Cynthia C. E. van Leeuwen

Modelling of soil processes is dependent on the availability of high-quality soil data. Soil properties that are considered difficult to measure are frequently determined through pedotransfer functions (PTFs). Here, readily available data are translated into data that are needed. Aside from these input soil properties, a reference wet chemistry dataset of the soil property of interest is required. However, these calibration and validation data are imperfect due to measurement error caused by various sources. Until now, the uncertainty of calibration and validation data has been ignored when deriving PTFs, and uncertainty quantification remains limited to the propagation of model input, parameter and structural uncertainty. In this contribution, we aimed to take uncertainty analysis one step further by studying how measurement error in wet chemistry calibration and validation soil data affects PTF predictions and associated prediction uncertainty. We focused on PTFs to predict the soil’s cation-exchange capacity (CEC), which is an important indicator of soil fertility and nutrient retention capacity. To predict CEC through PTFs, soil properties such as clay percentage, organic carbon content and pH are commonly included. We aimed to study the effect of measurement error in CEC data on the accuracy of multiple linear regression and random forest prediction models. PTFs were developed for the entire USA, subdivided per soil taxonomic order. Here, wet chemistry data from the National Cooperative Soil Survey’s (NCSS) Soil Characterization Database were used. The PTFs were fitted with and without including measurement error. However, the majority of the samples from the NCSS Soil Characterization Database were not measured in duplicate, which was needed to quantify measurement error. Alternatively, we used data from the Wageningen Evaluating Programmes for Analytical Laboratories (WEPAL) to provide a best estimate for the measurement error. Comparison of PTFs with and without measurement error showed significant differences in model accuracy metrics.

There is a growing demand for high‐quality soil data. However, soil measurements are subject to many error sources. We aimed to quantify uncertainties in synthetic and real‐world wet chemistry soil data through a linear mixed‐effects model, including batch and laboratory effects. The use of synthetic data allowed us to investigate how accurately the model parameters were estimated for various experimental measurement designs, whereas the real‐world case served to explore if estimates of the random effect variances were still accurate for unbalanced datasets with few replicates. The variance estimates for synthetic data were unbiased, but limited laboratory information led to imprecise estimates. The same was observed for unbalanced synthetic datasets, where 20, 50 and 80% of the data were removed randomly. Removal led to a sharp increase of the interquartile range (IQR) of the variance estimates for batch effect and the residual. The model was also fitted to real‐world and total organic carbon (TOC) data, provided by the Wageningen Evaluating Programmes for Analytical Laboratories (WEPAL). For , the model yielded unbiased estimates with relatively small IQRs. However, the limited number of batches with replicate measurements (5.8%) caused the batch effect to be larger than expected. A strong negative correlation between batch effect and residual variance suggested that the model could not distinguish well between these two random effects. For TOC, batch effect was removed from the model as no replicates were available within batches. Again, unbiased model estimates were obtained. However, the IQRs were relatively large, which could be attributed to the smaller dataset with only a single replicate measurement. Our findings demonstrated the importance of experimental measurement design and replicate measurements in the quantification of uncertainties in wet chemistry soil data. Highlights: Accurate uncertainty quantification depends on the experimental measurement design. Linear mixed‐effects models can be used as a tool to quantify uncertainty in wet chemistry soil data. Lack of replicate measurements leads to poor estimates of error variance components. Measurement error in wet chemistry soil data should not be ignored.

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.