Interpolation of polygons

[deleted-user-K_IRAXrpGKsG]

My boss asked me to give him an IDW interpolation of polygon data. I'm not sure if he knows if that is possible or not.

IDW of points is very easy and I already have that done, but does anyone know if you can do a IDW of polygons? Wouldn't
that essentially be a chloropleth?

Thanks,
Pat

[LucasDanzinger · Accepted solution]

Hi Pat,

It looks like IDW is limited to points as the input feature. Kriging and Spline also require points as the input feature. You might consider converting your polygons to points first. If you use the Feature to Point GP Tool, this will place a point at the centroid of the polygon and you could then interpolate based on these points. If you don't have ArcInfo, add an X (Double) and a Y (Double) field in your attribute table and calculate the geometry. This will calculate the location of the centroid of the polygon. Then create a feature class based on these XY points.

Hope this helps.

Luke

[toddsams]

Does anyone have another idea for how to accomplish this?

It seems that (if the polygons were somewhat large) you'd decrease the accuracy of the interpolation by representing the polygon as a centroid. If the polygon value corresponds to the entire area of the polygon, wouldn't it be better to convert the edges of the polygon to points and then use those points for interpolation?

This way, the points would be closer to each other and the interpolation routine would not have to cover as much distance.

The spacing of the points along the edge of the polygon and the number of points the IDW/Kriging tool uses for interpolation would likely have a big effect on the interpolated values though, so this might not be a great option.

It would be great to hear if anyone else has another suggestion.

[EricKrause]

If you have ArcGIS 10.1 and a Geostatistical Analyst license, you should consider using areal interpolation.  It works directly with polygons; there is no need to try to represent them as points.

You can see a video that takes you through a typical areal interpolation workflow here.

[toddsams]

Areal interpolation sounds like a good approach for this.

I noticed that a limitation of kriging is the assumption of stationarity. However, wouldn't using a cokriging variable help with nonstationarity in the variable to be interpolated?

[EricKrause]

That's a tough question to answer.  By pure theory, using a cokriging variable won't help with nonstationarity issues, but it is still likely to give better results.

A nonstationary variable will make the kriging equations non-optimal.  Using a cokriging variable will likely give better results, but the improvement has little to do with the nonstationarity.

[toddsams]

Thanks.

Does areal interpolation (as implemented in Geostatistical Analyst for Arc 10.1) allow the use of cokriging variables?

How does one chose a cokriging variable? Would the best cokriging variable be the one that has the highest correlation with the variable for interpolation?

Does the ESRI documentation provide an explanation and/or references for 1) how cokriging variables can provide better interpolation estimates and 2) how to go about selecting a cokriging variable? Do you have any recommended reading on these topics?

[EricKrause]

Areal interpolation allows you to use one cokriging variable.  For the cokriging variable to be effective, it should be highly correlated with the primary variable.  You can investigate the correlation with something like a scatterplot.

You can input the cokriging variable on the first page of the Geostatistical Wizard.  After selecting "Areal Interpolation," you can provide "Dataset" and "Dataset2".  "Dataset" is the primary variable, the one you will interpolate.  "Dataset2" is the cokriging variable.