THE INTEGRATED HYDROLOGICAL CATCHMENT MODEL EGMO. ALFRED BECKER Institut fur Wasserwirtschaft, Berlin, GDR

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1 Hydrological Sciences-Bulletin-des Sciences Hydrologiques, XXII, I 3/1977 THE INTEGRATED HYDROLOGICAL CATCHMENT MODEL EGMO ALFRED BECKER Institut fur Wasserwirtschaft, Berlin, GDR Abstract. A short description is given of the structure of the integrated catchment model EGMO, the flow components considered, the basic principles of the sub-models, and the procedure of the main program. Le modèle hydrologique intégré de bassin versant EGMO Résumé. Cet article décrit brièvement la structure du modèle hydrologique intégré de bassin versant EGMO, les composantes de l'écoulement considérées, les principes fondamentaux des sous-modèles, et la manière de procéder du programme principal. INTRODUCTION The basic principles of this model were presented in 1971 at the Warsaw Symosium (Becker, 1974). Additional details and modifications are described here. Applications of the model are reported separately (Becker, 1975). RUNOFF COMPONENTS AND LEVELS For the complex modelling of runoff in basins, especially in the mountainous areas of the GDR, it has been proved reasonable to consider three runoff components: (1) a quick response component, considered as overland flow AO occurring only during intense storm rainfall or snowmelt; (2) a delayed response direct runoff component, considered as direct lateral subsurface flow (interflow) or hypodermic flow AH, representing the main component of direct runoff in central Europe; (3) a gradually varying component, considered as baseflow QG mainly fed by the groundwater systems of the basin and representing the stable component of river flow also during dry periods. The consideration of these three runoff components requires a consideration of three corresponding runoff levels: (1) the surface (overland and channel flow system); (2) the soil (horizons of higher hydraulic conductivity); (3) aquifers (groundwater system). Within the surface and the soil system we distinguish the capillary water storage (WO, WB), which is not freely movable and can be reduced only by évapotranspiration, and the gravity water storage (SO, SB), which is only temporarily in storage, i.e. this water will become runoff, either as direct hypodermic flow AH into the channel system or groundwater recharge VG. 145

2 Two additional surface flow components have to be considered: (1) the runoff A U from impervious areas (streets, urban areas etc.) (2) the saturated area runoff AS generated in certain parts of the basin where, during rainfall or snowmelt periods, water saturation at the surface can be observed (depending on the soil gravity water storage SB). A schematic representation of the general structure of the resulting model of flow formation is given in Fig. 2. Additional information, especially on the structure and principles of the applied subsystem models are given in Fig. 1. The symbols used in the model are defined in Figs. 1 and 2. Interception, Wetting depression storage Infiltration V Soil capillary water Soil gravity water AB-SB/CLB -soil runoff Groundwater recharge VO Evapotranspiration ER > 1 I 1 I \ \ WMM Precipitation P tp F "T "ri wwfp~f~^~^-, b ' vo -Soil surface vo wafer supply SOMAX -.AO -Overland flow B> hnnr-!nnn inn [ -,r -,r! f-ir m i AU - Impervious R^ area runoff from Ft) FU I»'' > ' A'' / r \, m FS _ t SB hnnnn Ms* tt iff (AH) nnnn n n r-^.n n,n r i re i w Pi - Soil gravity water generation VB» -Saturated area runoff ASfFS) -[AH(FHB)] - Hypodermic flow AH Groundwater storage a6*(s6icq6) z =8ase flow Channel system " S" - AH (FH) - Direct runoftaû -AOfAU+AS+AH Fig. 1 - Schematic representation of the catchment model EGMO. 146

3 Runoff generation Legend linear system nonlinear system subdivision operator couplings Interception, Wetting depression storage, Infiltration Total discharge Sail capillary water Groundwater system Fig. 2 - Scheme of subsystem sequences in the integrated catchment model EGMO. RUNOFF GENERATING SUBMODELS Though the hydrological processes taking place in a basin are coupled in a complex manner, it is possible to simulate the different component processes by separate submodels. In the following, the runoff generating submodels are described first, while the next section deals with the flow concentration submodels. The runoff generating submodels determine (a) that part of precipitation falling during an interval which will recharge the catchment (the losses), and (b) the runoff as a residual. All submodels are listed under the name of the corresponding subroutines of the program according to Fig. 2: OSA (EOS) INF BOKA (EBOG) surface reservoir for capillary water (interception, wetting of the soil surface layer) Modelled by a cascade of two impermeable reservoirs, the first lumped, the second with a linear distribution of storage capacity WOMAX (see Fig. 1). Filled by rainfall or snowmelt, exhausted only by evaporation, overflow represents water supply VO from surface to soil. depression storage and infiltration model Lumped system, reservoir with infiltration capacity index VMAX and storage capacity SOMAX. Filled by surface water supply VO, outflow by infiltration V (less or equal to VMAX), overflow represents overland flow.40. soil capillary water storage The filling dwb/dt (+) which is possible during infiltration periods is assumed to be proportional to the actual soil capillary water storage deficit (WBMAX- WB), i.e. to the difference between storage capacity WBMAX and actual soil capillary water storage WB. (Similarly the exhaustion dwb/dt (-), which is only possible by évapotranspiration, is assumed to be proportional to WB). This relation can be interpreted as a statistical distribution of this storage capacity throughout the 147

