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The influence of landform and precipitation parameters on flood hydrographs
Journal of Hydrology 11 (1970) 393-411 ; © North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
THE INFLUENCE OF LANDFORM AND PRECIPITATION
PARAMETERS O N F L O O D HYDROGRAPHS* MICHAEL C. ROBERTS Department of Geography, Indiana University, Bloomington, Indiana, U.S.A. and PETER C. KLINGEMAN Department of Civil Engineering, Oregon State University, Corvallis, Oregon, U.S.A. Abstract: A laboratory watershed permitted carefully controlled experiments on important factors that affect stream hydrographs. The factors selected for experimental variation are: rainfall intensity, rainfall duration, storm movement, simulated permeability, and antecedent moisture conditions. Systematic changes in the flood hydrographs, brought about by controlled variation in the five factors previously mentioned, are described.
A striking p a r a d o x o f geohydrological research is the contrast between the relative abundance o f streamflow data, and the narrow range o f conditions to which it applies. The detailed data needed for a complete explanation o f a given p h e n o m e n o n , even that concerned with streamflow, is frequently inadequate. This situation is repeated when a review is undertaken o f the theory and empirical evidence o f the processes operative in m o v e m e n t o f water in a drainage basin. Certain processes, such as overland flow, have been treated with considerable rigor1), while other topics such as the expansion and contraction o f drainage nets are virtually unidentified. It is against this b a c k g r o u n d o f poverty and affluence, hydrologically speaking, that the use o f laboratory catchments should be placed. Models allow the replication o f rainfall-runoff situations in a way that is virtually impossible to duplicate with natural data. The holding constant of certain factors and the varying o f others gives this form o f model building consider* This study was made possible in part by funds received under the Water Resources Research Act of 1964, PL 88-397, administered by the Office of Water Resources Research, U.S. Dept. of the Interior, and in part from a Faculty Research Grant of the Graduate School, Oregon State University. The facilities of the Department of Civil Engineering, Oregon State University, were used for the experimental work. Help rendered by E. T. H. Chu and T. F. Basgen in the conduct of this study is gratefully acknowledged. 393
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
able power. Such relationships as storm movement and hydrograph shape can be clearly established even though natural data is too limited for this type of analysis. Many basin models containing intricate rain producing equipment often have the most simple landform geometry. This situation permits more controllable simulation of landforms, but it leaves to one side the possibility of utilizing basin characteristics in a way that has been done for natural drainage basins2). If the geomorphic parameters of the laboratory basin are quantified then comparative studies are possible.
Objectives A stream hydrograph offers considerably more than a history of water discharge; it is the integration of complexly interacting climatic and physiographic characteristics. When a given set of characteristics change, the effect is usually a modification of the hydrograph shape. However, it is not always possible to determine which of the variables has altered simply by a detailed examination of the hydrograph. To extract the critical variable, or set of variables, is often impossible because of the masking effect of all the interactions between the different factors. Overcoming this problem in natural basins is exceedingly difficult because of the cost and effort needed to obtain the necessary data. Were it possible to isolate the role of each parameter which influences the hydrograph, then one might be better able to predict, for example, the effect of watershed changes on floods, sedimentation, erosion, and the encroachmerits of man. Under the controlled conditions of laboratory research it is possible to isolate and modify selected variables. In this way, the role of a given variable on the shape of a stream hydrograph can be ascertained. This study uses a physical or iconic laboratory model 3) for the investigation of selected climatic and physiographic factors with the objective of studying their influence upon the runoff hydrograph. A literature survey was undertaken to establish the range of the various approaches taken to utilize laboratory watersheds in the study of hydrologic and geomorphic processes. The second part of the paper is concerned with the development of the model and the analysis of the data produced.
Previous studies An extensive literature exists in both geomorphology and hydrology dealing with rainfall-runoff relationships for natural watersheds. 4) The importance of this literature to laboratory studies is that it provides the insights,
THE INFLUENCE OF PARAMETERSON FLOOD HYDROGRAPHS
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generalizations and guidance for design of experimental models, whether iconic or mathematical. 5) The use of physical models as a method of simulation has long been commonplace in hydraulic research, unlike in geomorphology or hydrology. Dooge 6) discusses the place of simulation in hydrology and classifies the physical model as a form of direct simulation, as opposed to indirect simulation when mathematical or computer models are used. A threefold classification of laboratory watersheds for hydrologic research has been proposed by Amorocho and Hart: 7) 1) Model catchments. 2) Hydromechanic prototypes. 3) Prediction analysis prototypes. The laboratory model in the present research is best placed in category 1 above. It is worth noting in this context the cautionary note of Amorocho and Hart that: 8) considerable additional theoretical and experimental work is highly desirable before this tool of analysis can be put on a solid basis for routine hydrologic and engineering application. Concern with the practical matters of model construction has been the topic of several papers. Chery 9) discusses the similitude problems in connection with the laboratory modeling of a 97.2 acre watershed northwest of Albuquerque, New Mexico. A nozzle-type rainfall simulator was developed to give variable programmed rainfall intensities. A rainfall simulator of different design has been described by Chow and Harbaugh. 10) Raindrops were produced from a large number of closely spaced tubes extending from a plexiglas box. The overland flow and surface roughness aspects of watershed models have been examined through mathematical formulation by Grace and Eagleson 1) and by Harbaugh and Chow. 11) The latter authors define a "conceptual roughness"* which was evaluated for masonite laboratory watersheds of several shapes (square, triangular, and circular, all of approximately 1,040 sq. ft. area). To obtain experimental data for their study of systems analysis in hydrology, Chiang and Wiggert lz) built plywood catchments of simple rectangular design with the rainfall being simulated by spray nozzles.
* The Manning roughness coefficient (n) is an empirical measure of open channel roughness (see Chow, op. cit., ref. 2, pp. 7-24 and 7-25). Harbaugh and Chow (op. cit., pp' 11-12) found that (n) did not work in the modeling situation and were forced to evolve a new measure that they called conceptual watershed roughness. This coefficientintroduced the additional factors of depth of flow and resistance due to raindrop impact.
