Abstract
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 <em>sampling filter</em>, 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.
Highlights
Data assimilation (DA) is the process of combining information from models, measurements, and priors - all with associated uncertainties - in order to better describe the the true state of a physical system
Since Ensemble Kalman filter (EnKF) variations are the most popular ensemble-based algorithms in practice, we compare the new methodology against EnKF, maximum likelihood ensemble filter (MLEF), iterative ensemble Kalman filter (IEnKF)
We use the formulation of IEnKF presented in [47] to check the validity of the analysis produced by the sampling filter in the cases where nonlinear observation operators are used
Summary
Data assimilation (DA) is the process of combining information from models, measurements, and priors - all with associated uncertainties - in order to better describe the the true state of a physical system. A different approach to deal with nonlinear observations is to pose a nonlinear estimation problem in a subspace spanned by the ensemble members, and to compute the maximum a posteriori estimate in that subspace. This leads to the maximum likelihood ensemble filter (MLEF) proposed by Zupanski [60]. The “running in place” (RIP) EnKF scheme [33] uses a no-cost EnKS and repeatedly assimilates the observations over each assimilation window several times Another nonlinear extension of EnKF incorporates a non-linear change of variables (anamorphosis function) [50] and executes the analysis step in a space where the distributions of the transformed variables are Gaussian. The performance of EnKF, MLEF, and PF when observation operators are highly nonlinear was tested in [28, 29]
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