Ensemble neural network forecasts with singular value decomposition

Ensemble weather forecasts enable a measure of uncertainty to be attached to each forecast by computing the ensemble's spread. However, generating an ensemble with a good error-spread relationship is far from trivial, and a wide range of approaches to achieve this have been explored. Random perturbations of the initial model state typically provide unsatisfactory results when applied to numerical weather prediction models. Singular value decomposition has proved more successful in this context, and as a result has been widely used for creating perturbed initial states of weather prediction models. We demonstrate how to apply the technique of singular value decomposition to purely neural-network based forecasts. Additionally, we explore the use of random initial perturbations for neural network ensembles, and the creation of neural network ensembles via retraining the network. We find that the singular value decomposition results in ensemble forecasts that have some probabilistic skill, but are inferior to the ensemble created by retraining the neural network several times. Compared to random initial perturbations, the singular value technique performs better when forecasting a simple general circulation model, comparably when forecasting atmospheric reanalysis data, and worse when forecasting the lorenz95 system - a highly idealized model designed to mimic certain aspects of the mid-latitude atmosphere.