Soil spectroscopy improves mid infrared soil property prediction through optimized preprocessing and variable selection

Mid-infrared (MIR) spectroscopy is a powerful, eco-friendly, and cost-effective technique for predicting soil property. However, its predictive accuracy can be affected by factors such as moisture content, particle size, sensor variability, and the baseline noise. To address these limitations, this study investigated the impact of combining various preprocessing techniques with variable selection methods on the performance of partial least squares regression (PLSR) models. Soil samples from the Rhamna region of Morocco were analyzed to estimate key properties, including total nitrogen (TN), total carbon (TC), total organic carbon (TOC), clay, silt, sand, moisture content (MC), pH, phosphorus (P₂O₅), and cation exchange capacity (CEC). Spectral data were preprocessed using methods such as standard normal variate (SNV), Savitzky–Golay smoothing (SG smoothing), first and second derivatives (SG1D and SG2D), and their combinations (e.g., SNV + SG2D). The best-performing preprocessing combinations were then used with variable selection approaches, interval PLS (iPLS), variable importance in projection (VIP), and selectivity ratio (SR). The results indicated that Savitzky–Golay (SG) derivatives combined with SNV generally improved model performance across most soil properties. In particular, total nitrogen (TN) prediction improved primarily with the first SG derivative, with R²_cv increasing from 0.82 (raw spectra) to 0.88 (SG1D), while RMSEcv decreased from 0.03% to 0.01%. Further improvements were achieved through variable selection, with iPLS providing the most consistent enhancement across properties with a very low number of features compared to the other methods. Overall, the integration of optimal preprocessing and iPLS variable selection significantly improved the predictive accuracy and robustness of partial least squares regression (PLSR) models for soil property estimation compared with the full spectrum.

1 Introduction

Mid-infrared (MIR) spectroscopy has emerged as a powerful, non-destructive, eco-friendly, and low-cost soil analysis tool. It offers many advantages, such as high resolution, wide absorbance range, and strong signals, which make it popular and important in the study of soil environments (1). The combination of MIR data with machine learning, especially with partial least square regression as a mathematical model, is widely used to predict soil properties (2) and has proven excellent predictive capabilities for various properties such as total carbon, nitrogen, clay, potassium, pH, sand, and silt (3–5).

However, the accuracy of soil spectroscopy models based on infrared spectral data might be impacted by several factors, such as moisture. (6) found that the moisture level of the studied sample impacts the accuracy of the models for different soil properties. The soil particle size was also found to be an impacting factor for model accuracy (7). Baseline drift and background noise are similar factors that influence the model accuracy (8). The data source may also impact the accuracy of the predictive models, as benchtop, mobile, and homemade sensors perform differently in predicting soil properties (9).

These factors vary significantly across soil environments, potentially affecting the robustness and transferability of commonly applied preprocessing strategies. Most existing preprocessing workflows have been developed and validated using datasets from well-studied sources, leaving uncertainties regarding their generalized applicability across diverse and underrepresented soil contexts (10, 11). This highlights the need to evaluate variable selection approaches in combination with optimized preprocessing, especially for datasets originating from less-studied soil regions.

To overcome these challenges, data preprocessing is an efficient tool that can significantly increase the predictability of soil properties using mid-infrared spectral data (12). Different preprocessing methods were applied to the mid-infrared data, such as standard normal variate (SNV), normalization, Savitzky–Golay smoothing, and 1st and 2nd derivatives. These transformative approaches have shown excellent to acceptable results when predicting soil properties using the partial least square algorithm (13, 14). Likewise, combining pretreatments increases the accuracy of the predictive model (15); found that applying normalization after moving average is considered the best preprocessing step for MIR data to predict pH, organic carbon, Mg, and moisture content, while applying standard normal variate after moving average is the best approach to predict phosphorus. Further research by (16) suggests that the combination of normalization and the 1st derivative of Savitzky–Golay leads to better partial least squares regression (PLSR) performance.

The model’s development and behavior have been greatly influenced by the preprocessing techniques and combinations used; however, the variable selection is crucial to the model’s further enhancement and accuracy, and these variable selection techniques can provide even greater prediction accuracy in a shorter computing time than the full-spectrum model (17). Various studies have applied variable selection, such as interval-PLS and variable importance in projection (VIP) to predict soil properties using infrared spectral data, and these approaches have demonstrated their ability to achieve strong predictive performance in the model (18, 19). Nevertheless, recent work on Moroccan soils indicates that iPLS and VIP mainly contribute to model simplification rather than systematic accuracy improvements (20).

