2.1 Soil data: the Swiss SSL and the School of Agricultural, Forest and Food Sciences (HAFL) data set

The current Swiss SSL in the mid-IR range consists of 3723 topsoil (0 to 20 cm) samples from 1094 locations from the Biodiversity Monitoring program (BDM; e.g., FOEN, 2018; Meuli et al., 2017) and 572 topsoil samples from 71 locations from the National Soil Monitoring Network (NABO; Fig. 1 and Table 1; e.g., NABO, 2018; Gubler et al., 2015). The Swiss SSL is described in full detail in Baumann et al. (2021). Less than 2 % of the samples in the SSL originate from organic soils.

Figure 1Spatial grid of BDM locations (green dots), NABO long-term monitoring locations (gray squares) and the purposive sampling design of peatlands in the Seeland and St. Galler Rheintal regions, which constitute the HAFL locations (orange dots; NABO, 2018; Gubler et al., 2015; FOEN, 2018; Meuli et al., 2017; Baumann et al., 2021).

Table 1Summary statistics of all samples in the HAFL data set, which is, in this study, also referred to as the local data set, and the BDM and NABO data sets. The latter two together constitute the current Swiss SSL, which contains carbon reference measurements from 4295 samples from 1150 different locations (Baumann et al., 2021). Q1 and Q3 refer to the first and third quartiles, respectively.

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We introduce a data set from the Bern University of Applied Sciences, School of Agricultural, Forest and Food Sciences (HAFL), which was set up using a purposive sampling design to specifically study drained peatlands and organic soils. This local HAFL data set (n = 116) contains soil samples from between 0 and 2 m depth from a range of natural and disturbed Histosols from 26 different locations in the Seeland and St. Galler Rheintal regions of Switzerland (Fig. 1 and Table 1;  IUSS Working Group WRB, 2014). These samples originate from either undisturbed and waterlogged organic horizons, mineralized organic horizons under agricultural use, horizons with sandy or calcareous substrate material or horizons containing a mixture of these characteristics.

2.2 Mid-IR soil spectroscopy measurements and preprocessing

All samples were dried, sieved (<2 mm) and finely ground using a ball mill to maximize the signal-to-noise ratio (Guillou et al., 2015). The samples were measured with a VERTEX 70 Fourier-transform infrared (FTIR) spectrometer with a high throughput screening extension (HTS-XT) from Bruker (Massachusetts, USA). We used a spectral range of 7500 to 600 cm⁻¹ and a spectral resolution of 2 cm⁻¹ so that each spectrum comprised of reflectance values at 6901 wavelengths. On each 24-well plate, there is a fixed gold panel as the reflectance background, and three NABO standards and two subsamples of 10 different samples were measured using the HTS-XT extension. This means that 10 samples with two different measurements were analyzed per plate, maximizing the signal-to-noise ratio by averaging the two measurements. Reflectance spectra were transformed to apparent absorbance and recorded as such. OPUS software was used for correcting atmospheric water and CO₂.

We tested several preprocessing steps in order to increase the information content for modeling and to reduce the collinearity between consecutive wavelengths. We tested using a Savitzky–Golay (SG) filter with a first and second derivative, as well as a first-, second- and third-order polynomial (Savitzky and Golay, 1964). The window size (resolution) of 35 variables (70 cm⁻¹) was kept constant. Instead, we tested different resolutions by selecting either all variables, every fourth or every eighth variable to reduce collinearity and redundancy among predictors. The combination of preprocessing steps used for all final modeling approaches was chosen that resulted in the lowest root mean squared error (RMSE) across the cross-validated calibration (see Sect. 2.4 below).

We used the simplerspec package for the R statistical language for reading spectra and metadata from Bruker OPUS binary files into a R list, gathering spectra into a data structure of a list, resampling spectra to new wavenumber intervals, averaging spectra of replicate scans and preprocessing the raw spectra with the parameters described above (Baumann, 2020).

