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)

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 Unstructured Mesh Package (BUMP), which is one of the 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.