Combining semivariogram models

Often there are two or more processes that will dictate the spatial distribution of some phenomenon. For instance, the quantity of vegetation (the biomass) may be related to elevation and soil moisture. If this relationship is known, it is possible to use cokriging to predict biomass. You could use the measured values of biomass as dataset one, elevation as dataset two, and soil moisture as dataset three. You might fit different semivariogram models to each dataset because each exhibits different spatial structure. That is, the spherical model might fit elevation best, the exponential model might fit soil moisture best, and a combination of the models might fit biomass best. The models can then be combined in a way that best fits the structure of the data.

However, sometimes you don't know the causal relationships of the factors that are determining the spatial structure in some phenomenon. Using the same example of biomass above, you may only have the sample points measuring the biomass. When you examine the semivariogram, you notice distinct inflection points.

The points go up, straighten out, and bend again to level off to the sill. You suppose that there are two distinct structures in the data and a single model will not capture it. You can model the semivariogram with two separate models (for example, spherical and exponential), combining them into a single model. Three models can also be combined, if necessary.

Representing multiple distinct random processes through a single semivariogram is discouraged, and it is best to separate the spatial processes whenever possible. However, the causal relationships are not always understood. The choice of multiple models adds more parameters to estimate and is a subjective exercise that you perform by eye, then quantify by cross-validation statistics.

Learn more about cross-validation