Alexandre M.J.-C. Wadoux

Insights into the controlling factors of soil organic carbon (SOC) stock variation are necessary both for our scientific understanding of the terrestrial carbon balance and to support policies that intend to promote carbon storage in soils to mitigate climate change. In recent years, complex statistical and algorithmic tools from the field of machine learning have become popular for modelling and mapping SOC stocks over large areas. In this paper, we report on the development of a statistical method for interpreting complex models, which we implemented for the study of SOC stock variation. We fitted a random forest machine learning model with 2206 measurements of SOC stocks for the 0–50 cm depth interval from mainland France and used a set of environmental covariates as explanatory variables. We introduce Shapley values, a method from coalitional game theory, and use them to understand how environmental factors influence SOC stock prediction: what is the functional form of the association in the model between SOC stocks and environmental covariates, and how does the covariate importance vary locally from one location to another and between carbon-landscape zones? Results were validated both in light of the existing and well-described soil processes mediating soil carbon storage and with regards to previous studies in the same area. We found that vegetation and topography were overall the most important drivers of SOC stock variation in mainland France but that the set of most important covariates varied greatly among locations and carbon-landscape zones. In two spatial locations with equivalent SOC stocks, there was nearly an opposite pattern in the individual covariate contribution that yielded the prediction – in one case climate variables contributed positively, whereas in the second case climate variables contributed negatively – and this effect was mitigated by land use. We demonstrate that Shapley values are a methodological development that yield useful insights into the importance of factors controlling SOC stock variation in space. This may provide valuable information to understand whether complex empirical models are predicting a property of interest for the right reasons and to formulate hypotheses on the mechanisms driving the carbon sequestration potential of a soil.

For decades scientists have produced maps of biological, ecological and environmental variables. These studies commonly evaluate the map accuracy through cross-validation with the data used for calibrating the underlying mapping model. Recent studies, however, have argued that cross-validation statistics of most mapping studies are optimistically biased. They attribute these overoptimistic results to a supposed serious methodological flaw in standard cross-validation methods, namely that these methods ignore spatial autocorrelation in the data. They argue that spatial cross-validation should be used instead, and contend that standard cross-validation methods are inherently invalid in a geospatial context because of the autocorrelation present in most spatial data. Here we argue that these studies propagate a widespread misconception of statistical validation of maps. We explain that unbiased estimates of map accuracy indices can be obtained by probability sampling and design-based inference and illustrate this with a numerical experiment on large-scale above-ground biomass mapping. In our experiment, standard cross-validation (i.e., ignoring autocorrelation) led to smaller bias than spatial cross-validation. Standard cross-validation was deficient in case of a strongly clustered dataset that had large differences in sampling density, but less so than spatial cross-validation. We conclude that spatial cross-validation methods have no theoretical underpinning and should not be used for assessing map accuracy, while standard cross-validation is deficient in case of clustered data. Model-free, design-unbiased and valid accuracy assessment is achieved with probability sampling and design-based inference. It is valid without the need to explicitly incorporate or adjust for spatial autocorrelation and perfectly suited for the validation of large scale biological, ecological and environmental maps.

Pedometrics, the application of mathematical and statistical methods to the study of the distribution and genesis of soils, has broadened its scope over the past two decades. The primary focus of pedometricians has traditionally been on spatial and spatio-temporal soil inventories with numerical soil classification, geostatistical modelling of spatial variation and mapping. The rapid development of remote and proximal soil sensing as well as data-driven statistical modelling techniques have had a major impact on pedometrics over the past decades. During this time, a general demand for quantitative digital soil information for environmental modelling and management has compelled pedometricians to address other soil-related questions from a quantitative point of view: soil genesis and utility and quality of soil. While scientific progress is largely an autonomous process that is difficult to steer, research efforts could benefit from an agenda with pressing pedometric research topics. This paper defines and discusses ten recent or longstanding pedometrics challenges, with the attempt to identify knowledge gaps and suggest new concepts and methods to overcome them. The ten challenges were selected through a collaborative effort and may serve as a guidance for future pedometrics research and to foster collaboration among soil scientists. The challenges discussed in this paper are also indicators of the current understanding and state of knowledge from which progress can be measured in the future.

This book provides a didactic overview of techniques for inferring information from soil spectroscopic data, and the codes in the R programming language for performing such analyses. It is intended for students, researchers and practitioners looking to infer soil information from spectroscopic data, focusing mainly on, but not restricted to, the infrared range of the electromagnetic spectrum. Little prior knowledge of the R programming language or digital soil spectra is required. We work through the steps to process spectroscopic data systematically.