*Oana Lang (Imperial, UK)*

The aim of the talk/poster is to present a stochastic filtering problem consisting of a signal that models the motion of an incompressible fluid below a free surface whenthe vertical length scale is much smaller than the horizontal one. The evolution of the two-dimensional rotating system is represented by an infinite dimensional stochastic PDE and observed via a finite dimensional observation process. The deterministic

part of the SPDE consists of a classical shallow water equation (with an added viscosity term) and a new type of noise, namely the one introduced in [2]. Although this is a single layer model, therefore it does not completely reflect the complex stratification of the real atmosphere, it allows for important geophysical phenomena such as gravity and Rossby waves, eddy formation and geophysical turbulence.

References:

[1] A. Bain, D. Crisan, Fundamentals of Stochastic Filtering, Springer, 2009

[2] D. Holm , Variational Principles for Stochastic Fluid Dynamics, 2015

[3] G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics, 2005

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