Determining Sensitivities, Impacts and Error Covariances from Very Large Ensembles with Randomly Perturbed Initial Conditions

2 ABSTRACT This paper explores the use of large ensembles of model runs with randomly perturbed initial conditions for the calculation of error covariance fields, initial condition sensitivity fields, and perturbation impact fields. The calculation of error covariances from ensembles is familiar from ensemble Kalman filter (EnKF) techniques, but the calculation of sensitivity and impact fields from ensembles is new. This work is unlike previous EnKF work in that the ensemble members are randomly perturbed in each degree of freedom (DOF) of the model, rather than having perturbation fields based on expected errors in the analysis. In this work, all the DOFs of the model (or a subset) are independently and simultaneously perturbed and the response of the model to each perturbed DOF is sought by statistical technique. Sensitivity results are conceptually comparable to adjoint calculations. Error covariance, impact, and sensitivity fields constitute the three distinct kinds of fields that can be found from an ensemble. These fields can be found equivalently to first order as either covariances or partial derivatives from regression analysis. This paper makes use of ensembles of 2000 members of a mesoscale model, run for 6 hours over a domain in the Southern Plains, for a dryline-cold front convective initiation case. Results for sensitivity and impact fields are much noisier than those for error covariance fields, due to the weaker connection between variables at different model times. Results for sensitivity fields are found to be insensitive to perturbation magnitudes in the range tested, unless multiple physical variables are perturbed simultaneously. In the latter case, the physically strongest sensitivities dominate the results, with weak sensitivities being lost in noise. However, weak sensitivities could still be found if variables leading to strong sensitivities were not randomly perturbed.