  Ensemble forecasting is, so far, the most successful approach to produce
relevant forecasts with an estimation of their uncertainty. The main
limitations of ensemble forecasting are the high computational cost and the
difficulty to capture and quantify different sources of uncertainty,
particularly those associated with model errors. In this work we perform
toy-model and state-of-the-art model experiments to analyze to what extent
artificial neural networks (ANNs) are able to model the different sources of
uncertainty present in a forecast. In particular those associated with the
accuracy of the initial conditions and those introduced by the model error. We
also compare different training strategies: one based on a direct training
using the mean and spread of an ensemble forecast as target, the other ones
rely on an indirect training strategy using an analyzed state as target in
which the uncertainty is implicitly learned from the data. Experiments using
the Lorenz'96 model show that the ANNs are able to emulate some of the
properties of ensemble forecasts like the filtering of the most unpredictable
modes and a state-dependent quantification of the forecast uncertainty.
Moreover, ANNs provide a reliable estimation of the forecast uncertainty in the
presence of model error. Preliminary experiments conducted with a
state-of-the-art forecasting system also confirm the ability of ANNs to produce
a reliable quantification of the forecast uncertainty.