2.3 Reference chemical analysis

In order to guarantee that reference data for all mid-IR spectroscopy models were measured using the same standard soil chemical analysis methods, we prepared and measured SC in the local HAFL data set using the same procedures as for the Swiss SSL (Baumann et al., 2021). Briefly, all the dried, sieved (<2 mm) and finely ground samples were measured for total carbon content by dry combustion, using the CHN628 Series Elemental Determinator from the Laboratory Equipment Corporation (LECO Corporation, St. Joseph, MI, USA). We used a soil standard sample with a mean total carbon content of 2.372 %. In order to compare the measurement accuracy and accordance between the two different CHN628 Series Elemental Determinator machines used for the Swiss SSL and HAFL samples, representative samples were selected using a two-step process. The data were separated into two clusters using the K-means clustering algorithm (Hartigan and Wong, 1979), followed by using the Kennard–Stone (KS) algorithm for each cluster separately (Kennard and Stone, 1969). The KS algorithm is a deterministic approach that uses Euclidean or Mahalanobis distance to select a set of samples uniformly distributed in principal component (PC) space (Kennard and Stone, 1969). Within the Swiss SSL, NABO and BDM samples used the same machine (Baumann et al., 2021).

2.4 Spectroscopic modeling

We resampled the data using five repetitions of a location-grouped, 10-fold cross-validation for all of our models to determine the optimal number of components in model tuning, as well as evaluating the model performance using the hold-out samples. The predicted carbon content was calculated in each model using the hold-out values of the measured, preprocessed and averaged mid-IR spectra. For the final models, the calculated average (mean) predictions over these five repetitions with the chosen number of components are shown. To avoid overfitting, we used the one standard error rule, i.e., instead of choosing the tuning parameter associated with the lowest RMSE, we chose the simplest model within one standard error (SE) of the empirically optimal model (e.g., Hastie et al., 2009).

We used partial least squares regressions (PLSRs; e.g., Wold, 1975; Wold et al., 1983, 1984, 2001) to predict SC. We tuned the PLSR using 1 to 10 components, and the final model for the number of components was chosen according to the one SE rule.

All spectroscopic models were evaluated for their performance using the RMSE, the ratio of performance to deviation (RPD; Williams and Norris, 1987, Eq. 5), the ratio of performance to interquartile range (RPIQ), the bias and R². The RPD is suitable for normal distributions, while the RPIQ is more suitable for non-normal distributions (Bellon-Maurel et al., 2010). Since different definitions of R² exist, we used the equation of the mean squared error skill score (SS_mse; Wilks, 2011), also known as the model efficiency coefficient (MEC; Nash and Sutcliffe, 1970) to indicate the R².

Given the large range of SC in these data sets, we also assessed the RMSE, RPD and RPIQ by increments of 10 % SC for all model validations. Hence, we calculated these metrics for all samples for which the measured SC values are between 0 % and 10 % SC, 10 % and 20 % SC and so on. In this manner, we expected to detect for which range of SC prediction error increases or decreases.

One advantage of repeated cross-validation is that model imprecision can easily be assessed for each prediction ($\widehat{Y}$) using the standard deviation (SD) and mean ($\overline{Y}$) of the predictions across five repetitions, respectively. In this study, the SD is shown as error bars for each prediction ($\widehat{Y}$) and was also calculated for each overall summary statistic assessing the model performance.

2.5 Calibration schemes

2.5.3 Models using RS-LOCAL subsets

In the third approach, we tested whether representative subsets of the SSL using the RS-LOCAL algorithm improved the accuracy of predicting SC of the local HAFL samples (Fig. 2). The RS-LOCAL algorithm was used to data-mine the SSL for samples suitable for local or location-specific calibrations according to similarities of spectral signatures between the local HAFL and SSL soil samples (Lobsey et al., 2017). Local HAFL samples were selected in the same manner as in local and SSL spiked models, resulting in iterations of the same samples as before (Fig. 2). This variable was defined in the RS-LOCAL algorithm as m (Lobsey et al., 2017); so, in our case, m=3, 5, 7, 10, 15, 20, 25, 30, 40, 50 and 58 for each respective iteration. RS-LOCAL used m data to resample, evaluate and then remove irrelevant data from the SSL so that only the most appropriate data for deriving a local calibration remained in a new SSL subset K. K and m together formed a RS-LOCAL data set, which was used for a calibration. In addition to the SSL and m data, three parameters were needed for RS-LOCAL as follows (Lobsey et al., 2017):

• k – the number of SSL samples randomly selected in the resampling step and also the target number of SSL samples returned by the algorithm

• b – the number of times each sample in the SSL was tested, on average, in each iteration of the algorithm

• r – the proportion of SSL samples removed in each iteration of the algorithm.

