FLO-2D USERS MANUAL Version 2003.06 July 2003
FLO-2D USERS MANUAL Version 2003.06 2003 .06 July 2003
P. P.O. Bo 66 Nu!rioso" A# $%&32 $%&32 P'one (n) FA*+ ,&2$ 33&-&3% E/(il+ lo2)1yer!r(ils.o/
FLO-2D USERS MANUAL Version 2003.06 2003 .06 July 2003
P. P.O. Bo 66 Nu!rioso" A# $%&32 $%&32 P'one (n) FA*+ ,&2$ 33&-&3% E/(il+ lo2)1yer!r(ils.o/
A e4 o//en!s on /o)elin5 ree ree sur(e sur(e lo4s
Modeling unconfined free surface flood flows flows can be complex. Having knowledge of the study area fluvial system, some modeling experience and a set of plausible assumptions will help get you started. With With faster faster computers computer s and high resolution digital terrain models, flood routing models are becoming very detailed. It is necessary for the user to find a balance between model resolution, resolution , computer resources resource s and budget. budget . When applying a two-dimensional flood routing model, a number of factors should be considered including the accuracy of the flood hydrology, map resolution, spatial variability of channel cross section data, and limited calibration data. lood ha!ard delineation is dependent on hydraulic models and too often we are not critical enough of the model engines, modeling assumptions, limited data bases or the modeling results. While finite difference models have expanded in versatility with increasing computer resources, inade"uate hydrographic data bases still limit the accuracy of flood ha!ard delineation. #igital terrain models are become the foundation of high resolution mapping, but post-flood event surveys of high water marks and aerial photography of the area of inundation are either unavailabl unavailablee or perhaps were collected long after the flood waters have receded. $orrelating the area of inundation to flood discharge can lead to the harsh reali!ation that our best discharge measurements or gaging data have limited accuracy accura cy or applicability applicability at flood high flows. %ur modeling and mapping results are only as good as our ability to calibrate the model to available post-flood data. &s flood modeling advances with hydrograph routing and mapping of unconfined flows, improved graphic tools and more extensive flood data bases will be necessary to support accurate models. If it appears appea rs that flood modeling complexity is becoming overwhelmin overwh elming, g, take heart in the comments comments of $unge et al. '()*+, “The “The mode modele lerr must must resis esistt the the temp tempta tati tion on to go back back to one-d one-dim imen ensi sion onal al schematization because of lack of data otherwise otherwise necessary for an accurate twodimensional dimensional model calibrati calibration. on. If the flow pattern pattern is truly two-dimens two-dimensional ional,, a one-dimensi one-dimensional onal schematiza schematization tion will will be useless useless as a predicti predictive ve tool...” “It is better to have a two-dimensional model partially calibrated in such situations than than a one-dim one-dimens ension ional al one whic which h is unable unable to pred predict ict unobser unobserved ved events events.. Indeed, the latter is of very use while the former is an approimation approimation which may always be improved by complimentary survey.” &s a final word, please remember that software models have glitches and re"uire constant updating. updating . ven when a hydraulic model engine is fine tuned, adding ad ding components can introduce conflicts with unrelated subroutines or identify bugs that were previously undetected. undetec ted. %-/# is certainly no exception. We will immediately immediately address all "uestions concerns co ncerns over model mo del application, application, accuracy or problems. %n occasion, there is a pro0ect application application that pushes the model to new limits. limits. 1uch modeling problems can lead to new developments that benefit all users. 2he modeler is encouraged encoura ged to share any interesting pro0ects with us. We aspire to make the %-/# model a productive and enlightening tool.
i
FLO-2D SOFTWARE LICENSE AGREEMENT PLEASE READ CAREFULLY 2his end user license agreement '3&greement4 is a legal contract between you 'either an individual or a single business entity '3icensee4 and %-/# 1oftware, Inc. 5y clicking the 3I &gree4 button below or b y installing or otherwise using the software application, you agree to be bound by the terms and conditions of this &greement. If you do not agree to the terms and conditions of the agreement, do not install or use the %-/# 1oftware. 2he following %-/# 1oftware license terms are binding upon any purchaser or icensee who uses this software.
GRANT OF RIGHTS %-/# 1oftware Inc. grants to icensee, and icensee hereby accepts, a non-exclusive, non-transferable, royalty-free license, for use by icensee only, of the %-/# 1oftware package that includes the %-/# computer model and processor programs commonly known and referred to as %-/#. 2he license includes the right to copy the %-/# icensed 1oftware only as it is necessary for use within the home or office of purchase and for archival purposes. 2he license permits the use of the software by icensee or its regular employees on any and all computers owned by icensee within or located at the home or office of purchase as indicated by the icensee6s address appears in documents submitted to %-/#. 2he license granted above does not include the right to copy or distribute the %-/# icensed 1oftware outside the home or office of purchase or to any other person. 2he license does not permit the use of the %-/# icensed 1oftware on a laptop or portable computer outside of the h ome or office of purchase. 2he license granted above does not provide for any free updates of the icensed 1oftware even though updates may, from time to time, be made available to icensee. 1hould such updates be provided to icensee, this license agreement shall apply to the updated version of the software, unless superseded or supplemented by other license terms provided with the updated version. 2he parties agree that all rights, including, but not limited to, rights under the federal copyright laws in and to modifications, if any, to the %-/# icensed 1oftware shall remain the sole and exclusive property of %-/#. 2he parties further agree that all rights, including but not limited to rights under the federal copyright laws in and to the icensed 1oftware shall remain the sole and exclusive property of %-/# 1oftware, Inc. 7o rights or licenses to the icensed 1oftware, other than those granted herein are granted, whether expres sly, by implication, estoppels or otherwise. 2he term of this license shall be perpetual. 7o modification of this icense shall b e binding on the pa rties h ereto unless such modification is in writing and duly signed by both parties. &ny attempted assignment of this icense or any rights or obligations hereunder, without the prior written consent of %-/#, shall be null and void and of no effect and a material breach and default of this license agreement.
RESTRICTIONS 2he %-/# model and its accompanying software and processor programs may not be sold, resold, leased, lent, rented or distributed to any other individual or organi!ation outside the home or office of purchase. 2he %-/# model and accompanying software and processor programs can not be copied outside the home or office of purchase or to any other person, decompiled, disassembled, reverse engineered, recreated as a derivative program or otherwise used except as stated in this agreement.
DISCLAIMER OF WARRANTIES AND LIMITATIONS OF LIABILITY %-/# 1oftware, Inc. does not make any warranty, either express or implied with respect to the licensed software, its "uality, merchantability, or fitness for a particular purpose. &ll the %-/# icensed 1oftware provided hereunder is licensed 3&1 I14 and does not warrant that the licensed software is free from claims of infringement or patents, copyrights, trade secrets, or other proprietary rights of others. 2here are no warranties, either express or implied, and any and all such warranties are hereby disclaimed and negated. %-/# 1oftware and its employees do not warrant the performance or results that you may obtain by using the %-/# 1oftware or any results generated by the software. 2he user assumes the entire risk of using the %-/# 1oftware. 7o oral or written information or advice given by %-/# 1oftware Inc. or its employees shall create a warranty or make any modification, extension or addition to this warranty. In no event whatsoever, shall %-/# 1oftware, Inc. or its employees be liable to the icensee or to any third parties for any damages caused, in whole or in part, by the use of the licensed software or for any lost revenues, damages to computers or other computer software, lost profits, lost savings or other direct or indirect, incidental, special, or conse"uential damages incurred by any person, even if advised of the possibility of such damages or claims, arising out the use or application of the %-/# 1oftware or the inability to use the software.
ii
2he liability of %-/# 1oftware, Inc. for a defective copy of the %-/# 1oftware will be limited exclusively to the replacement of the originally purchased copy of the %-/# 1oftware with another copy of the software or the refund of the initial license fee if the originally purchased copy is returned within 8+ days of the date of purchase.
DEFAULT Without pre0udice to any other rights, %-/# 1oftware, Inc shall have the right to terminate this &greement and the license granted herein if the icensee fails to comply with or commits a material breach of the terms and conditions of this &greement or commits an act of or is sub0ect to a #efault. & 3#efault4 means any one or more of the following events9 2he distribution, exchange, or offer or promise to distribute or exchange one or more copies of the %-/# 1oftware by the icensee, whether by sale, license, lease or otherwise, and whether or not any consideration is received for any such transfer or offer or promise. :pon the occurrence of a #efault, %-/# shall provide written notice of the icensee and the icensee shall have fifteen '(; days from the icensee6s receipt of said notice of #efault to cure the same. If the icensee does not affect such a cure within the prescribed time, then this &greement and the %-/# license shall be terminated. Within fifteen '(; calendar days after the icensee6s receipt of notice as provided for above, I$71 shall deliver to %-/# 1oftware, Inc. all copies, including but not limited to, all archival and backup copies for the %-/# 1oftware and all documentation related thereto.
GOVERNING LAW 2his icense shall be deemed made and accepted in and governed by the laws of the 1tate of &ri!ona. 2he state and federal courts located in &ri!ona shall have non-exclusive 0urisdiction and venue to hear all disputes arising out of or related to this icense.
COPYRIGHT < $opyright ()*), ())8. %-/# is copyrighted by =. 1. %65rien. &ll rights reserved. 2he %-/# software and manual are protected by :.1. $opyright aw '2itle (> :1 $ode. :nauthori!ed reproduction and?or sales may result in imprisonment and?or fines '(> :1$ ;+@. $opyright infringers may also be sub0ect to civil liability.
iii
BRIEF OVERVIEW
%-/# is a simple volume conservation model that distributes a flood hydrograph over a system of s"uare grid element 'tiles. It is a two-dimensional flood routing model that can be valuable tool for delineating flood ha!ards, regulating floodplain !oning or designing flood mitigation. %-/# numerically routes a flood hydrograph while predicting the area of inundation and simulating floodwave attenuation. 2he model is effective for analy!ing river overbank flows, but it can also be used to analy!e unconventional flooding problems such as unconfined flows over complex alluvial fan topography and roughness, split channel flows, mud?debris flows and urban flooding. $onventional one-dimensional, single discharge flood analysis can be replaced with a detailed %-/# model that includes rainfall and infiltration, levees, hydraulic structures, streets, hyperconcentrated sediment flows and the effects of buildings or flow obstructions. %-/# simulates unconfined overland flow using topographic data files that have been developed from a digital terrain model or digitali!ed base map. 2he %-/# software package includes a grid developer system 'A#1 that will overlay a s"uare grid system on a set of random digital terrain '#2M points. 2he A#1 will filter #2M points, interpolate the #2M data and assign elevations to grid elements. &s an option, topographic digital maps prepared with a computer-aided design and drafting '$&## program can also be assigned a grid system. 2he user has control over the creation of spatial and temporal output data files. 2he %/# results including maximum flow depth and velocity can be viewed graphically in the M&BBC post processor program. M&BBC will generate very detailed flood inundation color contour mapping by subtracting the #2M points from the predicted %-/# water surface elevations to generate an array of flow depths associated with every #2M point. 2he M&BBC program automates flood ha!ard delineation. 2he results can also be re-imported to the original mapping using $&## software to produce maximum depth and velocity contours. 2he %-/# manual is divided into two sections. 2he first half of the manual is devoted to a model description, theory and components. 2he users is encouraged to read this section to become familiar with the overall model attributes and e"uations. 2he second half of the manual is subdivided into a series of data files with variable descriptions and comments. 2he user should consult this portion of the manual when constructing data files. 2hese data files can be viewed in any &1$II text editor. & graphical user interface 'A:I has been developed to assist the user in preparing and editing the data files. %-/# is on M&6s list of approved hydraulic models for both riverine and unconfined alluvial fan flood studies. It has been extensively by a number of federal agencies including the $orps of ngineers, 5ureau of Ceclamation, :1A1, 7C$1, ish and Wildlife 1ervice and the 7ational Bark 1ervice. %-/# has been used on hundreds of pro0ects by consultants worldwide. 2he user can keep current on %-/# model and processor updates, short courses and other modeling news at the website9 www.flo/d.com. TABLE OF CONTENTS
Bage iv
ist of igures.................................................................................................................... ........................................................................................................................................ ist of 2ables........................................................................................................................viii I.
I72C%#:$2I%7.................................................................................................................... ......................................................................................................................................... (.( (./ (.8
volution of the %-/# Model....................................................................................( Modeling the Hydrologic 1ystem with %-/#............................................................/ Aetting 1tarted on a Bro0ect...........................................................................................@
II. %-/# M%# 2H%CD.................................................................................. ....................* /.( /./ /.8
Aoverning "uations......................................................................................................* %-/# ogic How the Model Works........................................................................(+ 2he Importance of Eolume $onservation.....................................................................(;
III. M%# $%MB%7721.......................................................... .......................................... (@ 8.( 8./ 8.8 8.F 8.; 8.@ 8.> 8.* 8.) 8.(+ 8.(( 8.(/ 8.(8 8.(F 8.(; 8.(@
Model eatures and Arid 1ystem ................................................................................(@ %verland low............................................................................................................. (> $hannel low................................................................................................................// loodway Coutine......................................................................................................../@ $hannel-loodplain Interface......................................................................................./> imiting roude 7umbers............................................................................................/> evees........................................................................................................................../* Hydraulic 1tructures...................................................................................................../) 1treet low...................................................................................................................8+ loodplain 1urface 1torage &rea Modification............................................................8( Cainfall................................................... .............................................. ........................ 88 Infiltration and &bstraction..................................................................................... ......88 vaporation..................................................................................................................8@ %verland Multiple $hannel low..................................................................................8@ 1ediment 2ransport - 2otal oad.............................................. ....................................8> Mud and #ebris low 1imulation........................................................ .........................F+
IE. M%# $%7$B2:&IG&2I%7......................................................... ............................. ;( F.( F./ F.8
imitations and &ssumptions....................................................................................... ;( inite #ifference Couting &lgorithm............................................................................ ;/ Barameter 1ensitivity................................................................................................... ;; v
F.F
loodplain and $hannel Inflow and %utflow Hydrographs......................................... ;> TABLE OF CONTENTS 'cont. Bage
F.;
loodplain $ross 1ections........................................................................................... ;> F.@ Araphical :ser Interface and Working nvironment................................................... ;* F.> Arid #eveloper 1ystem 'A#1.................................................................................... ;* F.* Araphical %utput #isplays........................................................................................... @+ F.) #ata %utput %ptions................................................................................................... @( F.(+ 1tarting the Brogram................................................................ ................................... . @@ F.(( $ode anguage and Hardware Ce"uirements............................................................. @> E. %-/# &BBI$&2I%71 &7# M2H%#1.............................................. ...........................@* ;.( ;./ ;.8
Civer &pplications........................................................................................................@* %verland low and &lluvial an &pplications...............................................................@) Bro0ect Cesults - What is a 1uccessful lood 1imulation.............................................>+
EI. %-/# M%# ECII$&2I%7...................................................... ................................>/ @.( @./ @.8 @.F @.; @.@ @.>
Aeneral.........................................................................................................................>/ Eerification 2est (. $hannel Hydraulics in the $alifornia &"ueduct............................ >8 Eerification 2est /. Eariable $hannel Aeometry Hydraulics....................................... .>; Eerification 2est 8. Civer loodplain 1imulation - 2ruckee Civer, Ceno, 7evada..... .>> Eerification 2est F. Civer lood Couting - Areen Civer, :tah....................................*/ Eerification 2est ;. loodplain Inundation - Middle Cio Arande, 7ew Mexico..........*@ Eerification 2est @. Eerification of Mudflow Hydraulics.............................................**
EII. %-/# BC%=$2 &BBI$&2I%71.................................................... ..............................)+ >.( >./ EIII.
lood Ha!ard #elineation, Mapping and Cesults.........................................................)+ Bartial ist of %-/# Bro0ects...................................................................................)+
CC7$1...................................................................................................................)*
vi
LIST OF FIGURES
Bage igure (.
Bhysical Brocesses 1imulated by %-/#...............................................................F
igure /.
$hannel - loodplain Interface................................................................................;
igure 8.
%-/# low $hart................................................................................................>
igure F.
#ischarge lux &cross Arid lement 5oundaries................................................. (8
igure ;.
%-/# 1tability $riteria low $hart.................................................................. (F
igure @.
$onceptual %ctagonal for the 5oundary Widths and low engths..................... (>
igure >.
%verland low 1ubroutine low $hart................................................................. /(
igure *.
$hannel xtension over 1everal Arid lements.................................................... //
igure ).
evees #epicted in Ced and Civers in 5lue in the %7EIC Brogram............. /)
igure (+.
1treets #epicted in Areen in the %7EIC Brogram........................................8(
igure ((.
&rea and Width Ceduction actors....................................................................... 8/
igure (/.
1hear 1tress as a unction of 1hear Cate for luid #eformation Models............. F8
igure (8.
#ynamic Eiscosity of Mudflow 1amples Eersus Eolumetric $oncentration......... F>
igure (F.
Dield 1tress of Mudflow 1amples Eersus Eolumetric $oncentration....................F*
igure (;.
$lassification of Hyperconcentrated 1ediment lows........................................... F*
igure (@.
$hannel Brofile...................................................................................................... >@
igure (>.
$omparison of %-/# and H$-/ low #epths for ;,+++ cfs #ischarge......... >@
igure (*.
$omparison of %-/# and H$-/ low Eelocities for ;,+++ cfs #ischarge..... >>
igure ().
Bredicted 2ruckee Civer Water 1urface Brofiles for H$-/ and %-/#............ >)
igure /+.
2ruckee Civer %bserved and %-/# Bredicted &rea of lood Inundation......... *+
igure /(.
%-/# Bredicted 1tage for the ())> lood vent at the Ceno Aage................ *(
igure //.
%-/# Bredicted 1tage for the ())> lood vent at the 7ew Eista Aage........ *(
igure /8.
())> High low 1eason Hydrograph at =ensen, :tah.......................................... *8
igure /F.
7ovember ())* Bower Blant #ischarge Celease from laming Aorge #am........ *F
igure /;.
%-/# Bredicted vs. Measured #ischarge, =ensen :1A1 or Bower Blant Celeases at laming Aorge #am.................................................*;
igure /@.
&rea of Inundation, Middle Cio Arande, May, ())/............................................*>
igure />.
Cudd $reek Mudflow Maximum low #epth $ontours.......................................*)
vii
LIST OF TABLES
Bage 2able (.
Auidelines for 1electing a lood Couting Method..................................................)
2able /.
%verland low Mannings n Coughness Ealues.....................................................(*
2able 8.
Initial &bstraction ................................................................................................. 8F
2able F.
Areen-&mpt Infiltration Barameters - Hydraulic $onductivity and Borosity........ 8;
2able ;.
Areen-&mpt Infiltration Barameters - 1oil 1uction............................................... 8;
2able @.
Areen-&mpt Infiltration Barameters - Eolumetric Moisture #eficiency................ 8@
2able >.
Cesistance Barameters for aminar low.............................................................. FF
2able *.
Dield 1tress and Eiscosity as a unction of 1ediment $oncentration....................F@
2able ).
Mudflow 5ehavior as a unction of 1ediment $oncentration.............................. F)
2able (+.
$alifornia &"ueduct Bredicted Hydraulics............................................................ >F
viii
Two Dimensional Flood Routing Model
I. INTRODUCTION
2he first portion of the manual is a reference document that describes the physical processes of flooding. It is designed to ac"uaint the user with the model theory, finite difference algorithms, model components, modeling assumptions and limitations, and potential flood scenarios. & reference list is also provided for further reading. 2he second half of the manual provides a detailed description of the re"uired input and output data files. & series of processor programs is provided to assist data file development and to graphically view results. 1ome example pro0ect applications are provided for the user to test and modify. 2hese examples can be used as templates for developing your own pro0ect. 2he website9 www.flo-/d.com has additional information on model updates and other example pro0ects.
1.1
Evoluto! o" t#$ FLO-2D Mo%$l
2he first version of the %-/# model was called M:#%W. Its development was initiated in ()** to conduct a ederal mergency Management &gency 'M& flood insurance study 'I1 of an urbani!ed alluvial fan in $olorado. M& had re"uested the investigation of flood routing models that might be suitable for simulating mudflows. 2he #iffusive Hydrodynamic Model '#HM created by Hromadka and Den '()*> was considered to be a simple finite difference model that might serve as a template to develop a more sophisticated hydraulic model for mudflows. 2he selection of the #HM model as a template for the M:#%W model was based on its availability in the public domain, its simple numerical approach and a finite difference scheme that permitted modification of the grid element attributes. 2he original M:#%W model was only a few hundred lines of ortran code and was limited to /;+ grid elements. & six hour hydrograph took over (/ hours to run on an 2 computer. With the advent of faster pc6s, additional components were added and the numerical routing algorithm was improved. &fter (; years of development, the program code has grown to be in excess of /;,+++ lines, @+ subroutines and a number of processor programs. It has been integrated into a Windows format. Eirtually none of the original simplistic #HM concept remains in the current %-/# model. %-/# computes overland flow in *-directions, reports on mass conservation, utili!es a new timestep incrementing and decrementing scheme, incorporates efficient numerical stability criteria, has unlimited array allocation 'unlimited overland and channel grid elements and includes graphical editing and output display processor programs. %-/# has grown into a physical process model that routes rainfall-runoff and flood hydrographs over unconfined flow surfaces or in channels using either a diffusive or dynamic wave approximation to the momentum e"uation. 2he model now has a number of components to (
simulate street flow, buildings and obstructions, sediment transport and mobile bed, spatially variable rainfall and infiltration, floodways and many other flooding details. Bredicted flow depth and velocity between the grid elements represent average hydraulic flow conditions computed for a small timestep 'on the order of seconds. 2ypical applications have grid elements that range from /; ft to ;++ ft on a side and while number of grid elements is unlimited, the user is cautioned to avoid extremely large models. %ne model of over F++,+++ grid elements took several days to simulate a three hour hydrograph flood.
1.2
Mo%$l!& t#$ H'%(olo&) S'*t$+ ,t# FLO-2D
2o model the hydrologic system, %-/# consists of a series of components and processor programs that break up a flood simulation into a number of discreti!ed small units. 2he Arid #eveloper 1ystem 'A#1 generates a grid system that represents the topography as a series of small tiles. 2he %-/# flood model has components for rainfall, channel flow, overland flow, street flow, infiltration, levees and other physical features. 2he A#1 and the %7EIC processor programs are used to spatially edit the grid system attributes. BC%I1 is a processor program to edit channel slope and shape. lood routing results can be viewed graphically in the M&B%2, M&BBC and HD#C%A 'view hydrographs programs. %-/# is an effective tool for delineating flood ha!ards or designing flood mitigation. 2he model utility is discovered through its application to diverse flooding problems. 1tarting with a basic overland flood scenario, details can added to the simulation by turning on or off switches for the various components shown in igure (. Multiple flood hydrographs can be introduced to the system at any number of inflow points either as a floodplain or chann el flow. &s the floodwave moves over the floodplain or down channels or streets, flow over adverse slopes, floodwave attenuation, ponding and backwater effects can be simulated. In urban areas, buildings and flow obstructions can be simulated to account for the loss of storage and redirection of the flow path. 2he levee component can be used to select a preferred mitigation design. $hannel flow is one-dimensional with the channel geometry represented by either by natural, rectangular or trape!oidal cross sections. 1treet flow is modeled as a rectangular channel. %verland flow is modeled two-dimensionally as either sheet flow or flow in multiple channels 'rills and gullies. $hannel overbank flow is computed when the channel capacity is exceeded. &n interface routine calculates the channel to floodplain discharge exchange including return flow to the channel. 1imilarly, the interface routine also calculates flow exchange between the streets and overland areas within a grid element 'igure /. %nce the flow overtops the channel, it will disperse to other overland grid elements based on topography, roughness and obstructions. or flood pro0ects with specific re"uirements, there are several uni"ue components such as mud and debris flow routing, sediment transport, a floodway option, open water surface evaporation and others. 2he user is encouraged to utili!e all these components while understanding the importance of each component to the overall flood distribution. It is important to assess the level of detail re"uired on a given pro0ect. %-/# users have a tendency to put more detail into their models than is necessary. 2he modeling detail and accuracy predicted water surface elevations should be consistent with the resolution of the mapping, survey data and the hydrologic data base. 1imulating large flood events re"uires less detail than shallow flood models or the design of flood mitigation measures. 1election of the grid element si!e for most flood inundation pro0ects range /
from /; ft to ;++ ft. #ifferent scales of resolution can be applied on the same pro0ect. or example, a (; mile reach of river can be modeled using a ;++ ft grid system. & short one mile reach where levees are proposed can be modeled with a ;+ ft grid system to investigate the potential for levee failure. 2he hydrographic output from the (; mile reach will constitute the input to the one mile river reach. Breparation of channel flow, street flow, buildings and flow obstructions data files can be time consuming and should be tailored to meet the pro0ect needs.
8
igure (. Bhysical Brocesses 1imulated by %-/#
F
igure /. $hannel J loodplain Interface
;
1.
G$tt!& St(t$% o! P(o/$)t
2here are two important steps to starting a flood simulation, obtaining the topographic data base and developing the flood hydrology. or the first step, a digital terrain model '#2M or a topographic map with sufficient detail of the potential flow surface has to be overlaid with a grid system. 2he Arid #eveloper 1ystem 'A#1 processor program will overlay the grid system on a #2M data base and assign elevations to the grid elements. &erial photography, detailed topographic maps, orthographic photos and digiti!ed mapping can be used to locate important features on the grid system. 1treets, buildings, bridges, culverts or other flood conveyance or containment structures can then be located with respect to the grid system. igure 8 is a flow chart that outlines how various components interface with each other. 2he second step arises from the fact that each flood simulation re"uires an inflow flood hydrograph or a rain storm. 2he discharge inflow points might include the alluvial fan apex or a known discharge location in a river system. %-/# can be used to generate the flood hydrograph at a specific location using a rainfall-runoff simulation in the upstream watershed. ¬her approach is to use hydrologic program such as the $orps6 H$-( model to generate an inflow hydrograph for the %-/# model. Cainfall can be then simulated on the flood inundation
1.
