Hydrology of Warm Humid Regions (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no. 216, 1993. 231 Modelling of hydrological processes for estimating impacts of man's interventions TAKESHI HATA & EIJI TOYOKUNI Faculty of Agriculture, Kobe University, Nada-ku, Kobe, Japan 657 Abstract The characteristics of runoff processes in watersheds in a warm humid region are discussed, with emphasis on the role of the surface soil layer in such watersheds. It is important to represent the spatial distribution of the surface soil layer for an estimation of the impacts of man's interventions, which usually alter the state of the surface and subsurface layers. Basic runoff processes are modelled here like a distributed system according to the segmented sub-watersheds. The model can simulate long-term and short-term runoff processes using the same model parameters. INTRODUCTION The surface runoff and subsurface runoff are important components for the short-term and long-term runoff. These dominant components control the phenomena. It is necessary to estimate the state of the basic controller of the phenomena to predict the runoff change by watershed development. It is also important to reveal the unknown movement of water flow in a watershed to evaluate and manage water resources (Shaw, 1989). Many conceptual models originating with Sugawara's tank model have been developed and used for various problems in water resources (Kadoya & Nagai, 1988; Braun & Renner, 1992). However, it is difficult to estimate the runoff change by the spatial alteration of a watershed. The basic equations of water flow are taken in simple equations of storage-flow relationship, which is derived from the kinematic wave equations (Hata & Kira, 1977). The runoff change due to the partial alteration of a watershed becomes predictable by a well-simulated model. It is also important to estimate the return flow and groundwater recharge from irrigated water by using the model especially for water resources problems in watersheds where the water intakes to rice paddies are dominant in water use. THE STATE OF RAINFALL-RUNOFF The runoff occurrences in mountainous areas and hillslope areas in a watershed in a warm humid region play a different role compared with other areas. The largest part rainfall infiltration into the porous surface soil in forest areas, and surface flow - does not occur in such parts except on paths, rocks and brooks. These areas usually supply clean water during the long periods of low flows through the functions of the surface soil that contains numerous micro-organisms.
232 Takeshi Hâta & Eiji Toyokuni During the high water stage in a rainy season the areas sometimes generate pipe flow and surface flow together with soil erosion. The surface soil layers play an important role in the forested slope areas where porous terrestrial deposits and decayed humus are accumulated under the warm rainy weather. A large amount of water is stored in these layers and flows downward through them. In the lower land there are alluvial fans and plains, which are used by farms, cities and towns. The infiltration rate of the surface is usually low except in cultivated farm lands. Rainwater stands in depressions and flows into rivers. Water is diverted from river to be used in towns and farm lands. Groundwater is also used for agricultural, urban and industrial uses. Irrigation water in paddy fields returns to rivers or recharges groundwater. Rainwater in this region flows into rivers through drainage systems in towns and farm lands and partially percolates to the groundwater. The complicated system of these runoff processes can be divided into several basic components. The essential components in a watershed are the surface runoff system, the relationship between surface water and groundwater, their storage, évapotranspiration losses and channel system. The interflow in the stratified surface layer complicates the processes. There is sometimes no impervious layer in surface soil. In this case infiltrated water percolates unimpeded through pore spaces into the deeper beds. MODEL STRUCTURE It is important to give the characteristics of responses to the real processes especially for the simulation model of runoff changes by the watershed development. A distributed model in space is useful to represent the alteration of land use. The kinematic wave model for surface and subsurface flow has clear physical meaning in its parameters, and is easy to model for any watershed. However, this model needs to estimate effective rainfall for each runoff event before the simulation starts. It is usually difficult to have the exact estimation of effective rainfall. The state of a watershed changes with time, the volume of effective rainfall depending mainly on the soil moisture of the surface soil. It is possible, then, to estimate the preceding time period state of a watershed according to the time series of rainfall-runoff. In this way the model that is applicable both to short-term and longterm runoff simulation can be effective. In the model a watershed is divided into sub-watersheds according to the channel system. Rainfall-runoff processes in each sub-watershed are modelled by a channel with length l c and gradient i c, and two rectangular slope areas with length l s and width l c and gradient i s. Each channel usually has catchment areas on both sides, and each area has its surface soil layer. This is the basic component of the watershed model. Water in a channel flows into the next channel reach with different slope areas. These runoff processes continue until the rainwater reaches the river section concerned. The surface soil layer can be easily modelled as a layered one; however it requires the estimation of the parameter values of each soil layer. The surface layer is simplified here as one layer with the hydraulic conductivity k s. Each slope area has different characteristics of subsurface flow even in the case of the same value of k s, because each area has a different slope i measured from a topographical map.
