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The ArcGIS Help file says the Default Maximum Distance, when using the Variable Search Radius in IDW, is the extent's diagonal, however, no value is automatically filled in the corresponding box after I define the extent, so is ArcMap really using this default value if the box is empty?

Regarding coincident points (different measurements at the same location) when running IDW, it is possible to set the Environment "Geostatistical Analysis" to Min, Max, Mean, etc., but is this selection really honored when running IDW using Spatial Analyst, or does it only apply to tools from the Geostatistical Analyst extension? I am confused because the ArcGIS help says: "Tools that honor the Coincident Points environment define how coincident data is treated in Geostatistical Analyst". If the Coicident Point selection is not honored when using Spatial Analyst, how do I know what IDW is doing about them? Thanks a lot for your help!

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The IDW in Spatial Analysis is independent from Geostatistical Analyst and as such, the GA specific environmental setting do not apply to SA output. I would not expect a "data dependent" parameter to be populated in ArcToolbox and just because the box is empty does not mean that a default value is not applied. Some thought should be put into the search distance parameter and it should reflect some underlying spatial process in your data or the resulting error component.

As far as coincident points. As I recall from the IDW implementation in Arc/Info, duplicates are dropped based on order of input in the info table. Although somebody like @whuber would know for sure. A corollary in ArcGIS is if you have three coincided points the one with the lowest FID is retained. I am somewhat weary of just taking the min, max, mean of coincident points unless they actually represent repeated measurements. Coincident points should be identified before hand and investigated to ensure that they are not, in fact, data errors.

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