An algorithm is proposed to identify the best correlation between the variables of two data sets. The relationship among the variables could be linear or nonlinear and it can include time delays among the variables. This algorithm consists of: i) performing mathematical transformations to the original variables; ii) organize the information into small groups; iii) select the best predictors for each group; and v) perform integer random search to select the winner variables.

Forty rainfall stations located in Puerto Rico (PR) with 43 years of monthly observations were used to implement and assess the proposed algorithm. Meteorological indexes based on sea level pressure, and sea surface temperatures were used to identify teleconections between PR rainfall processes and global meteorological indexes. It was found that the major factors that drive the PR rainfall process are the North Atlantic Oscillation Index and the Artic Oscillation Index. The winner variables from the selection algorithm were also used to design and train an artificial neural network model to predict PR rainfall. Thirty-eight years were used for training and five years for model cross-validation. Results suggest that the proposed methodology is a potential tool to predict accumulated rainfall at any station, assuming that at leas 40 years of monthly rainfall observations are available.

A nonlinear dynamic system was simulated and modeled using an artificial neural network model. A feedforward neural network model with the Levenberg-Marquardt algorithm was successfully implemented. The structure of the neural network includes two layers with linear and nonlinear transfer functions. Simulation results show that a neural network model can properly represent a nonlinear dynamic system. It can be shown that an efficient identification procedure consists of selecting the transfer function and the number of the neurons that minimize the sum of square prediction errors.