Estimation of urbanization effects by a parallel cascades model

The influence of man on the hydrological regime with special reference to representative and experimental basins L'influence de l'homme sur le régime hydrologique avec référence particulière aux études sur les bassins représentatifs et expérimentaux (Proceedings of the Helsinki Symposium, June 1980; Actes du Colloque d'helsinki, juin 1980): IAHS AISH Publ. no. 130. Estimation of urbanization effects by a parallel cascades model M. H. DISKIN Technion - Israel Institute of Technology, Haifa, Israel Abstract. A prerequisite for the estimation of urbanization effects on the hydrological response of a basin is a model which treats the pervious and impervious components separately. The parallel cascades model is such a model, producing for each component its own rainfall excess hyetograph, runoff volume, and runoff hydrograph. The relative influence of the two components is represented in the model by the value of an impervious area factor. Changes in the degree of urbanization of a basin are reflected not only by changes in the value of this factor, but also in the values of the storage routing factors of the parallel cascades model. The effects of urbanization on the volume of runoff and on the shape of the runoff hydrograph can be estimated from the expected changes in the values of these two factors. Numerical examples, based on measured data, indicate the magnitude of the changes in the hydrological response of the basin. Evaluation des effets d'urbanisation par un modèle à cascades parallèles Résumé. Pour estimer les effets d'urbanisation sur la réponse hydrologique d'un bassin versant, il faut d'abord construire un modèle qui traite séparément les composantes perméables et imperméables du bassin urbanisé. Le modèle à cascades parallèles est un tel modèle, produisant pour chaque composante ses hyétogramme propre d'excès pluviométrique, volume de ruisseeement, et hydrogramme de ruissellement. L'influence relative des deux composantes est représentée dans le modèle par la valeur d'un facteur des surfaces imperméables. Les variations du degré d'urbanisation d'un bassin sont illustrées non seulement par les variations de la valeur de ce facteur, mais encore par les valeurs du facteur d'emmagasinement des crues du modèle à cascades parallèles. Les effets d'urbanisation sur le volume d'écoulement et sur la forme de Phydrogramme d'écoulement peuvent être évalués d'après les changements prévus des valeurs de ces deux facteurs. Des exemples numériques basés sur les données mesurées sur un bassin indiquent la grandeur des variations de la réponse hydrologique du bassin. INTRODUCTION The most significant feature of an urban basin is the fact that it is composed of two types of surfaces. One is the developed impervious area, consisting of paved roads and sidewalks, parking lots, rooftops, etc. The second type consists of mostly pervious areas of undeveloped land, lawns, parks, cemetries, etc. The process of urbanization of a natural basin manifests itself mostly in the growth in the relative size of the impervious areas and the decline in the extent of the pervious areas; other aspects of the urbanization process are of lesser significance hydrologically. The two components of an urban basin react differently to a rainfall input. The differences are expressed both in the production of rainfall excess and in its transformation to direct surface runoff. The depth of rainfall excess produced in a given storm is greater for the impervious than for the pervious parts, due mainly to lower infiltration rates and smaller depression storage of the impervious areas. The runoff hydrograph for the impervious area has shorter characteristic time parameters such as time to peak, time base, etc. than the corresponding hydrograph for the pervious areas. This is due to higher flow velocities and, often, shorter flow paths in the impervious area. The quantitative estimation of the hydrological effects of the urbanization process clearly requires a model in which the two components are represented by separate elements. Typically, such a model includes elements for producing rainfall excess hyetographs for each area from the total rainfall input, elements for converting these hyetographs to runoff hydrographs, and an element for combining the individual 37

38 M. H. Diskin hydrographs to a single runoff hydrograph which is the output of the model. Some of the parameters used to define the elements of the model depend on the degree of urbanization. Changing the values of these parameters according to the expected changes in the degree of urbanization gives an estimate of the expected hydrological response of the basin after the development takes place. THE PARALLEL CASCADES MODEL A model suitable for representing urban basins and studying the effects of urbanization is the parallel cascades model. Detailed descriptions of the model are available in the literature. A number of versions of the model exist (Wittenberg, 1975; Diskin et al., 1978; Wollman and Diskin, in press). They differ from each other in the method of production of rainfall excess, especially for the pervious area. The main feature of the model is the lumped representation of each of the two components of the urban basin by a cascade of linear reservoirs. The two cascades operate in parallel on rainfall excess hyetographs received as inputs and produce as their output two direct surface hydrographs, which are then combined to give the total response of the basin. The parameters involved in this part of the model are the numbers of linear reservoirs N A, N B and their storage constants K A, K B for each of the two cascades. The element used for producing the two rainfall excess hyetographs from the total rainfal input to the model is based on a simple representation of the infiltration process. The method adopted uses, for each part of the basin, an average infiltration loss rate which starts to operate after an initial loss for that part is satisfied. The initial loss consists mostly of depression and interception storage. The parameters involved in this part of the model are the values of the initial losses D A, D B and of the infiltration rates <p A, <p B for the impervious and pervious areas. The infiltration rates are held constant throughout any storm event, but the value of the infiltration rate <p B for the pervious area is taken to change from one storm to another, depending on antecedent rainfall and the characteristics of the total rainfall hyetograph of the storm considered. The runoff hydrographs produced by the two cascades of linear reservoirs are multiplied by weighting factors a and 0 = (1 - a) before adding them up to produce the total runoff hydrograph. The weighting factors represent the relative magnitude of the two component areas of the basin, the factor a is taken to be the proportion of the directly connected impervious area. I Rit) D A^A Rainfall Excess Separation R A(t) '' RJt) Q.It) N A' K A Cascades of Linear Reservoirs N.K,-QJt) " r FIGURE 1. Qlt) Structure of the parallel cascades model.

