Forcing singular vectors and other sensitive model structures

Model tendency perturbations can, like analysis perturbations, be an effective way to influence forecasts. In this paper, optimal model tendency perturbations, or forcing singular vectors, are computed with diabatic linear and adjoint T42L40 versions of the European Centre for Medium-Range Weather Forecasts' forecast model. During the forecast time, the spatial pattern of the tendency perturbation does not vary and the response at optimization time (48 hours) is measured in terms of total energy. Their properties are compared with those of initial singular vectors, and differences, such as larger horizontal scale and location, are discussed. Sensitivity calculations are also performed, whereby a cost function measuring the 2-day forecast error is minimized by only allowing tendency perturbations. For a given number of minimization steps, this approach yields larger cost-function reductions than the sensitivity calculation using only analysis perturbations. Nonlinear forecasts using only one type of perturbation confirm an improved performance in the case of tendency perturbations. For a summer experiment a substantial reduction of the systematic error is shown in the case of forcing sensitivity.