dS/dt is the fnstantaneous rate of change of storage. For cases where storage is a function of outflow (as in natural lakes, or for
channel storage £orshort reaches where wedge storage is negligible in comparison with prismatic storage)
S
=
T 0 swhere T is the time of storage, S is storage, and 0 is outflow.
s
(2)
CHAPTER
4 173
(3) Ts
dO/dt
The storage equation can then be expressed as It - 0t
By solving equation (3) in finite time increments, the outflow hydrograph can be developed as a continuous function, depending upon the input hydrograph. The time increment must be
small enough to represent the time variation of the inflow hydrograph.
Also, the time of storage, T , may be a variable as a non-linear s
function of outflow.
This basic solution of the storage equation may be applied to basin or channel storage evaluation by routing through successive increments of reservoir-type storage. This principle provides an extremely flexible and convenient method for'fitting streamflow data empirically. It should be pointed out that the time-of-storage
(T ) evaluation of time-delay effects can be computed from theoretical s
flow equations which, when· related to storage, provide a simplified rigorous solution of the differential time-rate equations of flow,.
Development of the routing techniques outlined briefly -above is described in reports by Rockwood and Nelson on computer ,application to streamflow synthesis (19,20).
4.4.13 Model Calibration As in hydraulic model practice, the hydrologic mathematical model of the genera~type discussed above must be calibrated by verification of observed streamflow data. By use of the computer, repetitive trial and error solutions can be easily and quickly. By use of this technique, the necessary coefficients can be derived which will define the particular basin runoff conditions.
It should be pointed out that the confidence that can be placed in the results of any simulation of streamflow is deuendent on the ability to reproduce observed streamfloH hydro graphs for a variety of meteorologic conditions. Tests of this type should be on data independent of those used in the derivation of the hydro-logic coefficients. This test phase of simulation by computer is the most important and time-consuming in the derivation of maximum floods. The amount of time required is largely a function of the amount of basic data available, the degree of breakdown of the drainage basin into hydrologic elements, and the degree of fit considered necessary in fitting historic streamflow data.
The verification should be based insofar as possible on hydrologic events which are in the range of the anticipated computed design flood event. \{hile, of course, the maximum observed floods are not as great as a probable maximum flood (often by a factor or 1/2 to 1/5 of the probable maximum), the model verification should include the reconstitution of the maximum observed floods.
The extrapolation of the coefficients and hydrologic methods to the design flood should lie within a reasonable range of conditions used in verifying observed flows in the model.
4.4.14 Basic Configuration In order to make full use of the computer technique of hydrologic simulation, the drainage basin should be subdivided into homogeneous hydrologic units, insofar as possible. The units. are usually defined by drainage sub-basin boundaries, but they may represent area lying within elevation
zones, areas of a particular forest cover, or areas of a particular geologic or soil character. The synthesis process is developed
175 CHAPTER
4individually for each component, and combined in do~mstreamsequence.
The definition of the basin configuration for the purpose
of synthesizing streamflow is determined from map studies, availability of hydrologic data, location of projects, channel and tributary
configuration, and general knowledge of the drainage basin. It is desirable for the hydrologist to make an aerial or ground
reconnaissance of the area in order to become familiar with the basin characteristics.
4.4.15 Application of Design Flood Parameters.. The
meteorological input can be supplied to the computer model in the form of rainfal'l amounts or rainfall excesses, by periods " for the duration of the design storm sequence. These input values are supplied by the Hydrometeorologist responsible for, the design storm analysis. Values must be supplied by individual basin sub-divisions and, accordingly, each sub-basin inflow may be varied, according to known or estimated variations in basin-ta-basin. rain-fall amounts.
