INTERCOMPARISON AND COUPLING OF ENSEMBLE-BASED AND VARIATIONAL DATA ASSIMILATION SCHEMES
Open Access
- Author:
- Zhang, Meng
- Graduate Program:
- Meteorology
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- October 04, 2010
- Committee Members:
- Fuqing Zhang, Dissertation Advisor/Co-Advisor
Fuqing Zhang, Committee Chair/Co-Chair
Eugene Edmund Clothiaux, Committee Member
Yvette Pamela Richardson, Committee Member
Xiaolong Zhang, Committee Member
Chris Snyder, Committee Member - Keywords:
- Data assimilation
EnKF
4DVar
Hybrid - Abstract:
- This dissertation aims to provide intercomparisons between ensemble-based and variational data assimilation schemes within a limited-area numerical weather prediction model. Hybrid algorithms that couple these two state-of-the-art data assimilation approaches are investigated in order to improve forecast skills. Firstly, an ensemble Kalman filter (EnKF) is compared with both three-dimensional and four-dimensional variational data assimilation methods (3DVar and 4DVar) for the weather research and forecasting (WRF) model over the contiguous United States in the warm-season month of June 2003. The data assimilated every 6 h include conventional sounding and surface observations as well as those from wind profilers, ships, aircraft and cloud-tracked winds. The performance of these data assimilation methods are evaluated through verifying the 12- to 72-h forecasts (initialized twice daily from the analysis of each method) against the standard sounding observations. It is found that the 4DVar has consistently smaller error than that of the 3DVar for winds and temperature at all forecast lead times except at 60 h and 72 h when their forecast errors become comparable in amplitude. Two schemes have similar performances for moisture at all lead times. The forecast error of the EnKF is comparable to that of the 4DVar at 12-to-36-h lead times, both of which are substantially smaller than that of the 3DVar, despite the 3DVar fitting the sounding observations much closer at the analysis time. The advantage of the EnKF becomes evident at 48-to-72-h lead times. A hybrid assimilation scheme, called E3DVar, that couples EnKF with 3DVar of the WRF model is implemented. The performance of this three-dimensional coupled system is examined in comparison with that of the standalone EnKF and 3DVar. In the control experiments with a 40-member multiple-physics-parameterization ensemble, the 12- to 72-h WRF forecasts initialized by the E3DVar analyses have slightly but noticeably smaller root-mean-square errors (RMSEs) than those initialized from the default-configured EnKF, especially in the wind and moisture fields. Both ensemble-based methods (i.e., EnKF and E3DVar), which estimate flow-dependent background error covariance, substantially outperform the default 3DVar with static background uncertainty. A series of sensitivity experiments are conducted and lead to following conclusions: the E3DVar may have similar performance to the standard EnKF but with a much smaller-size ensemble; the hybrid system is less demanding for using a multi-physics ensemble as a treatment of model error; additive inflation is helpful both for EnKF and E3DVar, due to the potential underestimation of the ensemble-based analysis errors. Coupling between EnKF and 4DVar is next implemented. This coupled scheme (E4DVar) benefits from using the flow-dependent uncertainty provided by EnKF while taking advantage of 4DVar in preventing filter divergence. The 4DVar analysis produces posterior maximum likelihood solutions through minimizing a cost function globally under linear dynamical constraints, about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an conceptual Lorenz (1996) model with simulated observations. The E4DVar outperforms the standalone 4DVar and the EnKF under both perfect- and imperfect-model scenarios. The performance of the E4DVar is also less sensitive to ensemble size and the assimilation window length than EnKF and 4DVar implementations, respectively. The E4DVar scheme is also implemented within the WRF model and again total on the warm season month of June 2003. In E4DVar, the ensemble-based multivariate background error covariance is incorporated into the 4DVar minimization via the alpha control transform, while the ensemble perturbations are updated in EnKF but their mean is replaced by the 4DVar analysis before the next forecast cycle. Therefore, the E4DVar can obtain flow-dependent information both from the explicit covariance matrix derived from ensemble forecasts and also its implicit counterpart modeled by the 4DVar trajectory. The capability of 4DVar in dealing with asynchronous and high-volume observations also makes the E4DVar more flexible and versatile. Based on the month-long statistical results, the E4DVar significantly outperforms the standalone assimilation methods; its 12-h forecast root mean square errors (RMSEs) that are consistently stay at a lower level than the others during the whole time period. The monthly mean results also demonstrate that the E4DVar leads to considerable forecast improvement against traditional data assimilation approaches up to a 60-h range, but becomes comparable to EnKF during the 60-72 h forecasts. The E4DVar is insensitive to tuning coefficients of background error covariance and has the capability to reduce sampling errors, which may make it more flexible for operational use. Finally, a case study exploring hurricane Katrina (2005) initialization and prediction is performed by 3DVar, 4DVar, EnKF and E4DVar via assimilation of Doppler radar observations into a high-resolution WRF model. The EnKF demonstrates great capability in delivering more accurate forecast at extended forecast-range up to 120 h. It is also shown a clear advantage of using the 4DVar method over the 3DVar both on improving the hurricane track forecast and resolving the dynamical structures. And the E4DVar method that couples the 4DVar and EnKF, is shown as a more robust and flexible data assimilation approach, which is insensitive to the quality of first-guess field.