89 8 Application of TOPMODEL for Streamflow Simulation andBaseflowSeparation Pei Wen, Xi Chen, and Yongqin Chen 8.1 INTRODUCTION The TOPMODEL concept (Beven and Kirkby 1979, Beven and Wood 1983, O’Loughlin 1986, Ambroise et al. 1996) has been a popular watershed modeling tool (e.g., Anderson et al. 1997, Lamb et al. 1998, Guntner et al. 1999, Scanlon et al. 2000). It is widely used because of its conceptual simplicity of runoff genera- tion, innovative use of topographical data, and demonstrated applicability to a wide variety of situations. In recent years, however, various hydrologists have noted the inappropriateness of TOPMODEL’s conceptual basis to meaningfully describe hydrologically shallow, hilly situations where transient, perched groundwater ow plays a substantial role in runoff generation processes (Moore and Thompson 1996, Woods et al. 1997, Frankenberger et al. 1999, Scanlon et al. 2000). Their observation in forested catchments has suggested the presence of such a storm ow zone perched above low-conductivity layers in the soil or a slowly moving wetting front (Hammer- meister et al. 1982a). A transient occurrence of storm ow through the macroporous region of the shallow subsurface may result in the rapid rise of the hydrograph. Data collected from subsurface weirs (Scanlon et al. 2000) showed that this ow occurs quickly enough to contribute to peak stream discharge, and that a greater percentage of precipitation is converted to subsurface ow in the lower hill slopes. Many efforts have been made to improve TOPMODEL structure in order to account for this runoff generation mechanism. Scanlon et al. (2000) believe that the soil water component may arise from saturated ow disconnected from the perma- nent water table while previous models relied on a conceptual model of one continu- ous water table (Robson et al. 1992, Hornberger et al. 1985), where stream water concentrations are determined by the position of this water table relative to an upper and a lower soil zone. They explicitly modied TOPMODEL to incorporate shallow, lateral subsurface ow by using two simultaneous TOPMODEL simulations, one describing deep baseow and the other describing shallow interow. © 2008 by Taylor & Francis Group, LLC 90 Wetland and Water Resource Modeling and Assessment The main objective of this study is to simulate streamow and to estimate base- ow in a hilly forest catchment in southeastern China using the modied TOP- MODEL. The model is calibrated and validated on the basis of daily and hourly observed streamow data. Simulated hydrological components reveal how much baseow contributes to the total runoff in the study region. 8.2 MODIFIED TOPMODEL The theory underlying the modied TOPMODEL relates hydrological behavior to the topography-derived variable ln(a/tanβ), where a is the area drained per unit con- tour, β is the local slope angle, and ln( ) is the Naperian logarithm. The model cal- culations are semidistributed in the sense that they are carried out for increments of ln(a/tanβ) for the catchment (Hornberger et al. 1985). TOPMODEL was modied to account for cases in which separate subsurface storm ow and groundwater storage mechanisms contribute to stream discharge, a generalized presentation of which is given by Clapp et al. (1996). The primary modication was the addition of a second subsurface state variable, although modications to associated uxes were conse- quently necessary. Vertical recharge to the groundwater zone is taken into account, and both the subsurface storm ow zone and the groundwater zone can contribute to episodic surface saturation near the stream (Figure 8.1). Q of $%" ' Q sf &"' Q gw #%' S gw ! S sf ! S rz S uz Q uz Q v S sf S gw FIGURE 8.1 Schematic diagram of the modied TOPMODEL. (After Scanlon et al. 2000. Shallow subsurface storm ow in a forested headwater catchment: Observations and model- ing using a modied TOPMODEL. Water Resources Research 36(9):2575–2586.) © 2008 by Taylor & Francis Group, LLC © 2008 by Taylor & Francis Group, LLC Application of TOPMODEL 91 8.2.1 suBsurfaCe floW Following Beven and Wood (1983), the local groundwater saturated storage decit S gwi for any value of ln(a/tanβ) is related to the average catchment storage decit, S gw , by S S m a gwi gw gwi = + −[ ln( /tan ) ]Λ β (8.1) where m is a scaling parameter, and L is the areal average of ln(a/tanβ). The subsurface storm ow saturation decit S sfi is determined (Ambroise et al. 1996) by S S a A a dA S S sfi sf A sf sf = − ( ) ( ) − ( ∫ max tan tan max β β1 )) (8.2) where Smax sf is the maximum subsurface storm ow zone decit, and S sf is the average subsurface storm ow zone decit for the catchment. Surface saturation is controlled by the interaction of both subsurface decits, S sf and S gw (Scanlon et al. 2000). Values of S gwi ≤ 0 and S sfi ≤ 0 indicate the area of groundwater saturation and storm ow zone saturation, respectively. For S gw ≥ 0 or S sf ≥ 0 , the soil is partially unsaturated. Unsaturated zone calculations are made for each ln(a/tanβ) increment. The calculations use two storage elements, SUZ and SRZ. SRZ represents a root zone storage, the decit of which is 0 at eld capacity and becomes more positive as the soil dries out; SUZ denotes an unsaturated zone stor- age that is 0 at eld capacity and becomes more positive as storage increases. Stor- age subject to drainage is represented by SUZ i for the i-th increment of ln(a/tanβ). When SUZ i > 0, vertical ow to the storm ow zone is calculated as QUZ SUZ S t i gwi d = (8.3) where SUZ i is the local unsaturated zone storage due to gravity drainage, and param- eter t d is a time constant. Vertical drainage that depletes the water in the subsurface storm ow zone and replenishes the water stored in the groundwater zone (Scanlon et al. 2000) is expressed as Q c S S S A v sf sfi gwi i N i = − ( ) = ∑ min max , 1 (8.4) where c[T −1 ] is a simple transfer coefcient, N is the number of topographic index bins, and A i [L 2 ] is the fractional catchment area corresponding to each bin. 92 Wetland and Water Resource Modeling and Assessment © 2008 by Taylor & Francis Group, LLC Evapotranspiration is taken from the SRZ i store. The maximum value of storage in this zone is described as parameter SRMAX. The rate of evapotranspiration loss E is assumed to be proportional to a specied potential rate Ep and the root zone storage SRZ, as E Ep SRZ SRMAX= * / (8.5) The sum of vertical ows Q v weighted by the area associated with each ln(a/ tanβ) increment is added to reduce the average saturated decit S gw . An outow from the saturated groundwater zone, QB, is calculated as QB e e Sgwi m = −Λ (8.6) or QB Q e Sgwi m = − 0 (8.7) where Q 0 is the initial stream discharge. The average subsurface storm ow zone decit S sf changes over each simula- tion time step with inputs from overlying unsaturated zone Q uz , and outow to the stream Q sf , and vertical drainage to the groundwater zone Q v . Discharge from this zone is expressed as Q Q S S sf sf sf sf = − 0 1 max (8.8) where Q sf0 is a storm ow zone recession parameter and inuences the storm ow recession slope. The water balance calculation for S gw or S sf produces a new end-of-time step value that is used to calculate a new value of S gwi or S sfi at the start of the next time step. There should be no water balance error involved since the incremental change in S gw or S sf is equal to the areally weighted sum of changes in S gwi or S sfi . 8.2.2 surfaCe floW Surface ow may be generated either due to a calculated value of S gwi = 0 or S sfi = 0 in the saturated zone or due to the unsaturated zone decit being satised by input from above (SRZ = SRMAX, SUZ > S gwi or SUZ > S sfi for any increment). Both cases represent saturation excess mechanisms of runoff production. Areas of high values of ln(a/tanβ), that is, areas of convergence or low slope angle, will saturate rst and as the catchment becomes wetter, the area contributing surface ow will increase. Calculated surface ow at any time step is simply the water in excess of any decit in each ln(a/tanβ) increment. Application of TOPMODEL 93 8.2.3 CHANNEL ROUTING After both surface and subsurface water ows into the stream channel, it is routed through the channel system to the stream outlet. Routing should determine the num- ber of time steps controlled by a specied maximum channel ow distance, D max , and a constant channel wave velocity parameter, V. It is assumed that all runoff pro- duced at each time step reaches the catchment outlet within a single time step. 8.3 APPLICATION 8.3.1 S TUDY SITE The study site is the Xingfeng catchment, which is situated in the forested headwater areas of the Dongjiang basin in South China. The catchment area is 42.6 km 2 and approximately 90% of the land surface is covered by forest. Soil is primarily red loam consisting of sandy loam and sand silt. Ground surface elevation varies from 42.6 to 508 m. The simulation program written by Beven and Wood (1983) is used for calculation