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
Experimental watershed BASIN DESCRIPTION No effect was made to model a particular prototype because the need to obtain information about a specific drainage basin was unnecessary. Therefore, the model represents a hypothetical basin. With the infinite range of possible basin and drainage configurations, it was decided to relate this work to an example in the geomorphic literature. 18) The basin shape and stream network are shown in Figs. 1 and 2. In Table 1 is a listing of some of the principal morphometric parameters. TEST VARIABLES The possible matrix of hydrologic and geomorphic factors that play a significant role in determining basin runoff is very large. Furthermore, several of these are highly time-dependent, as with snow, frozen ground etc. Table 2 is a summary of the matrix previously mentioned. Practical considerations, in terms of both time and money, make it necessary to limit the number of controlled variables. Consequently, the following factors were selected for experimental variation in this study: 1) Rainfall intensity; 2) Rainfall duration; 3) Storm movement; 4) Simulated permeability; 5) Antecedent moisture conditions. Three reproducible levels of precipitation intensity - high, moderate, and low * - permitted study of the effects of this variable. The moderate intensity was considered as a " n o r m " for the examination of the other variables. The simulation of rainfall duration was achieved by using five periods of 10, 15, 20, 30, and 45 sec. These values were arrived at by running a series of test durations up to and including that giving near-equilibrium between rainfall input and runoff outflow. In addition to the conventionally applied stationary storm over an experimental watershed, two directions of movement were introduced into this study. Up-basin and down-basin storm paths permitted examination of the influence of storm direction on the runoff hydrograph. Although impermeability is a relatively easy variable to establish in a *) The high, moderate, and low rainfall intensities used were 0.155, 0.131, and 0.112 inches/minute, respectively.
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
397
watershed model, differing degrees of permeability are much more difficult to simulate. In modelling, it is sometimes hard to separate permeability, infiltration, surface detention and surface retention. For this reason, the fourth variable can be taken to mean "interactions at the land surface". In this study, permeability was simulated by laying absorbent material*) over the surface of the basin. Two distributions of this material were applied, one
Fig. 1. The test basin showing the drainage network and contours.
covering 50 per cent and the other 100 per cent of the surface. Since the uncovered basin was impermeable, this offered a third condition of land surface interaction with rainfall. *) A double layer of cheesecloth was used to simulate permeability.
398
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
Fig. 2. The physical model showing the drainage and topography. The staff is in units of tenths of a foot.
Two antecedent moisture conditions for the basin were examined. With one, the basin surface was completely dry and with the other a wet condition was produced in that most of the surface storage capacity was filled. TEST FACILITY The test facility for this study is shown diagrammatically in Fig. 3.
Watershed Basin features were developed with layers of plywood and carved styrofoam sheets (see Fig. 4). The model was then made watertight with epoxy resin prior to final painting. The channel and immediately adjacent banks were covered with white latex paint. The channel bottom was defined with an additional finish of blue paint. The basin surface was covered with a coarse paint*) to simulate land roughness and irregularities.
Rain input equipment The rainfall generator consisted of seven fine spray nozzles arranged so *) Treadsure Slip Resistant Coating was used because of its particulate nature.
THE INFLUENCE OF PARAMETERSON FLOOD HYDROGRAPHS
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TABLE 1 Morphometric parameters of the laboratory watershed
Linear Aspects Basin stream order: Number of first-order stream segments: Number of second-order stream segments: Total length of first-order streams: Total length of second-order streams: Total length of third-order streams:
3 11 4 36.06 ft 5.81 ft 3.92 ft
Total length of streams:
45.79 ft
Length of basin, mouth to most distant perimeter point = 10.42 ft.
Areal Aspects Basin area: 44.44 sq. ft. ( Basin area Basin form factor \Basin length_ sq~uared]: 0.41 Basin length/width ratio: 1.6 (Total length of streams~ Drainage density \ Basi~ a-rea ] : 1.03 •Total No. of streams of all orders\ Stream frequency ~k Basin area ) : 0.36
Relief Aspects Maximum basin relief: 0.96 ft. ( Basin relief ~. Relief ratio \--Basin length]" 0.09
as to give a near-uniform areal rainfall distribution. The nozzles were m o u n t e d on a rail-guided carriage which could be m o v e d across the watershed. This equipment is shown in Fig. 5. Carriage m o t i o n was provided, at a steady rate, by means o f a winch. The water supply was controlled by a solenoid value for rapid starting and stopping o f the rainfall, and the adjustable flow rate was measured with a flowmeter.
Runoff output equipment R u n o f f was collected in a volumetric tank which has incorporated in it a stilling well by means o f h o n e y c o m b baffling (see Fig. 5). A staff gage in the stilling well permitted an absolute determination o f water volume and was used for calibration o f the graphical record for each test. A capacitance
400
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
TABLE 2 Major hydrologic and geomorphic variables affecting runoff
Precipitation
Basin Surface
Form & type Intensity Duration Time duration Areal distribution Frequency of occurrence Storm direction & movement Antecedent conditions
Interception
Land use & cover Soil type, texture & structure Soil moisture Surface condition & compaction Surface infiltration condition Temperature Lithology & structure Lakes & swamps
Geometric Features
Vegetation type & species Vegetation composition Vegetation age & density Disturbance of canopy & floor Land use Ground cover Season of year Storm size
Evaporation/Transportation Temperature of air & surface Wind Vapor pressure & humidity Atmospheric pressure Radiation Light Surface reflectivity Nature of surface Surface shape & form Soil moisture
Size Shape Slope & relief Orientation Aspect Elevation Stream density Stream lengths Overland flow lengths
Channel Characteristics Storage capacity Cross-section size & shape Slope Roughness Length Tributaries
Time
Source: Adapted from Chow2), op. eit., p. 14-15.
Time of day Season of year
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
401
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Fig. 3. A schematic diagram of the experimental equipment.
Fig. 4. Development of basin contours with plywood templates, prior to the placement and carving of styrofoam sheets. probe, also in the stilling well (Fig. 5), was connected to a graphical X-Y recorder to give a permanent record of water levels in the tank. Figure 6 shows the recorder as well as a cumulative hydrograph record from one of the tests. DATA COLLECTION
A typical test The experimental procedure can be better understood through description of a typical test run: 1) The rainfall simulator is moved off the model to check and set rain intensity and is then replaced over the basin.
402
Fig. 5.
Fig. 6.
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
The basin in testing position, with rainfall simulator overhead and with tank, staff gage, and capacitance probe at basin outlet.
The X-Y graphical recorder, showing a typical set of three superimposed cumulative hydrographs.
