Abstract
Under the motivation of the great success of four-dimensional variational (4D-Var) data assimilation methods and the advantages of ensemble methods (e.g., Ensemble Kalman Filters and Particle Filters) in numerical weather prediction systems, we introduce the implicit equal-weights particle filter scheme in the weak constraint 4D-Var framework which avoids the filter degeneracy through implicit sampling in high-dimensional situations. The new variational particle smoother (varPS) method has been tested and explored using the Lorenz96 model with dimensions N x = 40 , N x = 100 , N x = 250 , and N x = 400 . The results show that the new varPS method does not suffer from the curse of dimensionality by construction and the root mean square error (RMSE) in the new varPS is comparable with the ensemble 4D-Var method. As a combination of the implicit equal-weights particle filter and weak constraint 4D-Var, the new method improves the RMSE compared with the implicit equal-weights particle filter and LETKF (local ensemble transformed Kalman filter) methods and enlarges the ensemble spread compared with ensemble 4D-Var scheme. To overcome the difficulty of the implicit equal-weights particle filter in real geophysical application, the posterior error covariance matrix is estimated using a limited ensemble and can be calculated in parallel. In general, this new varPS performs slightly better in ensemble quality (the balance between the RMSE and ensemble spread) than the ensemble 4D-Var and has the potential to be applied into real geophysical systems.
Highlights
The Particle filter (PF) is a continuous-time sequential Monte Carlo method, which uses MonteCarlo sampling particles to estimate and represent the posterior probability density functions (PDFs).The advantage of PFs over variational methods and ensemble Kalman filter (EnKF) is that the PFs estimate the posteriors without the linear and Gaussian assumptions
The weight of each particle is proportional to the likelihood of these observations, which are the conditional PDFs of the observations given the model state
The particle smoother has a kind of natural connection to weak constraint 4D-Var formulation, and implicit sampling by Monte Carlo methods can be applied in the 4D-Var data assimilation system through the proposal transition density
Summary
The Particle filter (PF) is a continuous-time sequential Monte Carlo method, which uses Monte. The estimation of the posterior PDF becomes simplified under those assumptions, which means the mean value is close to the peak and the covariance becomes much easier to calculate These implicit conditions and assumptions of the variational methods and the EnKF methods are unlikely to be satisfied in most real geophysical systems. The particle smoother has a kind of natural connection to weak constraint 4D-Var formulation, and implicit sampling by Monte Carlo methods can be applied in the 4D-Var data assimilation system through the proposal transition density. We introduce the implicit sampling and proposal transition density in the weak constraint 4D-Var framework, using a scale factor α to slightly adjust the covariance of the proposal density (P matrix) for the purpose of fulfilling the equal-weights.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
