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 1 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 U.S. National Weather Service.

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, assume that the analysis resulting from the data assimilation lies in the same subspace as the expected forecast error. Under our hypothesis the dimension of this subspace is low. This implies that operations only on relatively low dimensional matrices are required. Thus, the data analysis is done 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. 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.

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The accuracy and computational efficiency of a parallel computer implementation of the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme on the model component of the 2004 version of the Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) is investigated. Numerical experiments are carried out at model resolution T62L28. All atmospheric observations that were operationally assimilated by NCEP in 2004, except for satellite radiances, are assimilated with the LETKF. The accuracy of the LETKF analyses is evaluated by comparing it to that of the Spectral Statistical Interpolation (SSI), which was the operational global data assimilation scheme of NCEP in 2004. For the selected set of observations, the LETKF analyses are more accurate than the SSI analyses in the Southern Hemisphere extratropics and are comparably accurate in the Northern Hemisphere extratropics and in the Tropics. The computational wall‐clock times achieved on a Beowulf cluster of 3.6 GHz Xeon processors make our implementation of the LETKF on the NCEP GFS a widely applicable analysis‐forecast system, especially for research purposes. For instance, the generation of four daily analyses at the resolution of the NCAR‐NCEP reanalysis (T62L28) for a full season (90 d), using 40 processors, takes less than 4 d of wall‐clock time.

Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively accounted for at low computational expense. In the case of linear dynamics, the technique is equivalent to instantaneously assimilating data as they are measured. The results of numerical tests of the technique on a simple model problem are shown.

The accuracy and computational efficiency of the recently proposed local ensemble Kalman filter (LEKF) data assimilation scheme is investigated on a state-of-the-art operational numerical weather prediction model using simulated observations. The model selected for this purpose is the T62 horizontal-and 28-level vertical-resolution version of the Global Forecast System (GFS) of the National Center for Environmental Prediction. The performance of the data assimilation system is assessed for different configurations of the LEKF scheme. It is shown that a modest size (40-member) ensemble is sufficient to track the evolution of the atmospheric state with high accuracy. For this ensemble size, the computational time per analysis is less than 9 min on a cluster of PCs. The analyses are extremely accurate in the mid-latitude storm track regions. The largest analysis errors, which are typically much smaller than the observational errors, occur where parametrized physical processes play important roles. Because these are also the regions where model errors are expected to be the largest, limitations of a real-data implementation of the ensemble-based Kalman filter may be easily mistaken for model errors. In light of these results, the importance of testing the ensemble-based Kalman filter data assimilation systems on simulated observations is stressed.

A B S T R A C T Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively accounted for at low computational expense. In the case of linear dynamics, the technique is equivalent to instantaneously assimilating data as they are measured. The results of numerical tests of the technique on a simple model problem are shown.

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