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
403
2) The ordinate scale of the X-Y plotter is adjusted to give nearly a fullrange deflection for the anticipated cumulative hydrograph. 3) For calibration purposes, an initial reading is taken at the staff gage. 4) The rainfall is started and its duration is timed by a stop watch. 5) The flowmeter is read periodically during the rainfall to confirm that there is a uniform rain intensity. 6) The rainfall is terminated. 7) A final reading on the staff gage is taken at a time well out on the recession limb of the hydrograph. 8) The interval between successive runs is carefully timed to insure consistent antecedent moisture conditions. 9) The next run is started. D a t a con version
Each test, with its given set of conditions, was repeated three times. The replicated runs were recorded on the same data sheet by superimposing the starting coordinates of the cumulative flow curves. The conversion of the three cumulative flow curves to a hydrograph was done by taking a mean curve for the three runs and differentiating this for short time increments. Presentation of results
Interpretation of the experimental results was based upon a comparison of various groupings of the graphical test records. Not all possible comparisons were made since over two hundred combinations of the controlled variables would be involved. Data points have been shown (see Figs. 7-11) except in those few instances where overlapping curves necessitated their elimination to maintain clarity. INFLUENCE OF RAINFALL INTENSITY
The intensity of rainfall during a storm is an important determinant of hydrograph shape. This is especially so for small basins where streamflow response is most sensitive to variations in intensity. Thus one finds intensity used to predict flood peak in many formulas, such as the Rational formula. The results of this study show that, given 100 per cent basin cover and wet antecedent conditions, the intensity of rainfall does indeed cause a marked difference in the magnitude of the discharge hydrograph. Experimental data for two durations of rainfall are presented in Fig. 7. With high and moderate intensities of rainfall over the test basin (Fig. 7A), the hydrograph shapes are quite similar, one being proportionately larger than the other. Both rain-
404
300
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
A. 45 SECOND RAINFALL DURATION
B. 30 SECOND RAINFALL DURATION I00 % Permeability Simulotion Wet Antecedent Conditions Stotionary Storm
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The effect of rainfall intensity on the runoff hydrograph.
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THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
405
fall intensities were sufficiently great to bring the antecedent situation to a saturated condition fairly early in the storm. When low intensity rainfall occurs over the basin, the resulting hydrograph shape exhibits important deviations from that for a higher intensity of rainfall. This is seen for the rising limbs of the hydrographs in Fig. 7B. At the low intensity of rainfall more time is required to create a saturated basin surface. Some volume of the rainfall must go to satisfy surface abstractions,
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Fig. 9. The effect of storm movement on the runoff hydrograph.
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Moderals Rainfall Intensity 45 Second Rainfall Duration nd't'°ns
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Fig. 10. The effect of simulated permeability on the runoff hydrograph.
406
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
such as interception, infiltration, and surface storage, and this requires a finite time controlled by the rate of input. It has been pointed out 14) that for increasing rainfall intensity an equilibrium condition*) is reached more rapidly between precipitation and runoff, given a sufficient rainfall duration, than for low or decreasing intensities. In Fig. 7A this situation may be observed. The hydrograph for high intensity rainfall has flattened out to show a near-equilibrium before the end of the rain, whereas at a moderate intensity the near-equilibrium condition is barely achieved at the rainfall termination. Natural watersheds rarely show an equilibrium condition because of storm rainfall variability as well as other interacting factors that prevent it from occurring.
3OO Moderate Rainfoll Intensity
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The effect of antecedent moisture conditions on the runoff hydrograph.
INFLUENCE OF RAINFALL DURATION
It is intuitive that the longer a rainfall of given intensity lasts, the greater will be the resulting flood. This concept of duration has application both in the design of river structures and in the understanding of the geomorphic aspects of fluvial erosion and deposition. Theoretically, under the conditions of laboratory experimentation, if a nested set of hydrographs is examined, differing only with respect to rainfall *) Here equilibrium refers to the steady state condition between rainfall and runoff, which is reflected on the hydrography by a constant peak discharge (see Fig. 8A for an illustration of this condition).
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
407
duration, the rising limbs of the hydrographs will be identical (see Figs. 8A and 8B). This is because the simplified basin characteristics permit repeated establishment of virtually identical starting conditions, especially if the surface is impermeable. The recession limbs should also retain a;general similarity of shape*), though displaced in time in accordance with the volume of runoff, which is a reflection of rainfall duration. The flood peak will increase with duration until a equilibrium condition is reached. When this happens a flat hydrograph peak will result (see Fig. 8A), with a crest width dependent upon the duration of rainfall. The rate of overland flow is retarded for permeable basins, so that the rising limb has a flatter slope than for a hydrograph from an impermeable surface. Similarly, a change in recession curve characteristics can be expected because of the slower release of water from the permeable surface after rainfall ceases. The above distinctions are illustrated by the theoretical models in Figs. 8A and 8B. The experimental evidence generally confirms the theoretical models that have been advanced. In Fig. 8C the longer rainfalls (20, 20, 45 sec) on this impermeable surface reached equilibrium. It should be noted that the deviation of the 20 second duration test is the result of experimental variation. An interesting feature observable for the 10 and 15 second duration hydrographs is the time lag of the flood peak after the termination of rainfall. The reason for this is that the up-basin contributions, whether overland flow or channel flow, are still building up when the rain stops and for a brief period maintain the rising limb. The major distinction between the results presented in Figs. 8C and 8D is the retardation effect of simulated permeability on the five hydrographs in Fig. 8D, preventing all of them from reaching equilibrium except the 45 second rainfall.**) iNFLUENCE OF STORM MOVEMENT The direction of storm travel over a drainage basin may be instrumental in aggravating or reducing flood peaks. It may be hypothesized that storms moving up-basin give an early rising limb to the hydrograph but a broad
*) The recession curves show the greatest similarity in shape for impermeable experimental basins, and are modified by permeability and related land surface interactions. *) One inference of the comparison of Figs. 8C and 8D is that the commonly used unit-hydrograph method is more suitable for relatively impermeable basins. It can be observed that the rising limbs of hydrographs from the impermeable basin showed much less variation than those from the permeable one. This rising limb variability is a reflection of slight differences in the carefully controlled experimental antecedent moisture conditions.
408
M I C H A E L C. ROBERTS A N D P E T E R C. K L I N G E M A N
crest of moderate peak and a gradual recession curve. The rapid rise is due to the rain first occurring at the basin outlet. As the storm moves farther up-basin, away from the mouth, down-basin runoffdiminishes and the runoff is from up-basin areas. This is modified by channel storage, so as to flatten and draw out the hydrograph. The corollary hypothesis for storms moving down-basin is that runoff is at first delayed, due to long travel times to the outlet from far up-basin, but then the hydrograph rises rapidly to a large peak value, caused by the arrival of streamflow from up-basin concurrently with rainfall at the mouth. The hydrograph falls fairly rapidly when the storm has passed off of the basin. The essence of these hypotheses has been presented in a descriptive form, 15) no previous experimental confirmation is known to the authors. The experimental results, presented in Fig. 9, give a very satisfactory confirmation of the hypothesized hydrograph shapes. It should be realized that the relative times of storm travel across a basin and of flood wave travel through a channel system vary for different storms or basins. Thus, the corresponding shapes of hydrographs resulting from storms moving in opposite directions across a given basin may have a range of possible shapes which depend upon prevailing meteorological conditions. In regions subject to generally recurrent directions for major storms, the predominant direction of storm movement would give definition to a "characteristic" hydrograph shape (assuming, for the moment, that other factors affecting runoff are invariant). Variations in this shape could result from differences in the rate of storm movement. I N F L U E N C E OF S I M U L A T E D P E R M E A B I L I T Y
In Fig. 10 are presented the results of the attempts to simulate permeability. The 50 per cent simulation involved an absorbent cover placed over that portion of the basin above an elevation of five inches (see Fig. 1) while the 100 per cent simulation was simply a covering of the complete basin. The rising limbs of the 0 per cent and the 50 per cent simulations are virtually superimposed for the first few seconds of runoff. A deviation between the two becomes apparent at the time of arrival of water from the upper half of the basin. This is because of saturation and flow retardation effects due to the simulated permeability. This hold-back of water is much more pronounced for the 100 per cent simulation of permeability since even the start of runoff is delayed. An equilibrium of rainfall and runoff occurred for the three simulations in Fig. 10 because of the long duration (45 sec). It is readily apparent that with an increasing degree of permeability there is an increasing time to equilibrium.
