Land Sea interface in global temperature averaging

Inhomogeneity is a problem when estimating an average. You have to sample carefully. In political polling, for example, men and women tend to think differently. So you need to get the proportions right in the sample (or re-weight).

In a global temperature average, a big inhomogeneity is the land/SST difference. For grid-based estimates, a land mask is often used. This tells how much of each cell is land and how much sea.

I haven't used a land mask with TempLS grid, because I think grid weighting has bigger problems. And with mesh weighting, there isn't any clear way to mask, especially as there is typically a new mesh for each monthly set of stations.

The mitigation is that there is a lot of cancelling effects. Some land areas may be in effect represented by sea, but also vice versa. Island temperatures tends to influence surrounding sea, but then again, they really should. If they were only representative of their own land area, it would generally not be worth including them.

I may still try to do something more elaborate. But in the meantime, I thought I would test what the current algorithm does, using what maths call a color function. This is 1 (red) for land stations, 0 (blue) for SST. I plot it as if it were temperature. I hope to see that land areas uniformly red, sea blue, and an in-between color tracking the shore. Insofar as it fails to track, I hope the failure is balanced, so that neither sea nor land is over represented on average. The result is an active WebGL plot below the fold.



This is the plot for the stations reporting in March 2015. I think it is quite good. There is some intrusion of sea effect where land is poorly covered, and there is the expected smudging of islands, but generally the demarcation follows the coastlines.