Data assimilation using an ensemble Kalman filter technique (original) (raw)
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Monthly Weather Review, 2007
This dissertation examines the performance of an ensemble Kalman filter (EnKF) implemented in a mesoscale model in increasingly realistic contexts from under a perfect model assumption and in the presence of significant model error with synthetic observations to real-world data assimilation in comparison to the three-dimensional variational (3DVar) method via both case study and month-long experiments. The EnKF is shown to be promising for future application in operational data assimilation practice. The EnKF with synthetic observations, which is implemented in the mesoscale model MM5, is very effective in keeping the analysis close to the truth under the perfect model assumption. The EnKF is most effective in reducing larger-scale errors but less effective in reducing errors at smaller, marginally resolvable scales. In the presence of significant model errors from physical parameterization schemes, the EnKF performs reasonably well though sometimes it can be significantly degraded compared to its performance under the perfect model assumption. Using a combination of different physical parameterization schemes in the ensemble (the so-called "multi-scheme" ensemble) can significantly improve filter performance due to the resulting better background error covariance and a smaller ensemble bias. The EnKF performs differently for different flow regimes possibly due to scale- and flow-dependent error growth dynamics and predictability. Real-data (including soundings, profilers and surface observations) are assimilated by directly comparing the EnKF and 3DVar and both are implemented in the Weather Research and Forecasting model. A case study and month-long experiments show that the EnKF is efficient in tracking observations in terms of both prior forecast and posterior analysis. The EnKF performs consistently better than 3DVar for the time period of interest due to the benefit of the EnKF from both using ensemble mean for state estimation and using a flow-dependent background error covariance. Proper covariance inflation and using a multi-scheme ensemble can significantly improve the EnKF performance. Using a multi-scheme ensemble results in larger improvement in thermodynamic variables than in other variables. The 3DVar system can benefit substantially from using a short-term ensemble mean for state estimate. Noticeable improvement is also achieved in 3DVar by including some flow dependence in its background error covariance.
A Data Assimilation Case Study Using a Limited-Area Ensemble Kalman Filter
Monthly Weather Review, 2007
Ensemble Kalman filter (EnKF) data assimilation experiments are conducted on a limited-area domain over the Pacific Northwest region of the United States, using the Weather Research and Forecasting model. Idealized surface pressure, radiosoundings, and aircraft observations are assimilated every 6 h for a 7-day period in January 2004. The objectives here are to study the performance of the filter in constraining analysis errors with a relatively inhomogeneous, sparse-observation network and to explore the potential for such a network to serve as the basis for a real-time EnKF system dedicated to the Pacific Northwest region of the United States. When only a single observation type is assimilated, results show that the ensemble-mean analysis error and ensemble spread (standard deviation) are significantly reduced compared to a control ensemble without assimilation for both observed and unobserved variables. Analysis errors are smaller than background errors over nearly the entire domain when averaged over the 7-day period. Moreover, comparisons of background errors and observation increments at each assimilation step suggest that the flow-dependent filter corrections are accurate in both scale and amplitude. An illustrative example concerns a misspecified mesoscale 500-hPa short-wave trough moving along the British Columbia coast, which is corrected by surface pressure observations alone. The relative impact of each observation type upon different variables and vertical levels is also discussed.
A local ensemble Kalman filter for atmospheric data assimilation
Tellus A, 2004
A B S T R A C T 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.
Russian Journal of Numerical Analysis and Mathematical Modelling, 2013
Recently, ensemble Kalman filters have come into practical data assimilation for numerical weather prediction models. We give an overview of ensemble Kalman filters and problems that arise with practical implementation of ensemble methods. We present our implementation of the local ensemble transform Kalman filter, one of ensemble square root filters using observation localization. Multiplicative and additive inflations are used to prevent filter divergence and to account for the model error. The implemented assimilation system is tested with the global semi-Lagrangian atmospheric model SL-AV using real observations for 2 months of cyclic assimilation (August and September 2012). The system works stably. Application of the ensemble filter significantly reduces first guess (background) errors and corrects the forecast biases. Numerical weather prediction models require estimates of the initial state of the atmosphere as input data. Data assimilation is a cyclic process to obtain such estimates (analyses) by improving first guess (also called background) estimates with available atmospheric observations. Data assimilation methods use the first guess and observations together with the information on their error distributions to seek for the best possible estimate in some sense (for example, maximum a posteriori estimate, or minimum variance estimate). Data assimilation consists of two steps, i.e., the analysis step: obtaining
2010
The quality of convective-scale ensemble forecasts, initialized from analysis ensembles obtained through the assimilation of radar observations using an ensemble Kalman filter (EnKF), is investigated for cases whose behaviors span supercellular, linear, and multicellular organization. This work is the companion to Part I, which focused on the quality of analyses during the 60-min analysis period. Here, the focus is on 30-min ensemble forecasts initialized at the end of that period. As in Part I, the Weather Research and Forecasting (WRF) model is employed as a simplified cloud model at 2-km horizontal grid spacing. Various observationspace and state-space verification metrics, computed both for ensemble means and individual ensemble members, are employed to assess the quality of ensemble forecasts comparatively across cases. While the cases exhibit noticeable differences in predictability, the forecast skill in each case, as measured by various metrics, decays on a time scale of tens of minutes. The ensemble spread also increases rapidly but significant outlier members or clustering among members are not encountered. Forecast quality is seen to be influenced to varying degrees by the respective initial soundings. While radar data assimilation is able to partially mitigate some of the negative effects in some situations, the supercell case, in particular, remains difficult to predict even after 60 min of data assimilation.
Proceedings of the …, 2007
This paper describes the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme and its implementation on the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model at the University of Maryland. Numerical results are shown for both simulated observations and observations of the real atmosphere. The role of flow-dependent information in data assimilation is discussed based on the results of the numerical experiments. Preliminary assimilation results with AMSU-A radiance observations are also presented.
Tellus A, 2005
A B S T R A C T 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 multi-model ensemble Kalman filter for data assimilation and forecasting
arXiv (Cornell University), 2022
Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi-model ensemble Kalman filter (MM-EnKF) based on this framework. The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner; it uses adaptive model error estimation to provide matrix-valued weights for the separate models and the observations. We apply this methodology to various situations using the Lorenz96 model for illustration purposes. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM-EnKF results in significant error reductions compared to the best model, as well as to an unweighted multi-model ensemble, with respect to both probabilistic and deterministic error metrics.
Initiation of ensemble data assimilation
2005
The specification of the initial ensemble for ensemble data assimilation is addressed. The presented work examines the impact of ensemble initiation in the Maximum Likelihood Ensemble Filter (MLEF) framework, but is also applicable to other ensemble data assimilation algorithms. Two methods are considered: the first is based on the use of the Kardar-Parisi-Zhang (KPZ) equation to form sparse random perturbations, followed by spatial smoothing to enforce desired correlation structure, while the second is based on the spatial smoothing of initially uncorrelated random perturbations. Data assimilation experiments are conducted using a global shallow-water model and simulated observations. The two proposed methods are compared to the commonly used method of uncorrelated random perturbations. The results indicate that the impact of the initial correlations in ensemble data assimilation is beneficial. The root-mean-square error rate of convergence of the data assimilation is improved, and the positive impact of initial correlations is notable throughout the data assimilation cycles. The sensitivity to the choice of the correlation length scale exists, although it is not very high. The implied computational savings and improvement of the results may be important in future realistic applications of ensemble data assimilation.