This study aimed to investigate the impact of combining preprocessing (standard normal variate, Savitzky–Golay smoothing, 1st and 2nd derivatives) with iPLS, VIP, and selectivity ratio as variable selection methods on the prediction accuracy of the PLSR model to predict total nitrogen (TN), total carbon (TC), total organic carbon (TOC), clay, silt, sand, moisture content (MC), pH, phosphorus (P₂O₅), and cation exchange capacity (CEC).

2 Materials and methods

2.1 Soil sample collection and preparation

Fifty soil samples were collected from different locations and depths in the Rhamna region, to assess the impact of combining statistical preprocessing and variable selection methods on the prediction accuracy of some soil properties. Each soil sample was finely ground, sieved, and oven-dried at 39°C for 48 h before analysis.

2.2 The structural framework of the study

The standard procedure for using spectral data to calibrate multivariate models to predict soil properties begins with the construction of a database. To ensure accuracy, one or more preprocessing techniques intended to improve the signals and reduce noise interference can be implemented. Subsequently, relevant variables were identified using suitable variable selection methods. The next stage involves developing a modeling framework and assessing the models that have been built. Statistical metrics, such as the root mean square error (RMSE) of prediction and the coefficient of correlation (R²), were used to evaluate the accuracy of these models (21).

This study aimed to examine the impact of preprocessing tools on predictive models; therefore, the procedure outlined below and in Figure 1 was adhered to. Models generated based on raw data and several preprocessing algorithms (standard normal variate, Savitzky–Golay smoothing, Savitzky–Golay 1st and 2nd derivatives, Savitzky–Golay 1st derivatives coupled with SNV, and Savitzky–Golay 2nd derivatives coupled with SNV) were evaluated. Furthermore, variable importance projection (VIP), selectivity ratio (SR), and interval-PLS (iPLS) were used to highlight important variables. The resulting data were then used to generate PLSR models to predict TN, TC, TOC, clay, silt, sand, MC, pH, P₂O₅, and CEC in Moroccan soils.

Figure 1

Figure 1. Workflow for evaluating the impact of preprocessing tools and their combinations with variable selection on PLSR models for estimating soil properties.

2.3 Wet chemistry

Soil physical–chemical properties (Table 1), such as total nitrogen (TN) via the combustion method (ISO 13878), soil total carbon (TC) via the combustion method (ISO 10694), total organic carbon (OC) (ISO 10694), sand, silt, and clay (Bouyoucos method ISO 13317), soil pH_{(1/5 in water)} (ISO 10390), moisture (MC) using the gravimetric method (ISO 11461), available phosphorus (P₂O₅) using the Olsen method (ISO 11263), and the hexamine-cobalt method for cation exchange capacity (CEC) (NF ISO 23470) were analyzed in the Soil Testing Laboratories of Mohammed VI Polytechnic University (UM6P).

Table 1

Table 1. Statistical summary of wet chemistry analysis.

2.4 Chemometrics analysis

2.4.1 Data processing

Chemometrics is essential for fully extracting the potential of contemporary instruments (22). In numerous investigations, it has been used to estimate different soil parameters using spectral data, such as near- or mid-infrared data, using various types of models, such as Partial Least Square Regression (2). As indicated by (23), the PLSR is the most employed learning modeling method. It has proven to be a good mathematical model for predicting various soil properties, such as soil organic carbon, total nitrogen, cation exchange capacity, clay, sand, pH, and other properties (3, 4). Predictions based on unprocessed soil sample laboratory spectra appear promising for quantitatively estimating soil chemical properties (24). However, the accuracy of this information can be affected by different factors, such as moisture, variations in soil roughness, and soil particle size. Therefore, data preprocessing methods that can enhance spectral information must be implemented (7, 24). Numerous preprocessing techniques, including standard normal variate, Savitzky–Golay smoothing, 1st derivative, and 2nd derivative, have been used in various studies and have demonstrated good prediction capabilities for soil properties (25, 26). The standard normal variate is an easy approach for spectral data normalization that works row by row, aimed at correcting for light scattering using the formula: $SNV=\frac{xi - \overline{x}i}{Si}$, where $xi$ represents the signal of the observation, $\overline{x}i$ is its mean, and $Si$ is its standard deviation (27).

The derivation of Savitzky–Golay pre-processing is one of the most extensively utilized drift-noise reduction strategies. The first and second are two orders, each with a special role. The second derivative is recommended to address the effect of the offset and linear trend of the baseline, while the first is intended only for a constant baseline effect (28). The Savitzky–Golay derivative uses the same procedure as the Savitzky–Golay smoothing described by (29), but with an added step. The derivative of this function is calculated after fitting the polynomial to a window around the moving point. This value was then used as the derivative estimate for the central point (29).

