How to Compare Slope Computations

 My comparison of slope computations has 21 combinations of algorithm and GIS program, requiring some thought on how to organize the results.  These four graphs show some preliminary results, without identifying any of the guilty parties.

These results are for a one arc second DEM, for which some of the programs are not well equipped to handle.

Rows and columns each have a slope grid produced by a different algorithm/program.  The white principal diagonal is where a grid would be compared with itself.  

We do not know the "correct" slopes, so we can only discuss differences.

The results suggest that using a 5x5 window requires a lot more thought since the results are so different compared to the traditional 3x3 window.


Pearson correlation coefficient between the slope grids computed by two methods.  Those in the top, dark green box in the legend, produce identical results.  This matrix is symmetrical. There can be a high correlation coefficient if there is an offset between the grids, or one is a multiple of the other.

Mean absolute difference, which means that positive and negative differences cannot cancel out, but you get a better sense of how often the results are different, and by how much.  This matrix is symmetrical.

Mean average difference, which means that positive and negative differences can cancel out, but you can see which methods are consistently high.  This matrix is not symmetrical; opposite sides of the principal diagonal differ by a factor of -1 because the color indicates which slope grid is consistently higher or lower, and by how much.


Mean average difference, removing the slope algorithms using the 5x5 window.


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