Slope calculations

The above image is on the mluri ftp site under task5. It illustrates 8 different derivations of slope for the DEM in your FireMap demo. (The original DEM is Wave 10 in the top left of the image).

The images have been normalized (0 to 1) by histogram so that the largest slope value found in any dataset is set to 1 and all other values re-scaled accordingly.

The darker values denote steeper slopes and the brighter tones denote level terrain.

The following key identifies which method was used to create each image and the maximum value produced for that method.

Wave 0: Fleming and Hoffers (Ritter's) method; maxslope score 0.7523
1: Horn's; 0.6746
2: One over distance; 0.6674
3: Sharpnack and Akins; 0.6607
4: Diagonal Ritter's; 0.6411
5: Averaged down-dip slopes; 0.7526
6: Simple method; 1.0
7: maximum downward gradient; 0.8931
8: Least squares paraboloid; 0.6607

A few points to notice:

1. The largest estimation of slope was derived using the `simple method' (1.0) and the lowest values were those derived using "Diagonal Ritter's" method (0.64). The range for Ritter's method is only 64% of that for the Simple approach.
2. The AREA of the land which is estimated to have the steeper slopes within each dataset is larger for the Diagonal Ritter's method than for the Simple method. Therefore, depending upon the method selected, the footprint of a feature such as a valley or a gulley will be much larger for the methods such as Ritter's, Horn's, Sharpnack and Akins, One over distance and least squares.
3. The method employed in Arc Info GRID is Horn's method, thus one of the most commonly used methods will provide a much "smoother" output image for slope than might be justified.
4. The scoring of 'risk' associated with individual pixels will vary depending upon the slope algorithm used, but the significance of this will only be determined by the wieghting of the slope images within the FireMap processing.

We are going to run the FireMap demo using the different slope images to see whether there are significant differences (aspect will be next). Are there particular elements that we should look for? For example, if the wind direction was altered would the geographical distribution of the output classes be more or less affected with respect to the shape of the topography?

What we wondered was whether or not we could code each cell according to method. That is, for each cell, which method would provide the highest or lowest estimation of slope?

Please let David know your opinion on the above. IF the outputs are sensitive to slope or aspect it would be useful to illustrate the consequences of using different routines within the WWW framework.

Press here to see the effect of the various slope algorithms on the calculated fire risk

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Last modified: Tue Aug 12 09:54:01 BST 1997