Exercise 5. TOPMODEL Simulation
DUE DATE: Dec. 2, 2003 (midnight)
TOPMODEL is described in section 9.5 as a tool for routing water through a catchment. It
allows us to make predictions of the hydrograph based on certain characteristics of the
catchment and using measurements of precipitation. TOPMODEL is based on the idea that
the land surface topography controls the nature of the surface and subsurface flow paths; the
fundamental runoff mechanism embodied in TOPMODEL is saturation-excess overland
flow (see section 9.4.2).
As discussed in sections 9.5.1 and 9.5.2, the important characteristics of a catchment or
hillslope that influence the likelihood of saturation developing at some point are the upslope
contributing area and the slope of the land surface at that point. The topographic index is
defined as:
(9.19)
where a is the upslope contributing area per unit contour length and tan is the local slope.
The distribution of values of TI throughout the catchment is the primary information
required for a TOPMODEL simulation of a hydrograph.
TOPMODEL separates stream discharge into subsurface flow and overland flow
contributions. Overland flow occurs from saturated areas, while subsurface discharge
depends on the topography (the mean of the TI distribution, ), the average catchment
saturation deficit ( ), and characteristics of the soil. The soil is assumed to be
homogeneous, with a vertical transmissivity profile described by Tmax (the transmissivity at
the soil surface), and m (which describes the rate at which transmissivity decreases
exponentially with depth):
(9.18)
Transmissivity is equal to soil thickness multiplied by hydraulic conductivity. A thick,
permeable soil will have a much larger transmissivity than a thin, relatively impermeable
soil. If the transmissivity decreases rapidly with depth, m will be small; conversely, a large
value of m means that the transmissivity decreases slowly with depth.
Exercise—TOPMODEL Calculations
Several parameters (described above) determine how the calculations in TOPMODEL
proceed. The M-file "TOPRUN.M" allows comparison of hydrograph calculations for some
combinations of the parameters m and Tmax. The precipitation and stream discharges are for
Watershed 36 (WS36) at the Coweeta Hydrology Laboratory in North Carolina as is the
topographic index distribution for the base case.
1. Setting CODE to zero results in a computation of a hydrograph for WS36 and a
comparison of calculated and observed discharges.
2. Setting CODE to 1 results in a comparison of computed hydrographs for two different
TI distributions – that for Watershed 36 and that for a hypothetical watershed with
higher TIs (Figure 1).
3. Setting CODE to 2 results in a comparison of computed hydrographs for WS36 using
two values of parameter m—the one you set and one half of that value.
4. Setting CODE to 3 results in a comparison of computed hydrographs or WS36 using
two values of Tmax—the one you set and one half of that value.
Figure 1 Distribution of topographic indices for base case (blue bars) and comparison
case (CODE = 1; gray bars).
Figure 2 Daily precipitation (top), stream discharge (bottom, black dashed line), and
potential evapotranspiration (bottom, red line) for an entire water year.
In this exercise, you will set CODE to 0, 1, 2, or 3 and set values for the parameters m and
Tmax. Execute the M-file "TOPRUN.M" to calculate the stream discharge and overland
flow, based on daily values of precipitation and potential evapotranspiration (Figure 2). The
results will be returned as plots of stream discharge and overland flow; observed stream
discharge will also be plotted as a dashed black line for comparison if you choose CODE =
0. Note that the data and calculations are for a complete water year; the time axis is days,
beginning with the start of the water year (October 1).
Hydrograph Simulation Using TOPMODEL
Parameter
Comparison Code,
Tmax (mm2 day1),
CODE
Tmax
Range,
0–3,
50,000–500,000,
increment
1
50,000
CODE = 0;
Tmax = 50000;
MATLAB
>>TOPRUN
m (mm1), m
100–300,
10
m = 100;
Overland Flow and Total Stream Runoff
8
Simulated (WS36)
6
4
2
0
50
100
150
200
250
300
350
150
200
Time, days
250
300
350
20
Simulated (WS36)
Observed (WS36)
15
10
5
0
50
100
Questions
 Begin by executing "TOPRUN" for the base case (set CODE to 0, m = 180 and Tmax =
250,000). How do the simulated and observed stream discharges compare? Does
overland flow occur? When is it most likely to occur? What parts of the topographic
index distribution (Figure 1) lead to overland flow?
 Try the WS36 simulation (i.e., CODE = 0) with several different values for m and
Tmax. (For example, try the combination m = 120, Tmax = 100,000.) Can you find
values that give a simulated hydrograph that is closer to the observations than the base
case?
 Now compare the results for the two different TI distributions (set CODE to 1). Which
catchment, WS36 or the hypothetical high-TI catchment, has the greater overland flow?
Both calculations are done with the same values of inputs—precipitation and
evapotranspiration—and the same soil parameters—m and Tmax. The only difference is
the TI distribution. Explain the results you obtained.


Examine the effect that parameter m has on the calculations by setting CODE = 2. Can
you explain the results on the basis of what m represents in the calculations?
Examine the effect that parameter Tmax (Tmax) has on the calculations by setting CODE
= 3. Can you explain the results on the basis of what Tmax represents in the calculations?