of the topographic index on the basis of a DEM with a resolution of 25 m. Precipitation from ve observation stations in Figure 8.2 is used to calculate the area’s mean precipitation between 1982 and 1987. Additional data of pan evaporation and stream discharge from the observation station of the catchment outlet are used for model parameter calibration and model validation. Xing Feng Scale (Kilometer) 0 1 0.5 Precipitation Station Evaporation Station Hydrologic Station FIGURE 8.2 Map of the study catchment. © 2008 by Taylor & Francis Group, LLC 94 Wetland and Water Resource Modeling and Assessment 8.3.2 MODEL CALIBRATION AND VALIDATION The observed daily precipitation, pan evaporation, and stream discharge from 1982 to 1985 are selected for model parameter calibration, and the daily data from 1986 to 1987 for model validation. Additionally, nine hourly ood events are cho- sen for the model simulation. The calibrated parameters are listed in Table 8.1. The Nash-Sutcliff efciency coefcient (NSEC) is 0.79 and 0.72 in the calibra- tion and validation periods, respectively. The root mean square error (RMSE) is 1.50 mm/d in the calibration period and 1.31 mm/d in the validation period. For the hourly simulation, ve ood events are selected for model calibration and the other four for model validation. Calibration results demonstrate that most of the model parameters in hourly simulation are the same as those in daily simulations, except for the routing velocity (V), which becomes larger in ooding periods. V is 1,650 and 4,000 m/h in daily and hourly simulation, respectively. NSEC for all ood events is between 0.77 and 0.96 in the calibration period and between 0.81 and 0.87 in the validation period (Table 8.2). Figures 8.3 and 8.4 show that the simulated and observed streamow discharges in the daily and hourly processes generally march well. Based on the modied TOPMODEL structure, baseow that comes from per- manent groundwater storage can be estimated by equation (8.6) or (8.7). Estimation of mean baseow from daily simulation is approximately 72% of the total discharge. Figure 8.5 shows the simulated hydrological components of surface ow, storm ow, and baseow for the ood (No. 053008) during May 30 and 31, 1984. The subsur- face stormow discharge is about 15.6% of the total discharge and the baseow is 23.4% in the ood event. For the nine ood events, calculated results in Table 8.2 demonstrate that the mean baseow is 47.0% of the total discharge, and storm ow and surface ow are 7% and 46%, respectively. TABLE 8.1 Model parameters after calibration. Parameter Description Value m Exponential storage parameter 0.16 m SRMAX Root zone available water capacity 0.22 m td Unsaturated zone time delay per unit storage decit 0.35 h Smax sf Maximum subsurface storm ow zone decit 0.125 m C Recharge transfer coefcient 1.15 m –2 h –1 V Catchment routing velocity 1650 m/h T0 Mean catchment value of ln(T0) 1.0 m 2 /h BC Evaporation rate from root system 0.8 Alpha Forestation coefcient 0.7 Silmax Maximum water intercepted by leaf and litter cover 0.007 m © 2008 by Taylor & Francis Group, LLC Application of TOPMODEL 95 8.4 CONCLUSIONS Traditionally, a main objective of hydrograph analysis is to decompose streamow into the three major components of surface runoff, interow, and baseow. Quan- tifying time-dependent volumetric contributions to total stream water from surface and subsurface hydrological pathways is critical for the development of remedial strategies in areas where contaminants may be present and is necessary for the proper conceptualization of solute transport at the catchment scale. Over the past decade, chemical and isotopic methods for the separation of stream hydrographs have been a rigorously explored topic in the eld of hydrology. Hydrological mod- els used for this purpose must take into account and be consistent with site-spe- cic observations of runoff-generating processes, and must be compatible with the theory derived from physical and geochemical observations in catchment studies. In this study, the modied TOPMODEL with an improvement in representing the runoff generation mechanism in the forest headwater area has successfully been applied in daily and hourly streamow simulation in the Xingfeng catchment. Model calibration and validation results demonstrate that this model is able to effectively reect watershed hydrological processes. By isolating the long-term groundwater recession and using a hydrograph transformation