4 basin (see Becker, 1974). That part of infiltration V, which will not become capillary water storage WB, will become soil gravity water VB. VB can be stored temporarily (SB), and later on become either hypodermic flow AH or groundwater recharge VG. The subroutines EOS and EBOG, which represent the counterpart of OSA and BOKA, calculate the real évapotranspiration ER (less or equal to potential évapotranspiration EP) during exhaustion periods. THE FLOW CONCENTRATION SUBMODELS These submodels simulate only temporary storage and time delay of flow generated by the runoff generation models (losses are only possible by direct évapotranspiration). During flow generation periods, free moving water occurs on the above-mentioned runoff levels (surface, soil horizons, groundwater). This water is temporarily stored, whereby areal variations of water supply are equalized, Regarding this, it is possible to use relatively simple flow models for the three runoff levels considered: ELS soil gravity water storage Single linear reservoir, containing temporary storage SB, resulting from excess water VB (as output of BOKA). The outflow AB of ELS is proportional to SB (AB = SB/CLB with CLB a storage constant). AB is subdivided into hypodermic flow AH (direct soil runoff into the channel system) and groundwater recharge VG. DAGBI: This submodel subdivides the soil gravity water outflow AB into the two runoff components AH (hypodermic flow) and VG (groundwater recharge). By special investigations, it was proved that the percentage of AH in AB increases (a) with increasing groundwater storage SG (Becker, 1976), and (b) with increasing soil gravity water storage SB (Becker, 1975). To model this dependence, the relations presented in Fig. 3 have been introduced: (a) a linear relation between the area producing hypodermic flow FH and groundwater storage SG (FH = FHMIN + FDGH SG/SGMAX, as indicated by the lower line in Fig. 3 where FDGH = F-FU-FHMIN-FGMIN). (b) a linear relation between FHB and gravity soil water SB (FHB = (F- FU)SB/SBGR, as indicated by"the middle line in Fig. 3). At each time step of the calculation the greater value (FH or FHB) is taken to calculate the hypodermic flow AH = AB-FH/F The remaining area FG = F- FH- FU produces the groundwater recharge The model parameters are (see Fig. 1) F FU FHMIN FGMIN SGMAX 148 FG = AB-FGIF total catchment area, impervious area, producing surface runoff AU, established minimum area producing hypodermic flow FH, established minimum groundwater recharge area FG, a parameter.

5 overland flow area hypodermic flow area groundwater recharge area FO FU ~^-FS - - FH FB SB SBMAX - SBGR - f 1 SG, J _ X 1 J CL ib _j* ^-^~^^ 1 1 \ S6MAX -! 1, FH -p, i 0 - FHMIN. FD8H PRMIN m - F - Fig. 3 - Principal scheme of the variability of different runoff generating areas. Besides this, the submodel DAGBI calculates the saturated areafs depending on the soil gravity water storage SB (upper line in Fig. 3): FS = FH-SBjSBMAX where SBMAX is a parameter. From FS overland flow is running off if VO is greater than the direct runoff (AB+ AO) which already had been generated in that area: AS = (VO-AB-AO)-FSjF All the above-mentioned partial areas of a basin are not to be considered as unique areas, but as the sum of different elementary areas. The introduction of these area-dynamic moisturedependent concepts for the calculation of direct runoff has proved to be useful, simple, and effective. The total direct runoff AD for each calculation time interval amounts to AD=AU+AO+AS+AH 149

