Analytical determination of optimal Hybrid parameters in realistic data-assimilation settings

Determine optimal parameters for Hybrid covariance models in realistic atmospheric data-assimilation contexts, where no analytical solution is known, including systems using realistic atmospheric models, nonlinear observation operators with sparse observational networks, simultaneous tuning of multiple parameters, and current or novel advanced Hybrid formulations.

Background

The paper introduces the hypervariational method as an automated procedure for tuning parameters of Hybrid covariance models using a time series of innovations and cost-function minimization. The analytical expression for the optimal ensemble-covariance weight derived in the paper is restricted to the synthetic experimental setting, which uses particular random-matrix generators and an identity observation operator. The authors explain that this analytical result does not extend to more general operationally relevant settings, motivating the unresolved problem of determining optimal Hybrid parameters analytically in those contexts.