Simple methods are formulated using an ensemble forecast to identify the sensitive initial perturbations that grow in a specified region at the verification time. These methods do not require the tangent-linear or adjoint models, but use an ensemble forecast to obtain approximated solutions. Input to the sensitivity calculation can be any ensemble forecast integrated from initial conditions perturbed with the bred vector, singular vector, or ensemble Kalman filter methods. Two formulations are presented here to approximate the adjoint and singular vector methods using an ensemble forecast. The ensemble singular vector sensitivity, which has already been applied in previous studies, is obtained with a single eigenvector calculation. The ensemble adjoint sensitivity only requires an even simpler matrix-vector multiplication.
To validate the formulations, ensemble-based sensitivity analysis has been conducted in a few cases. First, the two methods were applied to identify the sensitive initial perturbations that grow in the verification region over Japan in January and August 2003. The first singular vector mode indeed achieves the largest amplitude at the verification time, but that is not necessarily true after the verification time. Both methods can identify the sensitive regions more specifically than the regions with large ensemble spread in cases with a mid-latitude cyclone and with a tropical cyclone. The monthly-mean sensitivity in January 2003 indicates the effect of Rossby waves and synoptic disturbances in upstream sensitive regions over Siberia, Tibet, and a downstream sensitive region in the north-western Pacific; the sensitivity in August 2003 suggests the influence of the Asian summer monsoon. Next, for an August 2002 storm case in Europe, global 20-km resolution simulations were conducted from the initial conditions perturbed by the ensemble singular vector method to compare with the unperturbed simulation. In the perturbed simulation, the cyclone is deeper by a few hPa in its north-east sector with more precipitation north of the Alps more consistently with observations. These results indicate that reasonable sensitive regions can be identified with our methods.
2015 by Meteorological Society of Japan