Implicit ensemble tangent linear models (IETLMs) for model differentiation

Abstract

Ideally, tangent linear models (TLMs) predict the difference between perturbed and unperturbed non-linear forecasts of interest. The adjoint of a TLM gives the gradient of the non-linear model and is used in 4DVar data assimilation and in adjoint-based Forecast Sensitivity to Observation Impact (FSOI). The accuracy of the local ensemble TLM (LETLM) has been shown to be limited by its inability to account for implicit time stepping. Here we derive implicit ensemble TLMs (IETLMs) that, at most, require the number of independent ensemble members to be equal to the number of variables in the implicit computational stencil. The accuracy of the IETLM in the linear regime is confirmed using an impl..