2.4.2 Variable selection

In areas where datasets with many variables are available, variable and feature selection has attracted considerable interest in the research community. The variable selection process has many advantages, such as enhancing data comprehension and visualization, lowering the need for measurement and storage, shortening the time needed for application and training, and reducing the impact of dimensionality to increase prediction accuracy (30). The use of some variable techniques, such as variable selection with interval-PLS (iPLS) and variable importance in projection (VIP), has proven to be more effective and increases the accuracy of the model (31, 32). The selectivity ratio is also beneficial for increasing predictive accuracy by concentrating on a small, highly relevant subset of variables (33).

2.4.3 Variable selection with interval

Interval partial least squares (iPLS) is an approach for finding intervals of variables that are highly important for prediction. The algorithm splits the variables (predictors) into intervals and attempts to find the best combination of intervals that has the highest predictive accuracy. This interval selection can be performed using two methods: forward and backward. The forward method is when the intervals are included successively, whereas the backward method is when the intervals are excluded successively (34). In this study, forward iPLS was applied to the data after selecting the optimal preprocessing on R.

2.4.4 Variable importance in projection

Variable importance in projection-partial least squares (VIP-PLS) is a multivariate statistical methodology employed to evaluate the significance of individual indicators in influencing an aggregate index. The primary objective of VIP-PLS is to establish a hierarchical ranking of indicators based on their respective degrees of importance to an aggregate index. This facilitates a clear understanding of the relative contributions of individuals (35). The VIP score is calculated using the following equation: ${VIP}_j=\sqrt{\frac{{\sum }_{f=1}^F{W}_{jf}^2·{SSY}_{f·}J}{{SSY}_{total·}F}}$, where w_jf represents the weight value for j variable and f component, SSY_f is the sum of squares of explained variance for the fth component, and J is the number of X variables. SSY_total is the total sum of squares explained by the dependent variable, and F is the total number of components (36).

2.4.5 Selectivity ratio

The selectivity ratio is the ratio of the explained variance to the residual variance for each variable in a dataset, which is calculated after applying a target projection in a multivariate analysis. This ratio is based on the ability of a variable to discriminate between the different groups of samples. A high selectivity ratio indicates that a variable has a strong discriminative advantage (37). The selectivity ratio is defined as follows: $S{R}_i=\frac{S{S}_{i, explained}}{S{S}_{i, residual}}$. The SS_i,residual represents the portion of the variance of variable i that is explained by the target projection component, that is, the part aligned with the PLS regression direction. In contrast, SS_i,residual denotes the remaining or unexplained variance of that variable after subtracting the target-projected part (the residual variance in the model). Therefore, the ratio quantifies the relevance of each variable’s variance to prediction versus residual noise, with higher SR values indicating greater predictive importance (36).

2.5 Spectra collection and preprocessing

The spectral data acquisition was done at the soil spectroscopy laboratory of the Center of Sustainable Soil Sciences (C3S) Mohammed VI Polytechnic University (UM6P) of the Mohammed VI Polytechnic University, using a Bruker Tensor II bench-top spectrometer coupled with the Diffuse reflectance infrared Fourier transform spectroscopy (DRIFT) technology. The generated spectra were an average of 60 scans from each sample, at the 4,000 and 600 cm⁻¹ range, with a 4 cm⁻¹ resolution.

Prediction models were built using the entire FTIR spectra measured for the soil samples. Nine groups of PLS models were established, namely raw spectral data, SNV, SG smoothing (polynomial order = 0 and number of windows = 3), 1st SG derivative (polynomial order = 1, number of windows = 3, and derivative order = 1), 2nd SG derivative (polynomial order = 2, number of windows = 15, and derivative order = 2), SNV coupled with 1st SG derivative, 1st SG derivative coupled with SNV, 2nd SG derivative coupled with SNV, and SNV coupled with 2nd SG derivative data. The optimal number of wavelengths was identified by evaluating multiple configurations, with selection based on predictive accuracy. These models were validated using leave-one-out cross-validation (38), R², and the root mean square error (RMSE_cv), which were calculated to evaluate the accuracy of each model. Based on these metrics, the best prediction model was selected to apply iPLS, VIP, and SR as variable selection techniques. PLSR modeling was conducted in the R environment using the mdatools package (39). Spectral preprocessing was performed using prospectr (40) and variable selection techniques were implemented using the plsVarSel package (41).

