Exercise 2: Topmodel
Hydro GIS Short Course
University of Padua
Spring 2000
Prepared by David
Tarboton, Utah State University.
Purpose:
The purpose of this exercise is to learn how to perform practical runoff
calculations using the TOPMODEL concept.
Contents

Reference material [This is a list for extended reading.
You are not expected to read this before doing the homework, or even at
all in its entirety. You should skim this material and be ready to
search in this material for help or clarification when necessary.]

Installation [If SINMAP
and TARDEM are not installed from earlier exercises you need to install
them]

Exercise

Summary of material to turn in.

Single file, ex1.zip, with all datasets to be
used. These are the same datasets as for previous exercises.
Reference Material
This is a list for extended reading. You are not expected to read
this before doing the homework, or even at all in its entirety. You
should skim this material and be ready to search in this material for help
or clarification when necessary.

Tarboton, D. G., (1997), "A New Method for the Determination of Flow Directions
and Contributing Areas in Grid Digital Elevation Models," Water Resources
Research, 33(2): 309319. (available online at http://hydrology.usu.edu/dtarb)

Beven, K., (1991), "Spatially Distributed Modeling: Conceputal Approach
to Runoff Prediction," Chapter 17 in Recent Advances in the Modeling of
Hydrologic Systems, Edited by D. S. Bowles and P. E. O'Connell, NATO ASI
Series C: Mathematical and Physical Sciences  Vol. 345, Kluwer Academic
Publishers, Dordrecht, p.373387.

Beven, K., R. Lamb, P. Quinn, R. Romanowicz and J. Freer, (1995), "TOPMODEL,"
Chapter 18 in Computer Models of Watershed Hydrology, Edited by V. P. Singh,
Water Resources Publications, Highlands Ranch, Colorado, p.627668.
Some of these require Acrobat Reader which can be obtained from Adobe.
Exercise
The SINMAP software will be used to compute slope and contributing
area by the Dinfinity method. Open ArcView (with SINMAP extension
loaded) and open a new View. If the DEM grid 'reydem' is not available
from previous exercises, select File/Import Data Source/ASCII Raster then
select the file 'reydem.asc' to import it. Respond NO to cell
values as integers and NO to add grid as theme to the view.
From the SINMAP menu 'Select DEM grid for analysis'. Select grid
theme 'reydem'. This adds the theme to the view, providing names
that the remainder of SINMAP will recognize.
The processing is divided into two steps. Grid processing is only done
once since it depends only on digital elevation data. Stability analysis
requires iteration on parameters. We will not do stability analysis.
We are just using SINMAP to do grid processing with the Dinfinity method
(because it is easier than running TARDEM DOS command line programs dinf
and areadinf which do the equivalent).
Select 'Compute All Steps' from the 'Grid Processing' part of the SINMAP
menu. You should see the blue action bar at the bottom and various
messages flash by. Once this stops 4 themes (pit filled dem, flow
direction, slope and contributing area) have been added to the view.
These are from the Dinfinity method so are different from the results obtained
using TARDEM d8 and aread8 earlier. Flow direction is expressed as
an angle in radians, measured counterclockwise from east. Contributing
area is specific catchment area expressed in area per unit contour length,
i.e. it has the same units as 'map units' which for this work is meters.
The 'contour length' used for each grid cell is the cell size (30 m here).
The contributing area has been evaluated using the proportioning between
downslope cells, i.e. a multiple flow direction approach, that is part
of the Dinfinity method. This calculation also includes a check for
edge
contamination. This is the possibility that some terrain outside
the bound of the DEM analyzed could be part of the contributing area of
grid cells within the DEM analyzed. If the program detects this it
reports the contributing area as 'no data'. This is the reason for
gaps near the edges and along streams that come in from the edge of the
map.
To mask (isolate) the watershed of interest type the command
aread8 reydem xy 520170 4789800
This computes contributing area only upslope of the specified outlet, leaving
the rest of the area as 0. Add the theme reydemad8 to the
view. Use the map calculator from the analysis window to evaluate
reydemad8 > 0
This results in a theme with 1 in the watershed and 0 out of it.
Now do ( 1 .AsGrid/ [Map Calculation 1]) to change the 0's to no data (dividing
by zero is no data). Select theme 'Map calculation 2' and then
from the Theme menu Save Data Set, specifying grid name 'mask'.
Add the theme 'reydemsca' to the view. [This is the actual specific
catchment area computed using Dinfinity. The theme displayed as contributing
area 'reydemsca2' is the base 10 log of this to compress the scale and
avoid color mismapping due to range overflow in ArcView.] Use the
map calculator to evaluate ([mask] * [Reydemsca]) and ([mask]
* [Reydemslp]). Save the masked specific catchment area and slope
grids as 'reydemsca_m' and 'reydemslp_m'. Compute the exponential
TOPMODEL wetness index [ln(a/S)] using the map calculator (([reydemsca_m]
/ [reydemslp_m]).Log). Save the grid as 'reydemlnas'.
Double click on the legend for this theme. Click on the statistics
button. This should report various statistics. The mean is
the TOPMODEL parameter 'lambda'. Prepare a layout of the wetness
index, ln(a/S). Report the TOPMODEL parameter lambda for
this watershed. Report the number of flat cells in this watershed
(use map calculator for slope > 0) and statistics. The calculations
will need to account for this.
Now assume an initial baseflow of 10 m^{3}/s and TOPMODEL parameters,
K_{o} = 5 m/hr, f = 2 m^{1}.
Estimate R (the flow per unit area in m/hr) and mean depth
to saturation 'zbar'.
Use the map calculator to evaluate the depth to saturation
Beware that map calculator does not adhere to the common associations
of arithmetic. It evaluates expressions left to right. It is also
common to get syntax errors due to confusion between grids and numbers.
The way to avoid them is to use the AsGrid button a lot, and use a lot
of parentheses, e.g. (0.96.AsGrid(([reydemlnas]6.98.AsGrid)/5.AsGrid)).
Prepare a layout map depicting the depth to the water table z (overlaid
by 50 m contours) over part of the watershed. Depict the
saturated area (z < 0) is a distinct color. Be sure to include
flat spots in the saturated area. Report the initial saturated
area as a fraction of the total area. This is the initial runoff
coefficient by TOPMODEL, because rain falling on this area immediately
becomes runoff. Rain elsewhere can infiltrate. As rain
infiltrates z is reduced. Consider a storm of 50 mm. Assume
the soil has an effective porosity of 0.25. This means that z will
be reduced everywhere by 0.05/0.25=0.2m. Report the saturated
area fraction after this 50mm storm. Estimate the total runoff
from rain on saturated areas during this 50 mm storm.
Summary of material to turn in

layout of the wetness index ln(a/s) (overlaid by 50 m contours).

the Topmodel parameter 'lambda'

the number of flat cells

Estimate R (the flow per unit area in m/hr)

mean depth to saturation 'zbar'.

layout map depicting the depth to the water table z (overlaid by 50
m contours)

the initial saturated area as a fraction of the total area

the saturated area fraction after this 50mm storm
the total runoff from rain on saturated areas during this 50 mm
storm.
Ok, you're done!
These materials may be used for study, research, and education,
but please credit the authors and the Utah Water Research Laboratory, Utah
State University. All commercial rights reserved. Copyright 2000 Utah State
University.