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.
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.