Analytical Properties for a Stochastic Rotating Shallow Water Model Under Location Uncertainty

Abstract

The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class of rotating shallow water models which are stochastically perturbed in order to incorporate model uncertainty into the underlying system. The stochasticity is chosen in a judicious way, by following the principles of location uncertainty, as introduced in Mémin (Geophys Astrophys Fluid Dyn 108(2):119–146, 2014). We prove that the resulting equation is part of a class of stochastic partial differential equations that have unique maximal strong solutions. The methodology is based on the construction of an approximating sequence of models taking value in an appropriately chosen finite-dimensional Littlewood-Paley space. Finally, we show that a distinguished element of this class of stochastic partial differential equations has a global weak solution.

Noise calibration for SPDEs: A case study for the rotating shallow water model

“…equation (18) below). The form for the h equation we use in this work is common to both [7] and [14]. The model in [14] is based on the Location Uncertainty paradigm first introduced in [17], whilst the model in [7] is based on the Stochastic Advection by Lie Trasport paradigm first introduced in [11].…”