6 QAS The groundwater recharge is routed through a nonlinear storage element as follows: single quadratic reservoir, representing the groundwater system Input is the groundwater recharge VG. The relation between base flow QG and groundwater storage SG is QG = (SG/CQG) 0-5, with CQG a storage constant. The total direct runoff is routed through a linear storage element as follows: FALTI the surface flow system (overland and channel flow system) May be modelled as a linear system with constant response function H&. H& can be derived in first approximation on the basis of the isochrone method (linear translation system, see Becker and Leder, 1971). The direct channel flow is calculated by convolution of the total direct runoff ADj with the response function//^ QD I = Y J AD I _ K H K K Finally the baseflow QG is added, to get the total catchment outflow Qi=QGi+QD l MAIN STEPS OF THE CALCULATION PROGRAM The first step of the calculation for each time interval DT is to ask, whether potential évapotranspiration EPJ for the interval is greater than precipitation PJ for the interval. If it is greater, then the évapotranspiration cycle of the program will be called, otherwise the runoff generation cycle. If the runoff generation cycle is called, the interception and upper soil capillary water storage (WO) is wetted and/or filled first (subroutine OSA). The 'overflow' VO is supplied to the soil (see Figs. 1 and 2). On the impervious part FU of the total basin area (F) this supply results in direct surface runoff (AU = VO FU/F). This impervious area runoff A U is flowing directly into the channel system (subroutine FALTI). To calculate the runoff from the remaining permeable part (F-FU) of the catchment the subroutine INF is called. It calculates: (1) the actual infiltration F (less or equal to infiltration capacity VMAX), (2) the depression storage SO in the case of exceedance of VMAX by the supply VO), (3) the overland flow AO (in the case of exceedance of depression storage capacity SOMAX). Generated overland flow AO is flowing also directly into the channel system (FALTI). The infiltration V is supplied at first to the soil capillary water system (subroutine BOKA). The recharge of this storage is proportional to the actual soil capillary water deficit (WBMAX- WB). The residual of V is the input VB into the soil gravity water system (subroutine ELS). The subroutine ELS calculates the increase or decrease of soil gravity water storage SB (with the assumption of constant input intensity VB/DT during the calculation intervaldt), and after that the output AB (outflow). AB is subdivided by the subroutine DAGBI into two parts (with regard to the actual groundwater storage SG and soil gravity water storage SB), namely: hypodermic flow AH, and groundwater recharge VG. For this reason the SG, SB dependent areas FH (hypodermic flow area) must be determined (see Fig. 3). The saturated area FS, which depends on FH and SB, is calculated and from it the saturated area runoff AS. The groundwater recharge VG is input into the groundwater system, modelled as a single 150

7 quadratic reservoir (subroutine QAS). The subroutine QAS calculates the increase or decrease of groundwater storage SG during the calculation interval DT (also with the assumption of constant input intensity VG/DT) and the resulting baseflow QG (groundwater system output). The direct runoff components are then summarized, and the resulting total direct runoff (AD =AU+AO+AS+AH) is convoluted by the subroutine FALTI with the response function Hg of the surface flow system. The resulting direct flow QD is added to baseflow QG and to direct flow resulting from direct runoff AD of former calculation time intervals. Thus the total discharge Q of the catchment is determined (for the end of each calculation time interval). The évapotranspiration cycle is called, if potential evatranspiration EPJ in the interval is greater than precipitation PJ in the interval. The first step of this cycle is to ask, whether the surface capillary water storage system (interception etc.) contains storage WO. If WO is greater than zero, then the subroutine EOS calculates the reductions of WO, resulting from EPJ (ox EPJ-PJ, respectively). The residual EPB of EPJ must be taken from the following storage systems. A jump into the runoff generation cycle is possible, if EPB is less than the actual depression storage SO (this is only possible during intervals after intense rainfall or snowmelt). Usually the subroutine EBOG is called next. EBOG calculates the partial évapotranspiration EG from groundwater (with regard to the actual groundwater storage SG), and EB from soil capillary water storage (with regard to this storage WB). The model is similar to DAGBI (Becker, 1976). Finally the total real évapotranspiration of the interval is determined: ER = (EPJ-EPB) + EG + EB After this, a jump follows into the runoff cycle, namely to the subroutine ELS, if soil gravity water storage SB is greater than zero, else to the subroutine QAS. CONCLUSIONS The intention of development of the integrated catchment model EGMO was to get a model as complex as necessary, as simple as possible, usable for the solution of different tasks of operational hydrology, especially forecasting, and water resources control planning (process simulation), containing submodels and model parameters of physical significance. The application of the model for flow forecasting, water balance calculations and flow simulation is reported in another paper (Becker, 1975). REFERENCES Becker, A. (1974) Applied principles of catchment simulation. In Mathematical Models in Hydrology (Proceedings of the Warsaw Symposium 1971), vol. 2, pp ; and the discussion chapter in vol. 3 'Distributed parameter catchment models and input fields-if: IAHS Pubis, no. 101 and no Becker, A. (1975) Multipurpose use of catchment models for operational forecasting and planning studies. In Application of Mathematical Models in Hydrology and Water Resources Systems (Proceedings of the Bratislava Symposium 1975), pp : IAHS Publ. no Becker, A. (1976) Erfassung der feuchteabhàngigen Variation der Abflussbildungs- und Verdunstungsflâchen in hydrologischen Einzugsgebietsmodellen./4cto Hydrophysica, Berlin XX, no. 4, Becker, A. and Leder, A. (1971) Impulsantwort des Vorflutersystems von Gebirgseinzugsgebieten. Wasserwirtschaft-Wassertechnik, Berlin 21, no

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