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
409
INFLUENCE OF ANTECEDENT CONDITIONS
Antecedent moisture conditions for a basin are very important in determining the magnitude of an ensuing flood. The pre-storm moisture level is responsible for wide variations in peak discharge values resulting from similar storm events. Therefore, in hydrologic design it is common to assume a saturated or very wet antecedent moisture condition in order to deal with the greatest likely flood. The effect of antecedent conditions is shown very markedly by the experimental results presented in Fig. 11. A long duration (45 sec) has been chosen to illustrate the differing effects of wet and dry antecedent moisture conditions at several points in time. The duration is also sufficient to permit near-equilibrium to be reached in each case. The rising limb of the hydrograph having dry antecedent conditions is considerably delayed in time. Much more of the rainfall goes into storage on the basin surface initially, due to the greater available volume for holding water. Some rainfall must also go into storage on the initially wet basin, in order to give saturated conditions there and to provide a finite water depth for overland flow. The difference, between wet and dry antecedent conditions, in the volume of water taken into storage on the basin surface is shown by the shaded area in Fig. 11. At durations of less than 45 sec, the discharge ordinates of the two hydrographs are quite different, the relative difference becoming greater for successively shorter durations. In fact, a family of hydrographs, all with different discharges at a stated duration, would result from slightly different antecedent moisture conditions between the limits used for the curves in Fig. 11. Therefore it is evident why natural floods resulting from similar storms exhibit have such a variation in peak discharge value.
Concluding remarks In this study a set of pre-selected landform features were built into a laboratory watershed to form a "base" of constants for the hydrologic testing of the model. Inputs that could be experimentally varied in this model were of two groups: storm related factors (rainfall intensity, rainfall duration, storm movement) and basin surface conditions (simulated permeability, antecedent moisture conditions). Each variable was found to cause a significant change in the hydrograph shape. Certain factors were particularly influential in altering the rising limb of the runoff hydrograph, whereas others were more critical with respect to the flood crest. Rainfall durations were pre-programmed so that the equi-
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
l i b r i u m c o n d i t i o n between rainfall a n d runoff, which is extremely difficult to find with n a t u r a l l y occurring data, could be studied. F u t u r e research will a p p r o a c h the p r o b l e m s of this study in a different fashion. The l a n d f o r m or g e o m o r p h i c variables will be varied experimentally, as well as the hydrometeorological factors. Such a m e t h o d o l o g y will entail a m u c h more complex watershed model.
References 1) R. A. Grace and P. S. Eagieson, The modeling of overland flow, Water Resources Research, 2 (1966) 292-403 2) The bibliography of quantitative geomorphology is extensive and the following works are only a selection: L. B. Leopold, M. G. Wolman and J. P. Miller, Fluvial Processes in Geomorphology, W. H. Freeman, (San Francisco, 1964); M. E. Morisawa, Streams their Dynamics and Morphology, McGraw-Hill, (New York, 1968); A. N. Strahler, Quantitative Geomorphology of Drainage Basins and Channel Networks, Section 4, Part II in: V. T. Chow (Ed.), Handbook of Applied Hydrology, McGraw-Hill, (New York, 1964). 3) The terminology used to classify models in hydrology varies from author to author; we prefer that of M. E. Holland who divided models into three classes-iconic (lookalike), analog and symbolic; W. T. Dickinson, M. E. Holland and G. L. Smith, An Experimental Rainfall-Runoff Facility (Fort Collins, Colorado State University, Department of Civil Engineering, Hydrology Paper No. 25, 1967). 4) Among the more important recent works with comprehensive literature surveys are: Chow (1964) ref. 2; Dickinson et al. (1967) ref. 3; R. J. More, Chapter 5 in: R.J. Chorley and P. Haggett (Eds.) Hydrological Models in Geography (Methuen, London, 1967); S. T. Wong, A multivariate statistical model for predicting mean annual flood in New England. Annals Assoc. Amer. Geog. 53 (1963) 298-311 5) A study that illustrates the need for adequate generalizations for the basis of simulation is that by Norman H. Crawford and Ray K. Linsley, Digital Simulation in Hydrology: Stanford Watershed Model IV (Palo Alto: Stanford University, Department of Civil Engineering, Technical Report No. 39, 1966). 6) J. C. I. Dooge, The hydrologic cycle as a closed system. Bulletin International Association of Scientific Hydrology, 13 (1968) 5 -68 7) J. Amorocho and W. E. Hart, The use of laboratory catchments in the study of hydrologic systems. J. Hydrol. 3 (1965) 106-123 8) Amorocho and Hart, op. cit., p. 122. 9) Donald L. Chery, Jr., Design and tests of a physical watershed model. J. Hydrol. 4 (1966) 224-235 10) V. T. Chow and T. W. Harbaugh, Raindrop production for laboratory watershed experimentation. J. Geophys. Res. 70 (1965) 6111-6119 V. T. Chow, Laboratory Study of Watershed Hydrology, Paper 26, Vol. 1, pp. 194202, Proc. International Hydrology Symposium, Sept. 6-8, 1967, Fort Collins, Colorado.
THE INFLUENCE OF PARAMETERSON FLOOD HYDROGRAPHS
1l)
12) 13) 14) 15)
4l 1
V. T. Chow, R and D of a Watershed Experimentation System, Junior Eng. Tech. Soc. 15, 11-13 T. E. Harbaugh and V. T. Chow, A study of the roughness of conceptual river systems or watersheds, Proceedings, 12th Congress, International Association of Hydraulic Research, 1 (1967) 9-17 T. T. Chiang and J. M. Wiggert, Analysis of Hydrologic Systems, Blacksburg, Virginia Polytechnic Institute, Water Resources Research Center, Bulletin 12, 1968 Chow2), op. cit., Figure 4-I1-16(a) Harbaugh and Chow11), op. cit., p. 14. R.J.M. DeWiest, Geohydrology (J. Wiley, New York, 1965), p. 72, Fig. 2-43.
