In this study, different interpolation techniques are presented, assessed, and compared for the estimation of soil iron (Fe) contents in locations where observations were not available. Initially, 400 soil samples from the Kozani area, which is near Polifitou Lake in northern Greece, were randomly collected from 2013 to 2015 and were analysed in the laboratory to determine the soil Fe concentrations and pH. The soil Fe concentrations were examined for spatial autocorrelation, and semivariograms were used to determine whether pH and Fe exhibited spatial cross correlation. Three interpolation methods, including Ordinary Kriging, Universal Kriging, and Co-Kriging, were applied, and their results were compared with the use of two different cross-validation methods. In the current study, there was evidence of spatial cross correlation of soil Fe and pH for each year, which was subsequently used to improve the interpolation results in locations where there were no measurements. In nearly all cases, Co-Kriging, which takes advantage of the covariance between the two regionalized variables (Fe and pH), outperformed the other interpolation techniques each year.

In the current paper we assess different machine learning (ML) models and hybrid geostatistical methods in the prediction of soil pH using digital elevation model derivates (environmental covariates) and co-located soil parameters (soil covariates). The study was located in the area of Grevena, Greece, where 266 disturbed soil samples were collected from randomly selected locations and analyzed in the laboratory of the Soil and Water Resources Institute. The different models that were assessed were random forests (RF), random forests kriging (RFK), gradient boosting (GB), gradient boosting kriging (GBK), neural networks (NN), and neural networks kriging (NNK) and finally, multiple linear regression (MLR), ordinary kriging (OK), and regression kriging (RK) that although they are not ML models, they were used for comparison reasons. Both the GB and RF models presented the best results in the study, with NN a close second. The introduction of OK to the ML models’ residuals did not have a major impact. Classical geostatistical or hybrid geostatistical methods without ML (OK, MLR, and RK) exhibited worse prediction accuracy compared to the models that included ML. Furthermore, different implementations (methods and packages) of the same ML models were also assessed. Regarding RF and GB, the different implementations that were applied (ranger-ranger, randomForest-rf, xgboost-xgbTree, xgboost-xgbDART) led to similar results, whereas in NN, the differences between the implementations used (nnet-nnet and nnet-avNNet) were more distinct. Finally, ML models tuned through a random search optimization method were compared with the same ML models with their default values. The results showed that the predictions were improved by the optimization process only where the ML algorithms demanded a large number of hyperparameters that needed tuning and there was a significant difference between the default values and the optimized ones, like in the case of GB and NN, but not in RF. In general, the current study concluded that although RF and GB presented approximately the same prediction accuracy, RF had more consistent results, regardless of different packages, different hyperparameter selection methods, or even the inclusion of OK in the ML models’ residuals.

Machine learning (ML) algorithms are extensively used with outstanding prediction accuracy. However, in some cases, their overfitting capabilities, along with inadvertent biases, might produce overly optimistic results. Spatial data are a special kind of data that could introduce biases to ML due to their intrinsic spatial autocorrelation. To address this issue, a special resampling method has emerged called spatial cross-validation (SCV). The purpose of this study was to evaluate the performance of SCV compared with conventional random cross-validation (CCV) used in most ML studies. Multiple ML models were created with CCV and SCV to predict groundwater electrical conductivity (EC) with data (A) from Rhodope, Greece, in the summer of 2020; (B) from the same area but at a different time (summer 2019); and (C) from a new area (the Salento peninsula, Italy). The results showed that the SCV provides ML models with superior generalization capabilities and, hence, better prediction results in new unknown data. The SCV seems to be able to capture the spatial patterns in the data while also reducing the over-optimism bias that is often associated with CCV methods. Based on the results, SCV could be applied with ML in studies that use spatial data.

One of the core tasks in digital soil mapping (DSM) studies is the estimation of the spatial distribution of different soil variables. In addition, however, assessing the uncertainty of these estimations is equally important, something that a lot of current DSM studies lack. Machine learning (ML) methods are increasingly used in this scientific field, the majority of which do not have intrinsic uncertainty estimation capabilities. A solution to this is the use of specific ML methods that provide advanced prediction capabilities, along with innate uncertainty estimation metrics, like Quantile Regression Forests (QRF). In the current paper, the prediction and the uncertainty capabilities of QRF, Random Forests (RF) and geostatistical methods were assessed. It was confirmed that QRF exhibited outstanding results at predicting soil organic matter (OM) in the study area. In particular, R² was much higher than the geostatistical methods, signifying that more variation is explained by the specific model. Moreover, its uncertainty capabilities as presented in the uncertainty maps, shows that it can also provide a good estimation of the uncertainty with distinct representation of the local variation in specific parts of the area, something that is considered a significant advantage, especially for decision support purposes.