Moving Windows

Variography allows us to detect spatial dependencies. What it does not detect is whether or not these dependencies are uniform throughout the whole study area. There could be large regional differences and in that case, our variogram would not be representative for the entire area! It only provides information about the spatial variability of our data.

The simple technique of the "moving windows"-statistics can help. A "window" of defined size and shape is moved over the data, the moving distance is equal to the width of the window. All data located within the window section are statistically summarized: the number and average of all points inside the window, the minimum / maximum values, the standard deviation, the coefficient of variation (= standard deviation / mean), etc. The results are again points – the centers of the moving windows and as their attributes the statistical indicators of these windows. In the case of sparse data, the window is only moved by one half of the window width to obtain more data to calculate (= moving window with overlap). The principle is shown in this animation:

Both window size and form may be varied with this method. In practice, it is used in an explorative way accordingly: an analysis is performed with windows of varying dimensions and the statistics are compared. In particular, the coefficient of variation is a significant parameter – if its values are > 1, this indicates a high variation (= high spatial variability) in this window pane.