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The European Green Deal emphasizes the importance of healthy soils for our planet and society. In order to monitor soil health, modelling soil organic matter (SOM) in space and over time is necessary to assess changes in the fertility of agricultural soils, combat climate change and maintain ecosystem services. In digital soil mapping, most recent statistical modelling approaches have used time series of remote sensing data, which became available from the early 1980s onwards, together with soil observations to make predictions in space and over time. While this has clear advantages, it does not provide spatially explicit, explanatory information for time periods before the 1980s, even though observations in soil databases are often from beforehand. In this study, we modelled changes in SOM in 3D space over 65 years on a national scale in the Netherlands. We used SOM observations from 345 000 locations from 0 to 2 m depth between 1953 and 2018. The covariates were comprised of proxies of soil forming factors either considered to be static (e.g. relief, parent material) or dynamic over these 65 years. As dynamic covariates, we used indices of digitized historic (1960 – 1980) and more recent (1986 – 2018) land use maps. These dynamic covariates were chosen for two reasons. Firstly, land use and land cover change are the main drivers of SOM change over the time period of several decades. This is especially true in the Netherlands, where the anthropogenic influence on soils has been tremendous. Approximately 82 % of the land surface are agricultural, urban or infrastructure areas, while 15 % consists of (managed) peatlands and up to 20 % has been reclaimed from the sea. Secondly, by including carefully mapped historic land use, we were able to take advantage of a longer time series of soil data to make space-time predictions of SOM over a longer time period. Predictions were made using the quantile regression forest (QRF) algorithm, whereby sampling depth and year were included during calibration. SOM predictions were validated in two ways: a) over the 65-year period using a 10-fold cross-validation and b) specifically for 1998 and 2018, where designed-based statistical inference was possible using a probability sample. We computed the mean error (ME), root mean squared error (RMSE), model efficiency coefficient (MEC) as accuracy metrics and the prediction interval coverage probability (PICP) as an evaluation of the prediction uncertainty. Results showed that spatial patterns were realistic and properly reproduced but that prediction of temporal dynamics was more challenging. This research is also of interest for spatio-temporal soil modelling in other regions of the world that have soil data from the early and mid-19th century and historical land use and land cover data.

There is a growing demand for high quality soil data to model soil processes and map soil properties. However, wet chemistry measurements on soil properties are subjected to many error sources, such as the observer, the instrument and lack of standardised methodologies. Consequently, soil data are imperfect and uncertain because of these error sources. Uncertainties in measurements of fundamental soil properties can propagate through, e.g., pedotransfer functions, spectroscopic models and digital soil mapping algorithms. Therefore, it is important to provide detailed uncertainty information about soil measurements to potential data users. In practice, uncertainty estimates are rarely specified by providers of analytical soil data.In this research, we aimed to quantify uncertainties in synthetic and real-world pH (1:1 soil-water suspension) and Total Organic Carbon (TOC) measurements. We assumed that uncertainty can be represented by a normal distribution. A linear mixed-effects model was applied to estimate the parameters of the normal distribution, i.e., mean and standard deviation, of both synthetic and real-world datasets. The model included ‘sample ID’ as a fixed effect, and ‘batch’ and ‘laboratory’ as random effects. The use of synthetic datasets allowed us to investigate how well the model parameters could be estimated given a specific experimental measurement design, whereas the real-world case served to explore if the parameter estimates were still accurate for such unbalanced datasets.For a balanced dataset (n=20, n=100, n=200 and n=500), using synthetic pH data for three hypothetical laboratories (two batches per laboratory), the mean estimated standard deviations (σ) of the random effects were σbatch=0.10, σlaboratory=0.24 and σresidual=0.2. These estimates were in agreement with the σ for the respective random effects used to generate the synthetic dataset, meaning that the model could accurately estimate the model parameters. Subsequently, changes were made to the experimental measurement design by randomly removing 20%, 50% and 80% of the data, resulting in unbalanced datasets. In general, the interquartile range (IQR) of σ for each random effect increased with a larger percentage of removed data. However, the increase in IQR was larger for n=20 compared to, e.g., n=200. When comparing 0% and 80% randomly removed data, the IQR for the batch effect increased with 60.3%. Conversely, for n=200 an increase of only 23.5% was observed.Subsequently, the same model was fitted on real-world pH and TOC data, provided by the Wageningen Evaluating Programs for Analytical Laboratories (WEPAL). The unbalanced dataset structure was first reconstructed and filled with synthetically generated data, based on sample means and standard deviations derived from the measured data. The model was fitted on both datasets. For measured pH, the model yielded σbatch=0.27, σlaboratory=0.17 and σresidual=0.10. The IQRs of the estimated σ from synthetic WEPAL data were 0.04 (batch), 0.06 (laboratory) and 0.02 (residual). The model fitted on the measured TOC data estimated σbatch=5.3%, σlaboratory=2.8% and σresidual=2.1%. For the synthetic WEPAL data, IQRs of 1.3% (batch), 1.4% (laboratory) and 0.4% (residual) were determined for the estimated σ. These findings suggest that despite having a highly unbalanced dataset, realistic model parameter estimates can still be obtained.