Optimisation of pedotransfer functions using an artificial neural network ensemble method

Soil hydraulic properties, mainly saturated and unsaturated hydraulic conductivity and water retention, are crucial input parameters in any modelling study on water flow and solute transport in soils. However, direct measurement techniques remain relatively time consuming, labour intensive and expensive. Fortunately, they may be predicted by forming a mathematical relationship between relatively easily collected soil survey parameters, such as soil texture, bulk density and organic matter content, and less readily available soil properties, such as water retention or hydraulic conductivity. These mathematical relationships, pedotransfer functions (PTFs), allow the transfer of data we have into data we need. In recent years many PTFs have been created with the aid of artificial neural networks (ANNs). We describe a PTF modelling method that combines a number of individual ANNs – the ensemble method – and compare directly the results obtained with those achieved by a competing single ANN method. The ensemble method is shown to produce significantly more accurate and robust PTFs when compared to single ANN methods, under the same conditions. These ANN–PTF ensembles have been optimised to produce maximum benefits from the ensemble method, whilst minimising data correlations between training and test data. Consideration has been given to how much data is required in the training and testing phases of modelling, and how many individual ANNs should be combined to produce the ensemble. We also demonstrate that the current terminology used to describe various portions of the dataset in the single ANN method is insufficient when describing such portions in the ensemble method. As a consequence, new terminology is introduced. Furthermore, we establish that data may be recycled, i.e. used in both the training and testing phases of the ANN–PTF ensemble with virtually no loss of precision. This report shows that, for the water retention data investigated here, the ensemble method requires significantly less data than does the single ANN method – more than 2 1/2 times less – to produce results of equivalent precision. This is a crucial result because, since ANN–PTFs formed from local data produce more accurate predictions than those built from data spread from a wider area, the concept of data conservation becomes a critical factor in ANN–PTF construction.