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

• 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): 309-319. (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.373-387.
• 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.627-668.

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 m³/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

1. layout of the wetness index ln(a/s) (overlaid by 50 m contours).
2. the Topmodel parameter 'lambda'
3. the number of flat cells
4. Estimate R (the flow per unit area in m/hr)
5. mean depth to saturation 'zbar'.
6. layout map depicting the depth to the water table z (overlaid by 50 m contours)
7. the initial saturated area as a fraction of the total area
8. the saturated area fraction after this 50mm storm

the total runoff from rain on saturated areas during this 50 mm storm.