MARCH 23, 2!5 """""""""""""""""""""""""""" DATE OF SUBMISSION PROBLEMS
SUBMITTED
TO:
1. The average annual discharge at the outlet of a catchment is 0.5 m !s. The catchment is situated in a desert area "no vegetation# and the si$e is %00 &m' . The average annual (reci(itation is '00 mm!)ear. a. *om(ute the average annual eva(oration from the catchment in mm!)ear. +n the catchment area an irrigation (ro,ect covering 10 &m' is develo(ed. -fter some )ears the average discharge at the outlet of the catchment a((ears to e 0.1/5 m !s. . *om(ute the eva(otrans(iration from the irrigated area in mm!)ear assuming no change in the eva(oration from the rest of the catchment. '. or a 2atershed 2ith a si$e of 1'0 &m' the follo2ing data on (reci(itation P eva(oration E and runo3 4 are given in mm.
a. -t the end of 2hich month is the amount of 2ater stored in the asin largest and 2hen is the smallest amount of 2ater (resent in the catchment 6hat is the di3erence "m # in the amount of 2ater stored in the asin et2een these t2o e7tremes . +n 2hat climate "arid humid tem(erate or humid tro(ical# do )ou e7(ect this catchment to e located . - catchment has a si$e of 100 &m' . +n its original condition the average annual total runo3 from the catchment is 1.1 m !s. The average annual rainfall is %00 mm!a. +n an average )ear 508 of the rainfall in9ltrates and 1'.58 of the rainfall reaches the ground2ater. Tests have turned out that the average annual eva(otrans(iration from the unsaturated $one "eing the sum of the trans(iration and the are soil eva(oration# amounts to :0 mm!a. +n all 2ater alance com(utations over the )ear one ma) assume that the storage e3ects are small "dS!dt ; <0#. a. =o2 much 2ater in mm!a reaches the root $one through ca(illar) rise in an average )ear . =o2 much 2ater in mm!a see(s out from the ground2ater to the surface 2ater in an average )ear c. =o2 much 2ater in mm!a eva(orates directl) from interce(tion in an average )ear d. =o2 much in mm!a is the total eva(otrans(iration in the catchment in an average )ear - 2ell 9eld is (lanned to 2ithdra2 0.1> m !s from the
catchment for drin&ing 2ater consum(tion else2here . -s a result the ground2ater level is e7(ected to go do2n and ca(illar) rise into the root $one 2ill no longer e (ossile. The (ercolation ho2ever is e7(ected to remain the same. e. 6hat 2ill e the e3ect of the 2ithdra2al on the di3erent com(onents of the h)drological c)cle? the ground2ater see(age the total runo3 the eva(otrans(iration from the unsaturated $one and the total eva(otrans(iration Please @uantif) in mm!a.
:. - (older in the 6est of The Aetherlands is surrounded ) a canal. The 2ater level in the canal is 2ell aove the land surface of the (older. The si$e of the (older is 10 &m' and '08 of this area is o(en 2ater. The average annual o(en 2ater eva(oration is >00 mm!a. The land use in the (older is grass. The o(en 2ater level in the (older is &e(t high all )ear round conse@uentl) the eva(otrans(iration of the cro( e@uals its (otential value. Potential eva(otrans(iration of grass in The Aetherlands ma) e estimated as /58 of the o(en 2ater eva(oration. The average annual (reci(itation is %00 mm!a the average annual amount of 2ater (um(ed out is 5710> m !a 2hile 0./710> m !a is let in to the (older in order to maintain a high 2ater level in the summer (eriod. a. *om(ute the average annual ground2ater see(age into the (older in mm!a. . o )ou estimate the error of the com(uted amount of see(age to e less than 1 et2een 1 and 10 or greater than 10 mm!a c. The 6ater Board decides to lo2er the o(en 2ater level in the (older from the original high level to a much lo2er level. -s a result of this the annual amount of see(age as 2ell as the eva(otrans(iration change ) 108. The 2ater inta&e remains the same "0./ &m !a#. *om(ute for the ne2 situation the average amount that is (um(ed out in mm!a.
5. - tro(ical c)clone (roduces ':0 mm of rainfall during a (eriod of 5 da)s. The 9gure elo2 gives the (ercentage mass curve of this rainfall event. Plot the h)etogra(h using dail) time intervals.
>. or the rainfall gauging stations - B and * 2hich are all situated in the same climatic region the annual (reci(itation data "cm# for ten successive )ears are given elo2. The data of one station are not reliale. etermine this station 2ith the douleCmass curve anal)sis.
/. +n a rectangular area three raingauges - B and * are located as sho2n in the 9gure elo2. The recorded rainfall for Dune is as follo2s? Station -? /5 mm Station B? :0 mm and Station *? 0 mm. se the Thiessen method to com(ute the areal rainfall of the rectangle for the month of Dune.
