Geostatistics

Basics of Geostatistics
Geostatistics is a branch of statistics that is used to characterize spatial distributions and to produce estimates of variables at unsampled locations. The idea behind geostatistics is quite simple: samples taken closer together are more similar on average than samples taken farther apart. For example, if you have a grid of points over an area, and measure some variable at each point:

You might find that on average, points that are right next to each other have values that are more similar than points that are 2 or 3 units apart. A lot of environmental factors like soils, climate, tree growth, species distribution, topography, etc. show this characteristic.

Using this principle, we can make a mathematical model (variogram) of how dissimilarity changes with distance:

As the separation distance increases, the dissimilarity, on the vertical axis, increases and then levels off. This mathematical model can then used in a procedure known as kriging (named after a statistician named Krige) to help estimate values for variables at unknown locations; kriging is basically a weighted averaging approach, with weights coming from the variogram.

Kriging and its variants (e.g., cokriging, kriging with local means, indicator kriging, and various types of simulation) have been used for years in the mining industry, and only recently in the forestry community.
One useful aspect of the kriging-based simulation procedures is that the error estimate for a given point is not only based on the density of surrounding samples, but also on how similar those surrounding samples are. The resulting "error maps", which are associated with the estimates, are useful when evaluating the final map product.

NE-FIA has used variography and various forms of kriging to create maps of FIA attributes such as basal area, species importance, volume, and presence/absence probability. We are pursuing ways to improve the fine-scale accuracy of geostatistical maps by incorporating ancillary information, like satellite imagery, into the analyses.
One example of our geostatistically-derived maps can be found at species distribution