CE322 Basic Hydrology Jorge A. Ramirez Muskingum Routing - Example
The inflow and outflow hydrographs of a river reach are tabulated below.
Time (h)
Inflow (m!s)
"utflow (m!s)
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The ,us-ingum routing procedure is used for systems that have torage / 0ischarge relationships that are hysteretic. That is1 for systems for which the outflow is not a uni2ue function of storage. The S vs. O relationship for the river reach under consideration is graphed below.
A. Parameter Estimation
3se these observations to obtain the ,us-ingum routing p arameters k and x for this river reach. The initial storage in the system is #&1 m. rap!ical Procedure"
The graphical procedure consists in generating graphs of [xI + (1-x)O] vs. S for different values of x1 arbitrarily selected such that 4 x 4 .&. The optimal value of x is selected as that which produces the narrowest and straightest loop graph of [xI + (1-x)O] vs. S . The slope of the least s2uares linear fit to the resulting points is the estimate of k . a) 5enerate accumulated storage in the system. 3se continuity e2uation as follows6
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ased on these results1 a value of x 8 .#& is selected. The best least s2uares fit to the corresponding points yields a value of k 8 '. h.
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3sing the above e2uations yields6 A 8 #'&&.+'+#+* s > 8 '$.#&# s k 8 A;> 8 %'%*.'++ s 8 '. h x 8 A!(A ; >) 8 .#&#&&$#&* "bserve that these results for k and x are the same as those of the graphical procedure. :or comparison purposes1 the observed outflow hydrograph and that predicted using the estimated values of k and x are graphed below.
B. Muskingum Routing
3se the ,us-ingum routing procedure to route the hydrograph tabulated below through the same river reach of ?art A elect a ∆t 8 # h1 as suggested by the inflow data. @owever1 chec- that with the selected ∆t1 parameter values meet restrictions6 x 4 .& ∆t/k 4 # / x :or this case6 .#&#& 4 (.&) (+)!%'%*. 4 # / .#&#& Thus1 ". ?roceed with routing1 by obtaining
This yields6
obtain the outflow hydrograph as tabulated below. The resulting hydrographs are also graphed below. .
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