Modelling of hydrological processes for estimating impacts of man 233 The water flow from river to groundwater is influential in the water balance in the alluvial fan and in the lower part of a watershed where the stage of river water is higher than that of the adjacent land. However, the basic relationship between river water and groundwater is similar to that of the upper watershed. The flow is estimated by Darcy's equation according to the hydraulic conductivity and the gradient between the water stages of river water and groundwater. BASIC EQUATIONS The simplified storage-discharge relationship of each runoff component is the basis of this model. It is derived from kinematic wave equations. For the surface flow: Q s - a s sl /p «a s = (il a IN)l(l+P)WÏ P )-\ llp (2) where Q s = outflow from the surface storage S s on the imaginary rectangular surface, N equivalent roughness coefficient of soil surface, and/> equals 0.6 according to Manning's equation. For the subsurface flow: Q 8 = a s S s a g = 2k,ijl, (4) in which Q g = discharge from subsurface storage S g in a surface soil layer under the imaginary slope surface, k s = hydraulic conductivity of the soil layer. For the channel flow: Q c = * e s? & a c = F- 1/u (il /2 /ri)[(l + u)/l c ] ll:t (6) F = al{ar m ) u ( 7 ) where S c = storage volume in a channel reach, a and R = cross-sectional area and hydraulic radius of the flow respectively, n = Manning's roughness coefficient. The value of Fis about 2.5 for natural channels and u is approximately 0.7. In this model these values are used for every torrent and channel and 0.03 m" 1/3 s is used for n. The loss of water in surface soil is supposed to be proportional to the subsurface storage as follows: Qi = VA < 8 > in which L g is a coefficient largely depending on weather. Water loss occurs mainly due to the évapotranspiration and the percolation to the deep layer. The rate of évapotranspiration is usually greater than the deep percolation. Thus the value of L g varies with season. The amounts of Q g and <2/ will come to their maximum values when the quantity of S g reaches its full stage S h. The surface flow begins to occur when the storage is
234 Takeshi Hâta & Eiji Toyokuni over the value S h. The outflow from sub-watershed is computed by the previously noted equations and the following continuity equation: dsldlt = Q r Q 0 (9) where 5 = storage in a slope area or in a channel, Q i = inflow, and Q 0 = outflow. For the storage in the pervious slope area, observed rainfalls are directly applied to Qi in equation (9) in each time increment. The values of N, S h and k s can be estimated by field measurement in each subwatershed. However, it is difficult to decide the appropriate values employed in the model because of spatial variability. Accordingly, these three values and L g are estimated by an iteration procedure. Starting values of these four variables are selected. The values of S g in the sub-watersheds are set to give the initial discharge in the long-term calibration. Subsequently, S c values in each channel are obtained in the flow routing computations. The four variables of N, S h, k s and L s are adjusted within their physically meaningful limits, and the iterated results of their estimation are easily evaluated by using a graphic display unit accompanying convergence indices. In this manner, the simulated discharge in the calibration period is forced to follow the observed values. ROUTING METHOD Runoff from a sub-watershed can be computed as the discharge from a channel and imaginary rectangular slopes which have the mean values of gradients and lengths of the real area. Actual sub-watershed is composed of a large number of slopes and channels. In this model the representative units are considered the basic component of each sub-watershed for computational purpose. Such basic areas of runoff are thought of as representative slopes with channels of order 1 according to Strahler's stream orders. The order channel 2 receives outflows from order channels 1, as lateral inflows, and the channel of order 3 receives outflows from order channels 2 as lateral inflows. In this way, the discharge from a