THE INFLUENCE OF LANDFORM AND PRECIPITATION
PARAMETERS O N F L O O D HYDROGRAPHS* MICHAEL C. ROBERTS Department of Geography, Indiana University, Bloomington, Indiana, U.S.A. and PETER C. KLINGEMAN Department of Civil Engineering, Oregon State University, Corvallis, Oregon, U.S.A. Abstract: A laboratory watershed permitted carefully controlled experiments on important factors that affect stream hydrographs. The factors selected for experimental variation are: rainfall intensity, rainfall duration, storm movement, simulated permeability, and antecedent moisture conditions. Systematic changes in the flood hydrographs, brought about by controlled variation in the five factors previously mentioned, are described.
A striking p a r a d o x o f geohydrological research is the contrast between the relative abundance o f streamflow data, and the narrow range o f conditions to which it applies. The detailed data needed for a complete explanation o f a given p h e n o m e n o n , even that concerned with streamflow, is frequently inadequate. This situation is repeated when a review is undertaken o f the theory and empirical evidence o f the processes operative in m o v e m e n t o f water in a drainage basin. Certain processes, such as overland flow, have been treated with considerable rigor1), while other topics such as the expansion and contraction o f drainage nets are virtually unidentified. It is against this b a c k g r o u n d o f poverty and affluence, hydrologically speaking, that the use o f laboratory catchments should be placed. Models allow the replication o f rainfall-runoff situations in a way that is virtually impossible to duplicate with natural data. The holding constant of certain factors and the varying o f others gives this form o f model building consider* This study was made possible in part by funds received under the Water Resources Research Act of 1964, PL 88-397, administered by the Office of Water Resources Research, U.S. Dept. of the Interior, and in part from a Faculty Research Grant of the Graduate School, Oregon State University. The facilities of the Department of Civil Engineering, Oregon State University, were used for the experimental work. Help rendered by E. T. H. Chu and T. F. Basgen in the conduct of this study is gratefully acknowledged. 393
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
able power. Such relationships as storm movement and hydrograph shape can be clearly established even though natural data is too limited for this type of analysis. Many basin models containing intricate rain producing equipment often have the most simple landform geometry. This situation permits more controllable simulation of landforms, but it leaves to one side the possibility of utilizing basin characteristics in a way that has been done for natural drainage basins2). If the geomorphic parameters of the laboratory basin are quantified then comparative studies are possible.
Objectives A stream hydrograph offers considerably more than a history of water discharge; it is the integration of complexly interacting climatic and physiographic characteristics. When a given set of characteristics change, the effect is usually a modification of the hydrograph shape. However, it is not always possible to determine which of the variables has altered simply by a detailed examination of the hydrograph. To extract the critical variable, or set of variables, is often impossible because of the masking effect of all the interactions between the different factors. Overcoming this problem in natural basins is exceedingly difficult because of the cost and effort needed to obtain the necessary data. Were it possible to isolate the role of each parameter which influences the hydrograph, then one might be better able to predict, for example, the effect of watershed changes on floods, sedimentation, erosion, and the encroachmerits of man. Under the controlled conditions of laboratory research it is possible to isolate and modify selected variables. In this way, the role of a given variable on the shape of a stream hydrograph can be ascertained. This study uses a physical or iconic laboratory model 3) for the investigation of selected climatic and physiographic factors with the objective of studying their influence upon the runoff hydrograph. A literature survey was undertaken to establish the range of the various approaches taken to utilize laboratory watersheds in the study of hydrologic and geomorphic processes. The second part of the paper is concerned with the development of the model and the analysis of the data produced.
Previous studies An extensive literature exists in both geomorphology and hydrology dealing with rainfall-runoff relationships for natural watersheds. 4) The importance of this literature to laboratory studies is that it provides the insights,
THE INFLUENCE OF PARAMETERSON FLOOD HYDROGRAPHS
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generalizations and guidance for design of experimental models, whether iconic or mathematical. 5) The use of physical models as a method of simulation has long been commonplace in hydraulic research, unlike in geomorphology or hydrology. Dooge 6) discusses the place of simulation in hydrology and classifies the physical model as a form of direct simulation, as opposed to indirect simulation when mathematical or computer models are used. A threefold classification of laboratory watersheds for hydrologic research has been proposed by Amorocho and Hart: 7) 1) Model catchments. 2) Hydromechanic prototypes. 3) Prediction analysis prototypes. The laboratory model in the present research is best placed in category 1 above. It is worth noting in this context the cautionary note of Amorocho and Hart that: 8) considerable additional theoretical and experimental work is highly desirable before this tool of analysis can be put on a solid basis for routine hydrologic and engineering application. Concern with the practical matters of model construction has been the topic of several papers. Chery 9) discusses the similitude problems in connection with the laboratory modeling of a 97.2 acre watershed northwest of Albuquerque, New Mexico. A nozzle-type rainfall simulator was developed to give variable programmed rainfall intensities. A rainfall simulator of different design has been described by Chow and Harbaugh. 10) Raindrops were produced from a large number of closely spaced tubes extending from a plexiglas box. The overland flow and surface roughness aspects of watershed models have been examined through mathematical formulation by Grace and Eagleson 1) and by Harbaugh and Chow. 11) The latter authors define a "conceptual roughness"* which was evaluated for masonite laboratory watersheds of several shapes (square, triangular, and circular, all of approximately 1,040 sq. ft. area). To obtain experimental data for their study of systems analysis in hydrology, Chiang and Wiggert lz) built plywood catchments of simple rectangular design with the rainfall being simulated by spray nozzles.
* The Manning roughness coefficient (n) is an empirical measure of open channel roughness (see Chow, op. cit., ref. 2, pp. 7-24 and 7-25). Harbaugh and Chow (op. cit., pp' 11-12) found that (n) did not work in the modeling situation and were forced to evolve a new measure that they called conceptual watershed roughness. This coefficientintroduced the additional factors of depth of flow and resistance due to raindrop impact.
