A local ensemble Kalman filter for atmospheric data assimilation

2002

302 citations recorded by the source corpus.

In this paper, we introduce a new, local formulation of the ensemble Kalman filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth’s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region. Ensemble Kalman filters, in general, take the analysis resulting from the data assimilation to lie in the same subspace as the expected forecast error. Under our hypothesis the dimension of the subspace corresponding to local regions is low. This is used in our scheme to allow operations only on relatively low-dimensional matrices. The data assimilation analysis is performed locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states for advancement to the next forecast time. One advantage, which may take on more importance as ever-increasing amounts of remotely-sensed satellite data become available, is the favorable scaling of the computational cost of our method with increasing data size, as compared to other methods that assimilate data sequentially. The method, its potential advantages, properties, and implementation requirements are illustrated by numerical experiments on the Lorenz-96 model. It is found that accurate analysis can be achieved at a cost which is very modest compared to that of a full global ensemble Kalman filter.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/5306d13c279d967146e7a33a67f6cfbc63b08a9c

Citations in the corpus

• Ensemble Kalman filtering (2005, unknown): “This strategy, proposed by Ott et al. (2004), leads to a more efficient parallelization.”
• Bayesian inverse problems for functions and applications to fluid mechanics (2009, unknown): “A widely used approach is that based on the ensemble Kalman filter [23] which uses an ensemble of particles to propagate the dynamics, but incorporates data using a Gaussian approximation which is hard to justify in general (see also [7, 56 ]).”
• Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters (2008, unknown): “Following Lorenz and Emanuel (1998), each model time step in our tests is conducted by a single step of the standard fourth-order Runge–Kutta integrator.”
• A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters (2008, unknown): “This model has been used for testing ensemble-based assimilation methods in a number of earlier studies (Anderson, 2001; Whitaker and Hamill, 2002; Ott et al., 2004; Lawson and Hansen, 2004).”
• A review of operational methods of variational and ensemble‐variational data assimilation (2017, unknown): “The latter method is used for instance in the local ensemble Kalman filter (Ott et al., 2004; Szunyogh et al., 2005) and with other ensemble DA techniques (Bishop et al.”
• Sampling the posterior: An approach to non-Gaussian data assimilation (2007, unknown): “However even this approximation is impractical for large d and further approximations, primarily to effect dimension reduction on the covariance matrix, are performed; this leads to the ensemble Kalman filter (EnKF) [9] and its generalizations [30].”
• Data Assimilation: A Mathematical Introduction (2015, unknown): “An important reference which links this concept firmly with ideas from dynamical systems is [94].”
• Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter (2009, unknown): “Following Ott et al. (2004), we use a cut-off-based localization with a local patch l = 6 which covers 13 model grid points.”
• Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, unknown): “The numerical feasibility of the approach has been demonstrated by Ott et al. (2004) and Hunt et al. (2007).”
• Localization and regularization for iterative ensemble smoothers (2017, unknown): “It is commonly used for data assimilation in atmospheric and oceanographic applications [1, 19, 26], but although several authors in petroleum engineering have used “regional analysis” [12, 30] and one paper has used local analysis with an observation cutoff [32], it appears that local analysis with”
• A Reanalysis of Ocean Climate Using Simple Ocean Data Assimilation (SODA) (2008, unknown): “…sophisticated alternatives, such as the four-dimensional variational algorithm and full Kalman filter have limitations in terms of high computational expense, increased sensitivity to the quality of the statistical assumptions, and for the full Kalman filter the potential for stability problems.”
• Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter (2005, unknown): “Since we only need to evaluate H in the ensemble space (or equivalently to evaluate H(x̄b + Xbw) for w in S̃), the simplest way to linearize H is to apply it to each of the ensemble members xb(i) and interpolate.”
• Inverse problems: A Bayesian perspective (2010, unknown): “…Kalman filter (Burgers, Van Leeuwen and Evensen 1998, Evensen and Van Leeuwen 2000, Evensen 2006), which uses an ensemble of particles to propagate the dynamics, but incorporates data using a Gaussian approximation which is hard to justify in general; see also Berliner (2001) and Ott et al. (2004).”