Hierarchical modelling in digital soil mapping: Advantages for mapping bimodal soil pH

Maps of soil pH are an important tool for making decisions in sustainable forest management. Accurate pH mapping, therefore, is crucial to support decisions by authorities or forest companies. Soil pH values typically exhibit a distinct distribution characterized by two frequently encountered pH ranges, wherein aluminium oxides (Al₂O₃) and carbonates (CaCO₃) act as the primary buffer agents. Soil samples with moderately acid pH values (pH CaCl₂ of 4.5-6) are less commonly observed due to their weaker buffering capacity. The different strength of buffer agents results in a distinct bimodal distribution of soil pH values with peaks at pH of around 4 and 7.5. Commonly used approaches for spatial mapping neglect this often observed characteristic of soil pH and predict unimodal distributions with too many moderately acid pH values. For ecological map applications this might result in misleading interpretations.

This study presents a novel approach to produce pH maps that are able to reproduce pedogenic processes. The procedure is suitable for bimodal responses where the response distribution is naturally inherent and needs to be reproduced for the predictions. It is model-agnostic, namely independent from the used statistical prediction method. Calibration data is optimally split into two parts corresponding each to a data culmination, i.e. for soil pH values belonging to the ranges of the two principal buffer agents (Al₂O₃ and CaCO₃). For each subset a separate model is then built. In addition, a binary model is fitted to assign every new prediction location a probability to belong either to Al₂O₃ or CaCO₃ buffer range. Predictions are combined by weighted mean. Weights are derived from probabilities predicted by the binary model. Degree of smoothness is chosen by sigmoid transform which allows for optimal continuous transition of the pH values between Al₂O₃ and CaCO₃ buffer ranges. For each location uncertainty distributions may be combined by using the same weights.

We illustrated application of the new approach to a medium and strong bimodal distributed response (1) pH in 0–5 cm and (2) pH in 60–100 cm of forest soils in Switzerland (2 530 calibration sites). While model performance measured at 354 validation sites slightly dropped compared to a common modelling approach (drop of R² of 0.02–0.03) distributional properties of the predictions are much more meaningful from a pedogenic point of view. We were able to demonstrate the benefits of considering specific distributional properties of responses within the prediction process and expanded model assessment by comparing observed and predicted distributions.