To test whether the optimal preprocessing combined with variable selection has improved the model performance, a paired, non-parametric Wilcoxon signed-rank test on cross-validation metrics (R²_cv and RMSE_cv) comparing raw with the optimal preprocessing combined with best variable selection approaches (α = 0.05) (42, 43). The tests were performed collectively across all 10 soil properties.

3 Results and discussion

3.1 Raw data

Figure 2 illustrates the FTIR spectra of the soil samples for raw data and after each preprocessing technique. The raw spectra show all the studied samples’ original features, divided into four regions. The first, from 4,000 cm⁻¹ to 2,500 cm⁻¹ is characterized by single bond stretch (C–N, C–H, O–H), the second, is located between 2,500 and 2,000 cm⁻¹ which represents the triple bond (C≡N). Double bonds can be found in the third region, which starts from 2,000 cm⁻¹ to 1,500 cm⁻¹. The last region between 1,500 cm⁻¹ and 400 cm⁻¹ is defined as the fingerprint zone (C–C, C–O, C–N) (44). As shown in Table 2, the prediction model built using PLSR on raw data yielded good predictions for TN (R²_cv = 0.82), TC (R²_cv = 0.88), clay (R²_cv = 0.81), silt (R²_cv = 0.82), and MC (R²_cv = 0.8), and acceptable predictions for sand (R²_cv = 0.79), TOC (R²_cv = 0.87), pH (R²_cv = 0.66), and P₂O₅ (R²_cv = 0.6), whereas CEC was poorly predicted (R²_cv = 0.46).

Figure 2

Figure 2. FTIR spectra of the soil samples before preprocessing and after applying different statistical pretreatment methods (SNV, SG smoothing, Savitzky–Golay 1st and 2nd derivatives. SNV coupled with Savitzky–Golay 1st derivative, Savitzky–Golay 1st derivative coupled with SNV, Savitzky–Golay 2nd derivative coupled with SNV, and SNV coupled with Savitzky–Golay 2nd derivative).

Table 2

Table 2. Table of merit of the prediction of (TN), total carbon (TC), total organic carbon (TOC), clay, silt, sand, moisture (MC), pH, phosphorus (P₂O₅), and cations exchange capacity (CEC) using medium infrared (MIR) data and preprocessing data with the application of iPLS, VIP, and SR.

3.2 Preprocessed data

As shown in Figure 2, after the application of preprocessing, the spectra become different. The spectra shapes after SNV preprocessing seem similar, the spectra become tightly grouped and follow a consistent baseline, with a decrease in inter-sample variation, showing that these processes have scaled it to a common range and maintained the spectra. SG smoothing is expected to smooth the spectra and reduce the noise while preserving the peaks; however, this preprocessing does not seem to have any impact on the spectra because the raw spectra and SG smoothing spectra seem to be similar.

For the SG 1st derivative, the changes in absorption are highlighted, and the peaks become more pronounced, helping to observe spaced spectral features. The positions of the absorption changes positions are easier to identify, and the baseline of the derivative spectra tends to be flatter and closer to zero, despite the spectra being noisier. The 2nd derivative exhibited the same changes, except that it corrected the baseline drift more effectively and exaggerated some data points, making them noisier than the 1st derivative.

When the 1st derivative is applied to the SNV, the noise increases compared to the raw data, and the peaks are more pronounced when the baseline is corrected and a cleaner and more detailed representation of spectral variations is obtained. After the reverse procedure (applying SNV to the 1st derivative), properties similar to those in the previous plot appear, but the 1st derivative applied to the SNV is more effective in reducing the variability.

After applying the SNV to the 2nd derivative, the baseline was corrected with highlighted peaks. When applying the 2nd derivative to the SNV, this preprocessing yielded a more detailed spectrum with improved resolution. The slope differences and baseline drift were corrected compared to the raw data, while the previous preprocessing was still better at correcting the baseline drift. Small peaks were highlighted by low-frequency noise.

3.3 Soil property prediction

The analysis involves 12 developed models (raw data, SNV, SG Smoothing, SG1D, SG2D, SNV + SG1D, SG1D + SNV, SG2D + SNV, SNV + SG2D, iPLS, VIP, and SR) for each property from the studied 10 soil properties (TN, TC, TOC, clay, silt, sand, MC, pH, P₂O₅, and CEC), with each model’s predictive accuracy assessed through R² and RMSE, while the selection of the optimal preprocessing for variable selection application was done using two criteria, the R² and RMSE and model complexity.