watershed can be computed. In terms of the discharge summation in the entire catchment, the storage in a channel of order 1 in the representative slope area receives its lateral inflows from slopes with same geometric characteristics. These are expressed as follows: Qu = 2(Qs+Q g ) (10) The outflow Q ol from the channel is computed using a finite difference scheme of equation (9). The storage of the channel of order 2 receives its inflows as mentioned above, Q i2 = {A 2 IA x )Q ol (11) where A x = area of representative slope, and A 2 = catchment area of the order 2 channel. The outflow from the channel, Q o2, is also computed with equation (9). The storage of the channel of order 3 receives its inflows as follows: Qis = Qo3 a + (A3'A 2 )Q o2 (12) in which Q o3a = inflow from an upper sub-watershed (should one be present) and
Modelling of hydrological processes for estimating impacts of man 235 A 3 = area of sub-watershed. The outflow from the channel storage is computed in the same way, and the discharge from a channel in any order can be computed in this way; thus it becomes possible to simulate the runoff from basins of any scale. THE APPLICATION OF THE MODEL The above model is applied to the River Kako, which flows into the Seto Inland Sea in Japan and has a catchment area of 1679 km 2 at the Kunikane gauging station. The daily observed data for one and a half years in 1973 and 1974 are used for the calibration and the discharge in the following four years are computed for the verification by using only precipitation data. For the evaluation of the accuracy of the simulation results, some measures can be used including the following: M= l(\q c -Q 0 \/Q 0 )/n (13) where Q 0 = observed discharge, Q c computed discharge and n number of the data. The values of M in equation (13) are shown in Table 1 with the data for the observed and computed annual runoff. The accuracy of the computation is similar both in the calibration and verification years. This means a suitable model can be made using the limited data. The computed and observed hydrographs both on the logarithmic and normal scale in the verification period of 1977 are shown in Fig. 1. The parameter values are as follows; S h = 100 mm, N = 8.0 m" 1/3 s, k s = 0.0004 m s" 1. The value of L in equation (8) varies according to the weather and season. The basic value is 1.8 from November to March. In April, May, September and October the value is 2.7 (= 1.8 x 1.5). It is 5.4 (= 1.8 x 3) in June, July and August when the evaporation loss is great. In the case when a constant value L g = 2.0 is used during a whole year in 1974, M = 0.37 and TQ C = 907 mm. These values are not so different from the ones in Table 1. The water loss by évapotranspiration decreases on a rainy day. It is expressed by multiplying L g by 0.1 when the precipitation in a day is greater than 3 mm. This value was estimated from the calibrating computation by the model. The simulation of runoff processes by using the above-mentioned equations is possible in any unit of time. The hourly flow routing is done in the same program as daily flow routing by simply changing the time scale of a s, a g and a c in equations (1), (3), (5) and (8). The transformation from daily to hourly routing, for example, is as follows: Table 1 The accuracy of simulated runoff in the River Kako. 1974++ 1975+ 1976+ 1977+ 1978 + M 0.27 872 881 0.36 1026 974 0.26 1180 1042 0.33 663 640 0.30 506 517 + + Calibration period. + Verification period. TQ a = Observed annual runoff (mm); TQ C = simulated runoff (mm).
236 Takeshi Hâta & Eiji Toyokuni 100 50...nHliuMiilt.Ui<hLl m t M kluju. 300 100 30 500 JAN FEB MAR APRMAY JUN JULAUG SEPOCTNOV DEC Fig. 1 Observed (solid line) and computed (broken line) discharge in the verification year of 1977 (the River Kako). a h = aj24 (14) where a h = parameter values in hourly routing, a d = parameter values in daily routing. The storage S, a surrogate for the antecedent moisture condition of each subwatershed, is estimated from an application of the model based on the observed daily Fig. 2 Observed (solid line) and computed (broken line) discharge in the short-term simulation (the River Kako).
