Parametric representation, or parameterization, is used in the numerical modeling of various atmospheric variables. It involves a statistical analysis that enables the representation of the true processes by simpler parametric relations. Three purposes may motivate such an analysis: (i) getting a better understanding of the system, (ii) allowing a computation of the processes that is faster than the exact formulation, (iii) linking two sets of variables when the exact formulation is not known. Numerous applications in numerical weather prediction fall in to one of these categories. This is the case of all the components of an atmospheric and/or oceanic forecast model, of the retrieval of geophysical parameters from satellite data, and of the analysis of satellite imagery.

Artificial neural networks (ANN) like the multi-layer perceptron provide powerful solutions for these problems, but have been only marginally used in the operational weather centers. The novelty of the approach partly explains this situation. Several reasons can be found in some difficulties associated to the ANN approach as well. Among others, we may mention the remote link of a trained ANN with the physical laws, the difficulty of gathering an adequate (i.e. representative and correctly sampled) training dataset for high-dimension problem, the difficulty of having both the direct model and its derivatives right, or the difficulty of modifying the ANN once it has been trained.

The presentation will discuss the current strengths and limitations of ANN in the context of numerical weather prediction. It will be illustrated by several applications, including those developed by the author at the European Centre for Medium-range Weather Forecasts in the field of radiation modeling.