Geophysical fields can be characterized by an extreme variability over a wide range of scales. One way of studying this variability is the multifractal /multiscaling approach which describes it on all scales and all intensities.
In this theoretical framework we propose to study the important question of measurements, which are obtained averaging the field at a given scale. Several problems, which are not completely solved yet, arise when we want to understand the relationship between scales and instruments: the resolution dependence of instrumental data; the relations between time average at a given location and space average at a given time; and also the influence of a network of measurements on the data.
These questions will be studied in a statistical framework, and the theoretical hypothesis and derivations will be validated and tested on the numerous geophysical data series which are already available concerning temperature, rain, wind velocity and pressure fields.