Estimation of urbanization effects 39 FIGURE 2. Generation of rainfall excess hyetographs. The structure of the model is shown schematically in Fig. 1. The procedure used in the rainfal excess separation element is illustrated in Fig. 2. The routing of each rainfall excess through a corresponding cascade of linear reservoirs is obtained by a convolution integral evaluated for finite time intervals Af by Q n = ^R l U n + 1. 1 At (1) using unit hydrograph ordinates U computed by the equation (t/k) N - 1 exp(-t/k) KT(N) where N is the number of reservoirs in the cascade, K is their storage coefficient, and T (N) is the gamma function. THE URBANIZATION FACTOR The process of urbanization is actuaëy a very complex process involving many human activities. It includes construction and paving of roads, building houses and commercial buildings, installing sewage and drainage systems, changing the nature and extent of the vegetation, improving and regulating the natural water courses, and many others, including in some cases modification of some topographic features of the basin considered. It is obvious that it is impossible to characterize all these changes by a single factor. It is also clear that if the effect of each process is to be evaluated, the model representing the hydrological behaviour of the basin must be very detailed and complex. Such a model would require for its calibration extremely detailed data, minutely describing the spatial and temporal variation of rainfall and runoff. The normal practice in urban hydrology is to use lumped or semi-lumped models to simulate the hydrological response of the basin. The models are calibrated with regular, good quality data which are available in many basins. With these models it is necessary to represent the degree of urbanization by one or at most two factors which affect the parameter values. The effects of changes in the degree of urbanization will thus be represented by corresponding changes in the values of these parameters. The changes in the volumes and rates of runoff are then estimated by using the model with the modified values of the parameters. This can be done with respect to either past recorded storms or for design storms based on depth duration frequency analysis and an estimated critical rainfall distribution within the storm duration.

40 M. H. Diskin The natural choice for the urbanization factor is the size of the impervious area of the basin. However, some consideration of the hydrological processes taking place in the basin leads to the conclusion that the size of the impervious area directly connected to the drainage system in the basin is a more significant urbanization factor. This factor is represented in the parallel cascades model by the value of the parameter a used as the weighting factor for combining the runoff hydrographs due to the impervious and pervious parts. The improvement of the drainage system of the basin is another activity which influences its hydrological response. While it is difficult to express this activity quantitatively, its effect in the model can be represented by a reduction in the storage routing coefficients of the two cascades. The main drainage system of the basin is represented in the model by the number of reservoirs N A and their storage coefficient K A for the cascade representing the impervious area. Once the system has been established, the values ofthese parameters will be fairly constant. Further improvements in the drainage system are more likely to reduce the value of the storage constant K B of the reservoirs in the second cascade representing the impervious area. BASIN AND DATA The basin used for demonstrating the effects of urbanization is the High School basin in the city of Tucson, Arizona, USA. The basin has a roughly rectangular shape with an area of 2.46 km 2 and an average slope of 1.1 per cent. The main stream is 1.9 km long (2.7 km to the basin boundary). The area is mostly residential with some commercial development. The total impervious area is estimated to be 29 per cent of the basin area, some 20 per cent of which is the directly connected impervious area of paved streets and parking lots. The drainage system is based on the natural stream channels which receive the water directly from street gutters wherever they cross the streams. RainfaU and runoff data for the High School basin have been collected since 1968 by the Water Resources Research Center at the University of Arizona. The mean annual rainfall for the period 1968-1975 is 247 mm and the mean annual runoff is 44 mm. The mean rainfall for the series of annual maximum flow events in this period is 26 mm and the corresponding mean runoff depth is 10 mm, with an average maximum flow rate of 11.4 m 3 /s (4.63 m 3 s _1 km" 2 or 16.7 mm h" 1 ). Data from 10 storms were used to calibrate the parallel cascades model for the High School basin (WoËman, 1979). These were storms in which the total rainfall was between 12 and 42 mm with peak 5-min rainfall intensities in the range 40 150 mm h" 1. Rainfall excess produced by these storms was in the range 3.0-15.6 mm with peak flows in the range 3 23 m 3 /s. The optimal parameters of the model were as folows: D A =2.0 mm N A =2.14 #4 =3.9 min a = 0.19 D B = 3.1 mm N B = 2.95 K B = 13.1 min 3 = 0.81 The value of 4> A was taken to be zero and the value of <j> B was related to the antecedent rainfall and to a rainfall shape factor by a procedure described elsewhere (Wollman and Diskin, 1979). The largest storm on record, that of 12 August 1972, was used for the demonstration of the urbanization effect. Total rainfall for this storm is 42 mm and its duration is 80 min. However, the main part of the storm lasted 50 min during which the rainfall was 37 mm. The hyetograph for this part of the storm is shown in Fig. 3. The storm resulted in 13.3 mm of rainfall excess producing a peak flow which was originally