G$tt!& St(t$% o! P(o/$)t
2here are two important steps to starting a flood simulation, obtaining the topographic data base and developing the flood hydrology. or the first step, a digital terrain model '#2M or a topographic map with sufficient detail of the potential flow surface has to be overlaid with a grid system. 2he Arid #eveloper 1ystem 'A#1 processor program will overlay the grid system on a #2M data base and assign elevations to the grid elements. &erial photography, detailed topographic maps, orthographic photos and digiti!ed mapping can be used to locate important features on the grid system. 1treets, buildings, bridges, culverts or other flood conveyance or containment structures can then be located with respect to the grid system. igure 8 is a flow chart that outlines how various components interface with each other. 2he second step arises from the fact that each flood simulation re"uires an inflow flood hydrograph or a rain storm. 2he discharge inflow points might include the alluvial fan apex or a known discharge location in a river system. %-/# can be used to generate the flood hydrograph at a specific location using a rainfall-runoff simulation in the upstream watershed. ¬her approach is to use hydrologic program such as the $orps6 H$-( model to generate an inflow hydrograph for the %-/# model. Cainfall can be then simulated on the flood inundation surface as the flood processes over the grid system. 2he model inflow flood volume is the primary factor that determines an area of flood inundation. or that reason, it is suggested that a comparable effort be spent on the hydrologic investigation as is being expended on the flood routing analysis. In developing a flood routing model, the user should focus on the desired results and tailor the model accordingly. Cesults from a %-/# flood simulation include9 outflow hydrographs from the grid systemK hydrographs and flow hydraulics for each channel elementK flood hydrographs and hydraulics for designated floodplain cross sectionsK maximum flow depths and velocities for all grid elementsK changes in bed elevationK and a summary of the inflow, outflow, storage and volume losses in the system. 2he user can specify the temporal and spatial output file detail including the outflow hydrograph locations, the output time intervals and the graphical display of the flood progression over the grid system. 1tarting with the preliminary %-/# runs, the user should test the output options to determine re"uired level of output detail. In the following sections of this :ser Manual, modeling theory and a description of the %-/# components is presented. 2he user should refer to these sections when developing the individual data files. #ata tables are presented in the following sections that will guide the user in selecting various component parameters such as roughness values or hydraulic conductivity for infiltration.
@
FLO-2D Basic Components Flow Chart Start
Read Input Data "pdate #$draulics% &olu!es% Output Files% Increase i!estep
Decrease i!esteps% Reset #$draulics% Restart Flood Routing
Initiali)e &aria'les
Start Flood Routing Loop Channel/Street and Floodplain Interface
Channel Su'routine% #$draulic Structures% *udflow% Sedi!ent ransport% Infiltration
(es Channel Flow
No
Channel Sta'ilit$ Criteria Satisfied
No
Sedi!ent Distri'ution on Channel/Floodplain ,ed
(es Rainfall Runoff and Evaporation
(es
Outflow Nodes and Stagei!e Co!putations Rainfall and Evaporation Su'routines
No
Output Interval Co!plete
Overland Flow Sedi!ent ransport Infiltration% +ull$ Fl ow% #$draulic Structures% *udflow
(es
Si!ulation i!e Co!plete Nu!erical Sta'ilit$ Criteria Satisfied
No (es
(es
Street Flow
No
End
(es
Nu!erical Sta'ilit$ Criteria Satisfied
No
No
(es
igure 8. %-/# low $hart >
No
II. FLO-2D MODEL THEORY
%-/# is a simple volume conservation model. It moves the flood volume around on a series of tiles for overland flow or through stream segments for channel routing. loodwave progression over the flow domain is controlled by topography and resistance to flow. lood routing in two dimensions is accomplished through a numerical integration of the e"uations of motion and the conservation of fluid volume for either a water flood or a hyperconcentrated sediment flow. & presentation of the governing e"uations is followed by a discussion on mud and debris flow modeling. 2.1 Gov$(!!& E0uto!*
∂h ∂ h " ∂ h " y # # ∂t ∂ ∂ y
! i
2he general constitutive fluid e"uations include the continuity e"uation, and the two-dimensional e"uations of motion 'dynamic wave momentum e"uation9
∂h " y ∂" y " ∂" y $ ∂" y
% fy ! % oy - - - ∂ y g ∂ y g ∂ g ∂t
where h is the flow depth and Ex and Ey are the depth-averaged velocity components along the xand y-coordinates. 2he excess rainfall intensity 'i may be non!ero on the flow surface. 2he friction slope components 1fx and 1fy are written as function of bed slope 1ox and 1oy, pressure gradient and convective and local acceleration terms. & diffusive wave approximation to the e"uations of motion is defined by neglecting the last three acceleration terms. 5y neglecting the pressure gradient term, a kinematic wave representation of the momentum e"uation is derived. or a discussion of the kinematic wave application in numerical modeling see Bonce et al., ()>*. 2he kinematic wave e"uation is not used in the %-/# model. 2he %-/# user can select between the diffusive wave and the full dynamic wave versions of the momentum e"uation. 2he two-dimensional representation of the e"uations of motion in %-/# is better defined a "uasi two-dimensional model using a s"uare finite difference grid system. 2he e"uation of motion is solved by computing the average flow velocity across a grid element boundary one direction at time. 2here are eight potential flow directions, the four compass directions 'north, east, south and west and the four diagonal directions 'northeast, southeast, southwest and northwest. ach velocity computation is essentially one-dimensional in nature and is solved independently of the other seven directions. 2he individual pressure, friction, convective and local
*
acceleration components in the momentum e"uation are retained. More discussion of model solution and constitutive e"uations will be presented in the next section. 2he relative magnitude of the acceleration components to the bed slope and pressure terms is important. Henderson '()@@ computed the magnitude of momentum e"uation terms for a steep alluvial channel and a fast rising hydrograph as follows9 5ed 1lope
Bressure Aradient
$onvective &cceleration
ocal &cceleration LE?gLt
Momentum "uation 2erm9
1o
Ly?Lx
ELE?gLx
Magnitude 'ft?mi
/@
+.;
+.(/ - +./;
+.+;
2his comparison of terms illustrates that on most steep slopes, the application of the kinematic wave is sufficient to model floodwave progression and the contribution of the acceleration terms can be neglected. 2he addition of the pressure gradient term to create the diffusive e"uation will enhance overland flow simulation with complex topography. 2he diffusive wave e"uation with the pressure gradient is re"uired if the grid system has topographic depressions. xplicit numerical schemes to solve the diffusive wave e"uation generally re"uire relatively mild slopes. lat slopes may induce very small timesteps to achieve numerical stability. 2he local and convective acceleration terms are important to the solution for channel flow especially for flat or adverse slopes or very steep slopes. It is recommended that the full dynamic wave e"uation be applied in the %-/# model for applications except a simple overland flow simulation on a mild or steep slope. In this case, very little accuracy is sacrificed when the diffusive wave e"uation is used compared to the full dynamic model '&kan and Den, ()*(. $riteria for selecting a channel routing e"uation is given in the following table 'adapted from the $orps of ngineers, 2echnical ngineering and #esign Auidelines 7o. (), ())>. 2able (. Auidelines for 1electing a lood Couting Method Bhysical Brocesses (
Cecommended Couting "uation
(. 1teep alluvial fans, watersheds or floodplains
#iffusive wave, kinematic wave
/. Mild slope floodplains, backwater areas which influence hydrograph, overbank flows
#ynamic wave, diffusive wave
8. 5ed slope (+ ft?mile
#ynamic wave, diffusive wave, kinematic wave
and
21 v?d (>(
F. 5ed slopes N / to (+ ft?mile and 21v?d O (>(
#ynamic wave, diffusive wave
;. 5ed slope O / ft?mile
and
21 'g?d+.; 8+
#ynamic wave, diffusive wave
@. 5ed slope O / ft?mile
and
21 'g?d+.; O 8+
#ynamic wave
(
2 P hydrograph peak time of riseK 1 P bed slopeK v P average flow velocityK d P average flow depthK g P gravitational ac celeration '8/./ ft?s /
)
2.2 FLO-2D Lo&) - Ho, t#$ Mo%$l Wo(*
2he differential form of the continuity and momentum e"uations in the %-/# model is solved with a central, finite difference scheme. 2his explicit algorithm solves the momentum e"uation for the flow velocity across the grid element boundary one element at a time. xplicit numerical schemes are simple to formulate but usually are limited to small timesteps by strict numerical stability criteria. inite difference explicit numerical schemes re"uire significant computational time when simulating complex flows hydraulics such as slowly rising flood waves, channels with non-prismatic features, abrupt changes in slope, tributaries or split flow and ponded flow areas. 2he solution domain is discreti!ed into uniform, s"uare grid elements. 2he computational procedure for overland flows involves calculating the discharge across each of the boundaries in the eight potential flow directions. 2he flow directions include the four compass directions and the four diagonal directions 'igure F. ach grid element hydraulic computation begins with an estimate of the linear flow depth at the grid element boundary. 2he estimated boundary flow depth is an average of the flow depths in the two grid elements that will be sharing discharge in one of the eight directions. <hough a number of non-linear estimates of the boundary depth were attempted in earlier versions of the model, they did not significantly enhance or improve the results. 2he other hydraulic parameters are also averaged to compute the flow velocity including flow resistance 'Manning6s n-value, flow area, slope, water surface elevation and wetted perimeter. 2he floodplain flow velocity at the boundary is the dependent variable. %-/# will solve either the diffusive wave e"uation or the full dynamic wave e"uation to compute the velocity. Manning6s e"uation is then applied in one direction using the average difference in the water surface slope to compute the velocity. If the diffusive wave e"uation is selected, the velocity is then computed for all eight potential flow directions for each grid element. If the full dynamic wave momentum e"uation option is applied, the computed diffusive wave velocity is used as the first approximation 'the seed velocity in the 7ewton-Caphson second order method of tangents for determining the roots of the full dynamic wave e"uation which is a second order, non-linear, partial differential e"uation. 2he local acceleration term is the difference in the velocity for the given flow direction over the previous timestep. 2he convective acceleration term is evaluated as the difference in the flow velocity across the grid element from the previous timestep. 2he local acceleration term '(?gQLE?Lt for grid element /;( in the east '/ direction converts to9 R'Et J Et-(/;( S'g Q Rt where Et is the velocity in the east direction for grid element /;( at time t, E t-( is the velocity at the previous timestep 't-( in the east direction, Rt is the timestep in seconds, and g is the acceleration due to gravity. & similar construct for the convective acceleration term can be made.
2he discharge across the grid element boundary is computed by multiplying the velocity times the cross sectional flow area. &fter the discharge is computed for all eight directions, the net change in discharge 'sum of the discharge in the eight flow directions in or out of the grid element is multiplied by the timestep to determine the net change in the water volume 'see igure (+
F. 2his net change in volume is then divided by the available surface area 'storage area on the grid element to obtain the increase or decrease in flow depth for the timestep. 2he channel routing integration is performed essentially the same way except that the flow depth is a function of the channel cross section geometry and there are usually only one upstream and one downstream channel grid element for sharing discharge. 2he channel routing algorithm will be explained in more detail in a later section. 2he key to efficient finite difference flood routing is the numerical stability criteria that limit the magnitude of the timestep. %-/# has a variable timestep that varies depending on whether the numerical stability criteria are not exceeded or not. 2he numerical stability criteria are checked for the every grid element on every timestep to ensure that the model solution algorithms converge and that the solution is stable. If the numerical stability criteria are exceeded, the timestep is decreased and all the previous hydraulic computations for that timestep are discarded. 2he %-/# flood routing scheme proceeds on the basis that the timestep is sufficiently small to insure numerical stability. Most explicit schemes are sub0ect to the $ourantriedrich-ewy '$ condition for numerical stability '=in and read, ())> that related the floodwave celerity to the model time and spatial increments. %-/# uses the $ condition for the floodplain, channel and street routing. 2he timestep Tt is limited by9 Tt P $ Tx ? 'v U c where9 $ is the $ourant number '$ O (.+ Tx is the s"uare grid element width v is the computed average cross section velocity c is the computed wave celerity While the coefficient $ can vary from +.8 to (.+ depending on the type of explicit routing algorithm, a value of (.+ is employed in the %-/# model to allow the model to have the largest timestep under this criteria. 7MPOR8AN8 NO8E+ 8'e 9FL s!(ili!y ri!eri( is '(r)4ire) in !'e /o)el" !'e user )oes no! in:u! (ny )(!( or !'is s!(ili!y (n(lysis.
or full dynamic wave routing, another set of the numerical stability criteria is applied that was developed by Bonce and 2heurer '()*/. 2his criteria is a function of bed slope, specific discharge and grid element si!e. It is expressed as9 Tt O
V 1o Tx/ ? "o
where "o is the unit discharge, 1o is the bed slope and V is an empirical coefficient 'Bonce and 2heurer, ()*/. 2he coefficient V was created as a variable uni"ue to the grid element and is ad0usted by the model during runtime within a minimum and maximum range set by the user. 1imilar to the $1 criteria, when this numerical stability is exceeded the hydraulic computations for that timestep are dumped and the timestep is decreased. ((
5efore the $ and the full dynamic wave e"uation numerical stability criteria are evaluated in the %-/# simulation, the percent change in depth from the previous timestep for a given grid element is checked. 2his percent change in depth is used to preclude the need for any additional numerical stability analysis. If the percent change in depth is greater than that specified by the user, the timestep is decreased and all the hydraulic computations for that timestep are voided. If numerical stability using these three criteria is not sustained, the volume conservation over several output intervals will be violated and fluid volume will be either generated or lost by the model 'see igure ;. 7MPOR8AN8 NO8E+ A 30; :eren! in )e:!' or !'e DEP8<8OL =(ri(le in !'e 8OLER.DA8 ile is reo//en)e) or /os! (::li(!ions. A r(n5e o 20; !o 30; is su55es!e) or DEP8<8OL.
2imesteps generally range from +.( second to @+ seconds. 2he model starts with the minimum timestep and increases it until one of the three numerical stability condition is exceeded, then the timestep is decreased. If the stability criteria continue to be exceeded, the timestep is decreased until the minimum timestep is reached. If the minimum timestep is not small enough to conserve volume or maintain numerical stability, then the minimum timestep can be reduced, the numerical stability coefficients can be ad0usted or the input data can be modified. 2he timesteps are a function of the discharge flux for a given grid element and its si!e. 1mall grid elements with a steep rising hydrograph and large peak discharge re"uire small timesteps. &ccuracy is not compromised if small timesteps are used, but the computational time can be very long if the grid system is large.
(/
igure F. #ischarge lux &cross Arid lement 5oundaries (8
FLO-2D Timestep Incrementing and Decrementing Scheme Channel% Overland or Street Su'routine
Co!pute New Flow Depth
Decrease i!estep '$ 2 1 *ini!u! i!estep or Set i!estep to Nu!erical Criteria Co!puted i!estep
FLO-2D Timestep Incrementing and Decrementing Scheme Channel% Overland or Street Su'routine
Co!pute New Flow Depth
Incre!ental Depth Criteria Satisfied
Decrease i!estep '$ 2 1 *ini!u! i!estep or Set i!estep to Nu!erical Criteria Co!puted i!estep
No
Reset #$draulics% Restart Routing Seuence
(es
Nu!erical Sta'ilit$ Criteria Satisfied
No Increase i!estep '$ .0 1 *ini!u! i!estep
(es "pdate #$draulics and Continue with Flood Routing
igure ;. %-/# 1tability $riteria low $hart
(F
2. T#$ I+o(t!)$ o" Volu+$ Co!*$(vto!
& review of model flood simulation results begins with volume conservation. Eolume conservation indicates flood simulation numerical accuracy and confirms that the millions of calculations during a flood simulation are being consistently performed. 2he inflow volume, outflow volume, change in storage and infiltration and evaporation losses from the grid system are summed at the end of each time step. 2he difference between the total inflow volume and the outflow volume plus the storage and losses is the volume conservation. Eolume conservation results are written to the output files or to the screen at user specified output time intervals. #ata errors, numerical instability, inappropriate or inconsistent simulation techni"ues will cause a loss of volume conservation. or example, forcing subcritical or supercritical flow with poorly assigned n-values could effect the volume conservation. Eolume conservation can be used to debug a model and discern whether model dysfunction occurred in the channel or floodplain components. &ny simulation not conserving volume should be revised. It should be noted that volume conservation in any flood simulation is not exact. 2he user must decide on an acceptable level of error in the volume conservation, generally +.++( percent or less. 7MPOR8AN8 NO8E+ Re=ie4 !'e SUMMAR>.OU8 ile !o )e!er/ine 'o4 4ell !'e /o)el onser=es =olu/e or ( loo) si/ul(!ion. 7 ( si/ul(!ion )oes no! onser=e =olu/e" !'e user s'oul) )e!er/ine !'e lo(!ion o !'e )(!( :role/ y !urnin5 o !'e =(rious o/:onen!s (n) runnin5 !'e /o)el 4i!' only one o/:onen! ,su' (s s!ree!s or '(nnels !urne) on (! ( !i/e.
(;
III. MODEL COMPONENTS .1
Mo%$l F$tu($* !% G(% S'*t$+
2he primary features of the %-/# model are9
•
loodwave attenuation can be analy!ed through flood hydrograph routing.
•
%verland flow on unconfined surfaces is modeled in eight directions.
•
loodplain flows can be simulated over complex topography and roughness including split flow, shallow flow and flow in multiple channels.
•
$hannel, street and overland flow and the flow exchange between them can be simulated.
•
$hannel flow is routed with either a rectangular or trape!oidal geometry or natural cross section data.
•
1treets are modeled as shallow rectangular channels.
•
2he flow regime can vary between subcritical and supercritical.
•
low over adverse slopes and backwater effects can be simulated.
•
Cainfall, infiltration losses and runoff on the alluvial fan or floodplain can be modeled.
•
Eiscous mudflows can be simulated.
•
2he effects of flow obstructions such as buildings, walls and levees that limit storage or modify flow paths can be modeled.
•
2he outflow from bridges and culverts is estimated by user defined rating curves.
•
2he number of grid and channel elements and most array components is unlimited.
2he first step in undertaking a %-/# flood simulation is to define the potential flow surface. & grid system can be created with either the grid developer A#1 or a $&## program. 2he product of the A#1 is a topographic file 'B&I7.#&2 that identifies the contiguous grid elements and contains the floodplain roughness and grid element elevation. 2he ma0or portion of the model data re"uirements are presented in this automated and error free file. 2he procedures for creating the grid system and the B&I7.#&2 file as well as all the data files are discussed in detail in the second portion of the manual. #ata file preparation and computer run times vary according to the number and si!e of the grid elements, the inflow discharge flux and the duration of the inflow flood hydrograph being simulated. Blease keep in mind that the flood events being modeled are generally large enough that the grid elements do not have to be excessively small. Most flood simulations can be accurately performed with grid elements (++ ft to ;++ ft on a side. Bro0ects have been undertaken with grid elements as small as (+ ft, although models with grid elements this small are exceedingly slow. %ne pro0ect simulated flow in a street intersection and the grid system was generated inside the streets. Arid system si!e selection and data ac"uisition should accommodate the pro0ect (@
needs. It is important to balance the pro0ect detail and the number of model components applied with the mapping resolution and anticipated level of accuracy in the results. It is often more valuable from a pro0ect perspective to have a model that runs "uickly enabling many simulations to be performed from which the user can learn about how the pro0ect responds to flood scenarios rather than invest a ma0or effort into creating a huge grid system that takes days to run. 2he selection of the grid element si!e is discussed in detailed in 1ection /.@ of the #ata Input portion of the manual. Model component selection should focus on those physical features that will significantly effect volume distribution. & brief description of the %-/# components follows.
.2
Ov$(l!% Flo,
2he simplest type of %-/# model is overland flow on an alluvial fan or floodplain. It re"uires only the topography files and a hydrograph along with the two control files $%72.#&2 and 2%C.#&2. %verland flow is routed in eight possible flow directions 'the four compass directions and the four diagonal directions. In this manner, %-/# treats each grid element as an octagon rather than a s"uare 'igure @. 2he conceptuali!ed grid element octagonal geometry is important primarily to the flow width across the grid element boundaries and diagonal flow lengths. 2he grid element surface area is still a s"uare.
igure @. $onceptual %ctagon for the 5oundary Widths and low engths 2he B&I7.#&2 file defines the potential flow surface and grid element linkages. It contains the data that identify the grid elements and their neighbors, hydraulic roughness and elevations. 2he hori!ontal positive of the grid elements is defined by the $&#B21.#&2 file that lists the grid element number and x- and y-coordinates. With these two data files all the coordinate geometry 'including elevation of the entire grid system is defined. If the B&I7.#&2 and $&#B21.#&2 file were created with the A#1 processor, these data files will be error free and no further modifications to these data files are necessary to start a simulation. 2he data files necessary to conduct a simple overland flow simulation are9 B&I7.#&2
$&#B21.#&2 $%72.#&2 I7%W.#&2%:2%W.#&2
2%C.#&2
%verland flow velocities and depths vary with topography and the grid element roughness. 1patial variation in floodplain roughness can be assigned through the %7EIC processor. 2he (>
assignment of overland flow roughness must account for vegetation, surface irregularity and flow path redirection. %verland roughness can be two or three times conventional open channel flow n-values and is a function of flow depth. 2ypical roughness values 'Manning6s n coefficients for overland flow are shown in 2able /. &n n-value of +.+>+ is suggested for most overland flow applications.
2able /. %verland low Mannings n Coughness Ealues( 1urface
n-value
#ense turf
+.(> - +.*+
5ermuda and dense grass, dense vegetation
+.(> - +.F*
1hrubs and forest litter, pasture
+.8+ - +.F+
&verage grass cover
+./+ - +.F+
Boor grass cover on rough surface
+./+ - +.8+
1hort prairie grass
+.(+ - +./+
1parse vegetation
+.+; - +.(8
1parse rangeland with debris + cover /+ cover
+.+) - +.8F +.+; - +./;
Blowed or tilled fields allow - no residue $onventional tillage $hisel plow all disking 7o till - no residue 7o till '/+ - F+ residue cover 7o till '@+ - (++ residue cover
+.++* - +.+(/ +.+@ - +.// +.+@ - +.(@ +.8+ - +.;+ +.+F - +.(+ +.+> - +.(> +.(> - +.F>
%pen ground with debris
+.(+ - +./+
1hallow glow on asphalt or concrete '+./;X to (.+X
+.(+ - +.(;
allow fields
+.+* - +.(/
%pen ground, no debris
+.+F - +.(+
&sphalt or concrete
+.+/ - +.+;
(
&dapted from $%, H$-( Manual, ())+ and the $%, 2echnical ngineering and #esign Auide, 7o. (), ())> with modifications.
7MPOR8AN8 NO8E+ S'(llo4 o=erl(n) lo4 ,less 0.2 ! or 0.06 / is )eine) y ( s'(llo4 lo4 n-=(lue ,S
%verland flow depths and velocities will vary with grid element topography and roughness. 2he grid element attributes can be further modified to add detail to the predicted area of inundation. or example, the surface storage area or flow path on grid elements can be ad0usted for buildings. :sing the area reduction factors '&Cs, a grid element can be completely removed from receiving any inflow. &ny of the eight flow directions can be partially or (*
completely blocked to represent flow obstruction. 2he area of inundation can also be affected by levees, channel breakout flows, flow constriction at bridges and culverts, or street flow in urban areas. Cainfall and infiltration losses can add or subtract from the flow volume on the floodplain surface. 2hese overland flow components are shown in a computational flow chart in igure >. & number of %-/# pro0ect simulations have been created using the floodplain elements inside of the channel. In the case, the channel component is not used and instead the %-/# grid system is draped over the channel portion of the topography. While these pro0ects have been conducted with some success, there are several modeling concerns that should be addressed. 2he %-/# model was developed to be able to exchange (-# channel overbank discharge with the floodplain grid elements. or this reason, the model works well on large flood events and large grid elements. When small grid elements are used inside of a channel with confined flow and large discharges and flow depths, the model will run very slow. In addition, there will be variable bed topography that will result in !ero water surface slope between some grid elements and spatially varied roughness should be used. It should be noted that the application of the open channel Manning6s e"uation for a !ero water surface slope is no long valid as the velocity approaches !ero 'ponded flow condition. Moving blocks of fluid volume with the channel grid elements in a finite timestep in * directions, has to result in variation of the water surface elevations in contiguous grid elements. 2he resulting water surface elevations can be accurately predicted but will display some variation of +.( ft '+.+8 m across the channel. 2herefore, it is recommended, that the results for these in-channel detailed models be carefully reviewed. It is also important that the grid element si!e not exceed the resolution of the available #2M mapping data base. 7MPOR8AN8 NO8E+ A si/:le (::ro(' !o 5ri) ele/en! si@e sele!ion is !o use !'e ri!eri(+ :e( CAsur 0.% sC! 2 ,0.% / 3 C/2 . 8'is 4ill resul! in re(son(le !i/es!e:s on !'e or)er o (ou! seon). 7 !'e =(lue o :e( CAsur sC! 2 ,0.3 / 3 C/2 " !'e /o)el 4ill run eee)in5ly slo4. Asur sur(e (re( o ( sin5le 5ri) ele/en!.
or overland flow, the specific energy, impact pressure and static pressure are computed and reported to file on an output interval basis 'see the list of output files. 2he specific energy is computed by adding the flow depth velocity head 'E/?/g to the flow depth. 2he maximum specific energy is reported to the file 1B$7CAD.%:2 by grid element. or some M& alluvial fan pro0ects, the specific energy is to be reported and plotted as contours. 2he impact pressure by floodplain grid element is reported as a force per unit length 'impact pressure x flow depth. 2he user can then multiply the impact pressure by the structure length within the grid element to get a maximum impact force on the structure. Impact force is a function of fluid density, structure materials, angle of impact, and a number of other variables. 2o conservatively estimate the impact pressure, the empirical e"uation for water is taken from #eng '())@9 Bi P k Yf E/ where Bi is the impact pressure, coefficient k is (./* for both both nglish and 1I units, Yf P water density and E is the maximum velocity regardless of direction. or hyperconcentrated sediment flows such as mud floods and mudflows, the fluid density Y f and coefficient k is a function of sediment concentration by volume. 2he coefficient k is based on a regressed relationship as a ()
function of sediment concentration from the data presented in #eng '())@. 2his relationship is given by, k P (./@( e$w where $w P sediment concentration by weight. 2he impact pressure is reported in the file IMB&$2.%:2. 2he static pressure for each grid element is also expressed as a force per unit length. It is given by the maximum flow depth times the specific weight of the fluid. 2he static pressure is then multiplied by the flow depth to compute the static force per unit length of structure. 2he maximum static pressure is written to the 12&2I$BC11.%:2 file.