In order to optimize the tuning parameters, we performed a full factorial combination of k (50, 100, 150 and 300), b (40, 50 and 60) and r (0.05 and 0.01) based on recommendations of the developers (Lobsey et al., 2017). The size of K remains the same for all values of m, only as long as k, b, r and the size of the entire SSL remain constant. As in the other modeling approaches, each iteration was validated using the same 58 remaining local samples never used for any of the calibration iterations.

Figure 2The number of samples used in each calibration (C) and validation (V) scheme using HAFL, BDM and NABO data sets for (a) local, (b) SSL spiking and (c) RS-LOCAL approaches. The same 58 local HAFL samples never used in calibration were used to validate each modeling approach and iteration. Note different the scales on the y axes.

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3.1 Spectral preprocessing and analysis of local HAFL spectra

The lowest RMSE was achieved in the cross-validated calibration when using a SG filter with a first derivative and second-order polynomial (Savitzky and Golay, 1964) in combination with a window size of 35 points (70 cm⁻¹) and selecting only every eighth variable. This resulted in 209 variables between 634 and 3962 cm⁻¹, which formed the predictors for subsequent modeling. Reducing the number of variables did not have an effect on model performance but reduced collinearity and redundancy, increased the simplicity of the model and decreased the computation time (Appendix A). An example of the PLSR tuning based on the number of chosen components in each repetition according to the one SE rule is shown using all local HAFL samples in Appendix B.

Figure 3The raw (a) and preprocessed (b) mid-IR spectra of all the local HAFL soil samples (n = 116) colored by total carbon content (percent).

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The raw and preprocessed measured mid-IR spectra of the local HAFL soil samples (n = 116) were clearly distinct in relation to the SC content, ranging from 1 % to 52 % (Fig. 3a and b). Mineral and organic soil samples showed different absorbance patterns in both the raw and preprocessed mid-IR spectra. Preprocessed absorbance values showed a clear pattern according to the SC content almost across the entire spectrum and particularly, but not exclusively, around 800, 1050, 1900, 2050, 2900 and 3600 cm⁻¹.

A principal component analysis (PCA) of the preprocessed spectra of the local HAFL samples clearly revealed a variance in the distribution of the soil samples related to the SC content (Fig. 4). The first two PCs together explained 53.5 % of the total variance in the preprocessed spectra. Figure 4 also exemplifies one possible local calibration scheme, whereby the HAFL data is split into 20 representative samples used for calibration, 58 samples used for validation and the remaining samples. We also compared the similarity of soil samples from different depths at the same location by coloring the first two PCs by location (Appendix C). However, the preprocessed spectra from the same locations generally showed little similarity; there was no distinct pattern as there was for the SC content.

Figure 4PC1 vs. PC2, computed via scaled and centered PCA, of the preprocessed local HAFL soil spectra (n = 116) colored by total carbon content (percent). The axes labels show the relative amount of variance explained (percent) in parentheses. In this example, n = 20 representative samples were selected using the KS algorithm for calibrating a local model.

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3.2 Comparing local HAFL to SSL data

When comparing the three data sets, we found that the local HAFL data set showed a different SC distribution and covered a different range in soil variability than the Swiss SSL (Table 1 and Fig. 5). The relatively small HAFL data set originating from peaty soils had a uniform continuous distribution, whereas the BDM and NABO data had a positively skewed distribution with regard to SC (Table 1). Although the BDM data set contained the highest single value of SC, over 98 % of soil samples in the Swiss SSL originated from mineral soils. In contrast, more than half of the HAFL samples ranging from 1 % to 52 % were classified as organic soils. The first and second PCs – which together covered 40.3 % of the total variance – also revealed a clear overlap of preprocessed mid-IR absorbance variance for the BDM and NABO data sets (Fig. 5). There was less overlap in the variance of the preprocessed mid-IR absorbance values of the Swiss SSL and the HAFL data set. In the PCA space, the BDM and NABO data sets show a similarly shaped convex hull and almost identical centroid (mean), whereas the centroid is very distinct for the HAFL data set (Fig. 5). In Fig. 5, 122 samples, of which 20 are the local HAFL samples, were used as a RS-LOCAL subset to calibrate a model.

