(excerpted from the Users' Manual)

The development of TOPMODEL was initiated by Professor Mike Kirkby at the School of Geography, University of Leeds under funding from the UK Natural Environment Research Council in 1974. The first versions were programmed by Keith Beven in Fortran IV on an ICL 1904S mainframe computer. The punched cards that were the program hard storage medium at the time have sadly (thankfully?) long since disappeared. Since 1974 there have been many variants of TOPMODEL developed at Leeds, Lancaster and elsewhere but never a "definitive" version.

This has been quite intentional. TOPMODEL is not intended to be a traditional model package but is more a collection of concepts that can be used where appropriate. It is up to the user to verify that the assumptions made are appropriate (see the discussion of limitations in Beven et al., 1994). This version of this program will be best suited to catchments with shallow soils and moderate topography which do not suffer from excessively long dry periods. Ideally predicted contributing areas should be checked against what actually happens in the catchment (at least qualitatively), so get your wellies on!! The program is quite simply and can easily be modified to try to match the observed distributed catchment response by thinking about how both catchment and model are working.

The TOPMODEL program requires ln(a/tanB) distributions for the catchment or for each subcatchment. These may be calculated using the GRIDATB program supplied which requires raster elevation data as input (see section 3). GRIDATB uses the techniques of digital terrain analysis reported in Quinn et al. (1991).

The model supplied here has deliberately not been provided with an automatic optimisation routine, although since the model source code is provided it will be easy to strip out the graphics code and link the model to any of the available optimisation routines (see for example, Press et al. (1989). This is for two reasons:

Firstly, the user is encouraged to view the output from the model and think about how the model is working. This is made possible, in part, by the fact that the results can be mappedback into space and viewed by the user in their correct spatial context. In this way, it may be concluded that this is not a good model to represent a particular catchment (but by thinking about why it may be possible to improve the representation in some relatively simple way. This is why the distributed nature of the model predictions, combined with a simplicity of structure, is very important. Use it firstly as an aid to understanding before it is used a a predictive tool.

Secondly, we do not believe that there is an optimum set of parameter values, even with a model that is as parametrically parsimonious as TOPMODEL (see discussion in Beven,1993) and do not want to encourage the practice of automatic optimisation. At Lancaster we are now using Bayesian Monte Carlo simulation to carry out calibration/sensitivity analysis/uncertainty estimation based on many thousands of runs (see Beven and Binley,1992).

We undertook the task of determining whether base flow alkalinity of surface waters in the northeastern United States is related to indices of soil contact time and flow path partitioning that are derived from topographic and soils information. The influence of topography and soils on catchment hydrology previously has been incorporated in the variable source area model TOPMODEL as the relative frequency distribution of ln(a/KbtanB), where ln is the Naperian logarithm, "a" is the area drained per unit contour, K is the saturated hydraulic conductivity, b is the soil depth, and tanB is the slope. Using digital elevation and soil survey data, we calculated the ln(a/KbtanB) distribution for 145 catchments. Indices of flow path partitioning and soil contact time were derived from the ln(a/KbtanB) distributions and compared to measurements of alkalinity in lakes to which the catchments drain. We found that alkalinity was, in general, positively correlated with the index of soil contact time, whereas the correlation between alkalinity and the flow path partitioning index was weak at best. A portion of the correlation between the soil contact time index and alkalinity was attributable to covariation with soil base saturation and cation exchange capacity, while another portion was found to be independent of these factors. Although our results indicate that catchments with long soil contact time indices are most likely to produce high alkalinity base flow, a sensitivity analysis of TOPMODEL suggests that surface waters of these same watersheds may be susceptible to alkalinity depressions during storm events, due to the role of flow paths.

full citation:

Wolock, D. M., Hornberger, G. M., Beven, K. J., and Campbell, W. G., 1989, The relationship of catchment topographic and soil hydraulic characteristics to lake alkalinity in the northeastern United States: Water Resources Research, v. 25, p. 829-838.

