Comparison of Hybrid-4DEnVar and Hybrid-4DVar Data Assimilation Methods for Global NWP

TLDR

The Met Office’s hybrid‑4DEnVar, an ensemble‑variational data assimilation scheme, was developed to replace the existing hybrid‑4DVar; both combine climatological and ensemble covariances but differ in error‑evolution modeling—hybrid‑4DVar uses a linear model and penalizes rapid analysis changes, whereas hybrid‑4DEnVar relies on localized nonlinear forecasts and lacks dynamical constraints. The study explores potential improvements to the hybrid‑4DEnVar method. The authors conduct idealized experiments comparing covariance evolution and introduce a four‑dimensional incremental analysis update (4DIAU) to suppress high‑frequency oscillations in hybrid‑4DEnVar increments. In operational trials, both hybrid methods outperform their 3D counterparts, but hybrid‑4DVar yields superior results, largely because it models climatological error evolution and penalizes rapid analysis changes, whereas hybrid‑4DEnVar does not.

Abstract

Abstract The Met Office has developed an ensemble-variational data assimilation method (hybrid-4DEnVar) as a potential replacement for the hybrid four-dimensional variational data assimilation (hybrid-4DVar), which is the current operational method for global NWP. Both are four-dimensional variational methods, using a hybrid combination of a fixed climatological model of background error covariances with localized covariances from an ensemble of current forecasts designed to describe the structure of “errors of the day.” The fundamental difference between the methods is their modeling of the time evolution of errors within each data assimilation window: 4DVar uses a linear model and its adjoint and 4DEnVar uses a localized linear combination of nonlinear forecasts. Both hybrid-4DVar and hybrid-4DEnVar beat their three-dimensional versions, which are equivalent, in NWP trials. With settings based on the current operational system, hybrid-4DVar performs better than hybrid-4DEnVar. Idealized experiments designed to compare the time evolution of covariances in the methods are described: the basic 4DEnVar represents the evolution of ensemble errors as well as 4DVar. However, 4DVar also represents the evolution of errors from the climatological covariances, whereas 4DEnVar does not. This difference is the main cause of the superiority of hybrid-4DVar. Another difference is that the authors’ 4DVar explicitly penalizes rapid variations in the analysis increment trajectory, while the authors’ 4DEnVar contains no dynamical constaints on imbalance. The authors describe a four-dimensional incremental analysis update (4DIAU) method that filters out the high-frequency oscillations introduced by the poorly balanced 4DEnVar increments. Possible methods for improving hybrid-4DEnVar are discussed.