Interpolating snowfall point data using a precipitation raster as a guide

[CodyOppermann]

I thought I'd post this in the Geostatistical Analyst section as I'm lead to believe this may be a cokriging issue.
I have a raster of precipitation data I've downloaded from Oregon State's PRISM (http://www.prism.oregonstate.edu/) which makes a pretty map of average annual precipitation across the country. I now have point data of average annual snowfall for some stations across Utah. I would do a simple interpolation using this data, but there are some mountain ranges where stations do not exist and a simple interpolation would gloss over the higher snowfall that would fall in those mountains.
I'm assuming this sort of thing is usually done with precipitation and elevation, with the assumption that the higher the elevation, the greater the precipitation. Is there a way I can use the snowfall point data and use the trends in the PRISM data to interpolate the snowfall data? Any help would be greatly appreciated.

-Cody

[EricKrause]

Yeah, this sounds like a case where cokriging might be effective.  Cokriging is most effective when the secondary variable is much more finely sampled than the primary variable, and it sounds like that is what you have.

If you find that cokriging is not effectively using the precipitation, you may want to try Geographically Weighted Regression.

[CodyOppermann]

As much as I fiddle with the cokriging parameters, much of which I don't understand, I can't seem to yield a reasonable-looking map. Any advice on what the parameters should be tuned to?
The Geographically Weighted Regression tool seems like it would be something I'm looking for, but I'm guessing the "explanatory" variable I'm looking for is the precip data, but that is in a separate file, and it doesn't appear a raster can be used as predictive locations or a variable. Thoughts?

[EricKrause]

To use Geographically Weighted Regression, you would need to convert the raster to points, then perform a spatial join to get them all in the same feature class.

[CodyOppermann]

Sorry, don't mean to ask to be spoon fed, but I'm still a little confused.
I clipped the raster to just cover Utah and this makes up over 300,000 individual grid cells. I then converted them to points.
To compare, there are only 180 sites in the area that reported average yearly snowfall. I performed a spatial join so that 180 of the points have a snow value and still over 300,000 report zero.
I then ran the GWR with average snowfall as the dependent variable and the average rainfall (or GRID_CODE which was spit out from the raster to point conversion) as the explanatory variable, selected FIXED kernel type, and selected the AICc bandwidth method. Doing so gives me a "severe model design" error. I ran an OLS, which a lot of the output means nothing to me, but there was an R-squared value of 0.000007 (is this due to all the zeroes involved?). Any ideas?

[EricKrause]

I think it has to do with the large areas of zero snowfall.  GWR needs local variability to compute estimates, and large areas of constant value will cause the tool to give that error.

As for what you can do, I honestly don't know.  Zero-inflation is a huge problem for statistical models.  You might find some success with performing GWR (or cokriging) only in the areas where you have snowfall, then trying to fit a different model to the areas with no snowfall.

[EricKrause]

This is a strange error to get from GWR if you only have one explanatory variable.  Is it possible to send your data to ekrause@esri.com so I can take a look?