Non-linear modelling of river levels using the Gamma test

We constructed non-linear predictive models for the River Kennet at Theale and the River Thames at Windsor using river and precipitation data from the Thames Valley region in the UK. Our approach used a novel non-linear data analysis technique called the Gamma test, combined with heuristic search techniques to provide a practical solution to the problem of constructing forward predictions of river levels and flows. Our three hour predictive model for the River Kennet at Theale calculated the level to a standard error of 1 cm, and our four hour predictive model for the River Thames at Windsor calculated the level to a standard error of 3cm. The Gamma test is used to examine the relationship between inputs and outputs in numerical data-sets. It is used prior to modelling to estimate the variance of the output that cannot be accounted for by the existence of any smooth model based on the inputs, even though the model is unknown. This error variance estimate provides a target Mean Squared Error that any smooth non-linear model should attain on unseen data. Building a model with greater accuracy than the error variance indicated by the Gamma test will result in a model that has overtrained on the data set and which cannot generalize well for unseen data.