/+
Overland Flow Routing Suroutine Flow Chart Call Overland Su'routine
Co!pute Outflow Discharge
(es "pdate Flow #$draulics
Inflow #$drograph "pdate ,oundar$ Inflow Discharge
No
(es
Floodplain Rainfall
Decrease i!estep% Reset #$draulics% Restart Routing Seuence
Infiltration/Evaporation (es
No Rainfall on Floodplain% Channel and Streets
No
Call Infiltration or Evaporation Su'routine
"pdate Sedi!ent Concentration (es
Levees or #$draulic Structures
Call Levee or #$draulic Structure Su'routines
Rill and +ull$ Flow
(es
No
(es
No
*udflow Routing Call *udflow Routing Su'routine
Call *ultiple Channel Su'routine
i!e-Stage Co!ponent
No
Overland 3 ater/*udflow Discharge Routing No
Sta'ilit$ Criteria Satisfied
(es Call i!eStage Su'routine
Increase i!estep Restart Routing Seuence
F&u($ 3. Ov$(l!% Flo, Rout!& Su4(out!$ Flo, C#(t /(
.
C#!!$l Flo,
$hannel flow is simulated as one-dimensional flow. &verage flow hydraulics of velocity and depth define the discharge between channel grid elements. 1econdary currents and dispersion are not modeled with a (-# channel component. 2he flow around bridge piers or superelevation in channel bends cannot be simulated. 2he average flow path length between two channel elements is on the order of the length of the grid element and this precludes the simulation of hydraulic 0umps over a short distance. 2he flow transition between subcritical and supercritical flow is based on the average conditions between two channel elements. Civer channel flow is simulated with either variable area, rectangular or trape!oidal cross sections and is routed with a dynamic wave approximation to the momentum e"uation. $ross section data can be assigned to represent the channel elements. 2he channels are represented in the $H&7.#&2 by a grid element, cross section geometry that defines the relationship between the thalweg elevation and the bank elevations, average cross section roughness, and the length of channel within the grid element. $hannel slope is computed as the difference between the channel element thalweg elevation divided by the half the sum of the channel lengths within the channel elements. $hannel elements must be contiguous to be able to share discharge. 2he channel width can be larger than the grid element and may encompass several elements 'igure *. If the channel width is greater than the grid element width, the model extends the channel into neighboring grid elements in the direction specified by the user. & channel may be (+++ ft wide and the grid element only 8++ feet s"uare. 2he channel in this case would extend through three grid elements and the center grid in the channel would be conceptually removed from the floodplain. 2he model also makes sure that there is sufficient floodplain surface area after extension. 2he channel interacts with the right and left bank floodplain elements to share discharge. ach bank can have a uni"ue elevation. If the two bank elevations are different in the $H&7.#&2 file, the model automatically splits the channel into two elements even if the channel would fit into one grid element.
igure *. $hannel xtension over 1everal Arid lements
//
2here are three options for establishing the bank elevation in relationship to the channel bed elevation 'thalweg and the floodplain elevation in the $H&7.#&2 file9 (. 2he channel grid element bed elevation is determined by subtracting the assigned channel thalweg depth from the floodplain elevation. /. 2he channel bed elevation is assigned the grid element floodplain elevation and the thalweg depth is then added to the channel bed elevation to compute a new floodplain elevation. 8. & bank elevation is assigned in the $H&7.#&2 file and the channel bed elevation is computed by subtracting the thalweg depth from the lowest bank elevation. Aenerally, only options ( and 8 are used. %ption / reflects a system where a channel may be confined by berms and the floodplain is lower than the berm crest. When using cross section data for the channel geometry, option 8 should be applied. 2he procedure for creating a river channel simulation is as follows9 (. %elect &hannel &ross %ections. 1urveyed river cross sections can be represented in the model. 2hese may be spaced to represent river reaches that encompass a number of grid elements, say ; to (+ elements. Aeoreferenced surveyed cross section station and elevation data can be entered directly into the model data files or the data can be defined by setting the highest bank to an arbitrary elevation 'e.g. (+++ ft. or channel design purposes, a rectangular or trape!oidal cross section may be selected. 2o use surveyed cross section data, a 1$.#&2 file has to be created with all cross section station and elevation data. ach channel element is then assigned a cross section in the $H&7.#&2. 2he relationship between the flow depth and channel geometry 'flow area and wetted perimeter is based on an interpolation of depth and flow area between vertical slices that constitute a rating table for each cross section. ¬her method to assign natural channel cross shape is to use the channel geometry routine with pre-assigned power regression relationships. 2he pre-processor program 1$ computes channel geometry relationships for the cross sections as a function of depth. 2his program 1$ transforms the cross section x- and y-coordinate data into the following relationships9
& P a d b Bw P a d b 2w P a d b
Where & is the cross section flow area, Bw is the wetted perimeter, 2w is the top width, d is the depth, 'a is the regression coefficient and 'b is the regression exponent. More than one relationship may be used to define a single channel. or example, one relationship may be /8
valid for flow depths less than ; ft and a second relationship used to represent flows greater than ; ft. 2his approach for representing the channel geometry in the %-/# is more computationally efficient than interpolating the flow from the cross section rating table data but is less accurate and is less numerically stable. 7MPOR8AN8 NO8E+ For ri=er :roGe!s 4i!' (=(il(le sur=eye) ross se!ion )(!(" !'e *SE9.DA8 ile is reo//en)e) o=er !'e '(nnel 5eo/e!ry re5resse) rel(!ions'i:s. 8'e /o)el 4ill e less inline) !o '(=e '(nnel sur5in5 (! l(r5e !i/es!e:s.
/. 'ocate the &hannel (lement with )espect to the *rid %ystem. 5y using the %7EIC processor program or by having a hard copy map with the grid system overlaid, the channels can be assigned to a grid element. or channel flow to occur through a reach of river, the channel elements must be neighbors. & channel extension direction can be defined and the channel length within the grid element can be assigned. 7MPOR8AN8 NO8E+ 8'e '(nnel len5!' 4i!'in ( 5ri) ele/en! (n e es!i/(!e) :lus or /inus 20 !o %0 !. ?'en !'e 9
2he %-/# model will automatically assign the grid elements necessary to contain the channel width. If the channel is to be contained within the grid element, the channel top width should not exceed ); of the grid element width. 2here should be sufficient floodplain surface area 'at least ; of the total grid element surface area for potential overbank flow storage. 2he model will extend the channel through enough grid elements to meet both of these conditions. 8. +dust the &hannel ed %lope and Interpolate the &ross %ections. ach channel element is assigned a cross section in the $H&7.#&2 file. 2ypically, there are only a few cross sections and many channel elements, so each cross section will be assigned to several channel elements. When the cross sections have all been assigned the channel profile looks like a stair case because the channel elements with the same cross section have identical bed elevations. 2he BC%I1 processor programs allows you to view and edit the cross sections. 2here are two important functions that BC%I1 will perform. irst, by opening, saving and closing the BC%I1 program, each channel element is assigned its own uni"ue cross section. 2he number of cross sections is not e"ual to the number of channel elements and the cross section number in both 1$.#&2 and $H&7.#&2 has been renumbered from top to bottom. 1econd, the cross sections and thalweg bed elevation can be interpolated. In BC%I1, the cross section editor has an interpolation button where the user can identify the upstream and downstream surveyed cross sections. 2hen the cross sections assigned to each channel element are interpolated between the two known cross sections. 2his accomplished as follows9 • inear interpolation of the thalweg bed elevation. • inear interpolation of the channel top widths. • Zuasi-linear interpolation of stations and elevations for the revised top width. • Weighted flow area ad0ustment of the cross section station and elevations to achieve a more uniform increase or decrease of flow area between the know cross sections. /F
2he product of this effort is an assigned ad0usted cross section and bed slope for each channel element. 2he assigned surveyed cross sections retain their original shape and elevations. Cectangular and trape!oid cross sections can be edited directly in the $H&7.#&2 file or using the %7EIC program. 2he bed slope for these two channel shapes can be ad0usted in the BC%I1 program. It is also possible to use the 1$.#&2 file to define rectangular or trape!oidal cross sections. 2he user has several other options for setting up the channel data file including grouping the channel elements into segments, specifying initial flow depths, identifying contiguous channel elements that do not share discharge, assigning limiting roude numbers and depth variable nvalue ad0ustments. In river simulations the important components include channel routing, the channel-floodplain interaction, overland flow and levees. 2hese components are described in more detail in the following sections 7MPOR8AN8 NO8E+ M(nnin5Hs eIu(!ion is (n e/:iri(l or/ul( !'(! 4(s )e=elo:e) on !'e (sis o !es!s on s!e()y" unior/" ully )e=elo:e) !urulen! lo4. 7!s use" 'o4e=er" '(s eo/e uni=ers(l or (ll lo4 (::li(!ions. 7n !'e ori5in(l )eri=(!ion" !'e e:onen! o !'e 'y)r(uli r()ius 4(s )e!er/ine) !o =(ry e!4een 0.6% (n) 0.$. 8'e use R 2C3 is only (n (::roi/(!ion !'(! /us! e (l(ne) 4i!' =(ryin5 n-=(lues. 8'ere (re o(sions in ( FLO-2D loo) si/ul(!ion 4'en !'e lo4 is nei!'er s!e()y nor unior/. Floo):l(in :on)e) 4(!er or '(nnel (4(!er ee!s (re !4o ins!(nes 4'en M(nnin5Hs eIu(!ion /(y no! e (::ro:ri(!e. 8'e !en)eny is !o un)eres!i/(!e n-=(lues in !'e FLO-2D /o)el. F(!ors !'(! (e! rou5'ness inlu)e sur(e rou5'ness" os!ru!ions" =e5e!(!ion" se)i/en! lo()" sour (n) )e:osi!ion" '(nnel si@e (n) s'(:e" s!(5e (n) )is'(r5e (n) r(:i)ly =(ryin5 lo4 ,'y)r(uli Gu/:s. Poor sele!ion o n-=(lues or (ilure !o :ro=i)e s:(!i(l =(ri(!ion in rou5'ness (n resul! in nu/eri(l sur5in5. 7! is reo//en)e) !o (ssi5n 'i5' n-=(lues !'(! re:resen! ( o/:osi!e o !'e (!ors lis!e) (o=e. A=oi) usin5 n-=(lues !'(! re:resen! :ris/(!i '(nnel lo4.
$hannel output can be reviewed in several ways. 2he channel output data is written to a series of &1$II output files including9 5&1.%:2, HD$H&7.%:2, $H&7M&.%:2, #B$H.%:2 and others. 2he HD#C%A program can be used to plot the hydrograph of each channel element. It also has a routine to review average hydraulic conditions 'flow area, bed shear stress, hydraulic radius, velocity, etc. in a channel reach covering several or many channel elements that user can select in the HD#C%A program. 2he BC%I1 program can be applied to review the water surface profile, the mobile bed profiles, or the cross section geometry changes associated with scour and deposition. inally M&B%2 and M&BBC will graphically define the relationship between channel and floodplain volumes by mapping the various inundated areas. .5 Floo%,' Rout!$ & new floodway routine has been implemented into the %-/# system. 2he purpose of floodway concept is to reserve an unobstructed area of flood conveyance passage while allowing for potential utili!ation of the floodplain. loodway boundaries are designed to accommodate a (++-yr flood within acceptable limits. 2he floodplain areas that can be eliminated from potential flood storage with violating the floodway criteria can be considered for potential development. 2he guidelines for floodway delineation are9 /;
• • • •
2he floodway is based on the (++-yr flood. 2he floodplain is divided into floodway and floodway fringe !ones. It is generally assume that all the flood conveyance in the floodway fringe is eliminated. 2he floodway will pass the (++-yr flood without raising the water surface elevation more than ( ft above the maximum floodplain water surface. 2he floodway is determined by means of e"ual reduction of conveyance on both sides of the channel.
2he general procedure in H$-C&1 is to apply encroachment conditions using one or more of the encroachment options and make reasonable ad0ustments until acceptable results are obtained both from a flood hydraulics standpoint and from a floodplain management perspective. loodway determination is difficult on streams with a mild slope and large floodplain, where there is split flow or overflow at drainage divides and levees, on alluvial channels with mobile boundaries, on high velocity channels and in developed floodplain areas with ineffective flow areas. %ne of ma0or concerns is that the floodway encroachment procedure using H$-C&1 ignores the effects of both floodwave attenuation and the effects of forcing more flood volume downstream by constricting the flood conveyance area upstre am. :sing a single discharge model to delineate a floodway can grossly underestimate the potential impacts of increased downstream flooding resulting from permitting encroachment on the upstream floodplain. 2he %-/# floodway component can address all the problems associated with floodplain encroachment. 2he procedure for identifying the floodway in %-/# is automated. irst it is necessary to complete an existing conditions flood ha!ard delineation using the %-/# model on the pro0ect area. &n output file 'I72CAW1.%:2 is created that lists the maximum water surface elevations for each floodplain grid element. 2o perform the floodway analysis, the user sets the I%%#W&D switch to 3on4 in $%72.#&2 and assigns the encroachment depth '7$C%&$H variable in $%72.#&2. 2ypically the encroachment depth is ( ft. 2hen the %/# model is re-run for the pro0ect. 2he model will add the encroachment depth to the maximum water surface elevation to compute an encroachment water surface elevation for a given grid element that must be exceeded in order for the model to exchange the discharge with other grid elements. &s the overbank flooding ensues, the model confines the flood to those floodplain grid elements whose encroachment waste surface elevation is not exceeded. 2his forces more water volume downstream enhancing the opportunity to inundate the downstream floodplain in response to upstream confined conveyance. 5oth floodwave attenuation and upstream confined conveyances are simulated in a %-/# flood model. 2his provides a significant opportunity to evaluate the potential impacts of past delineated floodways. .6
C#!!$l-Floo%l! I!t$(")$
When the channel or street conveyance capacity is exceeded, an overbank discharge is computed in the channel-floodplain interface subroutine. 2he computed velocity of either the outflow from the channel or the return flow to the channel is based on the difference in water surface elevations between the channel and floodplain. If the channel flow is less than bankfull discharge and there is no flow on the floodplain, then the channel-floodplain interface routine is not accessed. 2he interface routine is internal to the model and there are no data re"uirements for its application. 2his subroutine also computes the flow exchange for the street and the floodplain. /@
2he channel-floodplain exchange is based on the water surface elevation difference between the channel and the floodplain grid element containing either channel bank 'igure /. 2he channel bank elevation is established by the surveyed channel geometry and thus the channel water surface and floodplain water surface is known in relationship to the channel top of bank. 2he water surface slope can vary from positive 'flow out of the channel to negative 'return flow to the channel on a timestep basis. %verbank discharge or return flow to the channel is computed using the diffusive wave e"uation and the floodplain roughness. 2he channel-floodplain flow exchange is limited by the available exchange volume in the channel or by the available storage volume on the floodplain. 2his interface determines how much overbank discharge will be routed as unconfined floodplain flow. &n inflow hydrograph node can be located on the floodplain and the overland flow can enter a previously dry channel.
.7
L+t!& F(ou%$ Nu+4$(*
2he roude number has a number of physical implicationsK it delineates subcritical and supercritical flow, it is the ratio of average flow velocity to shallow wave celerity and it relates the movement of a translational wave to stream flow. stablishing a limiting roude number in a flood routing model can help sustain the numerical stability by forcing the model to have a reasonable representation this physical reality. In alluvial river channel flow, the practical range of roude numbers at bankfull discharge is +.F to +.@. %verland flow on steep alluvial fans can approach critical flow. In general, supercritical flow on alluvial fans is suppressed by high rates on sediment transport. High velocities and shallow depths on alluvial surfaces will dissipate energy with sediment entrainment. 1upercritical flow is more prevalent on bedrock or other hard surfaces. When a limiting roude is assigned for either floodplain flow, street flow or channel flow for a given reach, the model computes the grid element flow direction roude number for each timestep. If the limiting roude number is exceeded, the Manning6s n-value for hydraulic flow resistance is increased by +.++(. &s the flow slows down, the n-value is decreased by +.+++(. 2his increase in flow resistance mimics increasing energy loss as the flow accelerates. When the limiting roude is exceeded, the changes in the n-value are reported in the C%:AH.%:2 file. 2here is a uni"ue relationship that exists between slope, flow area and roughness. If there is a mismatch between these physical variables in a flood routing model, then high velocities can occur that may result in flow surging. &ssigning a limiting roude number has several practical advantages. irst, it helps to maintain the flow velocity within a reasonable range. 1econdly, a review of the increased n-values in C%:AH.%:2 will identify any trouble spots where the velocity exceeds a reasonable value. In this case, the roughness value is increased to offset an inappropriate flow area and slope relationship. 2he n-values in $H&7.#&2 and B&I7.#&2 can be ad0usted for the next simulation using the maximum values report in the C%:AH.%:2 file. inally, the increased n-values can prevent oversteepening of the frontal wave. 2he limiting roude number is assigned in $%72.#&2 for the floodplain, $H&7.#&2 for channel flow and 12C2.#&2 for street flow.
/>
7MPOR8AN8 NO8E+ 7! is su55es!e) !'(! !'e '(nnel (null lo4 Frou)e nu/er e es!i/(!e) or ( 5i=en '(nnel re(' or se5/en!. 8'is 4oul) ons!i!u!e !'e li/i!in5 '(nnel Frou)e nu/er (ssi5ne) in !'e 9
.3
L$v$$*
2he %-/# levee component confines flow on the floodplain surface by blocking one of the eight flow directions. evees are designated at the grid element boundaries 'igure ). If a levee runs through the center of a grid element, the model levee position has to be shifted to one or more of the eight grid element boundaries. evees often follow a series of consecutive elements. & levee crest elevation can be assigned for each of the eight flow direction s in a given grid element. When the flow depth exceeds the levee height, the discharge over the levee is computed using the broadcrested weir flow e"uation with a /.*; coefficient. Weir flow occurs until the tailwater depth is *; of the headwater depth. &t higher flows, the water is exchanged across the levees using the difference in water surface elevation. evee overtopping will not cause levee failure unless the failure component is invoked. evee failure is an option. 1imulated levee failure can occur with a breach that enlarges vertically or hori!ontally. Cates of breach expansion in feet or meters per hour can be specified for both the hori!ontal and vertical failure modes. & final levee base elevation that is higher than the floodplain elevation can also be specified. 2he entire grid element width for a given flow direction can fail. #ischarge through the breach is based on the levee width and the difference in water surface elevations on the two sides of the levee. evee failure can also be initiated by flood duration at a specified water surface elevation on the levee. 7MPOR8AN8 NO8E+ 8'e le=ee (n e e(sily re(!e) (n) e)i!e) 5r(:'i(lly in !'e KDS (n) FLOENV7R :roessor :ro5r(/s. ?'en !'e le=ee is si!u(!e) )i(5on(lly (ross ( series o 5ri) ele/en!s" use one si)e o one 5ri) ele/en! (n) !'e o::osi!e o !'e ne! 5ri) ele/en! so !'(! !'ere (n eIu(l (/oun! o !'e loo):l(in on e(' si)e o !'e le=ee.
/*
igure ). evees #epicted in Ced and Civer in 5lue in the %7EIC Brogram
.8
H'%(ul) St(u)tu($*
Hydraulic structures are simulated by specifying either rating curves or rating tables. Hydraulic structures can include bridges, culverts, weirs, spillways or any hydraulic facility that controls conveyance and whose discharge can be specifying by rating curves or rating tables. 5ackwater effects upstream of bridges or culverts as well as blockage of a culvert or overtopping of a bridge can be simulated. Hydraulic structures can be simulated in channels or on floodplains by appropriately identifying the structure location in the HD#C12C:$2.#&2 file. & hydraulic structure controls the discharge between channel or floodplain grid elements that do not have to be contiguous but may extend over several grid elements. or example, a culvert under an interstate highway may span several grid elements. & hydraulic structure rating curve e"uation specifies discharge as a function of the headwater depth h9 Z P a h b
/)
where 'a is a regression coefficient and 'b is a regression exponent. More than one power regression relationship may be used for a hydraulic structure by specifying the maximum depth for which the relationship is valid. or example, one depth relationship can represent culvert inlet control and a second relationship can be used for the outlet control. In the case of bridge flow, blockage can simulated with a second regression that has a !ero coefficient for the height of the bridge low chord. 5y specifying a hydraulic structure rating table, the model interpolates between the depth and discharge increments to calculate the discharge. 2he rating table can be more accurate than the regression relationship, if the regression is nonlinear on a log-log plot of the depth and discharge. low blockage by debris can be simulated by setting the discharge e"ual to !ero corresponding to a prescribed depth. 2his blockage option may useful in simulating worst case mud and debris flow scenarios where bridges or culverts are located on alluvial fans. ach bridge on an alluvial fan channel can have simulated blockage forcing all the discharge to flow overland on the fan surface.
.9
St($$t Flo,
1treet flow is simulated as flow in shallow rectangular channels with a curb height using the same routing algorithm as channels. 2he data input file 12C2.#&2 is organi!ed by street. & given grid element may contain one or more streets and the streets may intersect. 2he user specifies a street name followed by the number of grid elements that constitute a given section of street. 2he flow direction, street width and roughness are specified for each street section within the grid element. 1treet and overland flow exchanges are computed in the channel-floodplain flow exchange subroutine. When the curb height is exceeded, the discharge to floodplain portion of the grid element is computed. Ceturn flow to the streets is also simulated. 1treets are assumed to emanate from the center of the grid element to the element boundary in the eight flow directions 'igure (+. or example, an east-west street across a grid element would be assigned two street sections. ach section has a length of one-half the grid element side or diagonal. & given grid element may contain one or more streets and the streets may intersect. 1treet roughness values, street widths, elevations and curb heights can be modified on a grid element or street section basis in the %7EIC program.
8+
igure (+. 1treets #epicted in Areen in the %7EIC Brogram. .1: Floo%l! Su(")$ Sto(&$ A($ Mo%")to!
1ome of the uni"ueness of the %-/# model is embodied in its versatility to simulate diverse flow problems associated with flow obstructions. &rea reduction factors '&Cs and width reduction factors 'WCs are coefficients to modify the individual grid element surface area storage and flow width. &Cs can be used to reduce the flood volume storage on grid elements due to buildings or topography. WCs can be assigned to any of the eight flow directions in a grid element and can partially or completely obstruct flow paths in all eight directions simulating floodwalls, buildings or berms. 2hese factors can greatly enhance the detail of the flood simulation through an urban area. &rea reduction factors are specified as a percentage of the total grid element surface area 'less 8(
than or e"ual to (.+. Width reduction factors are specified as a percentage of the grid element side 'less than or e"ual to (.+. or example, a wall might obstruct F+ of the flow width of a grid element side and a building could cover >; of the same grid element 'igure ((. It is usually sufficient to estimate the area or width reduction visually without measurement on a map. Eisuali!ing the area or width reduction can be facilitated by plotting the grid system over the digiti!ed maps or underlaying an image in the A#1 or %7EIC programs to locate the buildings and obstructions with respect to the grid system. &s a guideline, the area or width reduction factors should be estimated within (+ to /+. It should be noted that only four width reduction factors need to be specified for the eight possible flow directions. 2he other four flow directions are assigned automatically by grid element correlation. 2wo of the specified width reduction factors are for flow across the diagonals. It is possible to specify individual grid elements that are totally blocked from receiving any flow in the &C.#&2 file.
igure ((. &rea and Width Ceduction actors .11 R!"ll
8/
&lluvial fan or floodplain rainfall can make a substantial contribution to the flood volume and peak discharge. 1ome the fan or floodplain surface areas are of the same order of magnitude as the upstream watershed area. In these cases excess rainfall on the fan or floodplain may e"ual or exceed the total volume of inflow hydrograph from the watershed. 2he excess rainfall and runoff on the fan or floodplain can precede the arrival of the floodwave from the upstream watershed. It will also dilute the mudflows from the upstream basin. 2he storm rainfall is discreti!ed as a cumulative percent of the total precipitation 'similar to H$-( data files for input to the model in the C&I7.#&2 file. 2his discreti!ation of the storm hyetograph is established through local rainfall data or through regional drainage criteria that defines storm duration, intensity and distribution. 1torm characteristics can significantly affect the excess runoff when simulating infiltration and a careful review of local published rainfall?runoff data is encouraged to establish the rainfall distribution. 2he first rainfall timestep may correspond to the first upstream flood inflow hydrograph timestep. 5y altering the storm time distribution on the fan or floodplain, the rainfall can lag or precede the rainfall in the upstream basin depending on the direction of the storm movement over the basin. 2he storm can also have more or less total rainfall than that occurring in the upstream basin. If no infiltration is being modeled, the user can still specify an initial abstraction. 1torms can be varied spatially over the grid system with areas of intense or light rainfall. 2he rainfall can be assigned on a grid element basis using real rainfall data. %7EIC can used to draw the storm shape and assign rainfall intensity factors. 1torms can also move over the grid system by assigning storm speed and direction.
.12 I!"lt(to! !% A4*t()to!
Brecipitation losses simulated in the %-/# model include abstraction 'interception and infiltration. 2he initial abstraction is filled prior to simulating infiltration and is assigned by the user in the I7I.#&2 file. 1ome typical initial abstraction values are presented in 2able 8. Infiltration is simulated using the Areen-&mpt infiltration model. 1patial variation of infiltration over the grid system can be modeled by assigning uni"ue hydraulic conductivity and soil suction values to each grid element. 2he infiltration parameters are assumed to be uniformly distributed over a grid element surface with the exception that no infiltration is calculated for streets, buildings or other impervious surfaces. 2he infiltration parameters are usually assigned a uniform value over a subbasin unless there is field data to support a detailed spatial variation. 1patially variable infiltration can be graphically assigned in the %7EIC program. $hannel infiltration can be simulated by setting the I7I switch in the I7I.#&2 file. <hough channel infiltration and bank seepage are generally very minor portion of the total infiltration losses in the system, they can affect the floodwave progression in an ephemeral channel. 2he surface area of a natural channel is used to approximate the wetted perimeter to compute the infiltration volume.