Figure 5PC1 vs. PC2 and the convex hulls and centroids (mean) in the PCA space of the preprocessed soil spectra of the local HAFL data set (n=116) and the BDM and NABO data sets, which make up the current Swiss SSL (n = 4295). Here, the PCs were computed via unscaled and uncentered PCA, since it showed the data distribution better than a scaled and centered PCA. The axes labels show the relative amount of variance explained (percent) in parentheses. In this example, the same representative local HAFL samples (n = 20) selected in Fig. 4 were used by RS-LOCAL to subset representative samples from the SSL (n = 102), which were used together for model calibration (n = 122).

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3.3 Predicted SC using (1) local, (2) SSL spiking and (3) RS-LOCAL subsets

We predicted SC content ($\widehat{Y}$) of the HAFL, BDM and NABO data sets using mid-IR soil spectroscopic PLSR models and compared them to the reference chemical measurements (Y). This is exemplified for each modeling approach in the case of 20 local HAFL samples in Fig. 6. For models using an RS-LOCAL subset, we found the best overall validation results using k=100, b=50 and r=0.05 and, therefore, chose these parameter values for all results shown here. The influence of RS-LOCAL parameter k on validation results is shown in Appendix D. Decreasing r to 0.01 had little influence on model performance and greatly increased the computation duration. There appeared to be no spatial correlation between chosen RS-LOCAL locations and target HAFL locations (Appendix E).

For calibration, all modeling approaches showed a high fit (R²>0.9) and low overall bias (≈0; Fig. 6a). The SSL spiking calibration scheme showed the lowest RMSE value. However, the accuracy of the spiked SSL calibration decreased and bias increased in the upper range of SC, which also explains the lower RPIQ value compared to local and RS-LOCAL calibration schemes. The RS-LOCAL calibration revealed the best model performance according to the RPD (6.92). The local PLSR, using only 20 samples, showed the lowest overall calibration accuracy based on the RMSE (3.72 % total carbon).

All model validations showed a similar fit (R² = 0.93 to 0.97). However, the bias, RMSE, RPD and RPIQ values differed among the three scenarios (Fig. 6b). The validation of the local PLSR had the lowest bias (0.53), but the validation of the RS-LOCAL subset had the best performance overall (RMSE = 2.82 % total carbon, RPD = 4.67 and RPIQ = 6.82). The validation of the spiked SSL scheme revealed the lowest prediction accuracy overall, especially with increasing values of measured SC. The error bars representing the SD of predictions across five resampled repetitions showed that there was the highest prediction uncertainty across repetitions in the validation of the local modeling approach. As with 20 local samples, validation statistics also show a good performance of PLSR models using RS-LOCAL subsets that contained as few as 5, 7 and 10 local samples (R² = 0.93 to 0.96; bias = 0.2 to 1.651; RMSE = 2.71 % to 3.89 % total carbon; RPD = 3.38 to 4.86; and RPIQ = 4.93 to 7.09; Appendix F).

Figure 6Predicted ($\widehat{Y}$) vs. observed (Y) total carbon content (percent) by calibrating a PLSR with 20 local HAFL samples (a) and validating it with the remaining local HAFL samples (n=96) (b). A PLSR was calibrated using only 20 local HAFL samples (1), adding the entire SSL to the 20 local HAFL samples (2) and using a RS-LOCAL subset of the SSL also containing the 20 local samples (3). The error bars signify the SD, and where none are present, the components remained identical across five repetitions and, thus, SD =0.

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We compared R², bias, RMSE, RPD and RPIQ as indicators of overall model performance depending on the number of local HAFL samples in each calibration scheme for all three modeling approaches, i.e., (1) local, (2) SSL spiking and (3) RS-LOCAL subsets (Figs. 7 and 8). R² was a poor indicator of model performance and did not show substantial differences between modeling approaches and calibration schemes (Fig. 7). Local models showed the lowest bias, regardless of the number of samples used during calibration (Fig. 7). The bias of validations of spiked SSL models only lowered slightly as the number of local samples was increased and remained large overall (>3). Bias was reduced significantly in validated models of RS-LOCAL subsets when at least five local samples were included and continued to decrease slightly with the increasing number of local samples. Models with five and 10 samples stand out with very little bias.