consistent with the TOPMODEL assumptions, the individual characteristics of both the subsurface storm ow and groundwater contributions to discharge have been evaluated. Simulation results demonstrate that baseow is approximately 72% of the total discharge in the area, and therefore baseow is very important for water resources utilization and further study on maintaining a basic baseow is very important for environmental and ecosystem protection. TABLE 8.2 Simulation results of hourly flood discharges. Flood number Period NSEC RMSE (m 3 /s) Flood discharge error (%) Stormflow (%) Baseflow (%) 052808 May 25–28, 1982 0.82 1.14 –2.9 7.0 50.2 020108 Feb. 1–3, 1983 0.86 1.46 7.3 4.0 52.6 052000 May 20–21, 1983 0.96 4.88 10.6 5.0 47.7 053008 May 30–31, 1984 0.77 4.58 –0.2 15.6 23.4 062500 Jun. 25–28, 1985 0.81 1.83 –1.9 1.0 42.2 070219 Jul. 2–4, 1985 0.90 3.31 5.4 6.0 38.9 091113 Sept. 11–13, 1985 0.87 2.35 9.1 1.0 49.4 092320 Sept. 23–26, 1985 0.88 2.58 –4.2 4.0 50.3 050712 May 7–24, 1987 0.81 15.84 12.1 16.0 68.7 Mean Nine ood events 0.85 4.22 3.9 6.6 47.0 © 2008 by Taylor & Francis Group, LLC 96 Wetland and Water Resource Modeling and Assessment ACKNOWLEDGMENTS The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK4247/03H), and partially supported by open funding from the Key Lab of Poyang Lake Ecological Environment and Resource Development, Jiangxi Normal University and by the Program for New Century Excellent Talents in University, China (NCET-04-0492). Discharge, m 3 /s 0 10 20 30 1 - 1 1982 1983 1984 1985 1 - 1 1 - 1 1 - 1 Time, Day (a) Observation Calculation Discharge, m 3 /s 0 10 20 1 - 1 1986 1987 1 - 1 Time, Day (b) Observation Calculation FIGURE 8.3 Observed and simulated daily discharges. © 2008 by Taylor & Francis Group, LLC Application of TOPMODEL 97 (a) (b) (c) (d) No. 053008 0 Date and Hour, 1984 10 20 30 40 50 60 70 80 Flood Discharge, m 3 /s 0 20 40 60 80 100 120 5/30 5/31 6/25 6/26 6/27 6/28 P, mm/hr Precipitation Observation Calculation Date and Hour, 1985 No. 062500 0 10 20 30 40 Flood Discharge, m 3 /s 0 10 20 30 40 50 P, mm/hr Precipitation Observation Calculation Date and Hour, 1985 0 10 20 30 40 50 60 70 80 90 100 Flood Discharge, m 3 /s 0 20 40 60 80 100 120 140 P, mm/hr No. 070219 Precipitation Observation Calculation 7-27-37-4 5/7 5/11 5/15 5/18 5/22 Date and Hour, 1987 No. 050712 0 20 40 60 80 100 120 140 160 180 200 Flood Discharge, m 3 /s 0 20 40 60 80 100 120 140 P, mm/hr Precipitation Observation Calculation FIGURE 8.4 Observed and simulated hourly ood discharges. No. 053008 0 10 20 30 40 50 5.30 5.31 5.31 5.31 Date and Hour, 1984 Flood Discharge, m 3 /s Stormflow Baseflow Observation Calculation FIGURE 8.5 Simulated hydrological components of surface ow, stormow, and baseow. © 2008 by Taylor & Francis Group, LLC 98 Wetland and Water Resource Modeling and Assessment REFERENCES Ambroise, B., K. Beven, and J. Freer. 1996. Toward a generalization of the TOPMODEL concepts: Topographic indices of hydrological similarity. Water Resources Research 32(7):2135–2145. Anderson, M., N. E. Peters, and D. Walling, eds. 1997. Special Issue: TOPMODEL, Hydro- logical Processes 11(9):1069–1356. Beven, K. J., and M. J. Kirkby. 1979. A physically based variable contributing area model of basin hydrology. Hydrological Sciences Bulletin 24(1):43–69. Beven, K. J., and E. Wood. 1983. Catchment geomorphology and the dynamics of runoff contributing areas. Journal of Hydrology 65:139–158. Clapp, R. B., T. M. Scanlon, and S. P. Timmons. 1996. 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Thongs, M. Zion, and E. Schneiderman. 2002. Rened conceptualization of TOPMODEL for shallow subsurface ows. Hydrol. Pro- cess. 16: 2041–2046. Woods, R. A., M. Sivapalan, and J. S. Robinson. 1997. Modeling the spatial variability of sub- surface runoff using a topographic index. Water Resources Research 33(5):1061–1073. © 2008 by Taylor & Francis Group, LLC . CALIBRATION AND VALIDATION The observed daily precipitation, pan evaporation, and stream discharge from 1 982 to 1 985 are selected for model parameter calibration, and the daily data from 1 986 . stormow, and baseow. © 20 08 by Taylor & Francis Group, LLC 98 Wetland and Water Resource Modeling and Assessment REFERENCES Ambroise, B., K. Beven, and J. Freer. 1996. Toward a generalization. of topographic index bins, and A i [L 2 ] is the fractional catchment area corresponding to each bin. 92 Wetland and Water Resource Modeling and Assessment © 20 08 by Taylor & Francis Group,