Introduction for ensemble based hybrid filtering

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 estimation of the current state of a dynamical system and its uncertainty. Due to the complexity of models it is not possible to compute the associate posterior analytically. The aim is to produce an empirical estimate via a Monte Carlo ansatz by generating an ensemble of samples of the posterior. Therefore It is crucial to have an efficient implementation for the forwarding step of the model and to pair it with a Bayesian update. There is a plethora of ensemble filters (often entailing an underlying Gaussianity assumption). Here we would like to employ filters from the family of Ensemble Square Root Filter (ESRF) and combine them with transport induced filters such as the Ensemble Transform Particle Filter (ETPF). These types of hybrid filters go beyond the restrictive Gaussian assumptions but maintain a high level of robustness which ultimately can lead to more precise estimates.