Comparison of hybrid four-dimensional data assimilation methods with and without an adjoint model for limited-area convection-permitting weather prediction: E4DVar vs. 4DEnVar

Recent advancements in data assimilation research have lead to the coupling of ensemble and variational methods that take into account both flow-dependent and climatological background errors. The current study investigates systematic differences between two commonly used strategies for incorporating ensemble information in 4DVar for limited-area modeling. The first method, denoted E4DVar (Zhang and Zhang 2012; Poterjoy and Zhang 2014), incorporates ensemble covariance in the cost function, which is then minimized in the same manner as the traditional 4DVar approach. The second method, denoted 4DEnVar (Liu et al. 2009), replaces the function of tangent linear and adjoint models with an ensemble of nonlinear model trajectories. The sampling approximation made in 4DEnVar improves the parallelization of the algorithm; however, it is still debatable whether avoiding the use of tangent linear and adjoint models to propagate the full-ranked covariance matrix could limit the effectiveness of this method. Issues related to sampling errors introduced in 4DEnVar, such as the need of a temporal localization scheme, clearly demand further comparison between E4DVar and 4DEnVar for their advantages and limitations.

In a recent study, Poterjoy and Zhang (2015) used E4DVar and 4DEnVar to generate a reanalysis of Hurricane Karl (2010) from the pre-genesis to mature stages of the storm's development. Both methods provided qualitatively similar synoptic and meso-α scale analyses of Karl's kinematic structure; however, subtle differences in moisture and inner-core storm structure in the analyses lead to significant differences in how well each method predicted Karl's intensification. These results motivate an investigation into how E4DVar and 4DEnVar assimilate observations at the convective-scale. In this study, we systematically compare E4DVar and 4DEnVar for limited-area convection-permitting numerical weather prediction based on the Weather Research and Forecasting (WRF) model. Both hybrid systems assimilate conventional and satellite-retrieved soundings and cloud-tracked winds every 3 h during the Dynamics of Madden-Julian Oscillation (DYNAMO) field campaign. The simulation period features an MJO active phase with finer-scale convectively coupled equatorial waves. Analyses and forecasts are verified using both standard sounding observations and extensive field observations from DYNAMO. Also considered will be the comparison of the two hybrid methods in assimilating Doppler radar observations for the convective scale.