Impact of surface data assimilation using an ensemble Kalman filter technique on the improvement of weather prediction

Abstract Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics. The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

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E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

Monthly Weather Review ◽

10.1175/mwr-d-11-00023.1 ◽

2012 ◽

Vol 140 (2) ◽

pp. 587-600 ◽

Cited By ~ 69

Author(s):

Meng Zhang ◽

Fuqing Zhang

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Prediction Model ◽

Ensemble Kalman Filter ◽

Weather Prediction ◽

Coupled System ◽

Limited Area ◽

Ensemble Forecasts ◽

Background Error ◽

Hybrid Data Assimilation

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

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Convective-Scale Data Assimilation for the Weather Research and Forecasting Model Using the Local Particle Filter

Monthly Weather Review ◽

10.1175/mwr-d-16-0298.1 ◽

2017 ◽

Vol 145 (5) ◽

pp. 1897-1918 ◽

Cited By ~ 20

Author(s):

Jonathan Poterjoy ◽

Ryan A. Sobash ◽

Jeffrey L. Anderson

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Weather Prediction ◽

Squall Line ◽

Monte Carlo Data ◽

Mixing Ratios ◽

Convective Scale ◽

Non Gaussian ◽

Mean Square Errors

Abstract Particle filters (PFs) are Monte Carlo data assimilation techniques that operate with no parametric assumptions for prior and posterior errors. A data assimilation method introduced recently, called the local PF, approximates the PF solution within neighborhoods of observations, thus allowing for its use in high-dimensional systems. The current study explores the potential of the local PF for atmospheric data assimilation through cloud-permitting numerical experiments performed for an idealized squall line. Using only 100 ensemble members, experiments using the local PF to assimilate simulated radar measurements demonstrate that the method provides accurate analyses at a cost comparable to ensemble filters currently used in weather models. Comparisons between the local PF and an ensemble Kalman filter demonstrate benefits of the local PF for producing probabilistic analyses of non-Gaussian variables, such as hydrometeor mixing ratios. The local PF also provides more accurate forecasts than the ensemble Kalman filter, despite yielding higher posterior root-mean-square errors. A major advantage of the local PF comes from its ability to produce more physically consistent posterior members than the ensemble Kalman filter, which leads to fewer spurious model adjustments during forecasts. This manuscript presents the first successful application of the local PF in a weather prediction model and discusses implications for real applications where nonlinear measurement operators and nonlinear model processes limit the effectiveness of current Gaussian data assimilation techniques.

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A Non-Gaussian Ensemble Filter Update for Data Assimilation

Monthly Weather Review ◽

10.1175/2010mwr3253.1 ◽

2010 ◽

Vol 138 (11) ◽

pp. 4186-4198 ◽

Cited By ~ 59

Author(s):

Jeffrey L. Anderson

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Sampling Error ◽

Weather Prediction ◽

Large Ensembles ◽

Stochastic Filter ◽

Pathological Behavior ◽

Non Gaussian ◽

Observation Space

Abstract A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability distribution in a fashion analogous to the use of rank histograms for ensemble forecast evaluation. This rank histogram filter can represent non-Gaussian observation space priors and posteriors and is shown to be competitive with existing filters for problems as large as global numerical weather prediction. The ability to represent non-Gaussian distributions is useful for a variety of applications such as convective-scale assimilation and assimilation of bounded quantities such as relative humidity.

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E3DVar: Coupling an Ensemble Kalman Filter with Three-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model and Comparison to E4DVar

Monthly Weather Review ◽

10.1175/mwr-d-12-00075.1 ◽

2013 ◽

Vol 141 (3) ◽

pp. 900-917 ◽

Cited By ~ 51

Author(s):

Fuqing Zhang ◽

Meng Zhang ◽

Jonathan Poterjoy

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Weather Prediction ◽

Three Dimensional ◽

Variational Data Assimilation ◽

Lead Times ◽

Limited Area ◽

Model Errors ◽

Mean Square Errors

Abstract This study examines the performance of a hybrid ensemble-variational data assimilation system (E3DVar) that couples an ensemble Kalman filter (EnKF) with the three-dimensional variational data assimilation (3DVar) system for the Weather Research and Forecasting (WRF) Model. The performance of E3DVar and the component EnKF and 3DVar systems are compared over the eastern United States for June 2003. Conventional sounding and surface observations as well as data from wind profilers, aircraft and ships, and cloud-tracked winds from satellites, are assimilated every 6 h during the experiments, and forecasts are verified using standard sounding observations. Forecasts with 12- to 72-h lead times are found to have noticeably smaller root-mean-square errors when initialized with the E3DVar system, as opposed to the EnKF, especially for the 12-h wind and moisture fields. The E3DVar system demonstrates similar performance as an EnKF, while using less than half the number of ensemble members, and is less sensitive to the use of a multiphysics ensemble to account for model errors. The E3DVar system is also compared with a similar hybrid method that replaces the 3DVar component with the WRF four-dimensional variational data assimilation (4DVar) method (denoted E4DVar). The E4DVar method demonstrated considerable improvements over E3DVar for nearly all model levels and variables at the shorter forecast lead times (12–48 h), but the forecast accuracies of all three ensemble-based methods (EnKF, E3DVar, and E4DVar) converge to similar results at longer lead times (60–72 h). Nevertheless, all methods that used ensemble information produced considerably better forecasts than the two methods that relied solely on static background error covariance (i.e., 3DVar and 4DVar).

