Rainfall Estimation Using Neuron-Adaptive Higher Order Neural Networks

Abstract

Real world data is often nonlinear, discontinuous and may comprise high frequency, multi-polynomial components. Not surprisingly, it is hard to find the best models for modeling such data. Classical neural network models are unable to automatically determine the optimum model and appropriate order for data approximation. In order to solve this problem, Neuron-Adaptive Higher Order Neural Network (NAHONN) Models have been introduced. Definitions of one-dimensional, two-dimensional, and n-dimensional NAHONN models are studied. Specialized NAHONN models are also described. NAHONN models are shown to be “open box”. These models are further shown to be capable of automatically finding not only the optimum model but also the appropriate order for high frequency, multi-polynomial, discontinuous data. Rainfall estimation experimental results confirm model convergence. We further demonstrate that NAHONN models are capable of modeling satellite data. When the Xie and Scofield (1989) technique was used, the average error of the operator-computed IFFA rainfall estimates was 30.41%. For the Artificial Neural Network (ANN) reasoning network, the training error was 6.55% and the test error 16.91%, respectively. When the neural network group was used on these same fifteen cases, the average training error of rainfall estimation was 1.43%, and the average test error of rainfall estimation was 3.89%. When the neuron-adaptive artificial neural network group models was used on these same fifteen cases, the average training error of rainfall estimation was 1.31%, and the average test error of rainfall estimation was 3.40%. When the artificial neuron-adaptive higher order neural network model was used on these same fifteen cases, the average training error of rainfall estimation was 1.20%, and the average test error of rainfall estimation was 3.12%.