Sub-basin losses a~e evaluated according to the particular flood estimate or design flood condition being synthesized. Criteria for probable maximum floods would involve minimum initial losses, consistent with conditions reasonably possible for the region being studied. With the computer program, it is possible to' test the effect of varying conditions of losses in the derived maximum flood, simply by varying the initial runoff conditions. Because of the
ease of computer simulation, it is feasible to obtain a range of values, from which the hydrologist may evaluate the relative
magnitude of effects of variable losses conditions they mav reasonably
be expected. Such repetitive computations of flood conditions are no"t generally feasible with hand computation methods.
For rain-type probable maximum floods, it is necessary to maximize the storm time distribution pattern to produce the most critical flood-producing sequence. This is most easily accomplished by trial solutions. The computer synthesis provides a ready means for testing various arrangeme~ts of storm patterns which will produGe the maximum flood peak.
In connection with design .of spillways and other appurtenant facilities .at dams, as well as for design of dm-mstream river contJ;"ol works, i t is necessary to route the derived inflow hydrograph through reservoir storage. Again, this is a problem which can be solved by the computer model. Various conditions of initial pool elevations can be tested, as well as varying conditions of spillway and
outlet works design. Analysis of multiple runs of the design flood inflow through varying amounts of reservoir storage and spillway conditions will enable engineers to select the spillway design which assures the ultimate safety of the structure for the most severe combination of hydrometeorologic conditions. It will also act in providing the most economical solution of spillway capacity in relation to height of dam, with due allowance for use of surcharge storage and necessary freeboard requirements.
4.4.16 Computation of Snowmelt Probable Maximum Floods For those drainage basins involving runoff from snowmelt, it is necessary to include in the mathematical model the ability to
compute snowmelt rates on a daily (or other period) basis. Such snowmelt rates may be computed from meteorologic parameters, either
CHAPTER 4
through use of snowrnelt indexes, or rational snowmelt equations which define the rates of heat transfer to the snowpack, as a
function of meteorologic parameters (see chapter 3).
A computer program can be designed to account for the relationship between snowpack ablation and decrease of the area covered by snow. Each day's computed snowmelt is an increment to the volume of runoff, which in turn is related to the decrease of snow-covered area. Thus, the computer program maintains a day-to-day inventory of 1;vater in storage and the -snow-covered area, until finally the last increment of the snowpack is melted.
Rainfall appropriate to the design flood condition is added to each day's snowmelt runoff for obtaining the. total water excess for each day's basin water input. The day's values may be subdivided into values for shorter periods, 1;vhen required. Evapo-transpiration loss, soil moisture increase, depression storage and-deep percolation may be accounted for either directly or indirectly.
The remaining water is then routed to produce the discharge hydro-graph.
As in the case of rainfall runoff synthesis, snowmelt coefficients, and basin runoff characteristics can be developed by the computer model, by reconstitution studies of historical stream-flow events. The characteristics thus developed are then used in the computer model for application to design flood conditions.
4.4.17 Summary From the preceding discussion, it ean be seen that the general approach of streamflow synthesis by
computer provides a means for developing design floods. Because of the capability of the computer to handle large volumes of input
177
data, make detailed computations very rapidly, and provide solutions on a repetitive trial basis, it enables the hydrologist to refine procedures far beyond his capability using "hand" computations.
A general streamflow synthesis computer model can be used to evaluate all natural and man-made effects on streamflow, and its application can be adjusted to any streamflow condition. The principal
deterrents to use of the electronic computer are the cost of using an adequate computer facility, and the need for training specialists in its use. These deterrents will be overcome in time, and it is anticipated that ultimately use of the computer will be universal for solution of hydrolog~c problems of this type.
REFERENCES (1) Boc1tpeCeHCKYlt'I
R.f[.:
r1ll,I~pOJ!orHtIeCKYle paCtIeTbI. rH~pOMeTeOl1a).IJ~TJIemmrpa,rr, 195(-i.
