I need to compute an aggregate index for vegetation density in certain (large) shapes, to assess desertification. I have NDVI data at a high spatial resolution (~100 NDVI-pixels per aggregation shape, based on MODIS NDVI version 6).
Initially my idea was to compute the arithmetic mean across all pixels in each shape, but that seems to be a bad idea: NDVI is a (unitless) ratio, ranging from -1 to 1, taking approximately the following values:
Clouds/Snow: ~ <0 Water: ~-0.1 to 0.1 Soil: ~ 0.1 to 0.2 Vegetation: ~ 0.3 to 0.8. Built-up areas: ~ ?
That scale is not even approximately linear in biomass, area covered in green, or similar natural scales. Taking the arithmetic mean across all pixels in a shape thus does not do what I want, and the resulting aggregation is difficult to intepret. In other words: The arithmetic mean of all pixel-NDVIs in a shape is not the NDVI of that shape. E.g. A change from bare soil (0.1) to concrete (-0.5) in one pixel will affect the average as much as several pixels going from loose to dense vegetation.
Are there any suggestions on how to proceed? In particular I'd like to know what the standard procedure in the remote sensing literature is. Are people actually using arithmetic means, if so, how do they argue? Are there alternatives that are commonly used?