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Data Assimilation Using an Ensemble Kalman Filter Technique

Monthly Weather Review ◽

10.1175/1520-0493(1998)126<0796:dauaek>2.0.co;2 ◽

1998 ◽

Vol 126 (3) ◽

pp. 796-811 ◽

Cited By ~ 967

Author(s):

P. L. Houtekamer ◽

Herschel L. Mitchell

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Filter Technique

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Pseudo-Orbit Data Assimilation. Part I: The Perfect Model Scenario

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-13-032.1 ◽

2014 ◽

Vol 71 (2) ◽

pp. 469-482 ◽

Cited By ~ 11

Author(s):

Hailiang Du ◽

Leonard A. Smith

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

State Estimation ◽

Ensemble Kalman Filter ◽

Weather Forecasting ◽

Weather Prediction ◽

Attractive Alternative ◽

Perfect Model ◽

Improved Performance ◽

Orbit Data

Abstract State estimation lies at the heart of many meteorological tasks. Pseudo-orbit-based data assimilation provides an attractive alternative approach to data assimilation in nonlinear systems such as weather forecasting models. In the perfect model scenario, noisy observations prevent a precise estimate of the current state. In this setting, ensemble Kalman filter approaches are hampered by their foundational assumptions of dynamical linearity, while variational approaches may fail in practice owing to local minima in their cost function. The pseudo-orbit data assimilation approach improves state estimation by enhancing the balance between the information derived from the dynamic equations and that derived from the observations. The potential use of this approach for numerical weather prediction is explored in the perfect model scenario within two deterministic chaotic systems: the two-dimensional Ikeda map and 18-dimensional Lorenz96 flow. Empirical results demonstrate improved performance over that of the two most common traditional approaches of data assimilation (ensemble Kalman filter and four-dimensional variational assimilation).

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Application of the Ensemble Kalman Filter to a One-Dimensional Linear Advection Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.804.287 ◽

2015 ◽

Vol 804 ◽

pp. 287-290

Author(s):

Somsiri Payakkarak ◽

Dusadee Sukawat

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Weather Prediction ◽

Atmospheric Model ◽

Ensemble Member ◽

Observation Data ◽

State Estimate ◽

One Dimensional ◽

Weather Forecasts

Data assimilation is used in numerical weather prediction to improve weather forecasts by incorporating observation data into the model forecast. The Ensemble Kalman Filter (EnKF) is a method of data assimilation which updates an ensemble of states to provide a state estimate and associated error at each step. The atmospheric model that is used in this research is a one-dimensional linear advection model. This model describes the motion of a scalar field as it is advected by a known speed field. The result shows that by selecting appropriate initial ensemble, model noise and measurement perturbations, it is possible to achieve a significant improvement in the EnKF results. The accuracy of the EnKF increases when the number of ensemble member grows. That is, the larger ensemble sizes perform better than those of smaller sizes.

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Assessing the Performance of the Ensemble Kalman Filter for Land Surface Data Assimilation

Monthly Weather Review ◽

10.1175/mwr3153.1 ◽

2006 ◽

Vol 134 (8) ◽

pp. 2128-2142 ◽

Cited By ~ 90

Author(s):

Yuhua Zhou ◽

Dennis McLaughlin ◽

Dara Entekhabi

Keyword(s):

Soil Moisture ◽

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

Land Surface ◽

Conditional Moments ◽

Surface Data ◽

Distributional Information ◽

Importance Resampling ◽

Efficient Option

Abstract The ensemble Kalman filter provides an easy-to-use, flexible, and efficient option for data assimilation problems. One of its attractive features in land surface applications is its ability to provide distributional information about variables, such as soil moisture, that can be highly skewed or even bimodal. The ensemble Kalman filter relies on normality approximations that improve its efficiency but can also compromise the accuracy of its distributional estimates. The effects of these approximations can be evaluated by comparing the conditional marginal distributions and moments estimated by the ensemble Kalman filter with those obtained from a sequential importance resampling (SIR) particle filter, which gives exact solutions for large ensemble sizes. Comparisons for two land surface examples indicate that the ensemble Kalman filter is generally able to reproduce nonnormal soil moisture behavior, including the skewness that occurs when the soil is either very wet or very dry. Its conditional mean estimates are very close to those generated by the SIR filter. Its higher-order conditional moments are somewhat less accurate than the means. Overall, the ensemble Kalman filter appears to provide a good approximation for nonlinear, nonnormal land surface problems, despite its dependence on normality assumptions.

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