3.3.1 Total nitrogen

The results of predicting TN using PLS and different preprocessing methods showed that the Savitzky–Golay 1st derivative was the preprocessing method that yielded the best prediction, with an R²_cv of 0.88 and an RMSE_cv of 0.01%. Savitzky–Golay 2nd derivative, SNV coupled with SG1D, SG1D coupled with SNV, and SNV with SG2D also yielded a good prediction higher than the raw data prediction ranging between 0.85 and 0.88 for the R²_cv and 0.02% and 0.03% for the RMSE_cv, respectively. SNV and SG smoothing yielded good predictions but were lower than the raw data (R²_cv <0.8 and RMSE_cv = 0.03%).

3.3.2 Total carbon

All preprocessing techniques employed did not show any improvement and generated R²_cv below the R squared of the raw data, except Savitzky–Golay smoothing, which yielded similar results with an R²_cv of 0.88 and an RMSE_cv (0.28%) higher than the RMSE_cv of the raw data. The inconsistent performance observed for total carbon using raw MIR spectra likely reflects fundamental spectroscopic limitations rather than deficiencies in model calibration. Total carbon includes both organic and inorganic carbon fractions, which exhibit different MIR spectral behaviors. Organic carbon is mainly associated with broad and chemically informative absorption features, whereas inorganic carbonates show more specific bands that may overlap with organic signals (45, 46).

Consequently, raw spectra may already capture the dominant organic carbon information, whereas common preprocessing techniques can unintentionally suppress or distort these broad features. This likely explains why preprocessing did not improve and, in some cases, reduced the predictive performance compared with the raw spectra.

3.3.3 Total organic carbon

The combination of Savitzky–Golay’s 1st derivative and SNV yielded good predictions for total organic carbon (R²_cv = 0.81, RMSE_cv = 0.13%), with a better calibration performance of SNV applied to SG1D (SG1D + SNV). Savitzky–Golay’s 2nd derivative and SG2D applied to SNV resulted in the same predictive performance as the raw data models (R²_cv = 0.78, RMSE_cv = 0.14%). Conversely, SNV, SG smoothing, and SG2D + SNV generated acceptable results (0.76 < R²_cv < 0.77, 0.14% < RMSE_cv < 0.15%) but did not show any improvement in predictive performance (lower than the raw data).

3.3.4 Clay

The results of predicting clay content using PLS and various preprocessing methods highlighted that SG1D + SNV was the optimal preprocessing method with the highest R²_cv (0.86) and lowest RMSE_cv (7.04%). SNV, SG1D, SG2D, SNV + SG1D, SG2D + SNV, and SNV + SG2D also exhibited good predictive performance, with an R²_cv higher than and an RMSE_cv lower than the raw data. SG smoothing demonstrated an R²_cv similar to raw data (0.81) but higher RMSE_cv (8.25%).

3.3.5 Silt

With an R² value of 0.86 and an RMSE_cv of 3.72%, the application of Savitzky–Golay 2nd derivative after applying SNV (SNV + SG2D) produced the highest accuracy in the silt content prediction results utilizing PLS. With R²_cv values of 0.81 and a slight difference in the RMSE_cv (4.27%), Savitzky–Golay smoothing had a predictive performance similar to that of the raw data. The SG1D, SNV + SG1D, SG1D + SNV, and SG2D + SNV techniques also elevated R²_cv to 0.86 and lowered RMSE_cv to 3.8%. In contrast, SNV and SG2D did not improve the predictive accuracy of the model and yielded inferior R²_cv and RMSE_cv values of R²_cv = 0.62, RMSE_cv = 4.07%, and R²_cv = 0.6, RMSE_cv = 3.74%, respectively.

3.3.6 Sand

As shown in Table 2, the results of the sand content prediction using PLS and multiple preprocessing methods showed that the SNV + SG2D combination yielded the highest R²_cv and the lowest RMSE_cv, 0.86% and 8.87%, respectively. Savitzky–Golay’s 1st and 2nd derivatives, SNV + SG1D, SG1D + SNV, and SG2D + SNV also yielded good prediction performance and higher than the raw data with an RMSE_cv of 9.78%, 9.48%, 9.36%, 9.4%, and 9.28%, respectively, and an R²_cv of 0.83 for SG1D and 0.84 for the other preprocessing methods. SNV did not improve the prediction, resulting in similar results as the raw data (R²_cv = 0.79, RMSE_cv = 10.78%). In contrast to all the previous preprocessing methods, SG smoothing lowered R²_cv to 0.78 and elevated RMSE_cv to 11.04%, suggesting that smoothing is unsuitable for the prediction of sand in this context.

