Heterogeneity and change of scale in models of remote sensing. Spatialization of multi-spectral models

Abstract

The multi-spectral reflectances measured from the satellite lead to soil surface information through models. Since these models arc defined and validated at local scale, where the soil surface is considered to be homogeneous, the usc of the models with satellite multi-spectral reflectances as inputs will create a gap between the corresponding output and the average of the local ill situ outputs.

We study the basis of the gap between the outputs of the model applied to global measurements and the average of its local outputs. This general problem in remote sensing is stated and approached without any a priori assumption on the measured parameter with respect to change of scale, as is made for example, with the fractal assumption.

Despite the very general and pragmatic statement of the problem, difTerent basic results are obtained which lead to new practical procedures. Different concepts are defined or clarified such as the spatialization of models, the degree of heterogeneity, the scale coherency. The point of view defined here leads to prospective ways to consider the respective role of the heterogeneity of natural media and the non-linearity of the model when the measured inputs are averaged values.