(2) AJIeH:Ce~B
P.A.:
POCtIeT sepoHTHhl)C MSKC1I1MaJI'hHhlX paCXO,IJ,OB BO,IlbI 111 OUb8Mon
err
OK::1 CHerOB11X III ~O)l{~eBbIX naBO~KOB 0 TpY~bI mm.38/92/, 1
~,s:2(3)
DemOB Dol""'.:
rl1~poJ[orwlecKl1e nporH03bI .f"11,n.pOMeTeol1B/.J;n'p .JleHIIlHrpa,n.1957.
(4) Cla~ke, C.O.
Storage and the Unit Hydrograph, Trans. Amer. Soc. Civ. Engineers 110, 1419-88, 1945
(5) Linsley, R.K., Kohler, M.A., Paulhus, J.L.H.
Applied Hydrology. New York, Toronto, London McGraw-Hill Book Company 1949.
C~PTER
4 179
(6) Balek, J., Holecek, .J.
Odvozovani tvaru a objemu povodnovych vln. Vodni hospodarstvi 4/1963, Praha.
(7) Johnstone, D., Cross, W.P.
Elements of Applied Hydrolog. New York 1949.
(8) A compilation of US Weather Bureau Un~t Hydrographs.
Washington 1960.
(9) Snyder, F.F.
Synthetic Unit Hydrographs: Trans.
Am.
Geophysic. Union Vol. 19, pp. 447-454, 1938(10) Dooge,
A General Theory of the Unit Hydrograph. Journal of Geophysical Research, Vol. 64, No. 2,1959.
(11) Remenieras, G.
L'hydrologie de l'ingeneur. Eyrolles 1964. (2nd edition).
(12) Anderson, D.V. and J.P. Bruce
The Storms and Floods of October 1954 in Southern Ontario. IUGG General Assembly, Toronto, lASH VIII pp 351-4, 1957.
(13) Ven Te Chow
Hydrologic Determination of Waterway Areas for the Design of
Drainage Structures in Small Drainage Basins. University of Illinois Bulletin 1962.
(14) Ven TeChow
Handbook of Applied Hydrology. McGraw-Hill 1964 (15) Wundt, W.
Gewasserkunde. Heidelberg 1953
(16)
(22) (21)
Ke11er, R.
Gewasser und Wasserhausha1t des Fest1andes. Leipzig 1962 (17) Bruce, J.P. and R.H. C1ark
Introduction to Hydrometeoro1ogy. Pergamon Press, Oxford, 1966 (18) Rockwood, David M.
Columbia Basin Streamf10w Routing by Computer, American Society of Civil Engineers, Transaction Paper No. 3119, 1961
(19) Rockwood, David M.
Program Description and Operating Instructions, 'Streamf1ow Synthesis and Reservoir Regulation '. Engineering Studies Project 171, Tech.
Bull. No., 22, Jan. 1964. U.S. Army Engineer Division, North Pacific, Portland, Oregon
(20) Rockwood, David M. and Mark. L,. Nelson
, Computer Application to Streamf10w Synthesis and Reservoir Regulation, The International Commission on Irrigation and Drainage, 6th Congress, New Delhi, India, January 1966.
Crawford, N.R., and R.K. Lindsey
The Synthesis of Continuous Streamf10w Hydrographs on a Digital Computer, Tech. Report No. 12, Dept. of Civil Engineering Stanford University, Pa10 Alto, Ca1if., U.S.A., 1962
McCa11ister, J.P.
Role of Digital Computers in Hydrologic Forecasing and Analysis,
General Assembly of Berk1ey, Int. Association of Scientific Hydrology, Vol. 63, pp. 68-76, 1963.
C~T~
4
181 (23) Corps of Engineers,North Pacific Division, Summary Report ofthe Snow Investigations, Snow Hydrology, 30 June 1956. D.S. Army Engineer Division, North Pacific, Portland, Oregon
(24) Corps of Engineers, Office, Chief of Engineers, Runoff from Snowme1t, Engineering Manual 1110-2-14-6, 5 Jan. 1960.