Maungawhau with a Gaussian process

The Maungawhau volcano dataset is an R classic, often used to illustrate 3d plotting.
Being on a Gaussian process kick lately, it seemed fun to try to interpolate the volcano elevation data using a subset of the full dataset as training data.
Even with only 1% of the data, a squared exponential Gaussian process model does a decent job at estimating the true elevation surface (code here):

The upper row of plots show the true elevation surface, estimated surface based on 1% of the data (53 of the 5307 cells), and the squared error in estimation.
The lower plots show the same data in heatmap form, with the location of sampled points shown as crosses.