3.3.7 Moisture content

All the derivative preprocessing and their combination with SNV improved the prediction accuracy of the moisture content, with R²_cv ranging between 0.8 and 0.85 and RMSE_cv between 0.68% and 0.7%. The highest R²_cv (0.85) and lowest RMSE_cv (0.67%) were generated by SG1D + SNV, ranking it as the best preprocessing methods to predict MC in this context. SNV alone could not enhance the model’s predictive accuracy and delivered results similar to raw data (R²_cv = 0.8, RMSE_cv = 0.79%). In contrast, SG smoothing increased the RMSE_cv to 0.82% and decreased the R²_cv to 0.78.

3.3.8 pH

The performance metrics showed that SG smoothing and SG2D + SNV decreased the predictive performance of the model compared to the raw data model, with R²_cv values of 0.61 and 0.58 and RMSE_cv values of 0.39 and 0.41, respectively. The SG1D + SNV also decreased the predictive performance, even though this preprocessing yielded a similar R²_cv (0.66) to the raw data but a higher RMSE_cv (0.37), which led to a higher predictive error. In contrast, SNV + SG2D generated a similar RMSE_cv but a higher R²_cv (0.67). The remaining preprocessing methods (SNV, SG1D, SG2D, and SNV + SG1D) improved the model performance by lowering the RMSE_cv and increasing the R²_cv, suggesting SNV + SG1D as the optimal preprocessing method for predicting pH (R²_cv = 0.73, RMSE_cv = 0.32).

3.3.9 Phosphorus

Overall, none of the used preprocessing methods improved or at least maintained the predictive raw data model, except for SNV and SG smoothing, which showed better performance and nearly identical results (R²_cv = 0.62 and RMSE_cv = 24.29 mg/kg for SNV and R²_cv = 0.61 and RMSE_cv = 24.74 mg/kg). The low MIR prediction accuracy obtained for soil phosphorus agrees with previous studies reporting unreliable spectroscopic prediction of phosphorus due to its weak association with MIR-active soil components (47).

3.3.10 Cation exchange capacity

In contrast to phosphorus, all preprocessing improved the prediction accuracy of the CEC model, except for SG smoothing, which yielded results similar to those of the raw model’s metrics (R²_cv = 0.46, RMSE_cv = 6.3 meq/100 g). The results also show that the best preprocessing for CEC prediction using PLSR is SG2D + SNV, with the highest R²_cv (0.59) and the lowest RMSE_cv (5.52 meq/100 g). The moderate predictive performance obtained for CEC can be explained by the limitations of MIR spectroscopy. The cation exchange capacity is not spectrally active, and its prediction relies on indirect correlations with clay mineralogy and soil organic matter rather than direct absorption features (48). explicitly highlights this limitation, showing that accurate MIR-based CEC prediction is strongly dependent on the dataset size and modeling strategy.

Overall, the results presented in Tables 2, 3 suggest that the application of Savitzky-Golay (SG) preprocessing, either alone or in combination with standard normal variate (SNV), improves the model performance for most soil properties. However, the order of SNV (applying SNV to the derivative or applying the derivative to the SNV) plays a crucial role in decreasing or increasing the model performance. This combination yielded strong predictive performance for most soil parameters, indicating that it was the most effective preprocessing technique tested, except for TN, TC, and P₂O₅. SNV and Savitzky–Golay derivatives and their combination offered the best results for different soil properties and for different regression techniques (partial least squares, support vector regression, cubist, and convolutional neural networks), as proven in a similar study by (49). In a study by (50), the optimal preprocessing to develop a model for total nitrogen monitoring in situ and in-door for different depths and the optimal preprocessing combinations for the best-performing models (both indoor and in situ) consistently included Standard Normal Variate and derivative preprocessing. Other studies have found other optimal preprocessing combinations to predict soil properties; however, their optimal combination always includes derivative pretreatment, which highlights its role in improving model accuracy (26, 51).

Table 3

Table 3. Optimal preprocessing with RMSE_cv and R²_cv for each soil property.

