Modelling the unsaturated hydraulic conductivity of a sandy loam soil using Gaussian process regression

Abstract

Unsaturated soil hydraulic conductivity is a main parameter in agricultural and environmental studies, necessary for predicting and managing water and solute transport in soils. This parameter is difficult to measure in agricultural fields; thus, a simple and practical estimation method would be preferable, and quantitative methods (analytical and numerical) to predict the field parameters should be developed. Field experiments were conducted to collect water quality data to model the unsaturated hydraulic conductivity of a sandy loam soil. A mini disk infiltrometer (MDI) was used to measure soil infiltration rate. Input variables included electrical conductivity and the sodium adsorption ratio of irrigation water. Suction rate (pressure head), soil bulk density, and soil moisture content acted as inputs, with unsaturated soil hydraulic conductivity as output. The performance of Gaussian process regression (GPR) was analysed, with multiple linear regression (LR) and multi-layer perceptron (MLP) models used for comparison. Free performance criteria were compared: correlation coeficient (r), root mean square error (RMSE), and mean absolute error (MAE). The simulations employed the Waikato environment for knowledge analysis (WEKA) open source tool. The results indicate that the GPR with Pearson VII function-based universal kernel (PUK kernel), cache size 250007, Omega 1.0 and Sigma 1.0 performs better than other kernels when evaluating test split data, with a correlation coeficient of 0.9646. The RMSEs for GPR (PUK kernel), MLP, and LR were 1.16 × 10⁻⁰⁴, 1.87 × 10⁻⁰⁴, and 2.22 × 10⁻⁰⁴ cm·s⁻¹, respectively. Predictive data mining algorithms (DMA) enable an estimate of unknown values based on patterns in a database. Therefore, the present methodology can be put to use in predictive tools to manage water and solute transport in soils, as the GPR model provides much greater accuracy than the LR and MLP models in predicting the unsaturated hydraulic conductivity of a sandy loam soil.

Keywords: multiple linear regression, multi-layer perceptron, data mining, infiltration rate, water management