Abstract
For many aspects of numerical weather prediction it is important to have good error statistics. Here one can think of applications as diverse as data assimilation, model improvement, and medium-range forecasting. In this paper, a method for producing these statistics from a representative ensemble of forecast states at the appropriate forecast time is proposed and examined. To generate the ensemble, an attempt is made to simulate the process of error growth in a forecast model. For different ensemble members the uncertain elements of the forecasts are perturbed in different ways.
First the authors attempt to obtain representative initial perturbations. For each perturbation, an independent 6-h assimilation cycle is performed. For this the available observations are randomly perturbed. The perturbed observations are input to the statistical interpolation assimilation scheme, giving a perturbed analysis. This analysis is integrated for 6 h with a perturbed version of the T63 forecast model, using perturbed surface fields, to obtain a perturbed first guess for the next assimilation. After cycling for 4 days it was found that the ensemble statistics have become stable.
To obtain perturbations to the model, different model options for the parameterization of horizontal diffusion, deep convection, radiation, gravity wave drag, and orography were selected. As part of the forecast error is due to model deficiencies, perturbing the model will lead to an improved ensemble forecast. This also creates the opportunity to use the ensemble forecast for model sensitivity experiments.
It is observed that the response, after several assimilation cycles, to the applied perturbations is strongly nonlinear. This fact makes it difficult to motivate the use of opposite initial perturbations. The spread in the ensemble of first-guess fields is validated against statistics available from the operational data assimilation scheme. It is seen that the spread in the ensemble is too small. Apparently, the simulation of the error sources is incomplete. In particular, we might have to generate less conventional perturbations to the model.
