Application of the implicit particle filter to a model of nearshore circulation

The implicit particle filter is applied to a stochastically forced shallow water model of nearshore flow, and found to produce reliable state estimates with tens of particles. The state vector of this model consists of a height anomaly and two horizontal velocity components at each point on a 1283 98 regular rectangular grid, making for a state dimension O(10). The particle filter was applied to the model with two parameter choices representing two distinct dynamical regimes, and performed well in both. Demands on computing resources were manageable. Simulations with as many as a hundred particles ran overnight on a modestly configured workstation. In this case of observations defined by a linear function of the state vector, taken every time step of the numerical model, the implicit particle filter is equivalent to the optimal importance filter, i.e., at each step any given particle is drawn from the density of the system conditioned jointly upon observations and the state of that particle at the previous time. Even in this ideal case, the sample occasionally collapses to a single particle, and resampling is necessary. In those cases, the sample rapidly reinflates, and the analysis never loses track. In both dynamical regimes, the ensembles of particles deviated significantly from normality.