| When we use statistical methods to study processes in the geosciences we treat variables
as realizations of random processes with particular, mathematically convenient,
properties. This option is commonly taken because of the complexity of the processes
of interest, and the inherent difficulties of attempting to predict their behaviour
mechanistically.
In this session we are asked to look towards joint interdisciplinary visions for how
progress might be made in the study of subsurface geosciences. On the face of it it might
seem that statistical processes close down such a joint vision because they use random
functions to model variables that we know arise from mechanisms. Is a statistical approach
compatible with process understanding?
In this paper I shall review the scope for synergy between statistical approaches and
process-based approaches to the study of multiscale variation in soil systems. How can
sampling and statistical analysis be structured so as to yield insight into processes
over multiple orders of scale, and so contribute to the modelling enterprise? At the
same time, can understanding of processes allow us to select appropriate spatial
statistical models whose parameters and structure are linked directly to processes,
and so, when estimated, provide process information and not merely convenient
statistical descriptors? In addressing these general questions I shall provide examples of
how understanding of the soil system has been enhanced by statistical analyses
which:
provide efficient sampling to permit analysis of the variation or covariation of
soil properties over strongly contrasting spatial scales,
allow spatial analysis over different scales without unrealistic statistical
assumptions about the stationarity (uniformity) of soil variation in space, and
avoid assumptions about the statistical distribution underlying soil variables, and
so permit more realistic spatial models, particularly for hydrological processes. |