Appendix A: Model Fact Sheets

TOPMODEL

Contact Information Keith Beven Department of Environmental Science Institute of Environmental and Natural Sciences Lancaster University Lancaster LA1 4YQ United Kingdom +44 (0)1524 593892 K.Beven@lancaster.ac.uk http://www.es.lancs.ac.uk/hfdg/TOPMODEL.html

Download Information Availability: Nonproprietary, (http://www.es.lancs.ac.uk/hfdg/TOPMODEL.html) Cost: None for non-commercial uses.

Contact the author for other uses.

Model Overview/Abstract TOPMODEL is a physically based, distributed watershed model that simulates hydrologic fluxes of water (infiltration-excess overland flow, saturation overland flow, infiltration, exfiltration, subsurface flow, evapotranspiration, and channel routing) through a watershed. The model simulates explicit groundwater/surfacewater interactions by predicting the movement of the water table, which determines where saturated land-surface areas develop and have the potential to produce saturation overland flow.

Model Features Rainfall-runoff modeling in single or multiple subwatersheds. The Windows version of the model allows Monte Carlo runs with parameter sets chosen from specified

parameter ranges. The Windows version of the model displays simulated hydrograph time seriesthe topographic index

derived from the elevation dataand map of saturated area in a watershed.

Model Areas Supported Watershed Medium Receiving Water Low Ecological None Air None Groundwater Medium

Model Capabilities

Conceptual Basis TOPMODEL is a rainfall-runoff model that bases its distributed predictions on an analysis of watershed topography. The model predicts saturation excess and infiltration excess surface runoff and subsurface stormflow. Since the first article was published about the model in 1979 (Beven and Kirkby, 1979) there have been many different versions.

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Appendix A: Model Fact Sheets

The idea has always been that the model should be simple enough to be modified by the user so that the predictions conform as far as possible to the user's perceptions of how a watershed works.

Scientific Detail TOPMODEL is defined as a variable contributing area conceptual model in which the dynamics of surface and subsurface saturated areas is estimated on the basis of storage discharge relationships established from a simplified steady state theory for downslope saturated zone flows. The theory assumes that the local hydraulic gradient is equal to the local surface slope and implies that all points with the same value of the topographic index, a/tan B will respond in a hydrologically similar way. This index is derived from the basin topography, where a is the drained area per unit contour length and tan B is the slope of the ground surface at the location. Thus the model need make calculations only for representative values of the index. The results may then be mapped back into space by knowledge of the pattern of the index derived from a topographic analysis.

The soil profile is defined by a set of stores. The upper one is the root zone storage, where rainfall infiltrates until the field capacity is reached. When forest canopies appear, an additional interception and surface storage may be necessary. In this store, evapotranspiration is assumed to take place at the potential rate to decrease at a linear rate when the root zone becomes depleted.

Once the field capacity is exceeded, a second store starts filling until the water content reaches saturation. The gravity drainage store links the unsaturated and saturated zones, according to a linear function that includes a time delay parameter for vertical routing through the unsaturated zone. An alternative approach based on the Darcian flux at the base of the unsaturated zone may be considered.

When the deficit in the gravity drainage store or the water table depth equals 0 the saturation condition is reached and the rainfall produces direct surface runoff. Hence the main goal of TOPMODEL is the computation of the storage deficit or the water table depth at any location for every timestep. The theory relates mean watershed storage deficit to local storage deficits using the local value of a function of the topographic index. In the original version of TOPMODEL the soil hydraulic conductivity, or by extension the soil transmissivity, is assumed to decay following a negative exponential law. In this case, the expression that estimates the value of the local storage deficit or the water table depth is given in terms of the topographic index ln(a/tan B). Other forms of soil hydraulic conductivity decay functions lead to different index functions. When distributed values of soil transmissivity (T0) are known a soil-topographic index may be considered, ln(a/T0 tan B).

The topographic index derivation was obtained by manual analysis of contour maps and hillslope streamtubes in the early versions of the model. The current version of the model provides a program to derive its distribution from a regular raster grid of elevations for any watershed or subwatershed using the multiple direction flow algorithm and the channel initiation threshold for positioning river headwaters.

To compute runoff according to the infiltration excess mechanism TOPMODEL uses the exponential Green-Ampt model. If infiltration excess does occur it does so over the whole area of the subwatershed (although alternatively a statistical distribution of hydraulic conductivity values in the watershed can be assumed). A parameter for controlling the fraction of watershed area that generates runoff by infiltration excess was considered recently by a few studies to compute runoff using the Philip two term-equation.

Subwatershed discharges are routed to the watershed outlet using a linear routing algorithm with constant velocity both in the main channel and in the internal subwatershed.

Model Framework Watershed and subwatersheds Watershed surface are divided into surface zone, root zone, and saturated zone. Channel networks

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Scale

Spatial Scale Grid or subwatersheds

Temporal Scale Variable, from 1 to 24 hours

Assumptions The hydraulic gradient of subsurface flow is equal to the land-surface slope. The actual lateral discharge is proportional to the specific watershed area (drainage area per unit length of

contour line). The redistribution of water within the subsurface can be approximated by a series of consecutive steady

states. The soil profile at each point has a finite capacity to transport water laterally downslope.

