|Stochastic Systems Group|
Yuhua Zhou - McLaughlin Research Group, MIT
Nonlinearity, high dimensionality, and complexity in the uncertainties of parameters and inputs of land surface model render land surface data assimilation a hard problem. Traditional approaches to assimilate measurements into a land surface model are based on Monte Carlo simulation of the nonlinear dynamics. Available estimation methods such as Ensemble Kalman Filters and Particle Filters use the simulated ensemble by the dynamic model as prior information. However, only a limited number of replicates can be generated for large problems. The resulting sampling errors are inevitable. Leaving the sampling error unattended would cause serious error in the estimates. Also, time varying spatial correlation of the states may exist across many scales due to moving rainfall input and land surface system dynamics. The resulting spectrum of the state covariance matrix would also change accordingly. To employ more spatial correlation and the feature of dynamic spectrum of the land surface system, a reduced rank approximation approach can be used to improve the efficiency of large scale estimation. An ensemble multiscale tree can be identified at any measurement time, and then fast estimation on the tree can be performed to generate posterior ensemble in order for the forward state propagation. The estimation on the tree is helped with the scale recursive innovation propagation and the internal tree model structure. It is feasible for large scale state estimation given any kind of correlated or uncorrelated multiresolution measurements. Preliminary results show that the new method is efficient and has higher accuracy. The improvements mainly depend on the tree identified for the approximation of the prior ensemble.
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