Topographic shape is a watershed attribute thought to influence the flow path followed by water as it traverses a catchment. Flow path, in turn, may affect the chemical composition of surface waters. Topography is quantified in the hydrological model TOPMODEL as the relative frequency distribution of the index ln(a/tanB), where "a" is the upslope area per unit contour that drains past a point and tanB is the local surface slope. Spatial distributions of ln(a/ tanB) were calculated for 8 catchments in Wales on a 25 by 25 m grid. Among the catchments, mean observed stream hydrogen ion concentration (H⁺) during high flow periods was highly correlated with the mean of the ln(a/tanB) distribution. The steady-state gain of a transfer function (time series) model relating H⁺ to discharge was positively correlated with the mean of the ln(a/tanB) distribution. These results suggest that during high flow periods, both the average stream acidity and the magnitude of fluctuations in H⁺ are conditioned by the topographic shape of the catchment. By performing a sensitivity analysis on TOPMODEL, we also show that as the mean of the ln(a/tanB) distribution for a catchment increases, so does its theoretical likelihood to produce significant quantities of surface and near-surface runoff. Our observed results in the Llyn Brianne catchments are consistent with this theoretical expectation in that surface or near-surface runoff is often higher in acidity than are deeper sources of hillslope runoff.

full citation:

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

The potential influence of increasing levels of atmospheric carbon dioxide (CO₂) on water resources includes changes in evapotranspiration that result from control of stomatal resistance by CO₂ and changes in precipitation and temperature caused by "greenhouse" warming. In this study, we investigate the potential effects of CO₂ change on the hydrological response of a forested catchment in Shenandoah National Park, Virginia. Steady temporal trends are superimposed on stochastically derived time series of precipitation and temperature. These input data, which account for the natural variability of the system and the hypothetical effects of climate change, are then used to drive TOPMODEL, a variable- source-area hydrological model. A variety of climate-change scenarios is simulated and temporal trends in annual average flow, peak flow, and basin yield are detected using Kendall's tau statistic. The direction and magnitude of the runoff trends are dependent on the relative magnitudes of the induced trends in precipitation, temperature, and stomatal resistance. Stochastic variability in temperature and precipitation obscure the runoff trends even when real trends in precipitation, temperature, and stomatal resistance are significant.

full citation:

Wolock, D. M., and Hornberger, G. M., 1991, Hydrological effects of changes in atmospheric carbon dioxide levels: Journal of Forecasting, v. 10, p. 105-116.

The effects of subbasin size on topographic characteristics and simulated flow paths were determined for the 111.5-km2 Sleepers River Research Watershed in Vermont using the watershed model TOPMODEL. Topography is parameterized in TOPMODEL as the spatial and statistical distribution of the index ln(a/tanB), where ln is the Napierian logarithm, "a" is the upslope area per unit contour length, and tanB is the slope gradient. The mean, variance, and skew of the ln(a/tanB) distribution were computed for several sets of nested subbasins (0.05 to 111.5 km2) along streams in the watershed and used as input to TOPMODEL. In general, the statistics of the ln(a/tanB) distribution and the simulated percentage of overland flow in total streamflow increased rapidly for some nested subbasins and decreased rapidly for others as subbasin size increased from 0.05 to 1 km2, generally increased up to a subbasin size of 5 km2, and remained relatively constant at a subbasin size greater than 5 km2. Differences in simulated flow paths among subbasins of all sizes (0.05 to 111.5 km2) were caused by differences in the statistics of the ln(a/tanB) distribution, not by differences in the explicit spatial arrangement of ln(a/tanB) values within the subbasins. Analysis of streamflow chemistry data from the Neversink River watershed in southeastern New York supports the hypothesis that subbasin size affects flow-path characteristics.

full citation:

Wolock, D. M., 1995, Effects of subbasin size on topographic characteristics and simulated flow paths in the Sleepers River, Vermont watershed: Water Resources Research, v. 31, p. 1989-1997.