Model Strengths It is a simple distributed watershed model and results can be visualized in a spatial context. It requires few watershed parameters and low level of expertise. It has been studied extensively. The model code is available for modification.

Model Limitations TOPMODEL only simulates watershed hydrology, although studies have been conducted to modify it to

simulate water quality dynamics. TOPMODEL can be applied most accurately to watersheds that do not suffer from excessively long dry

periods and have shallow homogeneous soils and moderate topography. Model results are sensitive to grid size, and grid size

Appendix A: Model Fact Sheets

The initialization of each run requires an initial stream discharge and the root zone deficit. Hydrological input data file: rainfall, potential evapotranspiration, and observed discharge time series in

m/h Topographic index map data file: the topographic index map may be prepared from a raster digital

elevation file using the DTM-ANALYSIS program. This file includes number of pixels in X direction, number of pixels in Y direction, grid size, and topographic index values for each pair of X and Y.

Users Guide Available online: http://www.es.lancs.ac.uk/hfdg/TOPMODEL.html

Technical Hardware/Software Requirements

Computer hardware: PC

Operating system: PC-DOS, PC-WINDOWS

Programming language: FORTRAN, Visual Basic

Runtime estimates: Minutes

Linkages Supported Links to GLUE (Generalized Likelihood Uncertainty Estimation) program for sensitivity/uncertainty/calibration analyses.

Related Systems TOPMODEL is integrated in GRASS GIS version 5. TOPSIMPL, another Windows version of the model written by Georges-Marie Saulnier can be downloaded directly from the main TOPMODEL site http://www.es.lancs.ac.uk/hfdg/TOPMODEL.html.

Sensitivity/Uncertainty/Calibration The Windows version of TOPMODEL allows the sensitivity analysis of the objective functions to changes of one or more of the parameters to be explored. An initial run of the model is made with the current values of the parameters. Then each chosen parameter is varied across its range, keeping the values of the other parameters constant. The results are displayed as graphs.

TOPMODELs Monte-Carlo simulation output can be exported for further sensitivity and uncertainty analyses on the model results using the GLUE (Generalized Likelihood Uncertainty Estimation) program.

TOPMODEL calibration procedures are relatively simple because it uses very few parameters in the model formulas. The model is very sensitive to changes of the soil hydraulic conductivity decay parameter, the soil transmissivity at saturation, the root zone storage capacity, and the channel routing velocity in larger watersheds. The calibrated values of parameters are also related to the grid size used in the digital terrain analysis. The timestep and the grid size also have been shown to influence TOPMODEL simulations.

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Appendix A: Model Fact Sheets

Model Interface Capabilities There are three options available in the program interface:

The Hydrograph Prediction Option: This option allows the model to be run and hydrographs displayed. If a Topographic Index Map File is available, then a map button is displayed that allows the display of predicted simulation, either as a summary over all timesteps or animated.

The Sensitivity Analysis Option: This screen allows the sensitivity of the objective functions to changes of one or more of the parameters to be explored.

The Monte Carlo Analysis Option: In this option a large number of runs of the model can be made using uniform random samples of the parameters chosen for inclusion in the analysis. Check boxes can be used to choose the variables and objective functions to be saved for each run. The results file produced will be compatible with the GLUE analysis software package.

References Beven, K J and M J. Kirkby. 1979. A physically based variable contributing area model of basin hydrology. Hydrologic Science Bulletin. 24(1):43-69.

Beven, K.J., M.J. Kirkby, N. Schofield, and A.F. Tagg. 1984. Testing a physically-based flood forecasting model (TOPMODEL) for three U.K. Catchments. Journal of Hydrology. 69:119- 143.

Hornberger, G.M., K.J. Beven, B.J. Cosby, and D.E. Sappington. 1985. Shenandoah watershed study: Calibration of a topography-based, variable contributing area hydrological model to a small forested catchment. Water Resources Research. 21:1841-1850.

Obled, Ch., J. Wendling, and K.J. Beven. 1994. The sensitivity of hydrological models to spatial rainfall patterns: An evaluation using observed data. Journal of Hydrology. 159: 305-333.

Robson, A.J., K.J. Beven, and C. Neal. 1992. Towards identifying sources of subsurface flow: A comparison of components identified by a physically based runoff model and those determined by mixing techniques. Hydrological Processes. 6:199-214.

Robson, A.J., P.G. Whitehead, and R.C. Johnson. 1993. An application of a physically based semi-distributed model to the Balquhidder Catchments. Journal of Hydrology. 145:357-370.

Wolock, D.M. 1995. Effects of subbasin size on topographic characteristics and simulated flow paths in Sleepers River Watershed, Vermont. Water Resources Research. 31(8):1989-1997.

Wolock, D.M., G.M. Hornberger, and T.M. Musgrove. 1990. Topographic effects on flow path length and surface water chemistry of the Llyn Brianne Catchments in Wales. Journal of Hydrology. 115:243-259.

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