| Sequential Monte Carlo (SMC) approaches are increasingly being used in watershed
hydrology to approximate the evolving posterior distribution of model parameters and states
when new streamflow or other data are becoming available. The typical implementation of
SMC requires the use of a set of particles to represent the posterior probability
density function (pdf) of model parameters and states. These particles are propagated
forward in time and/or space using the (nonlinear) model operator and updated
when new observational data become available. Main difficulty in applying particle
filters in practice is problems with ensemble degeneracy, in which an increasing
number of particles is exploring unproductive parts of the posterior pdf and assigned a
negligible weight. To ensure sufficient particle diversity at every stage during the
simulation, I will present an efficient SMC scheme that combines particle filtering with
importance resampling and DiffeRential Evolution Adaptive Metropolis (DREAM)
sampling. Our method is based on the DREAM adaptive MCMC scheme presented in
Vrugt et al. (2009), but implemented sequentially to facilitate posterior tracking of
model parameters and states. Initial results using the Sacramento Soil Moisture
Accounting (SAC-SMA) model have shown that our DREAM particle filter has
the advantage of requiring far fewer particles than conventional SMC approaches.
This significantly speeds up convergence to the evolving limiting distribution, and
allows parameter and state inference in spatially distributed hydrologic models. |