Climate models, in their effort to predict the weather properly, among other variables, require the aerosol size density. The determination of aerosol size density from aerosol optical depth is an ill-posed problem. A typical mathematical inversion approach consists of using a linear regularization method, which requires a smoothing operation on the penalty term associated with the regularization method. The severity of the smoothing operation itself is being optimized by a Lagrange multiplier to enable minimum error in the inversion calculations.

We propose solving this type of ill-posed problem using an artificial neural network (ANN), which will be trained with a typical pattern of Puerto Rico AOD and known size density, which will be used to take AOD data and generate size density on a continuous basis. This "typical pattern" may vary too drastically from season to season, so two networks may be used, to account for Puerto Rico's two major seasonal wind patterns. The network's reliability rests in obtaining the best training data possible that describes a relationship between AOD and aerosol size density in a given area of Puerto Rico. As a first attempt to generate size density, the training of ANN will be presented using AERONET data from nearby La Parguera for both AOD and size density.