All the features below have been normalized into \([0, 1]\), so the original units do not matter. What matters:
Have a look at the 3 different types of features, the question is in the end.
In the figures below, marginal plots (both on x- and y-axis) describe the the mean value over columns (x) and rows (y).
Feature is fairly evenly distributed over the whole area of interes with variation both globally and locally. Roughly speaking, value distributions on both x- and y-axes are multimodal (or even uniform).
Feature is very unevenly distributed over the area of interest. The values distribution is multimodal characterized by large relative differences in values (spikes). In other words, the occurrence is very localized. Note that the color scaling is different to those of A and C.
Feature can be found throughout the area of interest, but the distribution is concentrated in the central parts. Hence, local variation is medium or low, but global variation high. Approximating a little, the value distributions are unimodal.
Since the marginal plots in the figures above are not necessarily on the same scale (even if the data are after normalization), they cannot be directly compared to get and idea about how common/rare a given feature is. Visual inspection will already hint order floodregulation > carbon_sequestration > erosion_prevention. Another way of characterizing this is to have a look at the distribution sum (DS) of each feature, which is simply the sum of all values over the whole feature:
| Feature | Distribution sum |
|---|---|
| floodregulation | 1470616.9 |
| carbon_sequestration | 398752.1 |
| erosion_prevention | 2127.2 |
DS of floodregulation is ~4 and ~691 times greater than that of carbon_sequestration and erosion_prevention, respectively.
Given the different types (the typology is not exhaustive) of feature described above:
Do you know of any quantitative methods that would characterize both the spatial pattern and the occurrence levels of continuous rasters in some concise way? Furthermore, do you know software implementations of these methods?
Some sort of scalar measure, or set of measures would be best. It would have to take into consideration continuous data, so most e.g. most landscape ecological measures looking at discrete features are not ideal. Of course, it would be possible to categorize the features somehow. Any possible measures are probably going to be scale-dependent, but such is life. I keep coming back to two broad analysis categories: fractal analysis (e.g. lacunarity analysis) and pattern recognition (e.g. FFT methods). Unfortunately, I have very limited experience in either.