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Calculating a maximum slope

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I have a question regarding calculating maximum slope using a DEM. I am using ArcGIS 9.3.1. I also have access to TNTmips Pro 2009.

My supervisor, who is a biologist, would like me to calculate the maximum gradient between a cell and its 8 neighbors (or just the 4 adjacent--he hasn't decided--but we won't worry about that for now). We are mapping bird habitat and he would like to know what the highest slope a bird may encounter at any given point (pixel). To do this, I have determined the maximum elevation in a 3x3 window and assigned that value to each pixel. Then, I've taken that max elevation and subtracted the actual elevation for each pixel giving me the "rise." Finally, I calculated the rise/run (where run = cell size) * 100 for the percent slope.

Are there disadvantages of calculating slope in this way rather than, say, using the slope option in ArcGIS's Spatial Analyst that calculates the "average maximum" by fitting the 3x3 plane to elevation values using ordinary least squares? I feel there are disadvantages, but I can't place my finger on them.

Thank you for helping me understand this topic,

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