3.4 Preprocessed data with variable selection

3.4.1 Interval partial least square variable selection

The R²_cv and RMSE_cv of the models generated by the combination of optimal preprocessing and iPLS indicated a high level of prediction ability for most soil parameters, with an R²_cv over 90% for TN, TC, TOC, silt, sand, MC, and pH, and an R²_cv of 77% for CEC and 67% for P₂O₅, as illustrated in Figure 3. The resulting RMSE_cv was lower than that of the raw data and optimal preprocessing. Figure 4 illustrates that the selected intervals varied for different soil properties. Sand required the fewest intervals, utilizing 40 intervals. In contrast, P₂O₅ required the highest number of intervals (150). The remaining properties, TN, TC, TOC, Clay, silt, MC, pH, and CEC, required 45, 55, 110, 88, 60, 50, 66, and 70 intervals, respectively. These results indicate that the combination of iPLS and optimal preprocessing can improve the predictive accuracy of soil properties. Table 2 and Figure 3 show that the predictive performance improved for nearly all properties in this methodological integration. These values represent some of the highest accuracies among the preprocessing methods employed in this study. Demonstrating the robustness of the optimal preprocessing + iPLS method.

Figure 3

Figure 3. Reference vs. predicted values of different PLSR models for the prediction of total nitrogen (TN), total carbon (TC), total organic carbon (TOC), clay, silt, sand, moisture (MC), pH, phosphorus (P₂O₅), and cations exchange capacity (CEC) after the application of the optimal preprocessing and interval-PLS.

Figure 4

Figure 4. Selected intervals of total nitrogen (TN), total carbon (TC), total organic carbon (TOC), clay, silt, sand, moisture (MC), pH, phosphorus (P₂O₅), and cations exchange capacity (CEC) after the application of Savitzky–Golay 1st derivate and iPLS.

3.4.2 Variable importance in projection

Improved predictive accuracy for the studied soil attributes was also achieved by applying the variable importance in projection variable selection method to the optimal preprocessing, except for clay, moisture content, and phosphorus, which did not show any improvement using this technique. As shown in Table 2, VIP showed excellent predictive accuracy for TC with an R²_cv of 0.91 and an RMSE_cv of 0.24%, and good predictive accuracy for TN, TOC, silt, and sand, with an R²_cv ranging between 0.82 and 0.89. In comparison, pH and CEC exhibited acceptable accuracy with an R²_cv of 0.75 and an RMSE_cv of 0.31 for pH and 4.32% for CEC.

3.4.3 Selectivity ratio

Compared to VIP and iPLS, SR was not the best technique for improving the predictive accuracy of soil properties, as it did not show any improvement in total nitrogen, moisture content, clay, and pH. SR showed improved predictive accuracy of total organic carbon and silt with nearly similar R²_cv and RMSE_cv of VIP. The same case was observed for total carbon, but the R²_cv and RMSE_cv values were nearly similar to those of iPLS. Sand, P₂O₅, and CEC were improved using SR, with R²_cv values of 0.88, 0.63, and 0.73 and an RMSE_cv of 8.28%, 24.01%, and 4.43%, respectively.

Overall, the combination of optimal preprocessing with variable selection techniques has been shown to be effective in improving the accuracy of the developed models by increasing R²_cv and decreasing the models’ errors. However, when comparing the variable selection techniques, iPLS outperformed both VIP and SR. The iPLS method improved the metrics of all the properties. In contrast, VIP and SR could not improve certain properties, particularly the moisture content. In addition, the improvement rate of iPLS was higher than that of the other techniques (lowest RMSE_cv and highest R²_cv). In terms of model complexity, as illustrated in Figure 5, SR and VIP selected larger wavelength intervals, whereas iPLS selected shorter intervals, which means a less complex model. iPLS selected a lower number of intervals for some properties, such as total carbon, but for others, such as pH, a high number of intervals was needed to improve accuracy. Table 4 lists the intervals selected by iPLS and the number of selected wavenumbers for each property. Spectral interval selection using iPLS was conducted on the preprocessed data. As preprocessing methods modify the physical meaning of individual wavelengths, the selected intervals were used to optimize predictive performance and reduce model complexity rather than for direct chemical interpretation, which should be approached with caution when feature selection is applied (52). The proportion of selected MIR wavenumbers differed substantially among soil properties, highlighting the contrasting levels of spectral redundancy and information density. MC required the largest fraction of the spectrum (68.74%), indicating that predictive information for this property is distributed across the broad MIR regions. In contrast, properties such as P₂O₅ and clay were characterized by very limited spectral selections (3.15% and 5.50%, respectively), suggesting that their predictive signals are concentrated within narrow intervals. Intermediate selection levels were observed for organic-related properties (TN, TC, TOC), pH, and CEC, indicating an equilibrium between spectral coverage and reduced model complexity.

Figure 5

Figure 5. Selected MIR wavenumber ranges by variable selection techniques (iPLS, VIP, and SR). (When the technique is written in red it means that this technique could not show any improvement.).