88
2able 8. Initial &bstraction 1urface $over
&bstraction 'inches
7atural ( #esert and rangeland Hillslopes 1onoran desert Mountain with vegetation #eveloped J Cesidential ( awns #esert landscape Bavement &gricultural fields and pasture
+.8; +.(; +./; +./+ +.(+ +.+; +.;+
$onifers / Hardwoods/ 1hrubs/ Arass/ orest floor /
+.+( - +.8@ +.++( - +.+* +.+( - +.+* +.+F - +.+@ +.+/ - +.FF
(
Maricopa $ounty #rainage #esign Manual, ())/. W. 2. ullerton, Maste rs 2hesis, $1:, ()*8
/
2he Areen-&mpt '()(( e"uation was selected to compute infiltration losses in the %/# model because it was sensitive to rainfall intensity. It has an exponentially decreasing loss rate as the infiltration storage fills. If the rainfall exceeds the potential infiltration, then runoff is generated. 2he infiltration process continues after the rainfall has ceased until all the available water has run off or has been infiltrated. 2he Areen-&mpt e"uation is based on the following assumptions9
• • • • •
&ir displacement from the soil has a negligible effect on the infiltration process. Infiltration is a vertical process represented by a distinct piston wetting front. 1oil compaction due to raindrop impact is insignificant. Hysteresis effects of the saturation and desaturation process are neglected. low depth has limited effect on the infiltration processes.
& derivation of the Areen-&mpt infiltration modeling procedure can be found in ullerton '()*8 and in the H$-( Manual ':1$%, ())+. 2o utili!e the Areen-&mpt model, hydraulic conductivity, soil suction and the volumetric moisture deficiency must be specified in the I7I.#&2 file. 2ypical hydraulic conductivity, porosity and soil suction parameters are presented in 2ables F and ;. 2he volumetric moisture deficiency is evaluated as the difference between the initial and final soil saturation conditions. 2he initial saturation can be determined by subtracting the volumetric moisture deficiency '2able @ from the final saturation 'often assumed to be (. #epression storage is an initial loss from the potential surface flow. 2his is the amount of water in small surface depressions that does not become part of the overland runoff or infiltration. 2he depression storage or head 'ft is assigned by the 2% variable in the 2%C.#&2. & typical value of 2% is +.( ft. 7o discharge flux is computed for flow depths less than 2%.
2able F. Areen &mpt Infiltration Barameters J Hydraulic $onductivity and Borosity
8F
$lassification
'in?hr(
'in?hr/
'in?hr8
BorosityF
sand and loamy sand sandy loam oam silty loam 1ilt sandy clay loam clay loam silty clay loam sandy clay silty clay $lay very slow 1low moderately slow Moderate Capid very rapid
(./+ +.F+ +./; +.(; +.(+ +.+@ +.+F +.+F +.+/ +.+/ +.+(
(./( - F.(F +.;( +./@ +.(F
/.F( - *./> (.+/ +.;/ +./>
+.F8> +.F8> +.F@8 +.;+(
+.+) +.+; +.+8 +.+8 +.+/ +.+(
+.(> +.+) +.+@ +.+; +.+F +.+/ O +.+@8 +.+@-./+8 +./+-+.@88 +.@8-/.+8 /[email protected] @.88
+.8)* +.F@F +.F>( +.F8+ +.F>) +.F>;
(
Maricopa $ounty #rainage #esign Manual, ())/. =ames, et. al., Water Cesources 5ulletin Eol. /*, ())/. 8 W. 2. ullerton, Master s 2hesis, $1:, ()*8. F $% 2echnical ngineering and #esign Auide, 7o. (), ())> /
2&5 ;. AC7 &MB2 I7I2C&2I%7 B&C&M2C1 1%I 1:$2I%7 $lassification 'in( 'in/ 'in8 sand and loamy sand sandy loam loam silty loam silt sandy clay loam clay loam silty clay loam sandy clay silty clay clay 7ickel gravel-sand loam Ida silt loam Boudre fine sand Blainfield sand Dolo light clay $olumbia sandy loam Auelph loam Muren fine clay
/.F F.8 8.; @.@ >.; *.@ *./ (+.* ).F ((.; (/.F
(.)-/.F F.8 8.; @.@ *.@ *./ (+.* ).F ((.; (/.; /.+ - F.; /.+ - 8.; /.+ - F.; 8.; - ;.+ ;.; - (+.+ *.+ - ).; *.+ - (8.+ (;.+ - /+.+
(
Maricopa $ounty #rainage #esign Manual, ())/. =ames, W.B., Warinner, =., Ceedy, M., Water Cesources 5ulle tin Eol. /*, ())/. 8 W. 2. ullerton, Maste rs 2hesis, $1:, ()*8. /
2&5 @. AC7 &MB2 I7I2C&2I%7 B&C&M2C1 J E%:M2CI$ M%I12:C #I$I7$D
8;
$lassification
#ry ' #iff
7ormal ' #iff
sand and loamy sand ( sandy loam loam silty loam silt sandy clay loam clay loam silty clay loam sandy clay silty clay clay
8; 8; 8; F+ 8; /; /; 8+ /+ /+ (;
8+ /; /; /; (; (; (; (; (+ (+ ;
(
Maricopa $ounty #rainage #esign Manual, ())/.
.1 Evo(to!
&n open water surface evaporation routine was created for the %-/# model to account for evaporation losses in ma0or river systems for long duration flood flows. 2his component was implemented for the (>8 mile Middle Cio Arande model from $ochiti #am to lephant 5utte Ceservoir. 2he open water surface evaporation computation is based on a total monthly evaporation that is prorated for the number of flood days in the given month. 2he user must input the total monthly evaporation in inches or mm for each month along with the presumed diurnal hourly percentage of the daily evaporation and the clock time at the start of the flood simulation. 2he total evaporation is then computed by summing the wetted surface area on both the floodplain and channel grid elements for each timestep. 2he floodplain wetted surface area excludes the area defined by &C area reduction factors. 2he evaporation loss does not include evapotranspiration from floodplain vegetation. vapotranspiration is a function of the groundwater?surface water interaction and should be considered in relationship to the seepage 'infiltration loss and change in groundwater storage. 2he total evaporation loss is reported in the 1:MM&CD.%:2 file and should be compared with the infiltration loss for reasonableness.
.15 Ov$(l!% Multl$ C#!!$l Flo,
2he purpose of the multiple channel flow routine is to simulate the overland flow in rills and gullies rather than as overland sheet flow. Watershed surface water is often conveyed in small gully channels, even though they occupy only a fraction of the potential flow area. 1imulating rill and gully flow concentrates the discharge and improves the timing of overland runoff routing. 2he multiple channel routine calculates overland flow as sheet flow and routes it to the multiple channels within the grid element. low between the grid elements is then computed as rill and gully flow. 7o overland sheet flow is exchanged between grid elements if both elements have assigned multiple channels in the M:2.#&2 file. #ischarge can be conveyed as rill and gully flow from a grid with multiple channels to a grid element without them. 2he gully geometry is defined by a maximum depth, width and flow roughness. 2he multiple channel attributes can be spatially variable on the grid system and can be edited with the %7EIC program. If the gully flow exceeds the specified gully depth, the multiple channel can be expanded by a specified incremental width. 2his channel widening process assumes these gullies are alluvial
8@
channels and will widen to accept more flow as the flow reaches bankfull discharge. 2here is no gully overbank discharge to the overland surface area within the grid element. 2he gully will continue to widen until the gully width exceeds the width of the grid element, then the flow routing between grid elements will revert to sheet flow. 2his enables the grid element to be overwhelmed by flood flows. #uring the falling limb of the hydrograph when the flow depth is less than ( ft., the gully width will decrease to confine the discharge until the original width is again attained. If a grid element contains streets or river channels in addition to multiple channels such that the available surface area is less than /+ of the original grid element surface area, then the program will eliminate the gullies and reset that particular element to overland sheet flow.
.16 S$%+$!t T(!*o(t ; Totl Lo%
M& I1 studies are usually conducted using a rigid bed hydraulic model such as the $orps of ngineers H$-C&1 model. 2he 7ational Cesearch $ouncil '()*8 evaluated several movable-bed models without recommending any specific model for predicating channel geometry changes. When a channel rigid bed analysis is performed, any potential cross section changes are assumed to have a negligible effect on the predicted water surface. 2his is a reasonable assumption for large flood events on the order of a (++-year flood. %n steep alluvial fans, several feet of scour or deposition will usually have a minimal effect on the flow paths of large flood events. or small flood events, the potential effects of channel incision, avulsion, blockage, bank or levee failure and sediment deposition on the flow path should be considered. 2o address mobile bed issues, %-/# has a sediment transport component that can compute sediment scour or deposition. Within a given grid element, sediment transport capacity is computed for either channel flow or overland flow based on the flow hydraulics. 2he sediment transport capacity is then compared with the sediment supply and the resulting sediment excess or deficit is uniformly distributed over the grid element potential flow surface. 2he sediment transport capacity is computed using a choice of six possible e"uations for alluvial channels including Geller and ullerton '()*8, Dang6s e"uation, &ckers and White, nglund and Hansen, aursen or 2offeletti. ach sediment transport formula was derived for uni"ue fluvial geomorphic conditions and the user is encouraged to research the applicability of a selected e"uation to each pro0ect. %-/# can compute total load sediment transport in channels, streets and overland flow. 2he user has a choice of six sediment transport capacity methods and e"uations including Gellerullerton, Dang6s, &ckers and White, ngelund and Hansen, aursen and 2offaleti. ach sediment transport e"uation was developed to simulate specific channel or bed material conditions and has uni"ue attributes that may limit their applicability to certain river reaches. 2he user is encouraged to investigate each sediment transport e"uation and determine whether a given e"uation is appropriate for their modeling pro0ect. In the model, the sediment transport e"uation is used to compute the sediment transport capacity based on the predicted flow hydraulics between grid or channel elements. 1ediment continuity is tracked through the system on a grid element basis. 2he computed sediment load out of a grid element is compared to the sediment supply from other grid elements and the difference is deposited or scour from the grid element bed. 2he sediment excess 'deposition or deficit 'erosion is distributed uniformly on the floodplain element or non-uniformly on channel cross
8>
section based on a bed porosity of +.F+. 2he maximum scour, deposition and final bed elevations are recorded in the 1#B.%:2 and 1#$H&7.%:2 files. 1ediment transport is uncoupled from flow hydraulics. irst, the flow hydraulics are computed for all the grid and channel elements for the given time step and then the sediment transport is computed based on the completed flow hydraulics for that timestep. 2his assumes that the change in channel geometry resulting from deposition or scour does not have a significant effect on the average flow hydraulics for that timestep. Aenerally it takes several timesteps on the order of (+ seconds to result in average sediment deposition or scour that exceeds +.+; ft. ach sediment transport e"uation is briefly described. 2he user is encouraged to do further research to determine which e"uation is most appropriate for a specific pro0ect bed material and channel hydraulics. It should be noted that each e"uation may have been significant limitations that should be observed. When reviewing the 1#2C&71.%:2 file, it can be observed that the &ckers-White and ngelund-Hansen e"uations generate the highest sediment transport capacityK Dang and Geller-ullerton result in a moderate sediment transport "uantitiesK and aursen and 2offaleti compute the lowest sediment transport capacity. 2he apply any of the e"uations, the I1# switch in the $%72.#&2 file must be turned 3on4 and for channel flow the I1#7 switch must be set e"ual to ( in $H&7.#&2 file for each channel segment. +ckers-hite /ethod. &ckers and White '()>8 expressed sediment transport in terms of dimensionless parameters, based on 5agnold6s stream power concept. 2hey proposed that only a portion of the bed shear stress is effective in moving coarse sediment. $onversely for fine sediment, the total bed shear stress contributes to the suspended sediment transport. 2he series of dimensionless parameters include a mobility number, representative sediment number and sediment transport function. 2he various coefficients were determined by best-fit curves of laboratory data involving sediment si!e greater than +.+F mm and roude numbers less than +.*. 2he condition for coarse sediment incipient agrees well with 1heild6s criteria. 2he &ckers-White approach tends to overestimate the fine sand sediment transport '=ulien, ());.
(ngelund-0ansen /ethod. 5agnold6s stream power concept was applied with the similarity principle to derive a sediment transport function. 2he method involves the energy slope, velocity, bed shear stress, median particle diameter, specific weight of sediment and water, and gravitational acceleration. In accordance with the similarity principle, the method should be applied only to flow over dune bed forms, but ngelund and Hansen '()@> determined that it could be effectively used in both dune bed forms and upper regime sediment transport 'plane bed for particle si!es greater than +.(; mm. 'aursen1s Transport 2unction. 2he aursen '();* formula was developed for sediments with a specific gravity of /.@; and had good agreement with field from small rivers such as the 7iobrara Civer near $ody, 7ebraska. or larger rivers the correlation between measured data and predicted sediment transport was poor 'Araf, ()>(. 2his set of e"uations involved a functional relationship between the flow hydraulics and sediment discharge. 2he bed shear stress arises from the application of the Manning-1trickler formula. 2he relationship between shear velocity and sediment particle fall velocity was based on flume data for sediment si!es less than +./ mm. 2he shear velocity and fall velocity ratio expresses the effectiveness of the turbulence in mixing
8*
suspended sediments. 2he critical tractive force in the sediment concentration e"uation is given by the 1hields diagram. Toffeleti1s +pproach. 2offaleti '()@) develop a procedure to calculate the total sediment load by estimating the unmeasured load following the instein approach. 2he bed material load is give by the sum of the bedload discharge and the suspended load in three separate !ones. 2offaleti computed the bedload concentration from his empirical e"uation for the lower-!one suspended load discharge and then computed the bedload. Whereas in the instein approach, the bedload is determined first, then the suspended load is computed through integration. 2he 2offaleti approach re"uires the average velocity in the water column, hydraulic radius, water temperature, stream width, #@; sediment si!e, energy slope and settling velocity. 2offaleti6s procedure was consistently satisfactory for a comparison of 88) river and /*/ laboratory data sets '1imons and 1enturk, ()>@. 3ang1s /ethod. Dang '()>8 determined that the total sediment concentration was a function of the potential energy dissipation per unit weight of water 'stream power. 2he stream power was expressed as a function of velocity and slope. 2he total sediment concentration was expressed as a series of dimensionless regression relationships. 2he e"uations were based on measured field and flume data were made for sediment particles ranging from +.(8> mm to (.>( mm and for flows depths from +.+8> ft to F).) ft. 2he ma0ority of the data was limited to medium to coarse sands and flow depths less than 8 ft '=ulien, ());. Dang6s e"uations in the %-/# model can be applied to sand and gravel. 4eller-2ullerton (5uation. Geller-ullerton is a multiple regression sediment transport e"uation for sand bed channels or alluvial floodplains is used in the model. 2his empirical e"uation is a computer generated solution of the Meyer-Beter, Muller bed-load e"uation applied in con0unction with instein6s suspended load integration 'Geller and ullerton, ()*8. 2he bed material discharge "s is calculated in cfs per unit width as follows9 "s P +.++@F n(.>> EF.8/ A+.F; d-+.8+ #;+-+.@(
where n is Manning6s roughness coefficient, E is the mean velocity, A is the gradation coefficient, d is the hydraulic depth and #;+ is the median sediment diameter. &ll units in this e"uation are in the ft-lb-sec system except #;+, which is in millimeters. If the metric option is activated, no unit conversions are necessary. or a range of bed material from +.( mm to ;.+ mm and a gradation coefficient from (.+ to F.+, =ulien '()); reported that this e"uation should be accurate with (+ of the combined Meyer-Beter Muller and instein e"uations. 2he Geller-ullerton e"uation assumes that all sediment si!es are available for transport 'no armoring. 2he original instein method is assumed to work best when the bedload constitutes a significant portion of the total load 'Dang, ())@. %ummary. Dang '())@ makes the following recommendations for the application of total load sediment transport formulas in the absence of measured data. 2he recommendations have been limited to the six e"uations provided in the %-/# model and are slightly edited9
8)
• • • • •
:se Meyer-Beter and Muller and instein procedure 'Geller and ullerton e"uation when the bedload is a significant portion of the total load. :se 2offaleti6s method for large sand-bed rivers. :se Dang6s e"uation for sand and gravel transport in natural rivers. :se &ckers-White or ngelund-Hansen e"uations for subcritical flow in lower sediment transport regime. :se ausen6s formula for shallow rivers with silt and fine sand.
Dang '())@ reported that &1$ ranked the e"uations 'not including 2offaleti in ()*/ based on F+ field tests and (@; flume measurements in terms of best overall predictions as follows with Dang ranking the highest9 Dang, aursen, &ckers-White, ngelund-Hansen, and combined MeyerBeter, Muller and instein. It is important to note that in applying these e"uations, the wash load is not included in the computations. 2herefore, the wash load should be subtracted from any field measurements before comparing with the predicted sediment transport results from the e"uations. It is also important to recogni!e if the field measurements are supply limited. In this case, comparison with the sediment transport capacity e"uations would be inappropriate.
.17
Mu% !% D$4(* Flo, S+ulto!
%-/# routes hyperconcentrated sediment flows 'mud and debris flows as a fluid continuum by predicting viscous fluid motion. or mudflows, the motion of the fluid matrix is governed by the sediment concentration. & "uadratic rheologic model for predicting viscous and yield stresses as function of sediment concentration is employed and sediment volumes are tracked through the system. &s sediment concentration changes for a given grid element, dilution effects, mudflow cessation and the remobili!ation of deposits are simulated. Mudflows are dominated by viscous and dispersive stresses and constitute a very different phenomenon than those processes of suspended sediment load and bedload in conventional sediment transport. 2he sediment transport and mudflow components )!!ot be used together in a %-/# simulation. Initial attempts to simulate debris flows were accomplished with one-dimensional flow routing models. #eeon and =eppson '()*/ modeled laminar water flows with enhanced friction factors. 1patially varied, steady-state 7ewtonian flow was assumed and flow cessation could not be simulated. 1chamber and Mac&rthur '()*; created a one-dimensional finite element model for mudflows using the 5ingham rheological model to evaluate the shear stresses of a non7ewtonian fluid. %5rien '()*@ designed a one-dimensional mudflow model for watershed channels that also utili!ed the 5ingham model. In ()*@, Mac&rthur and 1chamber presented a two-dimensional finite element model for application to simplified overland topography. 2he fluid properties were modeled as a 5ingham fluid whose shear stress is a function of the fluid viscosity and yield strength. 2he description of the Mac&rthur and 1chamber model was published in a $orps of ngineers report ':1$%, ()** and included applications for mudflow on simplified, single plane topography. 2akahashi and 2su0imoto '()*; proposed a two-dimensional finite difference model for debris flows based a dilatant fluid model coupled with $oulomb flow resistance. 2he dilatant fluid
F+
model was derived from 5agnolds dispersive stress theory '();F that describes the stress resulting from the collision of sediment particles. ater, 2akahashi and 7akagawa '()*) modified the debris flow model to include turbulence. %5rien and =ulien '()**, Ma0or and Bierson '())+, and =ulien and an '())( investigated mudflows with high concentrations of fine sediment in the fluid matrix. 2hese studies showed that mudflows behave as 5ingham fluids with low shear rates 'O(+ s -(. In fluid matricies with low sediment concentrations, turbulent stresses dominate in the core flow. High concentrations of coarse particles combined with low concentrations of fine particles are re"uired to generate dispersive stresses. 2he "uadratic shear stress model proposed by %5rien and =ulien '()*; describes the continuum of flow regimes from viscous to turbulent?dispersive flow. 2o route mudflows, the rheological behavior of the flow must be treated as a continuum with mixed water and sediment components. Hyperconcentrated sediment flows such as mud and debris flows involve the interaction of complex fluid and sediment processesK turbulence, viscous shear, fluid-sediment particle momentum exchange, particle drag and sediment particle collision. 1ediment particles can collide, grind, and rotate in their movement past each other. ine sediment cohesion controls the non7ewtonian behavior of the fluid matrix. 2his cohesion contributes to the yield stress [y which must be exceeded by an applied stress in order to initiate fluid motion. 5y combining the yield stress and viscous stress components, the well-known 5ingham plastic model is prescribed. or large rates of shear such as might occur on steep alluvial fans '(+ s -( to ;+ s-(, turbulent stresses may be generated. In turbulent flow, an additional shear stress component, the dispersive stress, can arise from the collision of sediment particles under large rates of flow deformation. #ispersive stress occurs when large sediment particles dominate the flow and the percentage of cohesive fine sediment 'silts and clays is small. With increasing high concentrations of fine sediment, fluid turbulence and particle impact will be suppressed and the flow will approach being laminar. 1ediment concentration in a given flood event can vary dramatically and as a result viscous and turbulent stresses may alternately dominate, producing flow surges. 2he shear stress in hyperconcentrated sediment flows, including those described as debris flows, mudflows and mud floods, can be calculated from the summation of five shear stress components.
τ ! τ c # τ mc # τ v # τ t # τ d
where the total shear stress [ depends on the cohesive yield stress [c, the Mohr-$oulomb shear [mc, the viscous shear stress [ v 'η dv?dy, the turbulent shear stress [t, and the dispersive shear stress [d. When written in terms of shear rates 'dv?dy the following "uadratic rheological model can be developed '%5rien and =ulien, ()*;9 where
F(
τ ! τ y
# η
6
dv dv # & dy dy
τ y ! τ c # τ mc
and & ! ρ m l 6 # f 8 ρ m , & v 7 d s6
In these e"uations \ is the dynamic viscosityK [ c is the cohesive yield strengthK the Mohr $oulomb stress [mc P pstan] depends on the intergranular pressure ps and the angle of repose ] of the materialK $ denotes the inertial shear stress coefficient, which depends on the mass density of the mixture Ym, the Brandtl mixing length l, the sediment si!e ds and a function of the volumetric sediment concentration $v. 5agnold '();F defined the function relationship f'Ym, $v as9
f8 ρ m ,
& 9 $:; & v 7 ! a i ρ m & v
- $
where ai 'N +.+( is an empirical coefficient and $Q is the maximum static volume concentration for the sediment particles. It should be noted that 2akahashi '()>) found that the coefficient ai may vary over several orders of magnitude. gashira et al. '()*) revised this relationship and suggested the following9
< f8 ρ s , & v 7 ! $6 π π
$:; 6
sin α I ρ s 8$ -
6 en 7 & v
$:;
where the energy restitution coefficient en after impact ranges +.>+ O en O +.*; for sands, ^I is the average particle impact angle and Ys is the mass density of sediment particles. 2he first two stress terms in the shear stress e"uation are referred to as the 5ingham shear stresses and represent the internal resistance stresses of a 5ingham fluid 'igure @. 2he sum of the yield stress and viscous stress defines the shear stress of a cohesive, hyperconcentrated sediment fluid in a viscous flow regime. 2he last term is the sum of the dispersive and turbulent shear stresses, which is a function of the s"uare of the velocity gradient. & discussion of these stresses and their role in hyperconcentrated sediment flows can be found in =ulien and %5rien '()*>, ())8.
F/
igure (/. 1hear 1tress as a unction of 1hear Cate for luid #eformation Models & mudflow model that incorporates only the 5ingham stresses and ignores the inertial stresses assumes that the simulated mudflow is viscous. 2his assumption is not generally applicable because all mud floods and some mudflows are turbulent with velocities as high as /; fps '* m?s. ven mudflows with concentrations up to F+ by volume can be turbulent '%5rien, ()*@. #epending on the fluid matrix properties, viscosity and yield stresses for high sediment concentrations can still be relatively small compared to the turbulent stresses associated with high velocities. If the flow is controlled primarily by the viscous stress, it will result in lower velocities. $onversely, if the viscosity and yield stresses are small, the turbulent stress will dominate and the velocities will be higher. 2o delineate the role turbulent and dispersive forces in sand and water mixtures, Hashimoto '())> developed a simplified criteria involving only flow depth 'd and sediment si!e #i. When d?#i O 8+, the intergranular forces are dominant. If d?#i (++, inertial forces dominate. In the range 8+ O d?#i O (++ both forces play an important role in momentum exchange. It should be noted, however, that sediment concentration is a critical factor that is not accounted for in this criteria. 2o define the all the shear stress terms for use in the %-/# model, the following approach was taken. 5y analogy, with the work of Meyer-Beter and M_ller '()F* and instein '();+, the shear stress relationship is depth integrated and rewritten in the following form as a dimensionless slope9
F8
% f ! % y # % v # % t d
where the total friction slope 1f is the sum of the components9 the yield slope 1y, the viscous slope 1v, and the turbulent-dispersive slope 1td. 2he viscous and turbulent-dispersive slope terms are written in terms of depth-averaged velocity E. 2he viscous slope can be written as9 % v !
> η
"
= γ m
h
6
where `m is the specific weight of the sediment mixture. 2he resistance parameter for laminar flow e"uals /F for smooth wide rectangular channels but significantly increases 'up to ;+,+++ with roughness 'vegetation and irregular cross section geometry '2able >. or entucky 5lue Arass with a slope of +.+(, was estimated at (+,+++ '$hen, ()>@. & value of P /,/*; was calibrated on the Cudd $reek, :tah mudflow for a residential area and has been used effectively in most studies. or laminar and transitional flows, turbulence is suppressed and the laminar flow resistance parameter becomes important. 2able >. Cesistance Barameters for aminar low( 1urface
Cange of
$oncrete?asphalt 5are sand Araded surface 5are clay - loam soil, eroded 1parse vegetation 1hort prairie grass 5luegrass sod (
/F -(+* 8+ - (/+ )+ - F++ (++ - ;++ (,+++ - F,+++ 8,+++ - (+,+++ >,+++ - ;+,+++
Woolhiser '()>;
2he flow resistance ntd of the turbulent and dispersive shear stress components are combined into an e"uivalent Manning6s n-value for the flow9 6
% t d !
6
ntd " h
?:;
&t very high concentrations, the turbulent-dispersive stress arising from sediment particle contact increases the flow resistance ntd by transferring more momentum flux to the boundary. 2o estimate this increase in flow resistance, the conventional turbulent flow resistance n-value nt is increased by an exponential function of the sediment concentration.
FF
nd ! nt b e
m& v
where nt is the turbulent n-value, b is a coefficient '+.+;8* and m is an exponent '@.+*)@. 2his e"uation was based on 2he friction slope components that then be combined in the following form9
% f !
6 6 > η " τ y ntd " # # ?:; = γ m h6 γ m h h
& "uadratic e"uation solution to the friction slope e"uation has been formulated in the %-/# model for the velocity estimate in the momentum e"uation. 2he estimated velocity represents the flow velocity computed across each grid or channel element boundary using the average flow depth between the elements. Ceasonable values of and Manning6s n-value can be assumed for the channel and overland flow resistance. 2he specific weight of the fluid matrix `m increases with sediment concentration. 2he yield stress [y and the viscosity \ vary principally with sediment concentration. :nless a rheological analysis of the mudflow site material is available, the following empirical relationships can be used to compute viscosity and yield stress9
η ! α $ e
β $ & v
τ y ! α 6 e
β 6 & v
and
where ^i and i are empirical coefficients defined by laboratory experiment '%5rien and =ulien, ()**. 2he viscosity and yield stress are shown to be functions of the volumetric sediment concentration $v of silts, clays and in some cases, fine sands and do not include larger clastic material rafted along with the flow '2able * and igs. > and *.
