I have a question very similar to one asked by wxfox4god on 12th June 2013 ("Arcmap 10 restrict Flow Accumulation") that was answered by whuber. (I have had to post it as a new question as I do not have the reputation to post a comment.)

The original question was about performing a version of the ArcGIS flow accumulation tool that is restricted to only accumulating cells from within a given distance. So for every cell in the raster the process finds how many cells within a certain distance would flow into that cell. whuber suggested a clever workaround using focal statistics iteratively.

However, my problem differs in that I need to find the weighted flow accumulation for every cell in the raster based on cells only within a certain distance. So for every cell in the raster I need to know the sum of all of the values from the cells that flow into that raster from within a specified distance.

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    Isn't this the same question as before? How exactly does your distance restriction differ from the original one?
    – whuber
    Apr 21 '15 at 16:41
  • Hi. The same distance restriction applies but it is how to apply the distance restriction method you suggested to an accumulation weighted by another raster (rather than just accumulation of cells). I think I have worked out a way to do it on paper... Apr 22 '15 at 9:10
  • Finding the focal sum of the raster that the weighting is based on for irregular neighbourhoods focusing on each of the 8 directions, and then multiplying each of these by the outputs of your logical comparison between the directional irregular neighbourhood focal sums and each of the direction number (1 s and 0s) to identify the raster values that would be accumulated from each of the eight directions. Hopefully this is correct? I now need to learn how to use ModelBuilder to make it happen. Apr 22 '15 at 9:10
  • Could you elaborate on what the weights mean and how they are supposed to work?
    – whuber
    Apr 22 '15 at 15:44
  • Applying a flow accumulation using a weighted raster means that you are summing the weighted raster values from within all of the contributing cells, rather than just counting the number of contributing cells. It is useful for applications such as predicting pollutant concentrations within a river catchment - when the weighted raster would be the concentration of pollutants in the soil of each cell. Apr 24 '15 at 14:12