Quantification of uncertainty using artificial neural networks for mapping of soil properties in Germany

Machine learning models have been widely used in digital soil mapping to predict the spatial distribution of soil properties across the landscape. However, due to the unpredictable behavior of soil properties, insufficient training sample size, input data error, uncertainty in model parameters and structure, uncertainty inherently exists in machine learning predictions. Therefore, knowledge of prediction uncertainty is vital for decision-makers and end-users. This study quantifies the overall uncertainty of digital soil maps of Germany for soil acidity, organic carbon, cation exchange capacity, and clay using quantile regression forest (QRF) and artificial neural network (ANN) models. Here, we propose the use of a novel ANN model that directly estimates the lower and upper bounds of a prediction interval by using an architecture with two output neurons. A multi-objective evolutionary algorithm (i.e., non-dominated sorting genetic algorithm II) was employed to parameterize the ANN weights. The results of the modeling indicated that ANN performed better than the QRF for predicting soil properties. Additionally, the ANNs produced narrower prediction intervals in comparison to the QRF. Most importantly, ANN yielded prediction interval coverage probabilities that were more closely aligned to their associated confidence levels in comparison to the QRF. In general, the ANNs were not only effective in predicting soil properties, but they were also effective in constructing reasonable prediction intervals for soil characteristics; and therefore, it is recommended to be used for predicting soil properties and quantifying their uncertainty in digital soil mapping.

Keywords: uncertainty estimation, prediction interval, multi-objective optimization, artificial neural networks, machine learning, Germany