Artificial neural networks as a tool for spatial interpolation

This paper describes the spatial interpolation of daily minimum air temperature using a feed-forward back-propagation neural network. Simple network configurations were trained to predict minimum temperature using as inputs: (1) date and terrain variables; (2) temperature observations at a number of neighbouring locations; (3) date, terrain variables and neighbouring temperature observations. This is the first time that trend and spatial association are explicitly considered together when interpolating using a neural network. The internal weights given to different inputs to the network were analysed to estimate the degree of spatial correlation between neighbouring stations in addition to the most influential variables contributing to the underlying trend. The spatial distribution of daily minimum temperature was estimated with the greatest accuracy by a network trained on the most comprehensive data set (3). The best model for the prediction of temperature accounts for 93% of the variance, measured by the correlation between independent estimated and observed values over a full year. This is comparable to accuracies reported in the literature using other approaches such as ordinary kriging of the residuals of multi-variate linear regression or partial thin plate splines. An advantage of this method is that the guiding variables are not assumed necessarily to be linearly related with the data being interpolated, and combinative effects are taken into account. Analysis of the internal network weights confirms that the networks are able to select adaptively between trend and covariance components of the interpolation function. Example interpolated daily minimum temperature surfaces for a 100 km x 100 km area in Yorkshire, UK, were generated using the selected network architectures to illustrate the results achievable with an ANN.