Bayesian inference for fluid dynamics: A case study for the stochastic rotating shallow water model

In this work, we use a tempering-based adaptive particle filter to infer from a partially observed stochastic rotating shallow water (SRSW) model which has been derived using the Stochastic Advection by Lie Transport (SALT) approach. The methodology we present here validates the applicability of tempering and sample regeneration using a Metropolis-Hastings procedure to high-dimensional models appearing in geophysical fluid dynamics problems. The methodology is tested on the Lorenz 63 model with both full and partial observations. We then study the efficiency of the particle filter for the SRSW model in a configuration simulating the atmospheric Jetstream.