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
Experimental watershed BASIN DESCRIPTION No effect was made to model a particular prototype because the need to obtain information about a specific drainage basin was unnecessary. Therefore, the model represents a hypothetical basin. With the infinite range of possible basin and drainage configurations, it was decided to relate this work to an example in the geomorphic literature. 18) The basin shape and stream network are shown in Figs. 1 and 2. In Table 1 is a listing of some of the principal morphometric parameters. TEST VARIABLES The possible matrix of hydrologic and geomorphic factors that play a significant role in determining basin runoff is very large. Furthermore, several of these are highly time-dependent, as with snow, frozen ground etc. Table 2 is a summary of the matrix previously mentioned. Practical considerations, in terms of both time and money, make it necessary to limit the number of controlled variables. Consequently, the following factors were selected for experimental variation in this study: 1) Rainfall intensity; 2) Rainfall duration; 3) Storm movement; 4) Simulated permeability; 5) Antecedent moisture conditions. Three reproducible levels of precipitation intensity - high, moderate, and low * - permitted study of the effects of this variable. The moderate intensity was considered as a " n o r m " for the examination of the other variables. The simulation of rainfall duration was achieved by using five periods of 10, 15, 20, 30, and 45 sec. These values were arrived at by running a series of test durations up to and including that giving near-equilibrium between rainfall input and runoff outflow. In addition to the conventionally applied stationary storm over an experimental watershed, two directions of movement were introduced into this study. Up-basin and down-basin storm paths permitted examination of the influence of storm direction on the runoff hydrograph. Although impermeability is a relatively easy variable to establish in a *) The high, moderate, and low rainfall intensities used were 0.155, 0.131, and 0.112 inches/minute, respectively.
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
397
watershed model, differing degrees of permeability are much more difficult to simulate. In modelling, it is sometimes hard to separate permeability, infiltration, surface detention and surface retention. For this reason, the fourth variable can be taken to mean "interactions at the land surface". In this study, permeability was simulated by laying absorbent material*) over the surface of the basin. Two distributions of this material were applied, one
Fig. 1. The test basin showing the drainage network and contours.
covering 50 per cent and the other 100 per cent of the surface. Since the uncovered basin was impermeable, this offered a third condition of land surface interaction with rainfall. *) A double layer of cheesecloth was used to simulate permeability.
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
Fig. 2. The physical model showing the drainage and topography. The staff is in units of tenths of a foot.
Two antecedent moisture conditions for the basin were examined. With one, the basin surface was completely dry and with the other a wet condition was produced in that most of the surface storage capacity was filled. TEST FACILITY The test facility for this study is shown diagrammatically in Fig. 3.
Watershed Basin features were developed with layers of plywood and carved styrofoam sheets (see Fig. 4). The model was then made watertight with epoxy resin prior to final painting. The channel and immediately adjacent banks were covered with white latex paint. The channel bottom was defined with an additional finish of blue paint. The basin surface was covered with a coarse paint*) to simulate land roughness and irregularities.
Rain input equipment The rainfall generator consisted of seven fine spray nozzles arranged so *) Treadsure Slip Resistant Coating was used because of its particulate nature.
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399
TABLE 1 Morphometric parameters of the laboratory watershed
Linear Aspects Basin stream order: Number of first-order stream segments: Number of second-order stream segments: Total length of first-order streams: Total length of second-order streams: Total length of third-order streams:
3 11 4 36.06 ft 5.81 ft 3.92 ft
Total length of streams:
45.79 ft
Length of basin, mouth to most distant perimeter point = 10.42 ft.
Areal Aspects Basin area: 44.44 sq. ft. ( Basin area Basin form factor \Basin length_ sq~uared]: 0.41 Basin length/width ratio: 1.6 (Total length of streams~ Drainage density \ Basi~ a-rea ] : 1.03 •Total No. of streams of all orders\ Stream frequency ~k Basin area ) : 0.36
Relief Aspects Maximum basin relief: 0.96 ft. ( Basin relief ~. Relief ratio \--Basin length]" 0.09
as to give a near-uniform areal rainfall distribution. The nozzles were m o u n t e d on a rail-guided carriage which could be m o v e d across the watershed. This equipment is shown in Fig. 5. Carriage m o t i o n was provided, at a steady rate, by means o f a winch. The water supply was controlled by a solenoid value for rapid starting and stopping o f the rainfall, and the adjustable flow rate was measured with a flowmeter.
Runoff output equipment R u n o f f was collected in a volumetric tank which has incorporated in it a stilling well by means o f h o n e y c o m b baffling (see Fig. 5). A staff gage in the stilling well permitted an absolute determination o f water volume and was used for calibration o f the graphical record for each test. A capacitance
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
TABLE 2 Major hydrologic and geomorphic variables affecting runoff
Precipitation
Basin Surface
Form & type Intensity Duration Time duration Areal distribution Frequency of occurrence Storm direction & movement Antecedent conditions
Interception
Land use & cover Soil type, texture & structure Soil moisture Surface condition & compaction Surface infiltration condition Temperature Lithology & structure Lakes & swamps
Geometric Features
Vegetation type & species Vegetation composition Vegetation age & density Disturbance of canopy & floor Land use Ground cover Season of year Storm size
Evaporation/Transportation Temperature of air & surface Wind Vapor pressure & humidity Atmospheric pressure Radiation Light Surface reflectivity Nature of surface Surface shape & form Soil moisture
Size Shape Slope & relief Orientation Aspect Elevation Stream density Stream lengths Overland flow lengths
Channel Characteristics Storage capacity Cross-section size & shape Slope Roughness Length Tributaries
Time
Source: Adapted from Chow2), op. eit., p. 14-15.
Time of day Season of year
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
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Fig. 4. Development of basin contours with plywood templates, prior to the placement and carving of styrofoam sheets. probe, also in the stilling well (Fig. 5), was connected to a graphical X-Y recorder to give a permanent record of water levels in the tank. Figure 6 shows the recorder as well as a cumulative hydrograph record from one of the tests. DATA COLLECTION
A typical test The experimental procedure can be better understood through description of a typical test run: 1) The rainfall simulator is moved off the model to check and set rain intensity and is then replaced over the basin.
402
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Fig. 6.
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
The basin in testing position, with rainfall simulator overhead and with tank, staff gage, and capacitance probe at basin outlet.
The X-Y graphical recorder, showing a typical set of three superimposed cumulative hydrographs.
