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I have a raster of Zambia, 100m² resolution (about 650mb). Buffers (single) at 1,2,3,4,5,10,15,20,25,30,50 km.

I'm running "zonal statistics as table" in the model builder for all buffers (actually, the buffers are run in the model builder as well). How do I know the sums are wrong? Some of the larger buffers have smaller pixel sums than the smaller buffers. I've cut down the dataset so that there are about 150 points to buffer. I've run the problematic points/buffers individually and they returned identical results.
This might be related or suggest where the problem is coming from: When I tried to clip the buffers to the country outline (most of the problematic buffers are around the edges or where the points are in close proximity to each other). I get a Invalid Topology [Topoengine error.] message. How can I resolve this?

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Have you seen previous advice on Invalid Topology (Topoengine error)? If so, it would be worth editing the results of anything that you have tried from there into your Question. –  PolyGeo Nov 3 '13 at 1:46
    
If you are buffering points then a better approach is to compute focal sums (at the same buffer radii) and extract their values at the point locations. –  whuber Nov 3 '13 at 23:23

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