Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

By Brian R. Hunt, Eric J. Kostelich, Istvan Szunyogh. 2005

1,617 citations recorded by the source corpus.

Abstract Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, we describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “ensemble Kalman filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. We discuss both the mathematical basis of this approach and its implementation; our primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. We include some numerical results demonstrating the efficiency and accuracy of our implementation for assimilating real atmospheric data with the global forecast model used by the US National Weather Service.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/f465f81c6547c8688b414fbb7786eaba52527567

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Citations in the corpus

An Iterative EnKF for Strongly Nonlinear Systems (2012, methodology): “…EnKF can be easily adopted to assimilate asynchronous observations by simply using in the analysis the ensemble observations H(E) estimated at the time of each observation (Hunt et al. 2007), provided that propagation of the ensemble anomalies about the truth is mainly linear (Sakov et al. 2010).”
Data assimilation: making sense of Earth Observation (2014, methodology): “Advances in the EnKF include the square-root filter (Anderson, 2001; Whitaker and Hamill, 2002), the Ensemble Transform Kalman filter, ETKF (Bishop et al., 2001) and local Ensemble Kalman filtering (Ott et al., 2004; Hunt et al., 2007).”
A non-linear least squares enhanced POD-4DVar algorithm for data assimilation (2015, methodology): “…contrary, ensemble Kalman filter (EnKF; cf. Evensen, 1994, 2004; Houtekamer and Mitchell, 1998; Keppenne, 2000; Anderson, 2001; Houtekamer andMitchell, 2001; Whitaker and Hamill, 2002; Ott et al., 2004; Zhang et al., 2004; Hunt et al., 2007) provides another advanced method for data assimilation.”
The local ETKF and SKEB: Upgrades to the MOGREPS short‐range ensemble prediction system (2009, methodology): “Applying the method of Hunt et al. (2007) to remove this sharp jump would be a useful addition to our method.”
Localization and regularization for iterative ensemble smoothers (2017, methodology): “[20], the other is tapering of the local Kalman gain.”
Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter (2009, methodology): “More details about the LETKF are available in Hunt et al. (2007) and Szunyogh et al. (2008).”
The Non-hydrostatic Icosahedral Atmospheric Model: description and development (2014, methodology): “Furthermore, the local ensemble transform Kalman filter (LETKF) (Hunt et al. 2007) was developed based on the ensemble transform Kalman filter (ETKF) (Bishop et al. 2001) and used an algorithm that was designed for suitability with parallel computers by taking advantage of the independent local…”
Adaptive Ensemble Covariance Localization in Ensemble 4D-VAR State Estimation (2011, methodology): “To illustrate AECL methods within the context of a global numerical weather prediction model, Bishop and Hodyss (2007, 2009b) incorporated them into a large observation volume local ensemble Kalman filter (Ott et al. 2004; Hunt et al. 2007).”
Ensemble Kalman filtering without the intrinsic need for inflation (2011, methodology): “In the following, the focus will be on the ensemble transform Kalman filter (ETKF) variant, following Hunt et al.(2007).”
Enhanced Adaptive Inflation Algorithm for Ensemble Filters (2018, background): “Inflation has been introduced into stochastic (e.g., EnKF) and deterministic (e.g., Anderson 2001; Hoteit et al. 2002; Whitaker and Hamill 2002; Hunt et al. 2007; Sakov and Oke 2008) ensemble filters as a way to counteract the underestimation of the true variance.”
“Variable localization” in an ensemble Kalman filter: Application to the carbon cycle data assimilation (2011, methodology): “[3] The local ensemble transform Kalman filter (LETKF) [ Hunt et al., 2007 ], like other ensemble Kalman filter (EnKF) methods [e.g., Evensen, 1994; Houtekamer and Mitchell, 2001; Anderson, 2001; Bishop et al., 2001; Whitaker and Hamill, 2002; Ott et al., 2004, Zupanski, 2005], produces an analysis ”
A local particle filter for high-dimensional geophysical systems (2015, methodology): “While at first this may seem an advantage rather than a limitation, the computational cost of the local ensemble transform Kalman filter (LETKF) (Hunt et al., 2007), for example, increases at a rateO(k3) with the ensemble size k.”
Asynchronous data assimilation with the EnKF (2010, methodology): “Later, a simpler method called 4D-LETKF has been used in Hunt et al. (2007).”
Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation (2015, methodology): “With this restriction to N⊥, the prior of the ETKF defined over N⊥ is p(w̃)∝ exp ( − N − 1 2 ‖w̃‖2 ) , (17) whereas the prior pdf of the EnKF-N is p(w̃)∝ ( εN +‖w̃‖ 2 )−N 2 .”
Local Ensemble Transform Kalman Filtering with an AGCM at a T159/L48 Resolution (2007, methodology): “Initialization procedures to omit artificial fast oscillations caused by imbalance in initial conditions were not applied in this study as in Miyoshi (2005) and Szunyogh et al.”