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
403
2) The ordinate scale of the X-Y plotter is adjusted to give nearly a fullrange deflection for the anticipated cumulative hydrograph. 3) For calibration purposes, an initial reading is taken at the staff gage. 4) The rainfall is started and its duration is timed by a stop watch. 5) The flowmeter is read periodically during the rainfall to confirm that there is a uniform rain intensity. 6) The rainfall is terminated. 7) A final reading on the staff gage is taken at a time well out on the recession limb of the hydrograph. 8) The interval between successive runs is carefully timed to insure consistent antecedent moisture conditions. 9) The next run is started. D a t a con version
Each test, with its given set of conditions, was repeated three times. The replicated runs were recorded on the same data sheet by superimposing the starting coordinates of the cumulative flow curves. The conversion of the three cumulative flow curves to a hydrograph was done by taking a mean curve for the three runs and differentiating this for short time increments. Presentation of results
Interpretation of the experimental results was based upon a comparison of various groupings of the graphical test records. Not all possible comparisons were made since over two hundred combinations of the controlled variables would be involved. Data points have been shown (see Figs. 7-11) except in those few instances where overlapping curves necessitated their elimination to maintain clarity. INFLUENCE OF RAINFALL INTENSITY
The intensity of rainfall during a storm is an important determinant of hydrograph shape. This is especially so for small basins where streamflow response is most sensitive to variations in intensity. Thus one finds intensity used to predict flood peak in many formulas, such as the Rational formula. The results of this study show that, given 100 per cent basin cover and wet antecedent conditions, the intensity of rainfall does indeed cause a marked difference in the magnitude of the discharge hydrograph. Experimental data for two durations of rainfall are presented in Fig. 7. With high and moderate intensities of rainfall over the test basin (Fig. 7A), the hydrograph shapes are quite similar, one being proportionately larger than the other. Both rain-
404
300
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
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THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
405
fall intensities were sufficiently great to bring the antecedent situation to a saturated condition fairly early in the storm. When low intensity rainfall occurs over the basin, the resulting hydrograph shape exhibits important deviations from that for a higher intensity of rainfall. This is seen for the rising limbs of the hydrographs in Fig. 7B. At the low intensity of rainfall more time is required to create a saturated basin surface. Some volume of the rainfall must go to satisfy surface abstractions,
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406
MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
such as interception, infiltration, and surface storage, and this requires a finite time controlled by the rate of input. It has been pointed out 14) that for increasing rainfall intensity an equilibrium condition*) is reached more rapidly between precipitation and runoff, given a sufficient rainfall duration, than for low or decreasing intensities. In Fig. 7A this situation may be observed. The hydrograph for high intensity rainfall has flattened out to show a near-equilibrium before the end of the rain, whereas at a moderate intensity the near-equilibrium condition is barely achieved at the rainfall termination. Natural watersheds rarely show an equilibrium condition because of storm rainfall variability as well as other interacting factors that prevent it from occurring.
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INFLUENCE OF RAINFALL DURATION
It is intuitive that the longer a rainfall of given intensity lasts, the greater will be the resulting flood. This concept of duration has application both in the design of river structures and in the understanding of the geomorphic aspects of fluvial erosion and deposition. Theoretically, under the conditions of laboratory experimentation, if a nested set of hydrographs is examined, differing only with respect to rainfall *) Here equilibrium refers to the steady state condition between rainfall and runoff, which is reflected on the hydrography by a constant peak discharge (see Fig. 8A for an illustration of this condition).
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
407
duration, the rising limbs of the hydrographs will be identical (see Figs. 8A and 8B). This is because the simplified basin characteristics permit repeated establishment of virtually identical starting conditions, especially if the surface is impermeable. The recession limbs should also retain a;general similarity of shape*), though displaced in time in accordance with the volume of runoff, which is a reflection of rainfall duration. The flood peak will increase with duration until a equilibrium condition is reached. When this happens a flat hydrograph peak will result (see Fig. 8A), with a crest width dependent upon the duration of rainfall. The rate of overland flow is retarded for permeable basins, so that the rising limb has a flatter slope than for a hydrograph from an impermeable surface. Similarly, a change in recession curve characteristics can be expected because of the slower release of water from the permeable surface after rainfall ceases. The above distinctions are illustrated by the theoretical models in Figs. 8A and 8B. The experimental evidence generally confirms the theoretical models that have been advanced. In Fig. 8C the longer rainfalls (20, 20, 45 sec) on this impermeable surface reached equilibrium. It should be noted that the deviation of the 20 second duration test is the result of experimental variation. An interesting feature observable for the 10 and 15 second duration hydrographs is the time lag of the flood peak after the termination of rainfall. The reason for this is that the up-basin contributions, whether overland flow or channel flow, are still building up when the rain stops and for a brief period maintain the rising limb. The major distinction between the results presented in Figs. 8C and 8D is the retardation effect of simulated permeability on the five hydrographs in Fig. 8D, preventing all of them from reaching equilibrium except the 45 second rainfall.**) iNFLUENCE OF STORM MOVEMENT The direction of storm travel over a drainage basin may be instrumental in aggravating or reducing flood peaks. It may be hypothesized that storms moving up-basin give an early rising limb to the hydrograph but a broad
*) The recession curves show the greatest similarity in shape for impermeable experimental basins, and are modified by permeability and related land surface interactions. *) One inference of the comparison of Figs. 8C and 8D is that the commonly used unit-hydrograph method is more suitable for relatively impermeable basins. It can be observed that the rising limbs of hydrographs from the impermeable basin showed much less variation than those from the permeable one. This rising limb variability is a reflection of slight differences in the carefully controlled experimental antecedent moisture conditions.
408
M I C H A E L C. ROBERTS A N D P E T E R C. K L I N G E M A N
crest of moderate peak and a gradual recession curve. The rapid rise is due to the rain first occurring at the basin outlet. As the storm moves farther up-basin, away from the mouth, down-basin runoffdiminishes and the runoff is from up-basin areas. This is modified by channel storage, so as to flatten and draw out the hydrograph. The corollary hypothesis for storms moving down-basin is that runoff is at first delayed, due to long travel times to the outlet from far up-basin, but then the hydrograph rises rapidly to a large peak value, caused by the arrival of streamflow from up-basin concurrently with rainfall at the mouth. The hydrograph falls fairly rapidly when the storm has passed off of the basin. The essence of these hypotheses has been presented in a descriptive form, 15) no previous experimental confirmation is known to the authors. The experimental results, presented in Fig. 9, give a very satisfactory confirmation of the hypothesized hydrograph shapes. It should be realized that the relative times of storm travel across a basin and of flood wave travel through a channel system vary for different storms or basins. Thus, the corresponding shapes of hydrographs resulting from storms moving in opposite directions across a given basin may have a range of possible shapes which depend upon prevailing meteorological conditions. In regions subject to generally recurrent directions for major storms, the predominant direction of storm movement would give definition to a "characteristic" hydrograph shape (assuming, for the moment, that other factors affecting runoff are invariant). Variations in this shape could result from differences in the rate of storm movement. I N F L U E N C E OF S I M U L A T E D P E R M E A B I L I T Y
In Fig. 10 are presented the results of the attempts to simulate permeability. The 50 per cent simulation involved an absorbent cover placed over that portion of the basin above an elevation of five inches (see Fig. 1) while the 100 per cent simulation was simply a covering of the complete basin. The rising limbs of the 0 per cent and the 50 per cent simulations are virtually superimposed for the first few seconds of runoff. A deviation between the two becomes apparent at the time of arrival of water from the upper half of the basin. This is because of saturation and flow retardation effects due to the simulated permeability. This hold-back of water is much more pronounced for the 100 per cent simulation of permeability since even the start of runoff is delayed. An equilibrium of rainfall and runoff occurred for the three simulations in Fig. 10 because of the long duration (45 sec). It is readily apparent that with an increasing degree of permeability there is an increasing time to equilibrium.