2&5 *. DI# 12C11 &7# EI1$%1I2D &1 & :7$2I%7 % 1#IM72 $%7$72C&2I%7 η P αeβ$v τy P αeβ$v α β α β 1ource ield #ata &spen Bit ( &spen Bit / &spen 7atural 1oil &spen Mine ill
+.(*( /.>/ +.(;/ +.+F>8
/;.> (+.F (*.> /(.(
F;
+.+8@+ +.+;8* +.++(8@ +.(/*
//.( (F.; /*.F (/.+
&spen Watershed &spen Mine 1ource &rea Alenwood ( Alenwood / Alenwood 8 Alenwood F
+.+8*8 ().@ +.+++F); />.( +./)( (F.8 +.+++/+( 88.( +.+8F; /+.( +.++/*8 /8.+ +.+>@; (@.) +.+@F* @./+ +.+++>+> /).* +.++@8/ ().) +.++(>/ /).; +.+++@+/ 88.( Celationships &vailable from the iterature Iida '()8* +.++++8>8 8@.@ #ai et al. '()*+ /.@+ (>.F* +.++>;+ (F.8) ang and Ghang '()*+ (.>; >.*/ +.+F+; *./) +.++(8@ /(./ Zian et al. '()*+ +.+;+ (;.F* $hien and Ma '();* +.+;** ().(-8/.> +..(@@ /;.@ ei '()*( +.++F>+ //./ / &onversion@ 1hear 1tress9 ( Bascal 'B& P (+ dynes?cm Eiscosity9 ( B&s P (+ dynes-sec?cm / P (+ poises
Eery viscous, hyperconcentrated sediment flows are often referred to as either mud or debris flows. Mudflows are nonhomogeneous, non7ewtonian, transient flood events whose fluid properties change significantly as they flow down steep watershed channels or across alluvial fans. Mudflow behavior is a function of the fluid matrix properties, channel geometry, slope and roughness. 2he fluid matrix consists of water and fine sediments. &t sufficiently high concentrations, the fine sediments alter the properties of the fluid including density, viscosity and yield stress. 2he viscosity of hyperconcentrated sediment flow is a function of the properties of the fluid matrix including sediment concentration, percent and type of silts and clays and fluid temperature. Eiscous mudflows have high sediment concentrations and correspondingly high yield stresses and may result in laminar flow. ess viscous flows 'mud floods are always turbulent. 2he mudflow sample parameters in 2able * represent a full range of potential flow characteristics. 2o simulate mudflows with the %-/# model, the M:# switch in the $%72.#&2 must be set and the viscosity and yield stress variables in 1#.#&2 file must be specified. It is recommended that the viscosity and yield stress exponents and coefficients from 2able * be selected for inclusion in the 1#.#&2 file. 2he sample Alenwood F, for example, creates a very viscous mudflow. & volumetric sediment concentration or a sediment volume must then be assigned to the water discharge for a timestep in the discreti!ed inflow hydrograph in the I7%W.#&2 file. 2he inflow sediment volume may represent channel scour, bank erosion or hillslope failure. 2he incremental sediment volume is tracked through the routing simulation and reported as a total sediment volume in the summary volume conservation tables. 2his total sediment volume should be reviewed to determine if this is a reasonable sediment yield for the watershed. or a mudflow event, the average sediment concentration generally ranges between /+ and 8; by volume with peak concentrations approaching F; '2able ) and igure ). arge flood events such as the (++-year flood may contain too much water to produce viscous mudflow event. 1maller rainfall events such as the (+- or /;-year return period storm may have a greater propensity to create viscous mudflows. Most watersheds with a history of mud and debris flow
F@
events will have a substantial sediment supply. ven very small storms may generate mudflow surges. Mudflow and debris flows on semi-arid southwest alluvial fans usually average less than (; concentration by volume. 2he areal extent of mudflow inundation and the maximum flow depths and velocities can be determined by varying the sediment concentrations in the inflow hydrograph. & few trials will "uickly illustrate the effect of changing the sediment concentration. Most mudflows have a distinct pattern of flood development. Initially, clear water flows from the basin rainfall-runoff may arrive at the fan apex. 2his may be followed by a surge or frontal wave of mud and debris 'F+ to ;+ concentration by volume. When the peak arrives, the average sediment concentration generally decreases to the range of 8+ to F+ by volume. %n the falling limb of the hydrograph, surges of high concentration may occur.
igure (8. #ynamic Eiscosity of Mudflow 1amples Eersus Eolumetric $oncentration
F>
igure (F. Dield 1tress of Mudflow 1amples Eersus Eolumetric $oncentration
igure (;. $lassification of Hyperconcentrated 1ediment lows
F*
2able ). Mudflow 5ehavior as a unction of 1ediment $oncentration 1ediment $oncentration
low $haracteristics
by Eolume
by Weight
+.@; - +.*+
+.*8 - +.)(
Will not flowK failure by block sliding
+.;; - +.@;
+.>@ - +.*8
5lock sliding failure with internal deformation during the slideK slow creep prior to failure
+.F* - +.;;
+.>/ - +.>@
+.F; - +.F*
+.@) - +.>/
+.F+ - +.F;
+.@; - +.@)
+.8; - +.F+
+.;) - +.@;
+.8+ - +.8;
+.;F - +.;)
1eparation of water on surfaceK waves travel easilyK most sand and gravel has settled out and moves as bedload
+./+ - +.8+
+.F( - +.;F
#istinct wave actionK fluid surfaceK all particles resting on bed in "uiescent fluid condition
O +./+
O +.F(
andslide
Mudflow
Mud lood
Water lood
low evidentK slow creep sustained mudflowK plastic deformation under its own weightK cohesiveK will not spread on level surface low spreading on level surfaceK cohesive flowK some mixing low mixes easilyK shows fluid properties in deformationK spreads on hori!ontal surface but maintains an inclined fluid surfaceK large particle 'boulder settingK waves appear but dissipate rapidly Marked settling of gravels and cobblesK spreading nearly complete on hori!ontal surfaceK li"uid surface with two fluid phases appearsK waves travel on surface
Water flood with conventional suspended load an d bedload
When routing the mud flood or mudflow over an alluvial fan or floodplain, the %-/# model preserves continuity for both the water and sediment. or every grid element and timestep, the change in the water and sediment volumes and the corresponding change in sediment concentration are computed. &t the end of the simulation, the model reports on the amount of water and sediment removed from the study area 'outflow and the amount and location of the water and sediment remaining on the fan or in the channel 'storage. 2he volume of a debris detention basin upstream of the fan apex can be incorporated into the model. 1mall debris basins near the apex of alluvial fans may capture all or part of the mudflow event. 5y specifying the basin volume and grid element containing the basin in the 1#.#&2 file, the model will remove that portion of the hydrograph that is stored in the debris basin. If a large basin or reservoir exists, reservoir routing should be conducted prior to the application of the %-/# model. 2he reservoir outflow hydrograph can then be discreti!ed as an inflow hydrograph to the %-/# grid system.
F)
2here are several important sediment concentration relationships that help to define mud and debris flows. 2hese relationships relate the sediment concentration by volume, sediment concentration by weight, the sediment density, the mudflow mixture density and the bulking factor. When examining parameters related to mud and debris flows, it is important to identify the reported sediment concentration either by weight or by volume. 2he sediment concentration by volume $v is given by9 $v P volume of the sediment?'volume of water U sediment and $v is related to the sediment concentration by weight $w by9 $v P $w`? `s - $w'`s - `
where ` P specific weight of the water and `s P specific weight of the sediment 2he specific weight of the mudflow mixture `m is a function of the sediment concentration by volume9 `m P ` U $v'`s - `
1imilarly the density of the mudflow mixture Ym is given by9 Ym P Y U $v 'Ys - Y
and Ym P `m ?g
where g is gravitational acceleration. inally, the volume of the total mixture of water and sediment in a mudflow can be determined by computing the bulking factor 5 and multiplying the water volume by the bulking factor. 2he bulking factor is simply9 5 P (?'( - $v
It is apparent that the bulking factor is /.+ for sediment concentration by volume of ;+. 2hese basic relationships will be valuable when analy!ing and reporting the results of a %-/# simulation. Most studies re"uire estimates of the sediment concentration by volume and the bulking factor to describe the magnitude of the mudflow event. &verage and peak sediment concentrations for the flood hydrograph are important parameters for mitigation design.
;+
IV. MODEL CONCEPTUALI
2wo-dimensional overland flow in %-/# is analy!ed in a simple volume conservation, finite difference routing algorithm. It moves around blocks of fluids on a discreti!ed flow domain consisting of a system of tiles. With appropriate estimates of flow resistance, %-/# numerically distributes the volume in finite fluid blocks to mimic the floodwave progression and timing over the discreti!ed surface. $onceptually, %-/# is not a agranian fluid particle dynamics model involving streamlines or stream tubes and the movement of volume blocks around on the grid system is uni"uely limited by numerical stability criteria. 2he spatial and temporal resolution of the %-/# model is dependent on the si!e of the grid elements and rate of rise in the hydrograph 'discharge flux. 2he discharge flux is distributed over the available grid element surface area for a given timestep resulting in an incremental increase or decrease in the flow depth. iner grid resolution improves the accuracy of a flood simulation at the cost of increased computational time, more extensive data files and boundary conditions. & balance must be struck between the number of grid elements and an acceptable computational time. & grid si!e of (++ ft '8+ m to (+++ ft '8++ m is usually appropriate for most simulations. 1maller grid elements will not only significantly increase the number of grid elements 'the number of grid elements is "uadrupled each time the grid element si!e is divided by two, but the rate of discharge flux per unit area of the grid element increases. %-/# was developed to simulate large, infre"uent flood events on unconfined surfaces. 2he primary limitation of the %-/# model is the discreti!ation of the floodplain topography into a system of s"uare grid elements. 2he topography of each grid element is represented by a single elevation and roughness. Eariations in topography such as mounds and depressions within the element are obscured in the model. In large flood events, variations from the average node elevation will not significantly affect the inundated area because the water surface across the element will only vary on the order of a +.( ft. When simulating shallow flow, steep slopes and smaller discharges, smaller grid elements should be used. Map resolution and accuracy should be considered when selecting the grid element si!e. 1hallow flooding associated with fre"uent flood events may not have sufficient topographic resolution to support grid elements less than ;+ ft '(; m. 2he loss of floodplain topographic resolution through the grid system discreti!ation can generally be recovered in the M&BBC program when the #2M ground surface points are subtracted from the grid element water surface elevations and plotted in color contours. or one-dimensional channel flow, the spatial representation and variation in channel geometry is limited by the number of cross section surveys. Aenerally one cross section represents ; to (+ grid elements. 2he relationship between flow area, slope and roughness can be distorted by having an insufficient number of cross section surveys. 2his can result in numerical surges which commonly occur in cases of abrupt channel transitions. 2he ob0ective is to eliminate any discharge surges without substantially reducing the timestep so that the model runs as fast as possible. 2his can be accomplished by having gradual flow area and slope transitions between wide and narrow reaches. $onceptually, the %-/# model distributes flow between grid elements 'tiles in a simple volume conservation scheme. 5y using * flow directions 'with flow across the diagonals, the directional bias associated with F direction models is eliminated. our direction models such as
;(
the #HM model re"uire alignment of the grid elements with the primary flow direction to avoid a creating a model flow direction bias if the number of grid element rows are limited. In addition, in models that use only the diffusive wave approximation to the momentum e"uation, the flow will always follow the path of the steepest slope even if the flow has to turn at right angles. In this case, the artificial realignment of the grid elements may help to account for the missing convective acceleration momentum term. or this reason, an eight flow direction routing algorithm is clearly superior to one with only four directions. In an eight direction model, diagonal flow between two grid elements may crisscross, but this does not violate the principle of volume conservation. lood wave attenuation in the %-/# model is the result of simulating overbank and channel storage. 2his represents the interaction of the friction and bed slope terms with the diffusive pressure gradient. While the application of the dynamic wave e"uation can improve the flood routing, rapidly varying flow is still limited by the grid element resolution. 2he model does not have the ability to simulate shock waves, rapidly varying flow or hydraulic 0umps, and these abrupt changes in the flow profile are smoothed out in the model6s calculations. Eariable subcritical and supercritical flow transitions are assimilated into the average hydraulic conditions 'flow depth and velocity between two grid elements. 2he basic inherent assumptions in a %-/# simulation are9
• • • •
1teady flow for the duration of the timestepK Hydrostatic pressure distributionK Hydraulic roughness is based on steady flow resistanceK :niform channel geometry and roughness is represented with a channel element.
2hese assumptions are self-explanatory, but they help to envision that the model is simulating temporally and spatially averaged flow conditions between grid elements. inally, it should be noted that a rigid bed is assumed for a flood simulation, if sediment transport is not simulated. Cigid boundary conditions are appropriate for flow over steep slopes, urban flooding and mudflow events. 2he area of inundation associated with extreme flood events are generally unaffected by bed changes. It is assumed in rigid bed simulations that the average flow hydraulics are not appreciably affected by the scour and deposition that might occur in an individual grid element.
5.2 F!t$ D""$($!)$ Rout!& Al&o(t#+*
2he differential form of the continuity and momentum e"uations in the %-/# model is solved with a central, finite difference numerical integration method. 2he solution of the differential form of the momentum e"uation results from a discrete representation of the e"uation when applied at a single point. 2he finite difference numerical techni"ue for solving the momentum e"uation is an algorithm that advances the solution in time by solving for the unknown value of velocity of the dependent variables one grid element at a time. xplicit numerical schemes are simple to formulate, but are limited to small timesteps by strict numerical stability criteria. 2he %-/# re"uires large computational time when simulating slow rising flood waves, channels with non-prismatic features, abrupt slope change, and dead storage areas.
;/
2he solution domain for the nonlinear partial differential momentum e"uation is discreti!ed into uniform s"uare grid elements. 2he computational procedure for overland flow involves calculating the discharge across each of the boundaries in the eight potential flow directions. 2he discharge is estimated by assuming a linear trial function 'central average for depth, n-value and flow area between the two grid elements. 2he flow velocity across the boundary is then computed from the solution of the momentum e"uation. :sing an average flow area between two elements, the discharge for each timestep is determined as velocity times flow area. 2he net change in the volume of water in each floodplain grid element for each timestep is the sum of the eight individual discharges across the boundary. $hannel routing involves adding the inflow and outflow from the upstream and downstream channel elements. 2he channel and street routing algorithms are identical except that a rectangular channel is used for street flow. 2o compute the flow velocity at a grid element boundary using the full dynamic wave e"uation, initially the flow velocity is calculated with the diffusive wave e"uation using the average water surface slope 'bed slope plus pressure head gradient. 2his velocity is then used as a first estimate 'or a seed in the second order 7ewton-Caphson tangent method to find the root of the full dynamic wave e"uation '=ames, et. al., ()>>. 2he convective acceleration and local acceleration velocities used in the solution are those determined in the previous timestep. If the 7ewton-Caphson solution fails to converge after ; interations, the algorithm defaults to the diffusive wave solution. 2he solution algorithm incorporates the following steps where each grid element possesses a uni"ue roughness value, elevation and flow depth9 (. 2he average flow geometry and roughness values between two grid elements are computed. /. 2he flow depth d for computing the velocity across a grid boundary for the next timestep 'iU( is estimated from the previous timestep i using a linear trial function 'the average depth between two elements. i#$
d
! d i # d i +(
8. 2he velocity is computed using the diffusive wave e"uation as previous defined in 1ection /.(. 2he only unknown variable in the diffusive wave e"uation is the velocity. 2his is the case for overland, channel or street flow. F. If the full dynamic wave e"uation is selected by the user, the predicted diffusive wave velocity for that timestep is used as a seed in the 7ewton-Caphson solution. It should be noted that for hyperconcentrated sediment flows such as mud and debris flows, the velocity calculations include the additional viscous and yield stress terms. ;. 2he discharge Z across the floodplain boundary 'or between two channel elements is computed by multiplying the velocity by the cross sectional flow area. or overland flow, the flow width is ad0usted by the width reduction factors 'WCs. @. 2he incremental discharge for the timestep across the eight boundaries 'or upstream and downstream channel elements are summed,
∆ A i#$ ! An # Ae # A s # A w # A ne # A se # A sw # Anw ;8
and the change in volume 'net discharge x timestep is distributed over the available storage area within the grid or channel element to determine an incremental increase in the flow depth. where TZx is the net change in discharge in the eight floodplain directions for the grid element for the timestep Tt between time i and i U (. >. 2he numerical stability criteria is then checked for the new grid element flow depth. If any of
∆ d i#$
!
∆ A i#$ ∆t : +rea
the stability criteria are exceeded, the simulation time is reset to the previous time, the timestep increment is reduced, all the previous timestep computations are discarded and the velocity computations begin again. *. 2he simulation progresses with increasing timesteps until the stability criteria are exceeded. In this computation se"uence, the grid system inflow discharge and rainfall is computed first, then the channel flow is computed. 7ext, the street discharge is computed if streets are being simulated and finally, overland flow in *-directions is determined 'igure 8. &fter the flow routing for each of these components has been completed, the numerical stability criteria are tested for every floodplain grid, channel or street element. If stability criteria of any of the elements is exceeded, the timestep is reduced by two times the minimum timestep and the computation se"uence is restarted. If all the numerical stability criteria are successfully met, the timestep is increased by half the minimum timestep following the successful completion of the entire model computations. or each timestep the flow depth, velocity and the discharge across every grid element boundary are calculated. 2he model advances explicitly by solving for the new flow depths one grid element at time. #uring a single sweep of the grid system for a given timestep, discharge flux is added to the inflow elements, flow velocity and discharge between grid elements are computed and the change in storage volume in each grid element for both water and sediment are determined. &ll the inflow volume, outflow volume, change in storage or loss from the grid system area are summed at the end of each time step and the volume conservation is computed. Cesults are written to the output files or to the screen at user specified output time intervals.
5. P(+$t$( S$!*tvt'
2he success and accuracy of a flood simulation can be determined in part by volume conservation. ven small data errors can result in a significant loss of volume conservation. 2he 1:MM&CD.%:2 file reports on the volume conservation. It should be reviewed after each simulation to determine is the inflow volume matches the outflow volume plus storage on the grid system. While some numerical error is introduced by rounding numbers, approximations or interpolations 'such as with rating tables, volume should be conservation within a fraction of cubic meter. &cceptable limits of volume conservation error for a given flood simulation is on the order of plus or minus +.+++( to +.+++++( of one percent of the inflow.
;F
2here are no preemptive assumptions in the routing algorithm that limit the model application. It should be noted however, that the model was designed for open channel flow or steep slope overland flow applications and extensive ponding and backwater effects can re"uired very small timesteps. or overland flow, there are two flow conditions that warrant special attention. 1hallow overland flow where the flow depth is on the order of the roughness elements '+./ ft or +.+@ m can be more effectively modeled by assigning the 1H&%W7 parameter in the $%72.#&2 file. 1uggested n-values for the 1H&%W7 parameter range from +.(+ to +./+. or shallow overland flow less than +.; ft '+.(; m, ;+ of the shallow n-value assigned in the $%72.#&2 file is used. 2his roughness ad0ustment is invoked to account for higher flow resistance associated with shallow flows through vegetation. or ponded water conditions with water surface slopes less than +.++(, Manning6s open channel flow e"uation representing the friction slope has limited applicability. &d0ustments are made to the roughness n-value to reduce the velocities associated with such mild slope conditions. 2he ad0ustments increase the n-value from the original value at a slope of +.++( to (+ times the n-value at a slope of +.++++( based on a power regression relationship between the two slope values. low contraction and expansion between two channel elements is addressed by increasing the head loss as function of the ratio of the flow areas. 2he head loss coefficient is +.+ for a ratio of +.); for higher. or a contraction of up to @+, the head loss coefficient varies from +.+ to +.@. or flow expansion where the ratio of flows is @+ or less, the head loss coefficient varies from +.+ to (.+. 2he head loss is given by the velocity head E/?/g times the head loss coefficient and is expressed as slope between the two channel elements. 2he head loss reduces the available energy gradient between the channel elements. &s was discussed in 1ection 8.;, limiting roude numbers can be specified for overland flow, channel flow and street flow. When the roude number exceeds the maximum roude number in a grid element, the n-value is increased by +.++( for that element for the next timestep. 2he flow will only exceed the limiting roude number for that timestep. In this manner, the flow can be kept subcritical or below a specified subcritical or supercritical roude number. or example, in steep-slope sand bed channels, high energy flows will entrain more sediment and force subcritical flow. In this case, the limiting roude number might be set to +.). or flow down steep streets, a maximum roude number of (./ to (.; may be specified to limit the supercritical flow. 1ince %-/# does not simulate hydraulic 0umps, the limiting roude number should represent average flow conditions in a channel reach. #uring the falling limb of the hydrograph when the roude decreases to a value less than +.;, the flow resistance n-value decreases by +.+++; until the original n-value is reached. 2he %-/# model can simulate the complex detail of the hydrologic system including rainfall, infiltration, street flow, and flow through hydraulic structures. 2his level of detail re"uires a large number of variables. In terms of the channel and floodplain flood routing, the parameters having the greatest effect on the area of inundation or on the outflow hydrograph are as follows9
• • •
Inflow hydrograph discharge and volume directly affect the area of inundation. 2he overland flow path is primarily a function of the topography. 2he floodplain roughness n-values generally range from +.+8 to +.(; and control the floodwave speed over the flow domain.
;;
•
•
Civer channel roughness n-values general range from +.+/+ to +.+*;. 7-value ad0ustment will usually result in only minor variation of the water surface 'N +./ ft or +.+@ m. 2he channel n-values can be used to dampen numerical surging. 2he relationship between the channel cross section flow area, bed slope and roughness controls the floodwave routing, attenuation and numerical stability. low area and channel element storage have the most significant effect on channel routing stability. $hanges in the natural flow area between channel elements should be limited to /; or less. More cross section surveys may be necessary to simulated rapidly changing flow geometry. $onstructed rapid transitions in channel geometry can be model, but will re"uire smaller timesteps and more channel detail.
loodplain storage loss '&C values due to buildings, trees or topography can be generically assigned for the entire grid system using the &C parameter in the $%72.#&2 file. 2ypically, an &C value of ; to (+ can be applied to most floodplains. If inundation depths are relatively deep on the order of 8 ft '( m covering all of the grid system, the &C can be reduced or set e"ual to +.+. Watershed and alluvial fan flooding should be bulked for sediment loading. If it is assumed that the sediment loading will be relatively minor, the $%7$ factor in the $%72.#&2 file can be used to uniformly bulk all the inflow hydrograph volumes. &lluvial fans that do not exhibit mudflow depositional features can be conservatively bulked using an $%7$ value of (+ to (; by volume. 2ypically is not necessary to bulk river flood simulation as the sediment concentrations will rarely exceed ; by volume. 1etting $%7$ P ; for river flooding will conservatively bulk the inflow hydrograph volume by (.+;. Mud and debris flow simulations should be simulated by assigning concentrations by volume to the inflow hydrographs.
;@
5.5 Floo%l! !% C#!!$l I!"lo, !% Out"lo, H'%(o&(#*
2he data file for the inflow hydrographs is I7%W.#&2. & discreti!ed flood hydrograph from an upstream basin can be inflow either to the floodplain, channel or both. More than one grid element can have an inflow hydrograph. Hydrographs can be assigned as either direct inflow or outflow 'diversions from a channel by using the I7%:2$ switch in the I7%W.#&2 file. or example, an irrigation diversion can be assigned an outflow hydrograph from any channel element. 2his could be a simple constant diversion of (++ cfs or a variable hydrograph over the course of the simulation. If mudflows are being simulating then a volumetric sediment concentration or sediment volume must be assigned to each water discharge increment. In an urban area, the user can specify that the inflow hydrograph be received by the floodplain element or first enter a specific street segment within the floodplain element. %utflow control for the %-/# model is specified in the %:2%W.#&2 file. or flow out of the grid system, outflow grid elements must be specified for either the floodplain or channel or both. 2he outflow discharge from outflow elements is set e"ual to sum of the inflow to that outflow element and a flow depth is then assigned to the outflow element based on a weighted average of the upstream flow depths. In this manner, normal flow is approximated at the outflow element. 2he outflow discharge is totally removed from the system and is accounted by the model to the outflow volume. It is possible to specify outflow from elements that are not on the boundary of the grid system, but outflow elements should be treated as sinks 'all the inflow to them is lost from the flow system. %utflow elements should generally not be modified with &C6s or WC6s, levees, streets, etc. $hannel outflow can also be established by a stagedischarge relationship in the %:2%W.#&2 file. 2his option can be used when the channel outflow may occur at a hydraulic structure or when a known discharge relationship is available. 1tage-time relationships can be specified for either the floodplain or channel in the %:2%W.#&2 file. 2hese relationships can be assigned for outflow elements or for any elements in the system. When a stage-time relationship is specified, volume conservation is maintained when the discharge enters or leaves the stage-time designed grid element. 1tage-time relationships provide opportunity to simulate a wide variety of coastal flood simulations related to sea storm surge, hurricane surges or tidal waves. In addition, the backwater effects of tidal variation on river and estuary flooding can be simulated. It is possible to simulate the ocean stage in urban areas without inflow hydrographs or rainfall. 5.6 Floo%l! C(o** S$)to!*
& floodplain cross section analysis can be conducted by specifying grid elements in a cross section in the %:2%W.#&2 file. 2he grid elements must be contiguous in a straight line to constitute a cross section across a floodplain or alluvial fan. 5y designating one or more cross sections, the user can track floodwave attenuation across unconfined surfaces. 5oth the flood hydrograph and flow hydraulics can be analy!ed at cross sections. 2he average cross section hydraulics as well as the individual grid element hydraulics in the cross section are summari!ed in cross section output files, $C%11Z.%:2, HD$C%11.%:2 and $C%11M&.%:2. 5.7 G(#)l U*$( I!t$(")$ !% Wo(!& E!v(o!+$!t & graphical user interface 'A:I can be used to facilitate the data input. 2he A:I creates the &1$II text files used by the %-/# model and it re"uires only a few instructions to get
;>
started. 2o open the A:I, click on the %-/# Icon on your desktop or locate the %-/#. file in the %-/# subdirectory. 1pecific instructions for the A:I are presented in the #ata Input section of the manual. 2he A:I is series of forms that represent the individual %-/# data files. ach form consists of data dialog boxes, radio switch buttons or grid entry tables. 1ome of the data is nested in various levels of dialog boxes that are activated as the data is entered. 2he dependencies of nested tables are automatically filled as the user proceeds to develop the data base from bottom to top. &fter the data is entered in the A:I dialog boxes, the resulting &1$II text file can be viewed from the A:I or from any other &1$II editor such as M1 Word . Dou can run the model or any of the processor programs from the A:I, but the model doesn6t need the A:I to run a simulation. 2he model only re"uires that the data files are accessible and are constructed in the &1$II format specified in the #ata Input Manual. %nce the files have been created with the A:I, it may be easier to edit the %-/# data files with the %7EIC or A#1 programs. urther discussion of the A:I is presented in the #ata Input Manual. & working graphical environment '%7EIC can be used spatially edit the %-/# data base. It is possible to !oom, pan and !oom extents6 in the program. 2he %7EIC displays the grid system and allows selection of individual or groups of grid elements using the mouse. Arid element attributes can be edited by picking individual elements or by painting a group of elements with the mouse or by drawing a polygon around a group of elements and then modifying parameters in dialog boxes. $hannel, levee, streets, infiltration, area and width reduction factors, floodplain elevation and roughness, inflow and outflow nodes and rill and gully attributes can be edited. Cainfall can be spatially varied using the %7EIC. %7EIC saves the data in the &1$II format necessary to run the model. 2hese data files can also be started from scratch after the topographical B&I7.#&2 and $&#B21.#&2 files have been created. 2he %7EIC is a particularly useful tool for editing large groups of spatial variable data such as infiltration. 2his processor program is discussed more fully in the second portion of the manual.
