Gaussian Process Regression Models for Predicting Water Retention Curves

Abstract

An accurate representation of water retention curves is important for various reasons. Traditional models already exist for the representation of these curves, with one of them being the van Genuchten model. When soil parameters are available, the van Genuchten model can be used to plot water retention curves. However, when these soil parameters are not available, regression can be performed to estimate and predict the water retention curves. Commonly, the Non-Linear Least Squares regression method is used in combination with a certain water retention model. Problems arise for inhomogeneous soils as the traditional water retention models tend to break down. To improve the representation of water retention curves, Gaussian Process regression will be implemented. This method will be combined with the Non-Linear Least Squares method to obtain new representations of water retention curves. These new curves are better in terms of curve fit and uncertainty, when compared to the traditional method. These comparisons can be made visually, by observing the plots and their confidence intervals, as well as quantitatively by computing the log-likelihoods of the different methods. When comparing the results of the log-likelihood computations for both methods, it follows that the value of the log-likelihood is greater for water retention data with correlated residuals. In the case where the residuals are uncorrelated, the log-likelihoods are equal for both methods and no improvements are observed.