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I was wondering how does ArcMap10.2 calculate surface derivatives (slope, aspect) at the edge of the raster, since the Horn algorithm is used and uses the 8 neighboring pixels around each pixel. When beyond the raster there are pixels with NoData, do they contribute in the calculation of slope, aspect etc.

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This is what the ArcGIS help says about How Slope Works:

If there is a cell location in the neighborhood with a NoData z-value, the z-value of the center cell will be assigned to the location. At the edge of the raster, at least three cells (outside the raster's extent) will contain NoData as their z-values. These cells will be assigned the center cell's z-value. The result is a flattening of the 3 x 3 plane fitted to these edge cells, which usually leads to a reduction in the slope.

Most probably this is also valid for Aspect, though it's not clearly stated in the help page.

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