5.3 G(% D$v$lo$( S'*t$+ =GDS>
2he Arid #eveloper 1ystem 'A#1 will generate the %-/# grid system from a set of digital terrain model '#2M points. It is a pre-processor program that will overlay the grid element system on the #2M points, interpolate and assign elevations to the grid elements. It will automatically prepare the B&I7.#&2 and $&#B21.#&2 files for the %-/# model. 2he %-/# grid system is constructed interactively with the A#1 using mouse point and click events. 2he data is thoroughly validated in order to minimi!e common input errors. 2he A#1 supports both the nglish and the 1I system of units. &fter the A#1 overlays a grid element on the limits of the #2M points, the user selects the boundary grid elements that will constitute the outline of the %-/# system. 2he next step is to interpolate the grid element elevations from the #2M points. 2he user will select #2M filter criteria to interpolate the grid element elevations. ilters are available for both high and low #2M points. 2he need for filters arises from #2M points that may have been assigned to trees, bridges or channel beds. 2he A#1 replaces the need for a $&## program to assign grid element elevation and significantly improves the grid element elevations, by filtering points that may
;*
distort the average floodplain elevation. In addition to developing the %-/# grid 2he #2M also supports several important functions including the assignment of spatially variable n-value roughness, infiltration parameters, and the importation of images and AI1 shape files. 2he A#1 program incorporates 1CI Map%b0ects< AI1 software controls. & discussion of all the various tools and components related to the 1CI and AI1 interface is presented in #ata Input Manual. A#1 includes the following options9
•
1CI shape file format data such as land use, soil types, and Manning roughness coefficients can be imported.
•
1CI &rcInfo &1$II grid files containing terrain elevations and 7%&& rainfall isopluvial data can be imported.
•
Multiple geo-referenced aerial photos in various graphic formats such as 2I, 5MB, =BA, etc. can be imported and created as background.
•
Multiple 1CI &rcInfo &1$II grid files can be listed in a tile and index catalog file and referenced to a user defined polygon in the study.
•
Multiple image files like aerial photos can be listed in a tile and index catalog file and referenced to a user defined polygon in the study area.
• 7ew multiple layer capability is available including extensive control of layer properties. •
1patially variable Areen-&mpt infiltration parameters can be assigned to %-/# grid elements based on soil shape files, land use shape files, and soil and land use properties tables.
•
1patially variable Manning roughness coefficients can be assigned to %-/# grid elements based on Manning shape files.
•
1patially and time variable rainfall data can be computed and assigned to %-/# grid elements based on multiple 7%&& rain data files.
•
$hannel cross sections can be cut from regular or irregular elevation points and assigned to particular channel segments.
;)
5.8 G(#)l Outut Oto!*
& graphical display of the flow depths can be viewed on the screen during a %-/# simulation to visuali!e the progression of the floodwave over the potential flow surface. #ifferent color pixels represent different flow depth increments. 2he display is initiated by a variable switch AB%2 in the $%72.#&2 file. 2he user can specify the simulation time interval for updating or refreshing the graphical display. In addition to the predicted flow depths, an inflow hydrograph will be plotted. %nly one inflow hydrograph can be plotted and the user must specify which inflow channel or floodplain grid element hydrograph to view in the I7%W.#&2 file. If rainfall is simulated, the cumulative precipitation can also be plotted. If the flow depth graphics are not displayed, then a simple list of the model simulation time, minimum timestep and volume conservation are displayed on the screen. When the %-/# simulation is complete in the graphics mode, the maximum flow depths are displayed on the screen. If a further review of the grid element maximum depth and velocity for floodplain, channel and street flow displays are desired, a post-processor program M&B%2 will "uickly display the results including maximum and final depths and velocities. It also has a simple time series simulation whose time se"uence variables are specified in 2%C.#&2. &dditional graphic programs include HD#C%A, BC%I1 and M&BBC. HD#C%A is a post-processor program that will plot the hydrograph for every channel element. 2he user can "uickly move up and down the channel, viewing the channel hydrograph out of the channel element. 2he hydrographs can be printed or saved as an &1$II data file or Q.bmp image. HD#C%A can also be used to evaluate the average channel hydraulics in a given reach. 2he user can select the upstream and downstream channel elements and the program will compute the average of the hydraulics for all the channel elements in the reach including9 velocity, depth, discharge, flow area, hydraulic radius, wetted perimeter, top width, width to depth ratio, energy slope, and bed shear stress. &n optional data file of measured hydrographs 'HD#C%.#&2 can be prepared for comparison with the %-/# predicted hydrograph. 2hese two hydrographs are plotted together. 2he BC%I1 program plots channel water surface and bed slopes. It also displays survey cross section data in a profile plot and table so the channel cross section geometry can be edited and interpolated. BC%I1 is an important useful tool when building and editing the channel data file. Aenerally, one cross section is surveyed for every F to ; channel grid elements. It is necessary therefore to interpolate cross sections for channel elements without surveyed cross sections. 2his can be accomplished by simply selecting the upstream and downstream channel elements and clicking the interpolation button. low area weighted cross sections will be distributed to those channel element between the know cross sections. 5oth cross section shape and slope are interpolated. M&BBC is the primary program for displaying and utili!ed the %-/# flood simulation results. It can be used to develop production color contour plots of the %-/# results either on a grid element or #2M point basis including hydraulic variables and water surface elevations. 2hree types of maps can be created9 grid element or #2M point plots, contour maps and shaded contour maps. 2hese graphic maps may be created for ground surface elevations, maximum water surface elevations, maximum floodplain flow depths and maximum velocities. %ne of the most important features of M&BBC is its capability to create flood depth plots using the #2M topographic points. When the user activates the feature, M&BBC will subtract each #2M
@+
ground point from the grid element floodplain water surface elevation. 2he resultant #2M point flow depths can then be interpolated and plotted as color contours. M&BBC version 8.+ has the following features9
•
Incorporates 1CI Map%b0ects< AI1 software controls.
•
1CI shape file format data such as land use, soil types, and Manning roughness coefficients can be imported.
•
1CI &rcInfo &1$II grid files containing terrain elevations can be imported.
•
Multiple geo-referenced aerial photos in various graphic formats can be imported such as 2I, 5MB, =BA, etc.
•
Multiple 1CI &rcInfo &1$II grid files listed in a tile and index catalog file and referenced to a user defined polygon over the grid system can be imported.
•
Multiple image files such as aerial photos listed in a tile and index catalog file and referenced to a user defined polygon over the grid system can be imported.
• 7ew multiple layer capability, including control of layer properties is available. M&BBC can also export various types of graphic files for use in other $&## applications. AI1 shape files 'Q.shp are automatically created with any plotted results. 2his AI1 shape files can be then be imported into &rcEiew or other AI1 programs. &ll of these post-processor programs are described in detail in the input data section of the manual. 2he M&BBC tool will continue to be expanded in the future. M& I1 flood map templates are being prepared for the next version of %-/#.
5.9 Dt Outut Oto!*
2he %-/# model has a number of output options and files to help the user organi!e the results. loodplain, channel and street hydraulics are written to file. Hydraulic data include water surface elevation, flow depth and velocities in the eight flow directions. #ischarge and sediment concentration for specified output intervals 'hydrographs are written to various files. & mass conservation summary table comparing the inflow, outflow and storage in the system is presented in the 1:MM&CD.%:2 file and at the end of the 5&1.%:2 file. 1everal options available to format the output files to generate either temporally or spatially varied results. 1ome output files are created by simply initiating the various flow components 'e.g. 12C2.%:2 is created when street flow is simulated. & complete description of the output files are presented in the #ata Input Manual. %utput files that are generated by %-/# include9 +%(.BCT - 2his output file lists the inflow hydrograph, flow hydraulics for each output timestep, summary listing of the maximum flow hydraulics and summary mass conservation table. &ll the hydraulic output data for every grid element and timestep can be written to this file. :se the 7%BC2B and 7%BC2$ variable switches in the $%72.#&2 to limit the output in this file.
@(
&0+D*)IE.BCT - 2he channel elements that experience significant gains or losses of flow volume are listed in this file. 2hese channel elements can be reviewed for volume conservation problems. &0+D/+F.BCT - 2his output file lists the peak discharge for each channel element along with its corresponding time of occurrence. &0+D+D>('.&0> - When the bank elevations prescribed in the $H&7.#&2 do not match the corresponding floodplain grid element elevations, the difference in elevation is reported in this file. If the difference between the channel bank elevation and the floodplain grid element elevation exceeds ( ft '+.8 m, the model reports it in this file. 2his includes the channel extension grid elements. If the ( ft '+.8 m limit is exceeded during the simulation, the model assumes that the bank elevation is a more accurate representation of the floodplain for that grid element and resets the floodplain elevation to the bank elevation. &0+DD('.&0> - 2he grid elements which encompass a channel cross section are listed in this file. Ceview this file when the channel is wider than the width of a grid element. &0+D%.BCT - 2his output file contains a list of channel element, x- and y-coordinate and channel water surface elevation. &0D(E('.BCT - 2his file is a list of the channel element bed elevations used in the M&B%2 post-processor program. &0"B'C/(.BCT - Bresented in this file is a summary of the channel volume conservation including channel inflow, outflow, overbank flow, return flow from the floodplain, infiltration losses and channel storage. Ceview this file to discern if the channel volume is being conserved. &BD2'C(D&(.BCT - In this file there is a list of channel elements that constitute a confluence as defined by having three or more channel elements contiguous to a given channel element. 2he confluence may be a prescribed condition or it could constitute a data error in the $H&7.#&2 re"uiring 7%%$ definition. &)B%%A.BCT - 2he discharge hydrograph for the cross section grid elements listed in the %:2%W.%:2 file are presented. 2he floodplain cross section option must be initiated. &)B%%/+F.BCT - 2his is an output file created with the floodplain cross section option that will list the peak discharge for each floodplain cross section by grid element and time of occurrence. E(GT0.BCT - 2his file contains the predicted maximum flow depths for either floodplain, street or channel grid element whichever is the greatest. It lists the maximum flow depth for each grid element together with the x- and y-coordinate in a format that can be imported to $&## software. 2he $&## program can then be used to create maximum flow depth contours using the digital terrain model. Celated maximum depth output files with grid element number, coordinates and depth include9 E(G&0.BCT - Maximum channel flow depths. E(G2G.BCT - Maximum floodplain flow depths. E(GT0.BCT - Maximum combined channel, street and floodplain flow depths.
@/
2ID+'E(G.BCT - inal floodplain flow depths. E(GT0EC).BCT - 2he flood duration for a prescribed flow depth is written to this file along with grid element numbers and coordinates. 2he user specifies a floodplain flow depth and then the model tracks the time duration that the grid element is flooded above prescribed flow depth. E(GT0TB'.BCT - 2his file contains the maximum combined channel and floodplain flow depths greater than the 2% value. Ealues less than the 2% value are set to !ero. ())B).&0> - $heck this file for data input errors when the program prematurely terminates. 2he backup files 'Q.5&$ should be reviewed in con0unction with this file. 2G%CG().BCT - When the overland flow is supercritical, the grid elements, time of occurrence and roude 7umber are written to this file. 03&0+D.BCT - 2his output file lists the channel flow hydraulics including elevation, flow depth, velocity, discharge and sediment discharge by grid element in hydrograph form. It also lists the maximum discharge, stage and their time of occurrence. &dditional channel flow hydraulic and geometry parameters include9 flow area, hydraulic radius, wetted perimeter, top width, width-todepth ratio, energy slope, and bed shear stress. 03&)B%%.BCT - 2his file lists all the floodplain cross section hydraulic data including elevation, top width, flow depth, and velocity, discharge and sediment concentration. 2he floodplain cross section option must be initiated. 03E)B%T)C&T.BCT - 2he discharge hydrograph from any hydraulic structure listed in the HD#C%12C:$.#&2 file is presented in this output file. I/G+&T.BCT - 2his file list the impact force per linear foot of structure on the floodplain. 2he data is presented by grid element number, coordinates and force per linear foot. ID2I'03.BCT - 2he hydraulic conductivities are listed in this file to view the spatial variation. 2his file contains grid element number, coordinates and floodplain hydraulic conductivity. IDT()*%.BCT - 2he maximum floodplain water surface elevations based on the grid element elevation in the 2%B%.%CI are presented in this file. Ealues less than 2% are set to !ero. '("((.BCT - 2he E.%:2 file contains a list of the grid elements with a failed or overtopped levee. If the levee has failed, the failure width, levee elevation, discharge and the time of failure are listed. If the levee has only been overtopped without failure a output interval time and discharge are presented. /C'T&0D.BCT - &d0ustments to the multiple channel widths during the model simulation are listed in this file. 2hese ad0ustments are dependent on the gully bankfull discharge and incremental width increases. BCTDA.BCT - Hydrographs for the floodplain outflow grid elements are listed in this file.
@8
B"()+D>.BCT - When the flow exceeds bankfull discharge and begins to inundate the floodplain, the channel grid element and time of overbank flood occurrence are written to this file. )BC*0.BCT - 2his file can be reviewed for maximum n-values computed when the predicted roude number exceeds the specified limiting roude numbers. 2he final and original n-values are also written to this file. %(E&0+D.BCT - 2his file lists the maximum changes in the channel bed elevations resulting from the application of the sediment transport routing algorithm. 2he x- and y-coordinates, maximum deposition, maximum scour and final elevation changes by grid element are written to this file. %(E2G.BCT - 2his file is the companion output file to 1#$H&7.%:2 file for floodplain elements. 2he maximum changes in the bed elevation for each floodplain grid element are recorded. %(ET)+D.BCT - 2he sediment transport capacity 'cfs or cms computations for each of the six sediment transport e"uations are listed by output interval in this file. %G(&(D()*3.BCT J 2he specific energy is the sum of the depth plus the velocity head. 2his file lists the maximum specific energy for a floodplain grid element and includes grid element number, coordinates and maximum specific energy. %T+TI&G)(%%.BCT - 2he spatially variable static force per linear foot for each floodplain element is presented is this file by grid element number, coordinates and force per linear foot. %T)((T.BCT - 2his file is similar to the #B2H.%:2 file. It contains the grid element number, x- and y-coordinates and the predicted maximum street flow depths. %T)("('.BCT - 2his file is a list of the street elevations used in the M&B%2 post processor program. %C//+)3.BCT - 2he mass conservation table comparing inflow, outflow and storage is presented in this output file. 2his table is also listed at the end of the 5&1.%:2 file. %CG().BCT - When the floodplain or channel flow is supercritical, the grid elements experiencing supercritical flow, roude number, discharge and time of occurrence are written to this file. 2his file re"uires that the variable 1:BC P ( in the $%72.#&2 file. %C)2+)(+.BCT - 2his file summari!es all the available surface storage area by grid element in the system including the channel surface area, street surface area, multiple channel area, floodplain areas reduced with the area reduction factors and the remaining floodplain surface area available for flow storage. &t the end of the file is an output interval listing of the wetted area of inundation by floodplain, channel and combined maximum. 2his output will indicate approximately when the maximum surface area was inundated. TI/(.BCT - 2he twenty grid elements associated with the most timestep decreases are listed in this file. 2his file identifies which floodplain, channel or street elements are the most fre"uent in
@F
slowing down the model. 2hese are the grid elements whose attributes the user can modify to speed up the flood simulation. TI/E(G.BCT - 2he predicted flow depths are written to this file according to grid element together with the x- and y-coordinates for prescribed output intervals for a time lapse display of the flood progression. 2his file can be imported to the $&## drawing to create time lapse flow contours or a 8-dimensional display of the flood movement. M&B%2 will create an animation of the flood event using this file. "('B&.BCT - 1imilar to the #B2H.%:2 file, this file contains the predicted maximum velocity for each grid element along with the x- and y-coordinates. Maximum velocity contours can be plotted in M&B%2, M&BBC or in $&## software. Celated maximum velocity files with grid element number, coordinates and velocity data include9 2ID+'"('.BCT - inal overland flow velocities at the end of the simulation 2ID+'"('EI).BCT- inal maximum overland flow velocity components at the end of the simulation. %T"('.BCT - Maximum street flow velocity. %T"('EI).BCT - low direction of the maximum street flow velocity component. "('2G.BCT - Maximum floodplain flow velocity "('B&.BCT - Maximum combined channel, street and floodplain flow velocity. "('EI)(&.BCT - low direction of the maximum floodplain flow velocity component. F%(&+)(+.BCT - 2his output file contains cross section geometry data including bankfull flow area, wetted perimeter and top width. F%(&.BCT - 2his file is created by the sediment transport option 'I1# P ( in $%72.#&2 with channel cross section data. It contains the final cross section bed elevations after scour and deposition have been computed in a mobile bed simulation.
2he M&B%2 program uses the following %-/# output files for a graphical display of the maximum depths and velocities 'these files contain grid element number, x- and ycoordinates, and depth, velocity or elevation9 &0D(E('.BCT - $hannel element bed elevations. E(G&0.BCT - Maximum channel depths. E(GT0EC).BCT - #uration of flooding about the specified depth in hours. E(G2G.BCT - Maximum floodplain depths. E(GT0.BCT - Maximum combined channel, street and floodplain flow depths. 2ID+'E(G.BCT - 2he final channel or floodplain depths at the end of the simulation. 2ID+'"('.BCT - inal velocity at the end of the simulation. 2ID+'EI).BCT - inal flow velocity direction at the end of the simulation. %(E2G.BCT - Maximum changes in the grid element bed elevation. %T)((T.BCT - Maximum street flow depths. %T)("('.BCT - 1treet elevations. %T"('.BCT - Maximum street flow velocities. %T"('EI).BCT - low direction of the maximum street flow velocity components.
@;
"('EI)(&T.BCT - 2he maximum flow velocity directions. "('2G.BCT - 2he maximum flow velocities. "('B&.BCT - Maximum combined channel, street and floodplain flow velocities.
5.1: St(t!& t#$ P(o&(+
&fter the data files have been constructed with the A:I or with an &1$II editor, the model is ready to run. %nly six data files are re"uired to run an overland flow simulation, B&I7.#&2, $&#B21.#&2, $%72.#&2, 2%C.#&2, I7%W.#&2 and %:2%W.#&2. rom Windows xplorer, open the pro0ect subdirectory containing the data files, make sure that the %. is in the subdirectory and double-click on %. to start a flood simulation. 7o other commands are necessary. Most users will open the %-/# A:I by clicking on the desktop icon and then activate the %-/# model using the xecute6 button from the pull down menu to start a flood simulation. &ll the processor programs are accessible from the A:I pull down menus. In addition, any of the processor programs can be run by putting the Q. file for the processor into the pro0ect subdirectory and double-clicking on the processor name.
@@
5.11 Co%$ L!&u&$ !% H(%,($ R$0u($+$!t*
2he %-/# model software is written in ahey ortran ); computer language. Windows-based graphics code and subroutines have been written in the Winteracter 8.+ language from Interactive 1oftware 1ervices, td. of the :nited ingdom. 2he %-/# A:I, A#1 and M&BBC processor programs were written in Eisual 5asic. 2here are no hardware limitations for computers less than two years old with a clock speed greater than (.; MH! and either a Windows )*, /+++, B or 72 operating systems. &lmost all of the variable arrays are allocated at model runtime so the number of grid elements and associated components such as channels and streets are essentially unlimited. %n occasion an older computer may have a #%1 default to an integer array limitation of 8/,>@>. 2his means that the number of grids should be less than 8/,+++. 2he normal integer array si!e default is /,(F>,F*8,@F>. & complete list of data array si!e limitations and variable range is provided in the second portion of the %-/# manual.
@>
V.
FLO-2D APPLICATIONS AND METHODS
6.1 Rv$( Al)to!*
1imulating channel flow is one more difficult facets of applying the %-/# model. &brupt channel cross section transitions, flat bed slopes, confluences and limited data bases are some of the difficulties that have to be addressed. 2he key to effective %-/# river flood applications is correctly assessing the relationship between the volume stored in the channel and the volume distributed on the floodplain. 2his re"uires good definition of the relationship between channel flow area, slope and roughness. 2here are several considerations to defining channel volume and geometry. &n accurate estimate of the total channel length 'sum of the channel grid element lengths is critical to channel volume computation. In addition, the surveyed channel cross sections should be appropriately spaced to ade"uately model transitions between wide and narrow cross sections. inally, bankfull water surface elevations should be surveyed at cross sections to calibrate the channel roughness values. Modeling channel geometry with a limited data base can result in discharge surging, which can be observed in a plot of the channel element hydrographs. 2he conse"uence of an inade"uate channel data base is small timesteps and long flood simulations to reduce or eliminate the numerical surging. %nce the %-/# topography files B&I7.#&2 and $&#B21.#&2 have been created, the channel system can be laid out. 2his is easily accomplished in the %7EIC program by first selecting channel grid elements and then assigning the various channel attributes. &fter the $H&7.#&2 file has been created, the channel bed slope and cross sections can be ad0usted in the BC%I1 program. 2he program displays the channel profile and the cross section plots which can be edited directly in BC%I1. When one cross section has been assigned to several grid elements, the bed slope through this reach will be flat. 5etween channel elements with surveyed cross sections, the bed slope can be interpolated in the BC%I1 program to create a uniform bed slope. 1imilarly, between channel elements with surveyed cross sections, the assigned cross sections can be interpolated to create a smooth transition between wide and narrow surveyed cross sections. When preparing a channel simulation, the available cross section data is distributed to the various channel elements based on the top width observed on mapping, images or aerial photos. 2he bed elevation is then ad0usted between cross sections to achieve a uniform slope between the surveyed cross sections. 2he n-value assignment is estimated from either calibration of surveyed water surface elevations or from knowledge of the bed material, bed forms, vegetation or channel planform. 2he n-values also serve to correct any mismatched channel flow area and slope. 5y specifying a maximum roude number that represents bankfull flow conditions for a given reach, the model will increase the n-values gradually when the limiting roude number is exceeded. 2he maximum n-value can be reviewed in the C%:AH.%:2 file and then the n-values in the channel can be ad0usted. If the n-value ad0ustment appears to be outside an acceptable range, the flow area or the bed slope can be revised. :sing this approach, the relationship between the channel flow area, bed slope and n-value can be ad0usted to better represent the physical system, calibrate the water surface elevations, and reduce surging and speed-up the simulation. 2he limiting roude will also keep the average velocity in an acceptable range of the wave celerity. 2he floodplain inundation from channel overbank flow is a function of the channel conveyance and the floodplain roughness and topography. 2o improve the accuracy of a flood
@*
inundation analysis, the channel conveyance and water surface elevations should be calibrated by modifying the n-values, the flow area or the bed slope. 2he floodplain topography can then be checked to insure that the grid element elevations are appropriate. 2he speed of the floodwave progression over the floodplain can be ad0usted with the floodplain n-values. 2he two most important %-/# results are the channel hydrograph at a downstream location and the floodplain area of inundation. 2ypically if the area of inundation is correct, then the floodplain flow depths and water surface elevations will be relatively accurate. Ceplicating the channel hydrograph and the floodplain inundation while conserving volume is a good indication that the volume distribution between the channel and the floodplain is accurate. looding routing details for channel applications include simulating hydraulic structures, levees, infiltration, sediment transport and hyperconcentrated sediment flows. Hydraulic structure rating curves and rating tables are input in the HD#C%12C:$2.#&2 file and may include bridges, culverts, weirs, diversions or any other channel hydraulic control. evees are usually setback from the river on the floodplain, but can control the water surface in the channel if the flood is confined by the floodplain levees. $hannel infiltration is based solely on the hydraulic conductivity in the I7I.#&2 file and represents average bed and bank seepage conditions. 5ed scour or deposition associated with a mobile analysis is nonuniformly distributed on the channel cross section. inally, mudflows can be routed in channels.