The effects of basin size on low-flow stream chemistry and subsurface contact time were examined for a part of the Neversink River watershed in southern New York State. Acid neutralizing capacity (ANC), the sum of base cation concentrations (SBC), pH, and concentrations of total aluminum (Al), dissolved organic carbon (DOC), and silicon (Si) were measured during low streamflow at the outlets of nested basins ranging in size from 0.2 to 166.3 km2. ANC, SBC, pH, Al, and DOC showed pronounced changes as basin size increased from 0.2 to 3 km2, but relatively small variations were observed as basin size increased beyond 3 km2. An index of subsurface contact time computed from basin topography and soil hydraulic conductivity also showed pronounced changes as basin size increased from 0.2 to 3 km2 and smaller changes as basin size increased beyond 3 km2. These results suggest that basin size affects low-flow stream chemistry because of the effects of basin size on subsurface contact time.

full citation:

Wolock, D. M., Fan, J., and Lawrence, G. B., 1997, Effects of basin size on low-flow stream chemistry and subsurface contact time in the Neversink River watershed, New York: Hydrological Processes, v. 11, p. 1273-1286.

Forecasts of changes in watershed runoff in the Delaware River basin that result from a range of predicted effects of increased atmospheric carbon dioxide (CO2) on future precipitation, temperature, and stomatal resistance of plants, were examined. A deterministic hydrologic model, TOPMODEL, was driven with stochastic inputs of temperature and precipitation to derive the forecasts. Results indicate that the direction and magnitude of the changes in watershed runoff are dependent on the relative magnitudes of the induced changes in precipitation, temperature, and stomatal resistance. Natural variability in temperature and precipitation obscured the changes in watershed runoff even when the simulated changes in precipitation, temperature, and stomatal resistance were substantial.

full citation:

Wolock, D. M., Ayers, M.A., Hay, L.E., and McCabe, G.J., 1989, Effects of Climate Change on Watershed Runoff: Hydraulic Engineering '89 Proceedings, National Conference on Hydraulic Engineering, HY Div, ASCE, New Orleans, Louisiana, August 14-18, 1989. p 673-678.

(From the Users Manual)

Consistent with the philosophy of using an appropriate model structure for a particular catchment during the development of the TOPMODEL concepts many other versions of TOPMODEL have been tested in different catchments. Versions available or developed at Lancaster or elsewhere include:

1. A version as a component of the Institute of Hydrology's Water Information System (WIS) (see Romanowicz et al., 1993a,b; Beven et al., 1995).

2. A version that incorporates the "reference level" concept and subcatchment band structure outlined in Quinn et al. (1991).

3. Versions that use a more sophisticated root zone component including variable available water capacity and interception calculations and using water table depth rather than storage deficit as the internal state variable.

4. A version that is coupled to transport calculations for conservative solutes (see also Robson et al., 1992)

5. A version written in MATLAB/SIMULINK by Renata Romanowicz, complete with animated contributing areas.

6. A version using different transmissivity functions and incorporating a version of the ETH snowmelt component (see Ambroise et al., 1996a,b)

7. A version using a generalised recession curve storage/discharge relationship written by Rob Lamb. An interactive program for identification of a master recession curve from observed hydrographs (MRCtool) has been written in MATLAB.

In addition, various forms of the model have been developed elsewhere, notably at Princeton University where macroscale, dimensionless and fully distributed versions have been used (see Sivapalan et al., 1987; Wood et al., 1988; Famiglietti et al., 1992); at Grenoble where it has been combined with transfer function runoff routing (Obled et al., 1994); at the University of Virginia where a modular version has been linked to geochemical calculations and various optimisation strategies(e.g. Hornberger et al., 1985; Wolock and Hornberger, 1990).

Other TOPMODEL implementations within a GIS framework have been made using the SPANS Modelling Language SML (Stuart and Stocks, 1993); using GRASS routines (Chairat and Delleur (1993); the PVWave modelling and visualisation system (Clapp et al., 1992); the RHESSys system of Band et al. (1993) which also includes distributed ecological modelling components; the TAPES-G system of Moore et al. (1993) and the Modular Hydrological Modelling System (MMS) of Leavesley et al. (1992).

1. In any use for commercial or paid consultancy purposes a suitable royalty agreement must be negotiated with Lancaster University (contact Keith Beven).

2. In any publication arising from use for research purposes the source of the program should be properly acknowledged and a pre-print of the publication sent to Keith Beven.

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