Some problems are relatively easily modelled by the use of a simple fully connected MLP architecture: as an example accurate estimates of the wind speed at the sea surface have been successfully retrieved from scatterometer measurements. Other problems, addressed by the use of SOM maps, give the possibility to synthesize a large set of multi dimensional signals into a small number of informative synthetic ones that allow to extract pertinent characteristics of the geophysical data set: as an example, the SOM analysis of a large set of phytoplankton absorption spectra allow the retrieval of the different pigment concentration with respect to the spectrum characteristics. More sophisticated architectures can be used when the problem is ill posed. In order to determine the wind direction from the scatterometer measurements, which is a multi valued problem, one can connect two successive MLPs computing successively the wind speed and the a-posteriori probability of the direction given the estimated speed. The result is thus a distribution of possible direction. Using the same MLPs, with more sophisticated cost functions as the “maximum likelihood” permits to address new problems such as the variance covariance matrices estimation. This permits to improve the accuracy of the estimation of the different variables in complex problems and becomes necessary for extracting meaningful information from the simultaneous study of the different variables.
Now days, the major contribution of the NN approach in a large set of environmental studies is due to their use in combination with other statistical approach. The theoretical knowledge of the basic NN models are now well established and permits their connection with more traditional statistical method as the Probabilistic Principal Component Analysis (PPCA), the Markov Chain (MC) or the Variational Assimilation (VA). For example, in case of a non gaussian distribution of variables, which is more often the case in environmental applications, SOM allows to segment the distribution into a set of quasi-normal distributions. One can thus apply PPCA or use some inverse technique as VA to determine a possible solution on each subset. In case of multi-valued problem, one can determine the distribution of the physical parameters that have to be retrieved. This is done by the use of SOM linked with Markov Chain (MC) and VA.. A Random Walk based on a Markov Chain can be used to find the most appropriate subsets of the SOM map by taking into account a priori information on the unknown vectors and gives the distribution of the possible values of the control parameters.