Numerical Experiments with the Adjoint of a Nonhydrostatic Mesoscale Model

Abstract

For the purpose of assimilation of radar data into a nonhydrostatic mesoscale forecast model, the adjoint method is considered. For the case of dry convection, a set of identical twin experiments shows that it is possible to construct the initial conditions for the temperature only moderately well from observations of one velocity component only. This behavior can be explained with an ill-posedness of the problem in absence of temperature information caused by the discrete representation of gradients. Small pieces of additional thermodynamic information improve the results noticeably. Contamination of the data with random error has little impact on the quality of the retrieved initial state, as long as there are enough data available. Phenomena not resolved by the data are not retrievable by the algorithm. For the case considered, the adjoint method proves to be a robust tool for data assimilation purposes, but it also leaves the question of how to avoid the ill-posedness open.