m 150 E E Intensity ( c o o o - [ ', 1, 1 ^~x^ j, 1., 10 20 30 40 50-60 o Time (min ) FIGURE 3. Rainfall hyetograph for stonn on 12 August 1972. Estimation of u rbanization effects 41 measured as 185 m 3 /s (27 mm h ' ), but later revised to a value of 22.6 m 3 /s (33 mm h -1 ). RESULTS AND CONCLUSIONS The optimal values of the parameters listed above and a value of 4>B = 60.5 mm h -1 derived by the procedure developed, formed the basis for the present study. Two types of urbanization effects were considered. One is the increase in the directly connected impervious area and the second is a reduction of the reservoir storage coefficient for the cascade representing the pervious area. The optimal value of the impervious area parameter a = 0.19 was found to be approximately equal to the relative area of the paved streets and parking lots. Possible changes in these parameters were estimated to be either due to a change in the drainage practice, whereby all existing impervious area becomes directly connected giving a value of a = 0.29 or due to a transition to apartment buildings with accompanying parking facilities, resulting in doubling the size of the directly connected impervious area, a = 0.38. The other possible change in the existing conditions in the basin was considered to be a 20 per cent reduction in the value of K B, from 13.1 to 10.4 min, due to improvement in secondary channels conveying water to the main stream of the basin. This change, superimposed on the three possible values of a, resulted in six pairs of values for the two parameters, as listed in Table 1. The runoff hydrographs predicted by the parallel cascades model for the six pairs of parameter values are reproduced in Fig. 4. The main features of the hydrographs are listed in Table 1. It should be noted that the various changes assumed do not change the depth of rainfall excess for the two component parts, which are 37 mm and 11 mm for the impervious and pervious areas, respectively. The equivalent depth TABLE 1. Case no. 1 2 3 4 5 6 Parameters and resulting hydrograph features Model parameters a 0.19 0.19 0.29 0.29 0.38 0.38 K B [min] 13.1 10.4 13.1 10.4 13.1 10.4 Peak discharge ôpimv] 16.9 19.0 23.6 25.5 29.7 31.3 Rainfall excess R e [mm] 16.0 16.0 18.6 18.6 20.8 20.8

42 M. H. Diskin Time ( min ) Time ( min ) FIGURE4. Runoffhydrographsproduced FIGURE 5. Unit hydrographs for imperby the parallel cascades model. vious and pervious parts of the basin. of rainfall excess for the entire basin changes, however, with the value of a as listed in Table 1. The unit hydrographs for the impervious area and for the pervious area are shown in Fig. 5. The two unit hydrographs shown for the pervious area correspond to the two values of K B mentioned above. Examination of the results in Table 1 and Fig. 4 reveals that the relative effect of improvingthe stream channels decreases as the size of the directly connected impervious area increases. The increase in the peak discharge due to the change in the value of K B is about 12 per cent when a = 0.19 and about 5 per cent when a = 0.38. The change in the value of a from its present value to double this value causes an increase of 30 per cent in the depth of rainfall excess and 76 per cent in the value of the peak flow. Adding to this the effect of a reduction of 20 per cent in the value of K B causes the peak flow to reach a value of 31.3 m 3 /s (46 mm h _1 ) which is 85 per cent above the value predicted by the parallel cascades model for the existing conditions. REFERENCES Diskin", M. H., Ince, S. and Oben-Nyarko, K. (1978) Parallel cascades model for urban watersheds. /. Hydraul. Div., Amer. Soc. Gv. Engrs 104, (HY2), 261-276. Wittenberg, H. (1975) A model to predict the effects of urbanization on watershed response. Proceedings of National Symposium on Urban Hydrology and Sediment Control (University of Kentucky, Lexington, Kentucky), pp. 161-167. Wollman, S. H. (1979) A simple two component model for urban watersheds. MSc thesis, Technion - Israel Institute of Technology, Haifa, Israel. Wollman, S. H. and Diskin, M. H. (In press) A rainfall excess separation model for urban watersheds