Model accuracy (RMSE) varied considerably between calibrations and validations when SSL samples were used during calibration (Fig. 7). There was less of a difference between calibration and validation in local models, where the RMSE decreased with the increasing number of local samples in model calibration. As with model bias, the RS-LOCAL subsets again showed a threshold or minimum of five samples in order for the RMSE of model validations to lower significantly. Model validations of local and RS-LOCAL subsets showed very similar accuracy overall (RMSE ≈ 3 % total carbon). However, only five or 10 local samples were required to achieve an accuracy of RMSE = 3.16 % or 2.71 % SC, respectively (Fig. 7 and Appendix F). In contrast, local modeling approaches required 50 local samples to achieve a RMSE of <3 % SC.

Figure 7R², bias and RMSE values in percent of total carbon (RMSE in logarithmic scale) vs. the number of local HAFL samples used in local HAFL (a), local combined with SSL (b) and RS-LOCAL subsets (c), where k = 100. Error bars represent the SD between resampled repetitions, and where not present, there was no variation in the respective summary statistic across five repetitions. Dashed lines between data points do not represent real measurements and are only for visual guidance.

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Local and RS-LOCAL models also revealed similar and better model performance than SSL spiking modeling approaches (Fig. 8). Both RPD and RPIQ gradually increased in local models with increasing numbers of local HAFL samples in calibration. As with bias and RMSE, RPD and RPIQ values also indicate high-prediction accuracy with as few as five or 10 local HAFL samples when calibrating with RS-LOCAL subsets (RPD = 4.08 and 4.66 and RPIQ = 5.96 and 6.81, respectively).

Figure 8RPD and RPIQ vs. the number of local HAFL samples used in local HAFL (a), local combined with SSL (b) and RS-LOCAL subsets, where k = 100 (c). Error bars represent the SD between resampled repetitions, and where not present, there was no variation in the respective summary statistic across five repetitions. Dashed lines between data points do not represent real measurements and are only for visual guidance.

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Prediction accuracy in model validations was highest for mineral soils, or ranges of SC between 0 % and 20 % for all modeling approaches (Fig. 9). Local and RS-LOCAL modeling approaches showed better predictive performance for samples with higher SC. In local modeling approaches, samples with 0 % to 20 %, and especially 10 % to 20 % SC, were predicted increasingly well with an increasing number of local HAFL samples in the model calibration. Soils between 0 % and 10 % SC were predicted with the highest accuracy with the SSL spiking approach. However, samples with > 10 % were predicted with higher accuracy using local and RS-LOCAL calibration schemes. Validations of RS-LOCAL calibration schemes again showed a threshold around five local HAFL samples. After this threshold, RMSE, RPD and RPIQ results for samples with > 20 % remained constant with an increasing number of local samples during calibration. In contrast, samples containing 0 % to 20 % SC were considerably more unstable, depending on the number of local samples during calibration.

Figure 9RMSE (in percent of total carbon and logarithmic scale), RPD and RPIQ of validation results vs. the number of local HAFL samples used in local HAFL (a), local combined with SSL (b) and RS-LOCAL subsets (c), where k = 100. Observations (Y) were grouped in increments of 10 % SC, and the validation metrics were calculated separately for each group. Dashed lines between data points do not represent real measurements and are only for visual guidance.

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4.1 Spectral patterns reflect mineral and peat composition

The measured and preprocessed mid-IR soil spectra and PCA results of all local HAFL samples revealed a high correlation between the spectral absorbance values and a broad range of SC content overall (Figs. 3 and 4). According to past studies that assessed variable importance, we assumed that soil texture and mineralogical and organic composition influence mid-IR spectral absorbance the most (Madari et al., 2006; Bornemann et al., 2010; Calderón et al., 2011). SOC (soil organic carbon), for example, is known to be related to a variety of bands that represent absorptions due to organic molecules such as proteins with C–O, C=O and N–H bonds (Viscarra Rossel and Behrens, 2010). Local HAFL samples containing both a high number of organic compounds and carbonates created distinct absorbance bands around 1450, 1460, 2855 and 2930 cm⁻¹ for aliphatic C–H constituents (Madari et al., 2006) or around 1320 cm⁻¹ for hydroxyl groups bonded to carbon (C–O–H) (Bornemann et al., 2010) and around 2500 cm⁻¹ for carbonates (Calderón et al., 2011). Future studies should investigate whether the overlapping of spectral signals for organic and mineral components increases at high SC concentrations implies that spectral absorbance patterns above a certain threshold of SC no longer differentiate substantially.

