Large-scale snow data assimilation using a spatialized particle filter: recovering the spatial structure of the particles

Data assimilation is an essential component of any hydrological forecasting system. Its purpose is to incorporate some observations from the field when they become available in order to correct the state variables of the model prior to the forecasting phase. The goal is to ensure that the forecasts are initialized from state variables that are as representative of reality as possible, and also to estimate the uncertainty of the state variables. There are several data assimilation methods, and particle filters are increasingly popular because of their minimal assumptions. The baseline idea is to produce an ensemble of scenarios (i.e. the particles) using perturbations of the forcing variables and/or state variables of the model. The different particles are weighted using the observations when they become available. However, implementing a particle filter over a domain with large spatial dimensions remains challenging, as the number of required particles rises exponentially as the domain size increases. Such a situation is referred to as the "curse of dimensionality", or a "dimensionality limit". A common solution to overcome this curse is to localize the particle filter. This consists in dividing the large spatial domain into smaller portions, or "blocks", and applying the particle filter separately for each block. This can solve the above-mentioned dimensionality problem because it reduces the spatial scale at which each particle filter must be applied. However, it can also cause spatial discontinuities when the blocks are reassembled to form the whole domain. This issue can become even more problematic when additional data are assimilated. The purpose of this study is to test the possibility of remedying the spatial discontinuities of the particles by locally reordering them.