THE INFLUENCE OF PARAMETERS ON FLOOD HYDROGRAPHS
409
INFLUENCE OF ANTECEDENT CONDITIONS
Antecedent moisture conditions for a basin are very important in determining the magnitude of an ensuing flood. The pre-storm moisture level is responsible for wide variations in peak discharge values resulting from similar storm events. Therefore, in hydrologic design it is common to assume a saturated or very wet antecedent moisture condition in order to deal with the greatest likely flood. The effect of antecedent conditions is shown very markedly by the experimental results presented in Fig. 11. A long duration (45 sec) has been chosen to illustrate the differing effects of wet and dry antecedent moisture conditions at several points in time. The duration is also sufficient to permit near-equilibrium to be reached in each case. The rising limb of the hydrograph having dry antecedent conditions is considerably delayed in time. Much more of the rainfall goes into storage on the basin surface initially, due to the greater available volume for holding water. Some rainfall must also go into storage on the initially wet basin, in order to give saturated conditions there and to provide a finite water depth for overland flow. The difference, between wet and dry antecedent conditions, in the volume of water taken into storage on the basin surface is shown by the shaded area in Fig. 11. At durations of less than 45 sec, the discharge ordinates of the two hydrographs are quite different, the relative difference becoming greater for successively shorter durations. In fact, a family of hydrographs, all with different discharges at a stated duration, would result from slightly different antecedent moisture conditions between the limits used for the curves in Fig. 11. Therefore it is evident why natural floods resulting from similar storms exhibit have such a variation in peak discharge value.
Concluding remarks In this study a set of pre-selected landform features were built into a laboratory watershed to form a "base" of constants for the hydrologic testing of the model. Inputs that could be experimentally varied in this model were of two groups: storm related factors (rainfall intensity, rainfall duration, storm movement) and basin surface conditions (simulated permeability, antecedent moisture conditions). Each variable was found to cause a significant change in the hydrograph shape. Certain factors were particularly influential in altering the rising limb of the runoff hydrograph, whereas others were more critical with respect to the flood crest. Rainfall durations were pre-programmed so that the equi-
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MICHAEL C. ROBERTS AND PETER C. KLINGEMAN
l i b r i u m c o n d i t i o n between rainfall a n d runoff, which is extremely difficult to find with n a t u r a l l y occurring data, could be studied. F u t u r e research will a p p r o a c h the p r o b l e m s of this study in a different fashion. The l a n d f o r m or g e o m o r p h i c variables will be varied experimentally, as well as the hydrometeorological factors. Such a m e t h o d o l o g y will entail a m u c h more complex watershed model.
References 1) R. A. Grace and P. S. Eagieson, The modeling of overland flow, Water Resources Research, 2 (1966) 292-403 2) The bibliography of quantitative geomorphology is extensive and the following works are only a selection: L. B. Leopold, M. G. Wolman and J. P. Miller, Fluvial Processes in Geomorphology, W. H. Freeman, (San Francisco, 1964); M. E. Morisawa, Streams their Dynamics and Morphology, McGraw-Hill, (New York, 1968); A. N. Strahler, Quantitative Geomorphology of Drainage Basins and Channel Networks, Section 4, Part II in: V. T. Chow (Ed.), Handbook of Applied Hydrology, McGraw-Hill, (New York, 1964). 3) The terminology used to classify models in hydrology varies from author to author; we prefer that of M. E. Holland who divided models into three classes-iconic (lookalike), analog and symbolic; W. T. Dickinson, M. E. Holland and G. L. Smith, An Experimental Rainfall-Runoff Facility (Fort Collins, Colorado State University, Department of Civil Engineering, Hydrology Paper No. 25, 1967). 4) Among the more important recent works with comprehensive literature surveys are: Chow (1964) ref. 2; Dickinson et al. (1967) ref. 3; R. J. More, Chapter 5 in: R.J. Chorley and P. Haggett (Eds.) Hydrological Models in Geography (Methuen, London, 1967); S. T. Wong, A multivariate statistical model for predicting mean annual flood in New England. Annals Assoc. Amer. Geog. 53 (1963) 298-311 5) A study that illustrates the need for adequate generalizations for the basis of simulation is that by Norman H. Crawford and Ray K. Linsley, Digital Simulation in Hydrology: Stanford Watershed Model IV (Palo Alto: Stanford University, Department of Civil Engineering, Technical Report No. 39, 1966). 6) J. C. I. Dooge, The hydrologic cycle as a closed system. Bulletin International Association of Scientific Hydrology, 13 (1968) 5 -68 7) J. Amorocho and W. E. Hart, The use of laboratory catchments in the study of hydrologic systems. J. Hydrol. 3 (1965) 106-123 8) Amorocho and Hart, op. cit., p. 122. 9) Donald L. Chery, Jr., Design and tests of a physical watershed model. J. Hydrol. 4 (1966) 224-235 10) V. T. Chow and T. W. Harbaugh, Raindrop production for laboratory watershed experimentation. J. Geophys. Res. 70 (1965) 6111-6119 V. T. Chow, Laboratory Study of Watershed Hydrology, Paper 26, Vol. 1, pp. 194202, Proc. International Hydrology Symposium, Sept. 6-8, 1967, Fort Collins, Colorado.
THE INFLUENCE OF PARAMETERSON FLOOD HYDROGRAPHS
1l)
12) 13) 14) 15)
4l 1
V. T. Chow, R and D of a Watershed Experimentation System, Junior Eng. Tech. Soc. 15, 11-13 T. E. Harbaugh and V. T. Chow, A study of the roughness of conceptual river systems or watersheds, Proceedings, 12th Congress, International Association of Hydraulic Research, 1 (1967) 9-17 T. T. Chiang and J. M. Wiggert, Analysis of Hydrologic Systems, Blacksburg, Virginia Polytechnic Institute, Water Resources Research Center, Bulletin 12, 1968 Chow2), op. cit., Figure 4-I1-16(a) Harbaugh and Chow11), op. cit., p. 14. R.J.M. DeWiest, Geohydrology (J. Wiley, New York, 1965), p. 72, Fig. 2-43.