Ensemble-based Data Assimilation for high-dimensional shallow water s...

Data Assimilation serves multiple purposes, including estimating the model state and the initial state of a system for predicting its future state. It combines prior information from numerical model simulations with observed data to produce the most accurate description of a dynamical system and it uncertainty. Here we consider the highly nonlinear and spatially extended shallow water equations which are derived from depth-integrating the Navier-Stokes equations.  Once the model is developed, it can be integrated into various ensemble filters, such as the Ensemble Square Root Filter (ESRF), the Local Ensemble Transform Kalman Filter (LETKF) or the Ensemble Transform Particle Filter (ETPF) as a hybrid combination. These filters are commonly used in data assimilation to improve the accuracy of model predictions by incorporating observations of the system into the model. They work by generating a set of possible scenarios (or ensembles) that represent the uncertainties in the model, and then weighting and combining these scenarios based on their consistency with observed data. The evaluation of the high-dimensional dynamical model with a combination of these types of hybrid filters is novel and goes beyond the typical Gaussian assumptions, perhaps leading to even more precise estimates.