Jacobians of an Operational Prognostic Cloud Scheme

Abstract

A detailed examination of the Jacobian matrix of sensitivities of the prognostic cloud scheme operational at the European Centre for Medium-Range Weather Forecasts (ECMWF) is presented. These Jacobians exhibit sensitivities of output variables (e.g., cloud condensate) to small input perturbations on temperature and moisture. The coupling of the cloud scheme with the ECMWF convective mass-flux scheme is considered. The sensitivity of the cloud scheme is split into all its contributing parts in order to extract the dominant terms. A selection of contrasted convective cases normally present in a regular operational forecast is considered. Some comparisons are made with a simpler diagnostic cloud scheme. It is shown that the main contributing terms to the sensitivity in cloud condensate l are the following for cases of deep convection: detrainment from moist convection, evaporation processes, and conversion of cloud water into rain. The structure of the Jacobians in terms of temperature and moisture perturbations in such cases is strongly dominated by the structure of the Jacobians of the convective mass flux at cloud base. Because of this dominance, the Jacobians from a simpler diagnostic cloud scheme have similarities in shape with those produced by the prognostic scheme. For shallow convection cases, the same terms as for deep convective cases are important (convective effects still dominate), but now erosion of clouds becomes significant. Jacobians of integrated l produced by the diagnostic and prognostic cloud schemes here are also similar, still because of the dominance of convective effects. When moist convection plays a negligible role, the dominant terms are the condensation/evaporation effects and the conversion of cloud water into rain. Larger differences are found then between the Jacobians of the prognostic and diagnostic cloud schemes. In such situations, the sensitivity of l with respect to vertical motion plays an equally important role compared to temperature and humidity.