Spatial autocorrelation

The principle underlying spatial interpolation is the First Law of Geography. Formulated by Waldo Tobler, this law states that everything is related to everything else, but near things are more related than distant things.

The formal property that measures the degree to which near and distant things are related is spatial autocorrelation. According to this, if it is raining where you are, it is probably raining 10 feet away from you, is less likely to be raining on the other side of town, and might even be clear and sunny 20 miles away.

Most interpolation methods apply spatial autocorrelation by giving near sample points more importance than those farther away.

In this graphic, the darkest triangles indicate the most influential sample points.