6.2 Ov$(l!% Flo, !% Alluvl F! Al)to!*
&n unconfined flood simulation on a floodplain or alluvial fan without channels will usually have larger timesteps and be more numerically stable than channel flood simulations because the flood volume is distributed over a large surface area. & water flood simulation over a floodplain or alluvial fan surface re"uires only four additional files after topography files 'B&I7.#&2 and $&#B21.#&2 have been createdK $%72.#&2, 2%C.#&2, I7%W.#&2 and %:2%W.#&2. 2he $%72.#&2 and 2%C.#&2 files have 0ust a few lines of control and numerical stability data. 2he I7%W.#&2 file contains the inflow hydrograph and the %:2%W.#&2 lists the outflow nodes. If the flood hydrology is available, %-/# floodplain simulation without channels can be running within minutes after the topography files are created. 2he primary focus of an unconfined flood simulation is based on those factors that control volume distribution over the surface. 2he important flood routing details are accurate topography, spatial variation in infiltration and roughness and features such as flow obstructions and streets. 1treet flow is important for distributing shallow flooding in urban areas. 5uildings and walls that obstruct flow paths and or eliminate floodplain storage are important for flow path redirection. %ther flood routing details include levees, hydraulic conveyance facilities such as culverts, rainfall and gully flow. 2he levee routine can be used to simulate berms, elevated road fill, railroad embankments or other topographic features. It is possible to use the overland flow components to model the interior of various floodplain features such as detention basins, river channels or even streets. lood retention basins have been modeled as part of the entire floodplain system using either the grid element elevation or levees to define the basin storage area. &n appropriate grid element si!e should be selected to generate enough interior elements to ade"uately simulate the basin or channel. It should be noted
@)
that modeling the channel interior may re"uire very small timesteps. Manning6s steady flow, open channel flow e"uation for the friction slope may not be appropriate if the ponded water surface is very flat. %-/# can simulate an unconfined overland floodwave progression over a dry flow domain without any specifying any boundary criteria. 7o hot starts or prescribed water surface elevations are re"uired. 2here is no limit to the number of inflow hydrograph elements. %utflow nodes must be designated but re"uired no specific boundary conditions or water surface control. %utflow from the grid system is approximate as normal depth flow using a weighted average flow condition of the contiguous upstream grid elements. If no inflow flood hydrograph data is available, %-/# can perform as a watershed model. Cainfall can occur on the floodplain surface resulting in sheet runoff after infiltration losses have been computed. It is possible to simulate rainfall while routing a flood event and have rainfall occur on a flood inundated area. 2o improve concentration time, rill and gullies can be modeled to exchange flow between grid elements. 2his will reduce the travel time associated with sheet flow exchange between grid elements. 1patially variable rainfall distribution and a moving storm can be simulated. Ceal time rain gauge data can also be reduced and reformatted in the A#1 for real time storm runoff and flood simulation. . Mud and debris flows can be simulated on alluvial fan surfaces. 2here are two methods for loading the hydrograph with sediment. & sediment concentration by volume is assigned to a discreti!ed time interval of the inflow hydrograph. & second method is to load the inflow hydrograph with a volume of sediment. In this manner, spatially differential sediment loading in a watershed channel can be simulated. %nce the hydrograph is bulked with sediment, the mudflow is routing as a water and sediment continuum over the hydrograph. 2he same water routing algorithm is used for mudflows but the momentum e"uation is solved with the additional viscous and yield stress terms. 2he bulked sediment hydrograph is tracked through system conserving volume for both water and sediment. low cessation and flow dilution are possible outcomes of the mudflow routing.
6. P(o/$)t R$*ult* ; W#t * Su))$**"ul Floo% S+ulto!?
When a %-/# simulation is completed, how do you that the simulation was successful or accurate Where should you look first to determine if the results are meaningful 2he first output file that should be reviewed is the 1:MM&CD.%:2 file. In this output file, volume conservation results and the ultimate disposition of all the inflow hydrographs and rainfall can be examined. If the volume was not conserved, then it will be necessary to conduct a more detailed review of the 1:MM&CD.%:2 and other files to determine when the volume error was initiated and whether the channel volume was conserved '$HE%:M.%:2. If the volume was conserved, then the area of inundation can be "uickly reviewed in either M&B%2 or M&BBC programs. 2he area of inundation may be limited if the channel elements were disconnected or if a routing component did not have correct data. If the area of inundation seems reasonable and the flood appears to have progressed completely through the system, then the channel flow should be reviewed for surging in either $H&7M&.%:2 of by scanning the channel element hydrographs in the HD#C%A program.
>+
%nce the %-/# flood simulation is providing good results, the next step is to fine tune the model and add more detail. 2o speed up the model, review the 2IM.%:2 file to determine which channel floodplain or street elements are causing the most timestep reductions. If the number of timesteps reductions for a grid element is an order of magnitude or greater than the rest of the elements, its topography, channel geometry, slope or roughness in relationship to its neighbor grid elements can be ad0usted. Model speed is not critical if the simulation is accurate with respect to volume conservation, discharge surging and area of inundation unless a number of pro0ect scenario simulations are re"uired. #uring the review process, the C%:AH.%:2 file can provide insight into the model analysis. $hannel, street or floodplain elements with large increases in roughness in response to reasonable limiting roude numbers should be reviewed and ad0usted. High roude numbers may be the result of discharge surging and this can be initially addressed with more appropriate or spatially varied n-values. It may necessary to increase the n-values for several elements in a given reach or area. If the model does not respond to higher n-values, ad0usting the slope or flow area may be re"uired. or mudflow flow simulations, the sediment volume reported in the 1:MM&CD.%:2 file should be reviewed. Eery viscous mudflows should have an average concentration by volume in the range from /; to 8;. 2he total inflow sediment volume should represent the potential sediment yield from the watershed for the simulated return period volume. & rough check of the potential sediment supply should be reviewed including hillslope failure, bank erosion, channel scour and overland sediment yield. In the #ata Input portion of the manual, further discussion of model analysis and trouble shooting is presented. When it seem unclear as to where the pro0ect model is not functioning correctly, simplify the simulation by turning off components. or example, turn off all the peripheral model details except for the channel and the floodplain. Make certain that these two components are providing accurate results. 2hen add components back to the model, one component for each model simulation, turning off the previous reviewed components. In this manner, the model component that may be causing the problem will be revealed. Ceducing the timesteps should never be overlooked when addressing issues such as discharge surging and erratic results.
>(
VI. FLO-2D MODEL VERIFICATION 7.1.
G$!$(l
2he %-/# model has been applied on countless pro0ects by federal and state agencies, consulting firms and international users. Most users perform some sort of verification test to convince themselves of the validity of the flow routing algorithms. & 1wiss research organi!ation conducted a flume test to compare measured data with model predicted hydraulics. &ll users have to address the concern of whether the %-/# predicted hydraulics are reasonable and accurate for their pro0ects. %n occasion, an application may re"uire some code modification to address a uni"ue flow problem. In =anuary ())), the 1acramento #istrict $orps of ngineers accepted of the %-/# model for overland flow and alluvial fan flood studies. 2hey conducted a review of several model test applications, applied the model to a number of unconfined flood ha!ard pro0ects, developed the $alifornia &"ueduct test case and replicated of the &rroyo Basa0ero March ()); alluvial fan flooding. %ver a three-year period, the $orps actively engaged in model enhancement, code modification and model testing to expand the model applicability. In early /++(, the &lbu"uer"ue #istrict of the $orps of ngineers completed a review of the %-/# model for riverine studies. Much of the supporting documentation and application test cases are described in this section. 5oth the 1acramento and &lbu"uer"ue #istrict submitted acceptance letters to M& in support of using the %-/# for flood insurance studies. 2he %-/# model is on M&6s list of approved hydraulic models for both riverine and overland flow 'alluvial fan flood studies. Eerification of hydraulic models with actual flood events is dependent on several factors including estimates of flow volume and area of inundation, appropriate estimates of flow resistance, representative conveyance geometry, accurate overland topography and measured flow hydraulics including water surface elevation, velocities and flow depths. Ideally, the best model test involves the prediction of a flood event before it occurredK however, the probability of an actual flood having the exact volume of the predicted flood event is remote. Eerification 2est F, the Areen Civer routing model provides an opportunity to test the model with actual flow releases from a dam. 2he tools for verifying hydraulic models include physical model 'prototype studies, comparison with other hydraulic numerical models or replication of past flood events. 2o review the accuracy of the %-/# model all three verification methods are employed. 2he primary verification issues are the accuracy of the channel and the unconfined overland flow routing algorithms and the area of inundation. & series of application tests are presented for the %-/# model verification9
• • • • • •
$hannel flow using the full dynamic wave e"uation on the mild sloped $alifornia &"ueductK $hannel flow routing component compared to H$-/ model resultsK $hannel and floodplain flow routing for an actual river flood, 2ruckee Civer, ())>K $hannel routing in a ma0or river system 'Areen Civer with prediction of a dam release floodwave movementK $omparison of floodplain inundation with mapped wetted acreage 'Middle Cio ArandeK Eerification of mudflow hydraulics.
>/
2he results of these tests demonstrate that the %-/# computation algorithms are accurate for both channel and overland flood routing. 2he results also demonstrate the importance of routing the entire flow hydrograph. &ll the verification tests for &lbu"uer"ue #istrict review were rerun with the most recent version of the %-/# model.
7.2. V$(")to! T$*t 1. C#!!$l H'%(ul)* ! t#$ Cl"o(! A0u$%u)t
#ischarge in a (+ mile reach of the $alifornia &"ueduct near $oalinga, $alifornia was simulated using )@ channel elements in a ;++ ft s"uare grid system. 2he a"ueduct is essentially a large outdoor physical model and is one of the most difficult hydraulic simulations for a finite difference model because of the high discharge flux, very low roude number flow and very mild slope ';.> x (+-;. 2ypically numerical surging is difficult to control in such cases. 2his test application is comparable to modeling flow in the Mississippi Civer. 2he design discharge for this concrete lined trape!oidal channel was approximately *,(;+ cfs. 2he roughness n-values for most of the (+ mile reach ranged from +.+/+ to +.+/F with a few grid elements having slightly higher n-values of +.+/; or +.+/@. 2he variability in roughness accounted for the irregularities in the canal bed due to subsidence in the $entral Ealley resulting from long term groundwater extraction. 2he simulation time was > hours to create uniform flow throughout the reach for a constant discharge of *,(;+ cfs. &t the end of the simulation, the inflow discharge was *,(;+ cfs and the outflow discharge *,(F) cfs. Hydraulic design conditions for the canal reach were an average flow depth of approximately /@ ft and an average velocity of 8 fps. 2he prescribed operating water surface elevations were 8(>./@ at the start of the reach and 8(F./@ at the end of the reach. 2he %-/# predicted water surface elevations were 8(>.(; and 8(F.(@ for the inflow and outflow nodes. 2he results are presented in 2able (+ and show consistent discharge throughout the reach using the full dynamic wave momentum e"uation. 2he predicted velocities and flow depths are very uniform and precisely replicate the hydraulic design conditions. 2his application verified the %-/# dynamic wave routing algorithm for a large channel with a very mild slope.
>8
2able (+. $alifornia &"ueduct Bredicted Hydraulics
>F
7.. V$(")to! T$*t 2. V(4l$ C#!!$l G$o+$t(' H'%(ul)*
2his simulation test was performed in ()*) to verify the channel routing component by comparing the results with the $orps of ngineers H$-/ hydraulic model. 2he purpose of this test was to demonstrate %-/#s capability to replicate H$-/ flow hydraulics using an identical cross section data base and roughness values. 2he initial %-/# tests were conducted using only the diffusive wave approximation to the full momentum e"uation. 2he simulation test is reproduced for this document using the full dynamic wave e"uation to compute the flow velocities. Most hydraulic model testing involves the replication of pro0ect field data through the calibration of roughness parameters. 2hen to complete the test, the calibrated model may be applied to another field data base. & second, more stringent test compares the hydraulic computations from another accepted hydraulic model using identical data sets. <hough the %-/# model is a flood routing model and H$-/ predicts hydraulics using a step backwater calculation for one discharge at a time, the model comparison was accomplished by running %/# with the same discharge for a sufficiently long simulation time to achieve uniform, steady flow throughout the entire reach. & hypothetical channel //,;++ feet long with (; variable area geometry cross sections and four different slope reaches, two steep and two mild reaches was created 'igure (+. &ctual river cross sections were used in the test, but the roughness and slope were assigned fictitious values to create supercritical and subcritical flows in alternate reaches. 2he H$-/ model was run twice for each discharge, to analy!e both the subcritical and supercritical flow regimes. or the %/# simulation, the channel elements were ;++ ft in length. It should be noted that the crosssectional geometry did not necessarily correlate with the fictitious slope and roughness values and that the assumed associations between cross section, slope and roughness would not occur naturally. In the initial tests in ()*), discharges ranging from (++ cfs to (+,+++ were simulated with similar results. Cepresentative results from the ;,+++ cfs simulation are presented in igures (( and (/. &s shown in these figures, %-/# predicted flow depths and velocities that compare well with the H$-/ hydraulics. 2he differences in the results of the two models arise from interpreting the H$-/ hydraulics in the slope transitions as either subcritical or supercritical flow. %-/# predicted average transitional flow hydraulics between subcritical and supercritical regimes and any hydraulic 0umps are lost in the computation between ;++ ft grid elements. 2here is the added difficulty of interpolating the results at a given reach station since the H$-/ cross sections are not necessarily located at grid element node. Aiven the contrived channel geometry with artificial slope and roughness, the results show that natural channel routing can be conduced with %-/#. 2his test also demonstrates the consistency of the %-/# model as it evolved over the years.
>;
igure (@.
$hannel Brofile
igure (>. $omparison of %-/# and H$-/ low #epths for ;,+++ cfs #ischarge
>@
igure (*. $omparison of %-/# and H$-/ low Eelocities for ;,+++ cfs #ischarge
7.5. V$(")to! T$*t . Rv$( Floo%l! S+ulto! - T(u)$$ Rv$(@ R$!o@ N$v%
2he 2ruckee Civer has experienced significant flooding throughout its recorded history. In early =anuary ())>, rainfall on snowpack and unusually warm weather conditions resulted in flooding of the 2ruckee Civer through downtown Ceno, 7evada and the nearby $ity of 1parks. ifteen miles of river were simulated with %-/# to predict the area of inundation. & extensive hydrographic data base was compiled including over (++ channel cross section surveys. &dditional data for model calibration included two :1A1 river gages flood stage and discharge, estimated 2ruckee inflow hydrograph and numerous surveyed highwater marks through the inundated area. 2he inflow from three tributaries was estimated by the $orps of ngineers. In the 1parks 2ruckee Meadows area, significant overbank flooding occurred in a sparsely populated area before the river entered a bedrock canyon to the east. 2he 2ruckee Civer had been repeatedly analy!ed with H$-/ but the nature of the overbank flooding in 2ruckee Meadows is complex. 2he overbank flows from the river and two tributaries commingled and the floodplain discharge was e"uivalent to the channel conveyance. 1urging up and down the tributaries during the flood event was observed. 2his pro0ect provided an opportunity to review the accuracy of the %-/# channel-floodplain interface, the timing of overbank floodwave progression and the predicted area of inundation.
>>
2he 2ruckee 2ruckee Civer pro0ect task was to replicate replicate the ())> flood event. & total of ;,+*) ;++ ft grid elements with //( channel elements constituted constitu ted the %-/# grid system. Cainfall, infiltration, (* bridges and a number of streets and buildings were modeled to add detail to the simulation. 1patial variation in floodplain n-values and storage stora ge loss coefficients coefficients were imposed. 2he filling filling of large gravel pit was also simulated. simulated. $hannel roughness values were extracted extrac ted from previous H$-/ models models and calibrated calibrated to match the recorded stage at three :1A1 gages. Initially the %-/# model results were compared with those from H$-/ for an inchannel flow flow of (+,+++ (+,++ + cfs. %verbank flow ensues at approximately appro ximately ((,+++ in 2ruckee Meadows. 2he predicted water surface for (+,+++ cfs and the modeled bed profiles profiles for %-/# and H$-/ are shown in igure (8. In the upstream reach, the predicted predict ed water surfaces deviate slightly where the H$-/ cross cr oss sections are separated separ ated by a half mile or more. %ther small variations in the water surface profiles occur around aro und hydraulic structures structu res such as weirs and bridges. %verall, the match of the water surface profiles from the two models for (+,+++ cfs is excellent, especially in the sensitive flat slope at the downstream end of the reach. 2he predicted area of inundation matches matches the flooded developed from aerial photographs and observations observation s very well well as shown in igure igure (F. 2he gravel pit is noted by the maroon color co lor identifying identifying about /; ft or more of water storage. stora ge. 2he observed area of inundation is displayed as a black outline. & comparison of fifty surveyed high water marks and the %-/# predicted maximum water surface surfac e elevations resulted in an average difference of about +./ +. / ft. It should be noted that both the surveyed surveyed high water marks and the estimated area of inundation inundation were sub0ect to the observer6s interpretation. interpretation. &s an indication the accuracy of the channel-floodplain interface, igures (; and (@ display display the predicted versus measured stage reading for the two :1A1 gages in operation during d uring the ())> flood. 2hese stage recordings represent a accurate assessment assessment of the rise and fall fall of the hydrograph. hydrograph . 2he Ceno gage is located about abou t halfway through throu gh the simulated simulated reach and the new Eista Eista gage is located at the downstream do wnstream end of the system. system. :pstream :pstrea m of the Ceno gage, there the re is some overbank flooding and return flow from downtown Ceno. Ceno . 2he new Eista Eista gage includes almost all of the return flow from overbank discharge in the 2ruckee Meadows area 'the large flooded area in igure (F. 2here is some ungaged inflow that reaches the new Eista Eista gage that is not simulated in the model. urthermore, urthermor e, local rainfall intensity may have exceeded the th e rainfall simulated in the model. 7evertheless, the %-/# predicted stages stage s correlate well with the measured stage at both gages gag es in both magnitude and timing. 2his is important because becaus e the progression of the overland overland floodwave across across 2ruckee Meadows from from both the 2ruckee 2ruckee Civer and 1teamboat?5oynton 1loughs has a significant flood crest lag time of @ hours or more when compared to the t he floodwave movement in the river. 2he %-/# model must accurately predict the volume of overbank flow, the channel flood routing, the overland flood routing and channelfloodplain floodplain exchange exchange in order to match the stage at both :1A1 gages. 2his pro0ect indicates that %-/# can be applied to river flood simulations with confidence. It demonstrates demonstrat es the importance of accurately accura tely assessing and correctly analy!ing the relationship between channel conveyance volume and floodplain volume.
>*
igure (). Bredicted 2ruckee Civer Water Water 1urface Brofiles for H$-/ and %-/#
>)
igure /+.
2ruckee Civer Civer %bserved '5lack %utline and %-/# Bredicted &rea of lood Inundation *+
igure /(. %-/# Bredicted 1tage for the ())> lood vent at the Ceno Aage
igure //. %-/# Bredicted 1tage for the ())> lood at the 7ew Eista Aage
*(
7.6. V$(")to! T$*t 5. Rv$( Floo% Rout!& - G($$! Rv$(@ Ut#
& discharge routing model %-/# was developed for the Areen Civer system from laming Aorge to the $olorado Civer confluence, a river distance of F(/ miles. 2he model included the six ma0or Areen Civer tributaries upstream to the first :1A1 gaging station. 2his pro0ect was supported by the 7ational Bark 1ervice, ish and Wildlife 1ervice and the 5ureau of Ceclamation and it provided the opportunity to test a calibrated model with an actual discharge pulse of two days. 2o develop the %-/# data base, forty :1A1 >.; minute maps were digiti!ed and all the available cross section survey data was compiled from various researchers. 2his data was organi!ed by river reach and analy!ed for channel geometry relationships as a function of flow depth. $hannel geometry was assigned to the channel elements that did not have a surveyed cross section. 2he inflow discharge included all the available :1A1 tributary inflow data, laming Aorge #am releases and level logger discharge monitoring data at several locations throughout the river system. 2he %-/# model consisted of 8,@>( grid elements with (,8** channel elements. 2he initial calibration run encompassed (++ days of the ())@ high flow season. ollowing calibration of the roughness values and infiltration parameters and the ad0ustment of floodplain elevations and channel geometry, the model was applied to simulate (++ days of the ())> Areen Civer hydrograph 'igure (>. 2he flood simulations included the prediction of floodplain inundation. 5ased on the excellent correlation between the ())> recorded discharge data and the %-/# predicted discharge hydrograph at the :1A1 =ensen gage '); miles downstream of laming Aorge and Areen Civer gage '/)8 miles downstream of laming Aorge, the model was applied to various flow scenarios involving regulated releases of laming Aorge #am. inally, a series of six low flow scenarios were also simulated to examine the effects of power releases on the discharge at the =ensen gage. In 7ovember ())*, two days of power generating spike flows released from laming Aorge #am 'igure (* were used to test the %-/# model and predict floodwave attenuation for power operating conditions. 2he two spike releases of F,F++ cfs were about twice the normal daily release. :sing the calibrated model, the two floodwaves were routed through entire F(/ miles of river. &t the :1A1 =ensen gage, the shape and timing of the predicted floodwaves matches almost exactly the measured hydrograph 'igure (). 2he predicted flow is about /++ cfs less than the measured discharge because of ungaged tributary inflow that is unaccounted for in the model. =ones $reek in #inosaur 7ational Monument is responsible for most of the unmeasured flow. 2he Dampa Civer base flow contributes discharge that offsets some of the floodwave attenuation. 2he %-/# model was originally calibrated for bankfull conditions. 2he predicted early arrival of the two peaks at the =ensen gage can be attributed to the increased hydraulic roughness at lower flows through the steep odore $anyon. &t low flows, numerous boulders at exposed in the canyon channel. Most of the flow spike is attenuated through the relatively flat sloped %uray valley reach. 5y the confluence of the $olorado Civer, the two spike floodwaves had melded together in a single flood wave mound.
*/
igure /8. ())> High low 1eason Hydrograph at =ensen, :tah '%-/# vs. Measured #ischarge
*8
igure /F. 7ovember ())* Bower Blant #ischarge Celease from laming Aorge #am
*F
igure /;. %-/# Bredicted vs. Measured #ischarge, =ensen :1A1 Aage for Bower Blant Celeases at laming Aorge #am
*;
5y accurately predicting apriori an actual floodwave event, the %-/# model has been shown to be effective flood routing tool, and the channel routing algorithm has been validated. 2he Areen Civer %-/# routing model can now be used to simulate historic or predictive flow scenarios. It can be applied to evaluate the effects of laming Aorge releases on flood magnitude, timing and duration to benefit fish habitat and enhance floodplain inundation.
7.7. V$(")to! T$*t 6. Floo%l! I!u!%to! ; M%%l$ Ro G(!%$@ N$, M$)o
2he purpose of the %-/# model application to the Middle Cio Arande was to predict overbank flooding as function of discharge with the specific ob0ective to "uantify and locate the areas of inundation from 1an &cacia #iversion #am to the 1an Miguel gage 'approximately F* miles. igure /@ displays the %-/# predicted area of inundation of the active floodplain extending from the levee on the west to the bluff on the east. 2he pro0ect tasks included9
• • • •
$ompilation and preparation of the cross section data. $reation of a digital terrain model '#2M for the %-/# grid system. &nalysis of the inflow hydrology for various historic flows. $alibration of a rigid bed %-/# model with the 5ureau6s ())/ inundation mapping.
5y accurately predicting apriori an actual floodwave event, the %-/# model has been shown to be effective flood routing tool, and the channel routing algorithm has been validated. 2he Areen Civer %-/# routing model can now be used to simulate historic or predictive flow scenarios. It can be applied to evaluate the effects of laming Aorge releases on flood magnitude, timing and duration to benefit fish habitat and enhance floodplain inundation.
7.7. V$(")to! T$*t 6. Floo%l! I!u!%to! ; M%%l$ Ro G(!%$@ N$, M$)o
2he purpose of the %-/# model application to the Middle Cio Arande was to predict overbank flooding as function of discharge with the specific ob0ective to "uantify and locate the areas of inundation from 1an &cacia #iversion #am to the 1an Miguel gage 'approximately F* miles. igure /@ displays the %-/# predicted area of inundation of the active floodplain extending from the levee on the west to the bluff on the east. 2he pro0ect tasks included9
• • • • • •
$ompilation and preparation of the cross section data. $reation of a digital terrain model '#2M for the %-/# grid system. &nalysis of the inflow hydrology for various historic flows. $alibration of a rigid bed %-/# model with the 5ureau6s ())/ inundation mapping. &ssessment of the area of inundation as a function of discharge. Brediction of the area of inundation for various return period flood events.
2he model calibration was based on flood inundation mapping flown by the 5ureau of Ceclamation on May (/, ())/. 2he mean daily inflow discharge at the 1an &cacia gage during this period ranged from ;,8*+ cfs to ;,>/+ cfs. 2he mean daily discharge measured at 1an Marcial at the end of the simulated reach ranged from F,>++ cfs to ;,/8+ cfs. %n May (8, ())/, the mean daily discharge was ;,((+ cfs at 1an Marcial. 2he %-/# predicted discharge ranged from ;,(8+ cfs to ;,//+ cfs. 2he 5ureau6s mapped estimated wetted area was /,*(/ channel acres and 8,+(F floodplain acres at the time of the aerial photos. $omparably, the %-/# predicted /,)); wetted channel acres and 8,+8@ floodplain acres. 2his pro0ect verified that the %-/# model can accurately predict area of inundation as a function of discharge given an ade"uate channel cross section data base and an accurate river hydrograph. It confirmed that the channel-floodplain interface can accurately distribute the volume between the river and the floodplain. 2he actual area of inundation was mapped in detail and the river discharge was relatively uniform during the period of flooding. 2he %-/# volume conservation, overland floodwave routing, channel-floodplain interface and flow routing timing were tested in this application.
*@
igure /@. &rea of Inundation, Middle Cio Arande, May ())/
*>
7.3. V$(")to! T$*t 7. V$(")to! o" Mu%"lo, H'%(ul)*
2he prediction of mudflow hydraulics re"uires more engineering 0udgment than when simulating conventional water hydraulics. 2he simulation of hyperconcentrated sediment flows with the %-/# model was verified by using field data from the ()*8 Cudd $reek mudflow in #avis $ounty, :tah '%65rien, et al., ())8. 2he ()*8 Cudd $reek mudflow provided the best available actual mudflow data base. 2he flood hydrograph and other data used in the simulation were developed by the &rmy $orps of ngineers '$%, ()**. 2he field data included9
• • • •
2he area of inundation estimated from aerial photographyK & surveyed volume of the mudflow deposit of approximately *F,+++ yd8K & mudflow frontal velocity on the alluvial fan of approximately the speed that a man could walk 'eyewitness accountK %bserved mudflow depths that ranged from approximately (/ feet at the apex of the alluvial fan to approximately / or 8 feet at the debris front.
$lose examination of photos taken after the event showed that the boundaries of the mudflow deposit were slightly more irregular than reported by the $% '()** but the general area of inundation was reasonably accurate. 2he ma0or portion of the flood event was over in less than seven minutes, but the mudflow continued to creep and flow over the fan for days several days.
