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

Abstract. The use of particle filters for data assimilation is increasingly popular because of its minimal assumptions. Nevertheless, implementing a particle filter over domains of large spatial dimensions remains challenging, as the number of required particles rises exponentially as domain size increases. A common solution to overcome this issue is to localize the particle filter and consider a collection of local applications rather than a single regional one. Although this solution can solve the dimensionality limit, it can also create some spatial discontinuity inside the particles. This issue can become even more problematic when additional data is assimilated. The purpose of this study is to test the possibility of remedying the spatial discontinuities of the particles by locally reordering the particles. We implement a spatialized particle filter to estimate the snow water equivalent (SWE) over a large territory in eastern Canada by assimilating local manual snow survey observations. 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, in which SWE is indirectly estimated from snow depth. The two reordering solutions maintain the spatial structure of the individual particles throughout the winter season, which significantly reduces the 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 open-loop model, but we noted no significant improvement when both snow courses and the SR50 data were assimilated.