How to find the best kernel size statistically (in Focal statistics)

[KarolinaKorzeniowska]

I would like to find an appropriate kernel size for evaluation of mean for my raster DEM in Focal Statistics. Is there a way to select the best kernel size statistically without looking into the data?

[DanPatterson_Retired]

In short... No ... It is not only the size of the kernel, but its shape. If you happen to be analysing a raster with a directional pattern, then you would want to use one whose shape best reflects the directionality.  Focal statistics are often used to analyse the nature of the raster by varying the size and shape of the kernel

Focal Statistics—Help | ArcGIS for Desktop

other options entail converting your raster to numpy arrays and use numpy or scipy to look for other patterns

[KarolinaKorzeniowska]

Thank you for your answer. I thought that it might be possible to find a kernel size (as a threshold) which tells me that e.g. smoothing above this kernel size will not change the the results significantly more than smoothing using this kernel.

[DanPatterson_Retired]

That will vary with the input raster, the nature of the kernel and other factors...All I can tell you with any certainty as the kernel size increases, any value being calculated approaches that of the overall value for the raster as a whole.  As an example, you can verify this by setting kernel size so that it equal raster size and calculating the mean.  As you decrease kernel size, you begin...potentially... to introduce variation in the calculated values and they may become more diverse until each cell is unique at that location