7.3. V$(")to! T$*t 7. V$(")to! o" Mu%"lo, H'%(ul)*
2he prediction of mudflow hydraulics re"uires more engineering 0udgment than when simulating conventional water hydraulics. 2he simulation of hyperconcentrated sediment flows with the %-/# model was verified by using field data from the ()*8 Cudd $reek mudflow in #avis $ounty, :tah '%65rien, et al., ())8. 2he ()*8 Cudd $reek mudflow provided the best available actual mudflow data base. 2he flood hydrograph and other data used in the simulation were developed by the &rmy $orps of ngineers '$%, ()**. 2he field data included9
• • • •
2he area of inundation estimated from aerial photographyK & surveyed volume of the mudflow deposit of approximately *F,+++ yd8K & mudflow frontal velocity on the alluvial fan of approximately the speed that a man could walk 'eyewitness accountK %bserved mudflow depths that ranged from approximately (/ feet at the apex of the alluvial fan to approximately / or 8 feet at the debris front.
$lose examination of photos taken after the event showed that the boundaries of the mudflow deposit were slightly more irregular than reported by the $% '()** but the general area of inundation was reasonably accurate. 2he ma0or portion of the flood event was over in less than seven minutes, but the mudflow continued to creep and flow over the fan for days several days. 2he mudflow was initiated by a landslide and thus a relatively uniform sediment concentration was assumed. 2he concentration was increased slightly as the event progressed to simulate dewatering. %verland flow roughness values for the grid elements varied from +.+8; to +.(+ depending on vegetation and flow obstruction. &ppropriate viscous and yield stress parameters were selected from laboratory data mudflow data. 2he buildings which influenced the flow path were simulated with area and width reduction factors. & more detailed discussion of results is presented in %65rien, et al., ())8 . 2he maximum computed flow depth of ((.* ft downstream of the apex compared well with the (/ ft observed depth 'igure /(. Mudflow velocities predicted on the fan ranged from ( to F fps or approximately walking speed as was observed. 7ear the fan apex maximum predicted velocities were less than (+ fps. =ust upstream of the apex in the Cudd channel area predicted velocities approached /+ fps. Bredicted frontal lobe depths ranged from / to F ft depending on the location on the fan and correlated well with post-event photos. 2he predicted area of inundation is approximately the same as that reported by the $orps of ngineers. %-/# demonstrated that the streets played an important role in distributing the mudflow on the urbani!ed fan. & time lapse 8-# simulation of the mudflow progression over the Cudd $reek fan is presented in %65rien, et al. '())8.
**
igure />. Cudd $reek Mudflow Maximum low #epth $ontours
*)
VII. FLO-2D PROECT APPLICATIONS 3.1. Floo% H(% D$l!$to!@ M!& !% R$*ult*
%-/# has been applied to ma0or river systems, very flat slope river channel and floodplains, rivers with bridges and other hydraulic structures, floodplains with levees, desert alluvial fans, mountain mudflow alluvial fans, urban floodplains and alluvial fans, large rainfallrunoff watersheds, street intersections and mudflows associated with volcanoes. It has been used for flood ha!ard delineation, flood mitigation design, detention basin design and M& I1 studies on alluvial fans. & number of pro0ects have been conducted in foreign countries. & partial list of about over thirty %-/# pro0ects is presented in the following section. 2his list represents only a portion of the known %-/# pro0ects that have been completed. %-/# results can be displayed in temporal or spatial resolution. 2emporal results are available in the form of channel hydrographs, floodplain cross section hydrographs and hydraulic data 'flow depths and velocities for every grid element at specified output intervals. $hannel hydrographs can be plotted for every channel element. 1patial results in the form of the maximum area of inundation, maximum flow depths and velocities can be plotted with the M&B%2 program. In addition, there are output files that include the x- and y-coordinates along with the hydraulic variable 'such as maximum flow depth or velocity that can be imported to a $&## program for plotting results on the original mapping. With these imported files, the flow depth or water surface elevation contours can be plotted with the $&## interpretive mapping routines. #etailed flood ha!ard inundation maps can be prepared by subtracting the #2M points from the grid element water surface elevations. %n floodplain grid elements, the variation of the water surface elevation over a grid element is relatively minimal. 5y establishing the #2M points under the grid element water surface and computing the resulting flow depths, a colored contour plot of the flow depths can highlight the topographic detail within the grid element. 2hese flow depth plots reveal flooding in ditches, depressions, over berms and in streets. &ll of the topographic detail that is lost in assigning the representative grid element elevation is regained through this plotting process. 2hese color contour depth plots, when overlaid on photogrammetry maps, provide excellent detail for community flood ha!ard maps and M& I1 insurance rate maps.
3.2. P(tl L*t o" FLO-2D P(o/$)t*
&t the present time, %-/# has been applied in a number of foreign countries including9 Italy, 1wit!erland, &ustria, Mexico, cuador, Eene!uela, 1outh orea, 2aiwan and 2hailand. & brief description of some of the %-/# pro0ects completed by various agencies and consultants follows9
)+
(.
2elluride, $ornet $reek &lluvial an, $olorado
2his first %-/# pro0ect was a M& mudflow ha!ard delineation study. &pproximately 8++ grid elements, /++ ft s"uare were used to simulate mudflow over an urbani!ed alluvial fan. 7o buildings or streets were simulated since these components had not yet been created. 2he computer runs took six hours or more on a /*@ MHG computer. /.
Boudre Civer, ort $ollins, $olorado
&fter the 2elluride pro0ect, a river inundation test study was attempted. $ross section data from an H$-/ study was available for the Boudre Civer east of ort $ollins, $olorado. 2he flood inundation area was split by the I-/; embankment. 8.
1an 1evaine - tiwanda &lluvial ans, $alifornia
&lluvial fan mitigation design was simulated with the %-/# model. arge flood conveyance channels were designed for an urbani!ed alluvial fan. 2he model was used to establish channel geometry and freeboard for concrete lined channels. 2he area of inundation downstream of the channel was also predicted. F.
Hiko 1prings &lluvial an, aughlin, 7evada
Hiko 1prings Wash is severely incised into a broad alluvial fan flood terminating at the $olorado Civer. lood flows wander unconfined across the wash bottom. %-/# was applied to conduct a flood ha!ard delineation study for a M& $%MC. 2he model was also used to predict velocities and depths along a floodwall where sediment deposition was considered to be a potential problem. 2he model predicted flow accumulation along the floodwall, scour not deposition turned out to be the critical concern and the wall was buried eleven feet below the ground surface with footers. ;.
Whiskey Bete6s &lluvial an, 1tateline, 7evada
&n alluvial fan flood ha!ard delineation study was conducted above a casino resort. lows over the alluvial fan were collected at railroad berms and directed into culverts that could overtop the railroad embankment. 2he culvert outflows were directed at the casino. & concrete channel was designed to collect the flows upfan of the casino. 1ediment transport was analy!ed to determine the potential loss of channel conveyance laterally across the fan. low runup in the channel was a design consideration. 2he #esert Cesearch Institute in as Eegas also analy!ed the Whiskey Bete6s flows with %-/# to determine the potential for overtopping the railroad embankment. & master6s thesis was written on the application of %-/# and other flood models.
)(
@.
5arnard $reek Mudflow &lluvial an, $enterville, :tah
5arnard $reek is a completely urbani!ed alluvial fan with a small debris basin at the fan apex. %-/# was applied to delineate the potential water flood and mudflow ha!ard on the fan. 1treets, buildings and the debris flow overflow were simulated. 2he flood scenarios included water flooding, rainfall, mudflow, and rainfall and mudflow. 2he 5arnard $reek data files are provided as one of the example data file sets. >.
Cudd $reek Mudflow &lluvial an, $enterville, :tah
2he ()*8 Cudd $reek mudflow was well documented. 2he data base was used to calibrate some of the mudflow parameters in the %-/# model including the laminar flow resistance. 2he inflow hydrograph, area of inundation, maximum flow depths and velocities and flow cessation depths were known or observed. 1treet flow and building obstruction were simulated. *.
Mount 1t. Helen, Eolcano %bservatory, $ascade, Washington
2he Bine $reek mudflow on the south face of Mount 1t. Helen was simulated with %-/#. & comparison of volcanic mudflow parameters measured and computed by the Eolcanic %bservatory was made. 2he floodwave time to peak and predicted flow depths and velocities were compared with field observations. ).
5roadmoor &lluvial ans, $olorado 1prings, $olorado
xpensive residential units were planned for a series of steep coalescing alluvial fans along the front range of $olorado 1prings that had experienced numerous mud and debris flows in the past. arge boulder levees were evidence of the severity of the potential debris flow events. lood ha!ard delineation and mitigation design were based on %-/# mudflows simulations. (+. Bima $ounty, 2ucson, &ri!ona &t the re"uest of a local consulting firm, a %-/# application to an alluvial fan that was planned for development demonstrated the model6s capability to predict distributary flows over a broad alluvial fan surface. ((. Monroe $reek &lluvial an, Cichfield, :tah Monroe $reek flows over a large alluvial fan with a significant supply of boulders from the upstream watershed. 2he $orps of ngineers used %-/# to conduct an unconfined flood simulation of overbank flows. Cectangular, trape!oidal and natural shaped cross sections were used to represent the channel geometry. %verbank flooding and return flows to the channel were simulated to delineate the flood ha!ard. 2he data files for are included on the model as an example channel application.
)/
(/.
&rroyo Basa0aro &lluvial an, $olinga, $alifornia
In March ()); a significant flood filled the detention basin along the $alifornia &"ueduct forcing the release of water onto the alluvial fan downfan of the &"ueduct. 2he 1tate of $alifornia was sued by flooded farmers who lost crops and had buildings inundated. 2he #epartment of Water Cesources contracted to simulate the flooding from the detention basin outlet culverts. 1torm rainfall was also modeled. 2he results demonstrated that the flooding was due the rainfall first, then culvert releases. 5oth flood sources resulted in essentially the same area of inundation. (8. Cio Arande, $ochiti Ceservoir to lephant 5utte Ceservoir, 7ew Mexico & %-/# model of the Middle Cio Arande was developed for (>8 river miles using /),>*/ ;++ ft grid elements. In addition to flood inundation flows, an investigation was conducted to determine flooding potential for 5os"ue restoration flows. loodwave attenuation was an important facet of this study. evees were simulated. 2he 5ureau of Ceclamation, $orps of ngineers and the ish and Wildlife 1ervice participated in the study (F. Areen Civer Couting, F(/ Miles laming Aorge to $olorado Civer, :tah 2his Areen Civer flood routing study was a cooperative pro0ect between the 5ureau of Ceclamation, ish and Wildlife 1ervice and 7ational Bark 1ervice to develop a river discharge routing model and assess overbank flooding for endangered fish nursery habitat. 2he %-/# grid system was later extended up the Areen Civer tributaries to the first :1A1 gaging stations. &n excellent match was obtained between the predicted hydrograph and the :1A1 recorded discharges in the lower Areen Civer. (;. Eicee $anyon &lluvial an, $arson $ity, 7evada Eicee $anyon watershed debouches into an incised wash on the alluvial fan. & small debris basin was constructed at the terminus of the alluvial fan. %-/# simulated flows in the wash and through the debris basin. 5oth the existing basin and the proposed expanded basin were found to be inade"uate for the (++-year event. (@. Alenwood 1prings and %uray Mudflow &lluvial ans, $olorado 2he $ities of Alenwood 1prings and %uray are situated on a series of coalescing alluvial fans. 2he 1acramento #istrict of the $orps of ngineers applied %-/# to delineate the water flood and mudflow ha!ard on these two urbani!ed alluvial fan areas for a M& flood insurance study. or the Alenwood 1prings pro0ect, about ;+ small watersheds and their alluvial fans with the city limits were simulated. In %uray, two existing concrete channels were modeled.
)8
(>. Wailupe $reek, HawaiiK $orps of ngineers 2he Bacific #istrict of the $orps of ngineers conducted an urban alluvial fan flood ha!ard delineation study. 1everal channels flowed through the urban area that collected flows and debouched into the ocean. 1treets and buildings were modeled to assess the area of inundation. (*. &spen Mountain, &spen, $olorado WC$ ngineering, Inc. of #enver, $olorado performed an alluvial fan flood and mudflow ha!ard delineation study for the $ity of &spen. 1everal watersheds contributed to the flow the city. Mapping involved the assessment of street flow and building flow obstruction. 2etra 2ech later expanded this study for development mitigation.
(). #iamond &lluvial an, as Eegas B51= of as Eegas conducted an alluvial fan rainfall?runoff flood study above a proposed development. Cainfall was simulated in the upper basin and runoff was routed to the development site. 2his pro0ect represented a good example of simulating the entire hydrology of the basin and fan complex. /+. ehi and 7ephi &lluvial ans, :tah 2he $orps of ngineers, 1acramento #istrict conducted two alluvial fan flood ha!ard delineation studies involving culvert flows under an interstate highway. 2he culvert capacity was an integral part of the flood study involving culvert plugging, ponding and discharge onto an unconfined surface. /(. 2ruckee Civer, Ceno, 7evada In =anuary ())>, the 2ruckee Civer flooded downtown Ceno and the surrounding area. 2he 1acramento #istrict of the $orps of ngineers conducted a river flood ha!ard delineation study involving (; miles of the river and all of the urbani!ed floodplain. 1treets, buildings and the flow through (* bridges were modeled. 2he analysis included replication of the ())> flood including predicting river stages and discharge, area of inundation and water surface elevations on the floodplain. & full compliment of flood fre"uency events and pro0ect flood mitigation conditions were modeled. //. 1ection 8+, Baradise &lluvial an, as 7evada #eCoulhac $onsulting, Inc. conducted a detailed unconfined flood simulation for an alluvial fan upfan of a proposed subdivision.
)F
/8. Mc$oy Wash, 5lythe $alifornia 2he 7C$1 applied %-/# downstream of a proposed detention basin spillway to assess the pro0ect design flooding over an unconfined surface with the flow eventually returning to Mc$oy Wash. 2he %-/# sediment transport component was applied to determine the scour and deposition on the alluvial fan surface before the flow re-entered the wash. /F. Coaring ork $lub &lluvial ans, 5asalt, $olorado & golf course was constructed on a series of coalescing alluvial fans on both sides of the Coaring ork Civer. & channel mudflow ha!ard delineation was conducted and mitigation measures were recommended. 1everal cabin sites including one under construction were moved on the basis of the %-/# simulations. /;. Ceata Bass, 1an 5ernardino, $alifornia 2etra 2ech, I1A analy!ed flows on an alluvial fan in con0unction with the design of a concrete conveyance channel. %verflows from the channel were released into an alluvial fan channel for the purpose of maintaining the desert ecosystem on the alluvial fan. /@. ra!ier $reek &lluvial an, 1trathmore, $alifornia looding of ra!ier $reek inundated several property owners who claimed that the flooding was the result of upfan berms and channel improvements constructed by ranchers. %-/# was used to simulate historic conditions of the fan as they existed in ();( before the improvements were made. 2hen the model was applied to the existing conditions in support of a lawsuit filed by the flooded property owners. />. Howes 1treet Intersection, ort $ollins, $olorado idstone and &nderson $onsultants of ort $ollins used small grid elements of ten feet to simulate flows within a large street intersection in ort $ollins. 2he purpose of applying the %/# model was to predict the discharge split between the various streets at the intersection to design storm runoff. /*. Auagua Bichincha Eolcano Mudflows, Zuito, cuador Mudflows through the capital city Zuito were simulated to prepare a risk assessment plan for Zuito6s government and the :nited 7ations #evelopment Brogram. 1treets and buildings were modeled in flood scenarios involving volcanic ash mudflows of varying concentrations.
);
/). &vila Mountain Mudflows, 7orth $oast, Eene!uela In #ecember ())), the watersheds along the 7orth $oast of Eene!uela flooded under intense prolonged rainfall approaching a /;+ year return storm. Mudflows and flooding resulted in over (/,+++ deaths. %-/# was used to simulate the ())) floods and mudflows on a number of alluvial fans. It was then applied to test potential mitigation measures. 8+. %restimba $reek, near 7euman, $alifornia 2he ()); flood of %restimba $reek in the north $entral Ealley was simulated to conduct a flood delineation study. Cailroad embankment and county roads were simulated as small levees. %restimba $reek entered the 1an =oa"uin Civer with a mild slope. 2his pro0ect was conducted for the 1acramento #istrict $orps of ngineers. 8(. Ced &rroyo near &lamogordo, 7ew Mexico 2he &lbu"uer"ue #istrict $orps of ngineers conducted an alluvial fan and arroyo flood investigation to determine the mitigation effects of a proposed flood retention basin. 2he flooding included distributary channels. 8/. 1kunk $reek Wash, Maricopa $ounty, &ri!ona & pair of alluvial washes were controlled by a retention facility with an overflow spillway. & %-/# model was developed by 2etra 2ech I1A to simulate the flood distribution within the retention pond. 2he berm and spillway were simulated. 2he ponded flood waters overtopped the berms in several places for the design flood event. Mitigation measures were proposed. 88. ower Mission $reek, os &ngeles, $alifornia ower Mission $reek winds through an urban area before entering the ocean. & private development was elevated and was apparently out of the flood ha!ard. H$-/ and H$C&1 were ineffective in the urban area. %-/# was applied by a consultant with assistance from 2etra 2ech I1A to examine the flood ha!ard in detail by simulating the highway and railway embankments and the loss of storage due to the numerous buildings. 8F. Alenwood 1prings Hospital xpansion, Alenwood 1prings, $olorado 2he Alenwood 1prings Hospital is located on a series of coalescing alluvial fans created by mudflows. Mudflow mitigation for the hospital expansion was analy!ed with the %-/# model. Mudflow through an urban area with streets on a steep alluvial fan was simulated. 8;. Whitewater &lluvial an, near 5lythe, $alifornia 2etra 2ech I1A conducted an extensive alluvial fan study with the sediment component to determine the effects of a berm to redirect flood flows in a 7ational Wildlife Cefuge.
)@
8@.
West 1tanislaus Bro0ect, $entral Ealley, $alifornia
& series of interlacing river channels across the $entral Ealley were analy!ed by the $orps of ngineers. %-/# was applied to assess overbank flooding that entered other river channel segments as return flows. 8>.
Cogue Civer, %regon
idstone and &ssociates of ort $ollins conducted a complex multiple channel flood inundation study of the Cogue Civer that included gravel pits on the floodplain. 5oth split flow and channel confluence flows were simulated.
)>
VIII. REFERENCES
&ckers, B. and W.C. White, ()>8. 31ediment 2ransport9 7ew &pproach and &nalysis,4 =. of Hyd., &1$, E. )), no. HD((, pp. /+F(-/+@+. &kan, &.%. and 5.$. Den, ()*(. X#iffusive-wave flood routing in channel networks,X =. of Hyd., &1$, (+>'@, >()->8/. 5agnold, C.&., ();F. Xxperiments on a gravity-free dispersion of large solid spheres in a 7ewtonian fluid under shear,X Broc. of the Coyal 1ociety of ondon, 1eries &, E. /F), /8;-/)>. $hen, $.., ()>@. X:rban storm runoff inlet hydrograph study.X Brepared for the #ept. of 2ransportation, BCWA (+@-/, :tah 1tate :niversity, ogan :tah. $unge, =.&., .M. Holly =r., &. Eerwey, ()*+. 3Bractical &spects of $omputational Civer Hydraulics,4 Bittman &dvanced Bublishing Brogram, ondon, :. #eeon, &.&. and C.W. =eppson, ()*/. XHydraulic and numerical solutions of steady-state but spatially varied debris flow,X Hydraulics and Hydrology 1eries, :WC?H-*/?+8, :tah 1tate :niv. at ogan, :tah. #eng, G., ())@. 3Impact of #ebris lows and Its Mitigation,4 Bh.#. #issertation submitted to the #ept. of $ivil and nvironmental ngineering, :niv. of :tah, 1alt ake $ity, :tah. #M&, ()*;. X&lluvial fan flooding methodology and analysis,X Brepared for M& by #M& $onsulting ngineers, Cey, $alifornia, %ctober. gashira, 1., . &shida, H. Da0ima, and =. 2akahama, ()*). X$onstitutive e"uations of debris flow,X &nnuals of the #isaster Brevention Cesearch Institute, yoto :niv., 7o. 8/5-/, F*>-;+(. ngelund, ., and . Hansen, ()@>. 3& monograph on sediment transport in alluvial streams,4 2eknisk orlag, $openhagen. instein, H.&., ();+. X2he bed-load function for sediment transportation in open channel flows,X :1#& 2ech. 5ull. 7o. (+/@. ullerton, W.2., ()*8. XWater and sediment routing from complex watersheds and example application to surface mining,X Masters 2hesis, $ivil ngineering #ept., $1:, ort $ollins, $%. Araf, W.H., ()>(. Hydraulics of 1ediment 2ransport. McAraw-Hill, 7ew Dork, 7.D. Areen, W.H. and A.&. &mpt, ()((. X1tudies on soil physics, part I9 2he flow of air and water through soils,X =. of &griculture 1cience.
)*
Hashimoto, H., ())>. 3& comparison between gravity flows of dry sand and sand-water mixtures,4 Cecent #evelopments on #ebris lows, 1pringer, &. &rmanini and M. Michiue 'eds., 7D, 7D. Henderson, . M., ()@@. %pen $hannel low. MacMillan Bublishing $o., Inc., 7D, 7D. Hromadka, 2.E. and $.$. Den, ()*>. X#iffusive hydrodynamic model,X :. 1. Aeological 1urvey, Water Cesources Investigations Ceport *>-F(8>, #enver ederal $enter, $olorado. =ames, W. B., =. Warinner, and M. Ceedy, ())/. X&pplication of the Areen-&mpt infiltration e"uation to watershed modeling,X Water Cesources 5ulletin, &WC&, /*'8, @/8-@8F. =in, M. &nd #.. read, ())>. 3#ynamic flood routing with explicit and implicit numerical solution schemes,4 =. of Hyd. ng., &1$, (/8'8, (@@-(>8. =ulien, B.D., ());. rosion and 1edimentation. $ambridge :niversity Bress, 7ew Dork, 7.D. =ulien, B.D. and D.Z. an, ())(. 3%n the rheology of hyperconcentrations, =. of Hyd. ng., &1$, ((>'8, 8F@-8;8. usler, =., ()*@. XIntroduction9 flooding in arid and semi-arid regions,X Broc. of a Western 1tate High Cisk lood &reas 1ymposium, Improving the ffectiveness of loodplain Management in &rid and 1emi-&rid Cegions, &ssociation of 1tate loodplain Managers, Inc., as Eegas, 7E, March. aursen, .M., ();*. 32he total sediment load of streams,4 =. of the Hyd. #iv., &1$, E. *F, 7o HD(, pp. (;8+-(;8@. Mac&rthur, C.$. and #.C. 1chamber, ()*@. X7umerical methods for simulating mudflows,X Broc. of the 8rd Intl. 1ymp. on Civer 1edimentation, :niv. of Mississippi, (@(;-(@/8. Meyer-Beter, . and C. Muller, ()F*. Xormulas for bedload transport,X Broc. I&HC, /nd $ongress, 1tockholm, 8)-@F. 7ational Cesearch $ouncil, ()*/. X1electing a methodology for delineating mudslide ha!ard areas for the 7ational lood Insurance 5oard on the 5uilt nvironment,X 7ational &cademy Bress, Washington, #.$. 7ational Cesearch $ouncil, ()*8. X&n evaluation of flood-level prediction using computer based models of alluvial rivers,X 7ational &cademy Bress, Washington, #.$. %5rien, =.1., ()*@. XBhysical processes, rheology and modeling of mudflows,X #octoral dissertation, $olorado 1tate :niversity, ort $ollins, $olorado. %5rien, =.1. and B.D. =ulien, ()*;. XBhysical processes of hyperconcentrated sediment flows,X Broc. of the &1$ 1pecialty $onf. on the #elineation of andslides, loods,
))
and #ebris low Ha!ards in :tah, :tah Water Cesearch aboratory, 1eries :WC?g*;?+8, /@+-/>). %5rien, =.1. and B.D. =ulien, ()*>. #iscussion on XMountain torrent erosion,X 5y . &shida in 1ediment 2ransport in Aravel-5ed Civers, =ohn Wiley 1ons, ;8>-;8). %5rien, =.1. and B.D. =ulien, ()**. Xaboratory analysis of mudflow properties,X =. of Hyd. ng., &1$, ((F'*, *>>-**>. %5rien, =.1., B.D. =ulien, and W.2. ullerton, ())8. X2wo-dimensional water flood and mudflow simulation,X =. of Hyd. ng., &1$, (()'/, /FF-/;). %65rien, =.1. and 1imons, i &ssociates, Inc., ()*). Xlood ha!ard delineation for $ornet $reek, 2elluride, $olorado,X 1ubmitted to ederal mergency Management &gency, March. Bonce, E.M., C.M. i, and #.5. 1imons, ()>*. X&pplicability of kinematic and diffusion models,X =. of Hyd. #iv., &1$, (+F'(FF8, 8;8-@+. Bonce, E.M. and .#. 2heurer, ()*/. 3&ccuracy $riteria in #iffusion Couting,4 =. of Hyd. ng., &1$, (+*'@, >F>->;>. 1chamber, #.C. and C.$. Mac&rthur, ()*;. X%ne-dimensional model for mudflows,X Broc. of the &1$ 1pec. $onf. on Hydraulics and Hydrology in the 1mall $omputer &ge, E. /, (88F-8). 1imons, #.5. and . 1enturk, ()>@. 1ediment 2ransport 2echnology, Water Cesource Bublications, ort $ollins, $%. 2akahashi, 2., ()>). 3#ebris flow on prismatic open channel flow,4 =. of the Hyd. #iv., &1$, (+@'8, 8*( - 8)@. 2akahashi, 2. and H. 2su0imoto, ()*;. X#elineation of the debris flow ha!ardous !one by a numerical simulation method,X Broc. of the Intl. 1ymp. on rosion, #ebris low and #isaster Brevention, 2sukuba, =apan, F;>-F@/. 2akahashi, 2. and H. 7akagawa, ()*). X#ebris flow ha!ard !one mapping,X Broc. of the =apan $hina '2aipai =oint 1eminar on 7atural Ha!ard Mitigation, yoto, =apan, 8@8-8>/. 2offaleti, .5., ()@). 3#efinitive computations of sand discharge in rivers,4 =. of the Hyd. #iv., &1$, E. );, no. HD(, pp. //;-/F@. :.1. &rmy $orps of ngineers, ())+. XH$-(, lood Hydrograph Backage,X :sers Manual, Hydrologic ngineering $enter, #avis, $&. :.1. &rmy $orps of ngineers, ())+. XH$-/ Water 1urface Brofiles,X Hydrologic ngineering $enter, #avis, $&.
(++
