Forecasting cyanobacterium Anabaena spp. in the River Murray, South Australia, using B-spline neurofuzzy models

Abstract

Recently, artificial neural network (ANN) methods have been used successfully for ecological modelling. In most instances, multi layer perceptrons (MLPs) that are trained with the back-propagation algorithm have been used. The major shortcoming of this approach is that the knowledge contained in the trained networks is difficult to interpret. One way to increase model transparency is to use neurofuzzy approaches, which enable the information that is stored in trained networks to be expressed in the form of a fuzzy rule base. In this paper, B-spline associative memory networks (AMNs), which have been shown to be learning equivalent to certain types of fuzzy models, are used to forecast concentrations of the cyanobacterium Anabaena spp. in the River Murray at Morgan, South Australia, 4 weeks in advance. The ASMOD (adaptive spline modeling of observation data) algorithm is used to optimise the model structure and the number of model inputs. The sensitivity of the model to the order of the basis functions and a number of stopping criteria is investigated. The performance of the various models is assessed in terms of forecasting accuracy and model transparency, and compared with that of a MLP model developed in a previous study. It is found that lower order basis functions and Bayes' Information Criterion (BIC) give the best model performance, both in terms of forecasting accuracy and transparency. The accuracy of the forecasts obtained using the B-spline AMN and MLP models is comparable, although the AMN may be considered to perform marginally better overall. In addition, the AMN provides more explicit information about the relationship between the model inputs and outputs. The fuzzy rules obtained from the AMN model suggest that incidences of Anabaena spp. generally occur after the passing of a flood hydrograph and when water temperatures are high. © 2001 Elsevier Science B.V. All rights reserved.