Modelling of hydrological processes for estimating impacts of man 237 rainfall data. When a storm occurs, hourly or shorter-time flood routing starts on the initial storage computed from daily routing. The flood forecasting could be done by using all the possible rainfall data including forecast rainfalls as inputs to the watershed, which could be divided into sub-watersheds according to the rainfall stations. Figure 2 is an example of the discharge computation. Table 2 shows another example in which the model was applied to the catchment area of a dam reservoir. The Muro watershed has an area of 136 km 2. Figure 3 is the result for the data in 1977. The calibrated parameter values by the data in 1975 are as follows; S h = 120 mm, N = 3.0 m" 1/3 s, k s = 0.0006 m s' 1. The basic value of L g equals 1.4. Figure 4 shows examples of the application to the surface runoff from an experimental plot by using the observed parameter values of S h = 20 mm, AT = 0.1 m~ 1/3 s, k s = 0.0001 m s" 1 and estimated L g = 1.5. Rainfall and surface runoff are measured in the plot which is located at Kobe University and has the rectangular shape with the width 6 m and the length 20 m. The results of the application to different catchment such as mixed areas of forests, paddy fields and urban areas (Kako watershed), forests and rice fields (Muko watershed) and sparsely grassed area (experimental plot, Kobe) show that the model can be applied to other watersheds. When part of a watershed is artificially altered, the changes of runoff are computed by the model by the changes of variables of slopes i s and i c, surface storage capacity S h, roughness coefficient N and hydraulic conductivity k s in the area of concern. Table 2 The accuracy of simulated runoff in Muro watershed. 1975+ 1976+ 1977 + 1978 + M 0.48 776 762 0.39 909 930 0.65 542 542 + + Calibration period. + Verification period. TQ 0 = Observed annual runoff (mm); TQ C = simulated runoff (mm). 1.73 365 470 5 80 = +0 J 0 30 iwj^kiiiijilllhi.i.ii.uii lj.li ii CO S 10 v JAN FEB MAR APR MAY JUN JUL AUG SEP OCTNOV DEC Fig. 3 Observed (solid line) and computed (broken line) discharge in the verification year of 1977 (the Muro watershed).
238 Takeshi Hâta & Eiji Toyokuni 9 AUG'30 13 = 00 15 = 00 moo 19:00 21:00 Fig. 4 Observed (solid line) and computed (broken line) surface runoff in an experimental plot in Kobe. DISCUSSIONS AND CONCLUSIONS It is very important to estimate the storage and the role of a surface soil layer in watersheds in the warm humid region, where surface layer usually has large storage capacity. The state of the storage greatly affects the volume of effective rainfall in each runoff event. Man's interventions has led to the alteration in the state of the surface soil layer and its cover in watersheds. A model which can describe the spatial distribution of such surface layers is necessary for estimating the impacts by the development of a watershed. The model mentioned here represents the runoff processes as a distributed system. It has produced desired results when applied to watersheds, including a small experimental plot where surface flow was carefully measured. The basic processes of runoff, i.e. storage and flows on the surface and in the surface layer of a slope area, channel storage, channel flow, water losses, and their distribution are included in the model. These processes are easily able to be combined within the blocks of a subdivided watershed. The effect of a developed block-area on runoff is estimated by changing the storage capacity of surface layer S h, roughness coefficient N, surface slope i s and so on in the modified block-area. It is difficult to have satisfactory estimation of the storage and to connect those results with forecast runoff changes caused by alteration of the watershed in the usual discrete short-term analyses when models are not continuous. It is also difficult to predict effective rainfalls with these models where the watershed is developed. The current model circumvents both these problems of storage and effective rainfall estimation for individual events through the process of calibration of sequential data sets. The method outlined here in conjunction with the long-term simulation has advantages compared with the discrete runoff analysis or direct runoff analysis
Modelling of hydrological processes for estimating impacts of man 239 method. One advantage is the information about the storage of water in a catchment prior to a storm - a major influence on subsequent flood runoff. Acknowledgement The authors wish to thank John S. Gladwell for comments and helpful suggestions on the draft of this paper. REFERENCES Braun, L. N. & Renncr, C. B. (1992) Application of a conceptual runoff model in different physiographic regions of Switzerland. Hydrol. Sci. J. 37(3), 217-231. Hata, T. & Kira, H. (1977) Watershed modeling and estimation of runoff change. In: Modeling Hydrologie Processes, 691-702. Water Resources Publications, Fort Collins, USA. Kadoya, M. & Nagai, A. (1988) Development of the long and short terms runoff model. J. Japan. Soc. Irrig. Drain. Recla. Engrs 136, 31-38. Shaw, E. M. (1989) Engineering Hydrology Techniques in Practice. Ellis Horwood Ltd, Chichester, UK.