Three-dimensional variational assimilation with a multivariate background error covariance for the Model for Prediction Across Scales–Atmosphere with the Joint Effort for data Assimilation Integration (JEDI-MPAS 2.0.0-beta)

Abstract

Abstract. This paper describes the three-dimensional variational (3DVar) data assimilation (DA) system for the Model for Prediction Across Scales-Atmosphere with the Joint Effort for data Assimilation Integration (JEDI-MPAS). Its core element is a multivariate background error covariance implemented through multiple linear variable changes, including a wind variable change from stream function and velocity potential to zonal and meridional wind components, a vertical linear regression representing wind-mass balance, and multiplication by a diagonal matrix of error standard deviations. The univariate spatial correlations for the ``unbalanced'' variables utilize the Background error on an Unstructured Mesh Package (BUMP), which is one of generic components in the JEDI framework. The variable changes and univariate correlations are modeled directly on the native MPAS unstructured mesh. BUMP provides utilities to diagnose parameters of the covariance model, such as correlation lengths, from an ensemble of forecast differences, though some manual adjustment of the parameters is necessary because of mismatches between the univariate correlation function assumed by BUMP and the correlation structure in the sample of forecast differences. The resulting multivariate covariances, as revealed by single-observation tests, are qualitatively similar to those found in previous global 3DVar systems. Month-long cycling DA experiments using a global quasi-uniform 60 km mesh demonstrate that 3DVar, as expected, performs somewhat worse than a pure ensemble-based covariance, while a hybrid covariance that combines that used in 3DVar with the ensemble covariance, significantly outperforms both 3DVar and the pure ensemble covariance. Due to its simple workflow and minimal computational requirements, the JEDI-MPAS 3DVar can be useful for the research community.

Data assimilation for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS 2.0.0-beta): ensemble of 3D ensemble-variational (En-3DEnVar) assimilations

“…It is useful to further explore the impacts of using a hybrid BEC because that algorithmic enhancement is readily adaptable to future EDA applications. Therefore, we first compare eda75c25 to eda100 to demonstrate the benefits of additionally accounting for climatological BECs and then to gefs100 to show the total impact of developments herein and in Jung et al (2023).…”

“…There is one hybrid 3DEnVar experiment, eda75c25, that uses a mixture of 75 % EDA ensemble and 25 % climatological BEC. The climatological BEC, B c , is identical to the one described by Jung et al (2023). B c is trained using the National Meteorological Center (NMC) method (Parrish and Derber, 1992) with 366 samples of 48 h minus 24 h GFS forecast differences.…”

“…2.1 for more details) are scaled by 1/2 to account for differences between the sampled correlation versus separation distance relationship and the Gaspari-Cohn fitting function used in BUMP. More details can be found in Jung et al (2023).…”

“…A further refinement, which improves relative to using the EDA in EnVar alone and across almost all latitudes and heights, is the use of a hybrid BEC that is a weighted sum of the ensemble covariances and the static covariances of Jung et al (2023). With this refinement, the system is ready to produce research-quality ensembles for future sensitivity studies that aim to enhance JEDI-MPAS.…”

“…The ensemble BEC, B e , is represented by prior perturbations (before assimilation) in those same analysis variables with respect to the prior ensemble mean. As described in Jung et al (2023), B c is constructed by applying linear transformations that yield the analysis variables from stream function, velocity potential, and the "unbalanced" contributions to temperature and surface pressure together with the assumption that background errors in those underlying variables are mutually independent and have known isotropic covariances (Derber and Bouttier, 1999). B c is implemented via generic JEDI interfaces to the Background error on Unstructured Mesh Package (BUMP; Ménétrier, 2020).…”