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

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).

DEnKF–Variational Hybrid Snow Cover Fraction Data Assimilation for Improving Snow Simulations with the Common Land Model

“…For snow data assimilation (DA), a two-way coupled DEnKF-1DVar hybrid method (DEnVar) patterned after Zhang et al [36] is proposed. Two-way coupling re-centers the DEnKF analysis ensemble mean with the 1DVar analysis.…”

“…Such re-centering may help to prevent the divergence of the DEnKF analyses so that the ensemble perturbations empirically represent the distribution of the forecast errors. Unlike the EnVar method (hybrid ensemble-variational DA) of Zhang et al [36], the two-step DEnVar method without observation perturbations in Figure 1 includes three steps: (1) the DEnKF analysis is implemented to generate the analysis ensemble mean ̅ and the analysis error covariance , (2) the analysis ensemble mean ̅ is used as the first guess for the 1DVar and the analysis error covariance is introduced into the 1DVar hybrid cost function, and (3) the analysis ensemble mean ̅ of DEnKF is replaced with the 1DVar analysis for the next ensemble forecast. The hybrid error covariance is included in the hybrid cost function by separating the Jb in Equation (1) into two parts [28,51]: (11) where Jb1 stands for the traditional 1DVar background term as in Equation (1) and Jb2 for the ensemble-based term.…”

“…For the hybrid method, the ensemble covariance generated from the ensemble-based DA system is easily incorporated into the hybrid cost function of variational DA. The hybrid DA system can conform well to the existing variational framework and be more flexible than the conventional ensemble-based methods for exploring sampling errors and model errors [36]. Recent studies have also demonstrated the potential of the hybrid method as compared with the stand-alone EnKF and variational methods (e.g., [32,37,38]).…”

“…In recent decades, a hybrid DA method of utilizing advanced features of both ensemble-based and variational DA methods has been proposed (e.g., [28][29][30][31][32]) for numerical weather prediction (e.g., [33][34][35][36]). For the hybrid method, the ensemble covariance generated from the ensemble-based DA system is easily incorporated into the hybrid cost function of variational DA.…”

“…As a comparison with the other three DA methods-DEnKF, 1DVar, and EnVar (hybrid ensemble-variational DA)-the DEnVar method was used at five sites in the Altay region of China from November 2008 to March 2009. The EnVar method is similar to the method of Zhang et al [36]. We performed sensitivity tests on the hybrid error covariance weight and the observation errors.…”