[R] disparate data collections and resolutions in a GAM

Ateljevich, Eli@DWR Eli.Ateljevich at water.ca.gov
Tue Dec 1 18:58:43 CET 2015

I have point values of elevations on land (high resolution lidar) and in the water (some are lower resolution single beam soundings or even just prior elevation maps, others are high res multibeam). Let's say high resolution is 1m and low is 10m, although the coarse case can be worse.

>From this data I want to produce two smoothed datasets, one at 2m resolution where it is justified by the data and the other at 10m. Everywhere there is a 2m map there will be a corresponding 10m map, but not vice versa.

To do this in a mutually compatible way, I envision producing a GAM that does this:
1. partition the surface into variations at higher and lower frequencies, so that the 2m map could be considered the sum of a 10m general shape of the channel plus a zero mean higher frequency fluctuation due to features. The partition could be imperfect ... I'm sure frequencies will bleed and the terrain is inherently anisotropic (channels with long length scales in the downstream direction).
2. somehow deal with the fact that the data come from different collections, and are likely to be different in terms of bias, variance and point density. I'd be willing to call one of the datasets "true" and declare a collection effect for the others, but it would only be identifiable in a narrow region.

Any recommendations? I am most familiar with mgcv but flexible on approach. The GAM with tensors splines in the alongstream and cross-stream direction have worked well for us at 10m in similar terrain without the added twist.


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