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. We implement a spatialized particle filter to estimate the snow water equivalent (SWE) over a large territory in eastern Canada by assimilating local SWE observations from manual snow surveys. We apply two reordering strategies based on (1) a simple ascending-order sorting and (2) the Schaake shuffle and evaluate their ability to maintain the spatial structure of the particles. To increase the amount of assimilated data, we investigate the inclusion of a second data set (SR50), in which the SWE is indirectly estimated from automatic measurements of snow depth using sonic sensors. The two reordering solutions maintain the spatial structure of the individual particles throughout the winter season, which significantly reduces the spatial random noise in the distribution of the particles and decreases the uncertainty associated with the estimation. The Schaake shuffle proves to be a better tool for maintaining a realistic spatial structure for all particles, although we also found that sorting provides a simpler and satisfactory solution. The assimilation of the secondary data set improved SWE estimates in ungauged sites when compared with the deterministic model, but we noted no significant improvement when both snow courses and the SR50 data were assimilated.