%. The h)etogra(h in the 9gure aove "right# gives the rainfall intensit) in "mm!h# 2ith time "h# 2hich is recorded 2ith a raingauge at a height of 1'0 cm aove soil surface. a. *om(ute and (lot the mass curve "cumulative rainfall de(th 2ith time#. . S&etch roughl) in the same 9gure 2hat 2ould have een the mass curve for the situation that the (osition of the raingauge is changed in such a 2a) that the rim of the collector is at ground level
F. The follo2ing statistical characteristics "fre@uencies of occurrence# 2ere derived from a time series of dail) rainfall totals?
a. etermine the missing 9gures in the tale aove. . erive the intensit) duration curve for a return (eriod of 100 )ears.
10.
*onsider the follo2ing annual ma7imum dail) rainfall data?
Ma&e a gra(h of the e7treme rainfall de(th versus the logarithm of the return (eriod. o not use semiClog (a(er. Estimate the annual ma7imum dail) rainfall 2ith a return (eriod of '0 )ears.
11. The Gumel distriution of dail) e7treme rainfall data "mm# sho2s that? P"H I 100# ; 0.F0 P"H I 10# ; 0.F% a. *om(ute the dail) e7treme rainfall for a return (eriod of 100 )ears. "+f )ou 2ish )ou can chec& the ans2er )ourself gra(hicall) in 9gure '.'#. . Mention at least t2o re@uirements 2ith regard to the estalishment of the Gumel distriution that have to e ful9lled to ma&e the ans2er of the (revious @uestion meaningful. 1'. or a certain 2atershed the follo2ing monthl) data on (reci(itation P and (otential eva(otrans(iration E pot are given in mm.
The annual actual eva(otrans(iration Eact e@uals >10 mm. E7ce(t for one month the actual eva(otrans(iration e@uals the (otential eva(otrans(iration. a. +ndicate the month for 2hich Eact < E pot . b. *om(ute the actual eva(otrans(iration for this month. c. *om(ute the annual river discharge from the 2atershed assuming that the change in storage can e neglected. 1. or a large catchment the follo2ing data on (reci(itation P free 2ater eva(oration Eo (otential eva(otrans(iration E pot and actual eva(otrans(iration Eact are given in an aritraril) se@uence in mm!)ear as follo2s? :0 100 '500 and 000. a. Give the values for P, Eo, E pot and Eact . E7(lain )our ans2er. . +ndicate to 2hich climate these values (ertain? humid semiCarid or arid. 1:. The three data sets in the tale and chart elo2 refer to monthl) eva(oration values in mm!d for a shallo2 la&e a dee( la&e and a *lass (an in the same region in The Aetherlands.
a. 6hich data set elongs to the shallo2 la&e 2hich one to the dee( la&e and 2hich data set re(resents the (an eva(oration data Please e7(lain. . Estimate the (an coeJcient for the dee( la&e and for the shallo2 la&e.
15. Measurements in =odeidah "Kemen 15 oA altitude 1% m# of the gloal radiation results in the follo2ing data? -ugust 15 1FF0? RS ; '0.:%' MD!d!m' n ; >. hours -ugust 1> 1FF0? RS; 1>./5% MD!d!m' n ; :.' hours a. *om(ute the (arameters a and b in the radiation e@uation R s ; "a < n!A# R. *om(ute the eva(oration from a reservoir at =odeidah for the month of Dune according to Penman and Ma&&in& given the follo2ing data "': hour mean values at ' m height#? Sunshine duration ? 10.: hours -ir tem(erature ? 1.0 o* Relative humidit) ? %.: 8 6ind s(eed ? '.0 m!s 1>. -n in9ltrometer is used to determine the in9ltration ca(acit) of a cla) soil. The e7(eriment lasted 1'0 minutes. uring the e7(eriment 2ater 2as added to maintain a constant 2ater level in the ring. The total volume of 2ater added is taulated elo2. The area of the ring is >00 cm '. a. *om(ute for each time interval the in9ltration ca(acit) in cm!hr. . Plot the in9ltration ca(acit) "cm!hr# versus time "minutes#. c. Estimate the ultimate value of the in9ltration ca(acit).
1/. he relation et2een in9ltration ca(acit) in mm!hour and the time "in hours# since the start of the e7(eriment as measured 2ith an in9ltrometer is de(icted elo2. The relationshi( ma) e descried 2ith the em(irical formula of =orton "e@uation :.'# 2here f p, f c and f o in mm!h t in min. and k in minC1. a. erive the (arameter values relationshi(.
f o, f c and k from the measured
. Estimate from the gra(h elo2 the total amount of 2ater that 2ill in9ltrate into the soil during a rainstorm 2ith a duration '0 minutes and a constant intensit) of '0 mm!h. -ns2er the same @uestion for a constant rainfall intensit) of 1' mm!h.
