It has be recognized for a long time that stochasticity plays a large role in Geoscience. But how to separate the stochastic and deterministic effects has proven to be a difficult task. It has also not been clear how to quantify the stochastic influence on geosystems and how to use stochastic dynamics to make predictions that can be compared to field data.
In this lecture we will argue using the example of landsurface erosion that the deterministic and stochastic approaches are not as separate as many investigators in Geoscience seem to think. First we will show how the deterministic and stochastic approaches are linked through the instabilities ubiquitous in geosystems and secondly how the stochastic theory leads to a statistical theory. The statistical theory produces deterministic quantities that can be compared to field data.
The source of the stochasticity in Geoscience is frequently difficult to identify. We will argue that the source of the stochasticity of landsurfaces can be found in turbulent flow.
(Based on a joint work with T. Smith, G. Merchant, A. Bertozzi, E. Welsh, V. Pudkaratze, K. Mertens, and P. Vorbieff)