Local volume solvers for Earth system data assimilation: Implementation in the framework for Joint Effort for Data Assimilation Integration

The Joint Effort for Data assimilation Integration (JEDI) is an international collaboration aimed at developing an open software ecosystem for model agnostic data assimilation. This paper considers implementation of the model-agnostic family of the local volume solvers in the JEDI framework. The implemented solvers include the Local Ensemble Transform Kalman Filter (LETKF), the Gain form of the Ensemble Transform Kalman Filter (GETKF), and the optimal interpolation variant of the LETKF (LETKF-OI). This paper documents the implementation strategy for the family of the local volume solvers within the JEDI framework. We also document an expansive set of localization approaches that includes generic distance-based localization, localization based on modulated ensemble products, and localizations specific to ocean (based on the Rossby radius of deformation), and land (based on the terrain difference between observation and model grid point). Finally, we apply the developed solvers in a limited set of experiments, including single-observation experiments in atmosphere and ocean, and cycling experiments for the atmosphere, ocean, land, and aerosol assimilation. We also illustrate how JEDI Ensemble Kalman Filter solvers can be used in a strongly coupled framework using the interface solver approximation, which provides increments to the ocean based on observations from the ocean and atmosphere.