1%. The ca(acit) of the interce(tion storage of a forest is ' mm. -fter a dr) (eriod a rainstorm on this forest 2ith an intensit) of :0 mm!hr lasts one half hour. The in9ltration ca(acit) during the 9rst 1!: hour is :0 mm!hr and during the second 1!: hour is ' mm!hr. *om(ute the amount of 2ater that in9ltrates into the soil during the rainstorm.
1F. - s(rin&ling test is carried out on a (lot of '5 m '. The simulated rainfall intensit) "i# e@uals '0 mm!h. -fter : hours the surface runo3 from the (lot ecomes constant and e@ual to 0.05 l!s. a. *om(ute the ultimate in9ltration ca(acit) in mm!h. . S&etch in a gra(h the in9ltration ca(acit) 2ith time given an initial in9ltration rate at the start of the s(rin&ling rest e@ual to 1% mm!h. S&etch in the same 9gure the in9ltration ca(acit) 2ith time for the situation the e7(eriment is re(eated a fe2 hours later. '0. The rooting de(th of a cro( is >0 cm. a. *om(ute the "ma7imum# availale moisture for the cro( from the root $one "the amount et2een 9eld ca(acit) and 2ilting (oint# for sand loam and cla). se the soil moisture characteristics in )our lecture notes in 9gure :.>. ield ca(acit) corres(onds to ('. . +f all this 2ater has een used the cro( is dead "2ilting (oint condition#. +n order to (revent reduction in cro( )ield the farmer 2ill irrigate the cro( 2hen half of the availale moisture is used. +f the eva(otrans(iration rate of the cro( e@uals : mm!d com(ute the irrigation interval in the asence of (reci(itation. '1. +n a soil 2ith a dee( 2aterCtale the root $one has a de(th of 50 cm. The moisture content at 9eld ca(acit) for this root $one is '%8. Dust efore irrigation the moisture content in the root $one is 1'8. uring irrigation 110 mm of 2ater in9ltrates into the soil. =o2 much 2ater (ercolates from the root $one into the susoil ''. *onsider the 2ater alance of a reservoir during the last > 2ee&s of a long dr) season. The reservoir is receiving 2ater from one river onl). The river discharge into the reservoir at the start and at the end of the > 2ee& (eriod is 10 and 1.% m !s res(ectivel). The surface area of the reservoir is '0 &m'. a. *om(ute for each 2ee& the rise of the 2ater level in the reservoir due to the ino2 of river 2ater onl). The follo2ing (reci(itation "P# and eva(oration "E# data "mm!2ee a((l) for the >C2ee& (eriod.
-t the dam site 2ater is released 2ith a constant rate of 5 m !s. There are no other signi9cant o2s that should e considered for the 2ater alance of the reservoir. . *om(ute the 2ater level in the reservoir at the end of each 2ee& given a 2ater level of '0 m aove mean sea level at the start of the > 2ee& (eriod. '. *onsider a catchment of . &m' situated in an arid region. The outlet of the catchment is a 2adi "dr) river# that carries 2ater onl) after heav) rainfall. - rain storm 2ith a de(th of 100 mm falls uniforml) over the catchment during a (eriod of three hours. The rainfall de(th in the 9rst second and third hour are res(ectivel) :5 5 and '0 mm. The discharge at the outlet due to this rain storm is (resented as h)drogra(h - "solid line# in the chart elo2. a. *om(ute the runo3 coeJcient for this rainfall event. . *om(ute the constant loss rate "the Cinde7# c. +n the same chart the h)drogra(h oserved at a (oint B '0 &m do2n stream in the same river is (lotted. The average 2idth of the river section et2een - and B is 50 m. Estimate the average in9ltration rate into the river ed et2een - and B in mm!hr during the (assage of the ood 2ave.
':. or a certain catchment the de(letion curve of the h)drogra(h at the outlet ma) e descried 2ith the e@uation :.11. The ood h)drogra(h 4 "mm!d # at the outlet as given elo2 2as (roduced ) a rainstorm of 50 mm.
a. Plot the h)drogra(h and se(arate direct runo3 from ase o2 ) a straight line. "or the construction of this line semiClog (a(er ma) e used ut this is not re@uired#. . Estimate the direct runo3 in mm. c. Estimate the total ase o2 contriution from this rain storm. '5. *onsider a rainstorm 2ith a constant intensit) falling uniforml) over a catchment of > &m'. The time of concentration of the catchment is hours. The runo3 coeJcient is 0.:. The e(thCurationCre@uenc) curve for the T ; 10 )ears that a((lies to this catchment is given elo2. se the Rational Method to com(ute the ma7imum (ea& runo3 in m .sC1 2ith a return (eriod of 10 )ears.