4.2 RS-LOCAL improves model performance and increases efficiency

The RS-LOCAL approach, using representative local and SSL samples, was found to be the best of the three compared approaches. It significantly reduces the number of reference measurements that need to be made at new locations for five samples. In addition, the RS-LOCAL approach helps remove the strong bias of spiked SSL calibrations (Figs. 6 and 7), increasing the underestimated predictions of SC in the upper range. Finally, the additional samples provided from the SSL also reduce the uncertainty of SC predictions of resampled repetitions in the PLSR models, as can be seen from the smaller error bars of the residuals. Predictions of SC from 0 % to 10 % became more accurate when using additional samples from the SSL in the RS-LOCAL subset (Fig. 9).

We postulate that SC prediction accuracy of organic soil samples, using SSL-derived models, may be improved in future studies by adding more peat soil data to the Swiss SSL (Baumann et al., 2021), specifically for samples at different decomposition and mineralization stages. One of the most important characteristics of a high-quality SSL is that it contains the highest possible variation in soil characteristics within its designated area (Viscarra Rossel et al., 2016a). The SC distribution and the spectral principal component space of the HAFL compared to the BDM and NABO samples showed that the soil variability in the HAFL samples is only marginally covered by the current SSL (Table 1 and Fig. 5).

The use of our modeling approach, the PLSR of RS-LOCAL subsets, to predict soil properties at new locations for future studies and applications depends on the level of accuracy needed. For organic soils on a farm or landscape level, an accuracy of approximately 2 % to 3 % total carbon is suitable for quantifying SC. On the one hand, this range of accuracy is not useful for mineral soils, which, in Switzerland for example, contain average (mean) topsoil SOC concentrations of 2 % on arable locations and 2.5 % on temporary grassland locations (Leifeld et al., 2005). On the other hand, our validation results using the SSL spiking approach show that samples with 0 % to 10 % SC were constantly predicted with a RMSE < 1 % SC and RPD above 2 (Fig. 9). This implies that, when targeting mineral agricultural soils, mid-IR spectroscopic models making use of a SSL deliver the required accuracy for applications and end-users. These findings are supported by Baumann et al. (2021).

Few studies, to our knowledge, have predicted organic soils up to 52 % total carbon using mid-IR soil spectroscopy without splitting model calibration for mineral and organic soils. One exception is the mid-IR SSL of the United States, which contains about 2000 organic soil samples (Wijewardane et al., 2018; Dangal et al., 2019). Nocita et al. (2014) predicted SOC for croplands, grasslands, woodlands and organic soils separately from about 20 000 samples from the Land Use/Cover Area frame Survey (LUCAS) across Europe using vis-NIR spectroscopy. For the model using only organic soil data with a range of 12.0 % to 58.68 % SOC, predictions were less accurate (RMSE = 5.114 % SOC) than in this study (Nocita et al., 2014).

One advantage of the RS-LOCAL–PLSR approach used here is that the statistical modeling is simple and produces easy-to-understand models compared to other transfer and deep learning approaches (Padarian et al., 2019a, b). Using spectral- or model-based information from SSLs by spiking, subsetting and memory, instance and transfer learning may even be beneficial for parts of the world lacking legacy soil data or funding to establish their own SSL. In other words, the SSL of one region may be used to predict locally for another region that does not have a SSL. This is comparable to the concept of homosoil in digital soil mapping (Mallavan et al., 2010).

However, there are still some drawbacks. As mentioned by Padarian et al. (2019a), spiking and subsetting are dependent on the size of local and global data sets and may still bias the predictions towards the local data set rather than fully using valuable global information, which generates less robust models. Although transfer learning of model rules, or network weights, showed promising results on a continental scale (Padarian et al., 2019a), it has not been tested when transferring national spectral knowledge to a field scale.

Ultimately, soil spectroscopy has the potential to speed up the quantification of soil properties for soil mapping and monitoring. Several studies have shown how this affects soil maps and associated uncertainties (Brodský et al., 2013; Viscarra Rossel et al., 2016b; Ramirez-Lopez et al., 2019) but only on a farm scale. It still remains to be implemented in a large-scale soil information system.