The Ensemble Tangent Linear Model Applied to a Cloud Physics Parameterization

Abstract An ensemble tangent linear model (ETLM) is applied to a cloud physics scheme used in the Navy Global Environmental Model (NAVGEM). The ensemble is created using 3-h forecasts from the ensemble transform method used in the NAVGEM data assimilation system. The model states are saved before and after applying the cloud physics parameterization (which includes condensation/evaporation of cloud ice and cloud liquid water and stratiform precipitation), and these states are used to construct linearized model tendencies for temperature, specific humidity, cloud liquid water, and cloud ice water. We examine separately the application of the ETLM to cloud physics components that are explicitly local versus nonlocal. For the local components, an ETLM is built using a single grid point. ETLMs from 50 to 1000 members are tested, and skillful forecasts can be obtained for both local and nonlocal physics even with a moderate-sized ensemble (e.g., 100 members). At 1000 members, the globally averaged forecast error reductions (relative to persistence errors) are ∼40% for temperature, water vapor, and cloud liquid water and ∼30% for cloud ice. When initial perturbations are reduced by a factor of 0.1, the error reductions increase to ∼65% for all variables. For physics with nonlocal components (stratiform precipitation), the covariances that comprise the ETLM are localized with a Schur product matrix using a Gaussian localization shape with tunable length. The optimal lengths increased with an ensemble size from ∼2 to 3 km for 50 members to ∼10 km for 1000 members. ETLMs for “all cloud physics” are also constructed and evaluated.