AIMS Geosciences, 2015, 1(1): 41-78. doi: 10.3934/geosci.2015.1.41

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A Hybrid Monte Carlo Sampling Filter for Non-Gaussian Data Assimilation

Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24060, USA

Data assimilation combines information from models, measurements, and priors to obtain improved estimates of the state of a dynamical system such as the atmosphere. Ensemble-based data assimilation approaches such as the Ensemble Kalman filter (EnKF) have gained wide popularity due to their simple formulation, ease of implementation, and good practical results. Many of these methods are derived under the assumption that the underlying probability distributions are Gaussian. It is well accepted, however, that the Gaussianity assumption is too restrictive when applied to large nonlinear models, nonlinear observation operators, and large levels of uncertainty. When the Gaussianity assumptions are severely violated, the performance of EnKF variations degrades. This paper proposes a new ensemble-based data assimilation method, named the sampling filter, which obtains the analysis by sampling directly from the posterior distribution. The sampling strategy is based on a Hybrid Monte Carlo (HMC) approach that can handle non-Gaussian probability distributions. Numerical experiments are carried out using the Lorenz-96 model and observation operators with different levels of non-linearity and differentiability. The proposed filter is also tested with shallow water model on a sphere with linear observation operator. Numerical results show that the sampling filter performs well even in highly nonlinear situations where the traditional filters diverge.
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