Table 4

Table 4. Medium infrared wavelength ranges selected by iPLS of total nitrogen (TN), total carbon (TC), total organic carbon (TOC), clay, silt, sand, moisture (MC), pH, phosphorus (P₂O₅), and cations exchange capacity (CEC), from an initial set of 2,380 MIR wavenumbers (3,997 cm^−1–600 cm⁻¹).

To assess whether the improvement in model performance after variable selection was statistically significant, a two-sided Wilcoxon signed-rank test was conducted on the cross-validated R² values before and after applying the iPLS (α = 0.05). The test revealed a significant increase in predictive accuracy following iPLS variable selection (V = 55, p = 0.0029), confirming that the observed improvement in the R²_cv values was statistically significant. This supports the effectiveness of iPLS in enhancing the PLSR model performance.

The application of iPLS in the present study has proven to boost model accuracy and reduce model complexity. In parallel research by (34), the iPLS performed comparably to other variable selection methods (principal variables, forward stepwise selection, and recursively weighted regression), but the iPLS demonstrated its power in optimizing the prediction model compared to the full spectrum Partial Least Squares; this technique offers a beneficial advantage which is the graphical output that enhances data interpretation. The results of this study demonstrated the combination of optimal preprocessing with variable selection improves the predictive accuracy of the model, but when choosing the optimal preprocessing and optimal variable selection techniques, a better predictive performance is achieved, lowering the error of the model. The studied techniques (iPLS, VIP, and SR) are not commonly used in soil spectroscopy, which opens the window for further research and application and can guide future research in developing robustness and testing other preprocessing and variable selection techniques.

4 Conclusion

This study demonstrates that pairing mid−infrared spectroscopy with preprocessing and variable−selection strategies can substantially improve partial least squares regression (PLSR) models for routine soil diagnosis. This confirms the hypothesis that using preprocessing techniques, especially Savitzky–Golay derivatives combined with standard normal variate and variable selection approaches, such as interval Partial Least Squares, improves the predictive capability of the models.

With the iPLS pipeline, cross−validated coefficients of determination reached approximately 0.90 for TN, TC, TOC, silt, sand, MC, and pH (pH R²_cv = 0.91 with RMSE_cv = 0.19), while CEC and P₂O₅ remained moderate (R²_cv = 0.77 and 0.69, respectively), highlighting both the promise and limitations of MIR−based prediction in this dataset.

All models were evaluated with leave−one−out cross−validation, and the observed improvements from combining optimal preprocessing with variable selection were assessed using paired Wilcoxon signed−rank tests on fold−wise metrics (α = 0.05) that further confirmed that the improvements achieved through iPLS variable selection were statistically significant (p = 0.0029), reinforcing the reliability of the optimized modeling approach. Beyond accuracy, iPLS reduces model complexity by focusing on compact, property−specific spectral intervals, aiding mechanistic interpretation and easing deployment. This study highlights the best combinations, setting the stage for future research to explore more options. Combining MIR spectroscopy with chemometric tools has strong potential to improve soil property prediction, helping make soil management more precise and efficient in both agricultural and environmental monitoring.

5 Limitations, future perspectives, and recommendations

This study was designed around a small, locally homogeneous dataset collected in the Rhamna region of Morocco and measured using a single benchtop MIR instrument under controlled, oven−dry laboratory conditions. Although leave−one−out cross−validation (LOOCV) and a Wilcoxon signed−rank test provided internal evidence of improvement, the lack of an external prediction set or fully nested resampling means that the reported gains may be optimistic when transferred to other soils, moisture states, particle size distributions, or sensor platforms.

Finally, the model performance remained moderate for some targets (P₂O₅ and CEC), the outlier influence was non−negligible for CEC, and precision estimates for wet−chemistry references were unavailable, limiting our ability to benchmark the RMSE against analytical uncertainty.

Future work should prioritize broader and more diverse spectral libraries spanning soil types, texture classes, mineralogies, and field moisture conditions, coupled with either independent external validation or repeated nested cross−validation to de−bias performance estimates. Methodologically, population−based and stability−oriented selection schemes such as Monte Carlo uninformative variable elimination (MC-UVE), recursive weighted PLS (rPLS), competitive adaptive reweighted sampling (CARS), and variable iterative space shrinkage approach (VISSA) alongside alternative learners such as support vector machine (SVR), Random Forests, and/or cubist can be explored.

Derivative along or combined with SNV is often beneficial, but the order matters. It is recommended to embed all model−selection steps, preprocessing choices, the number of latent variables, variable selection, and selected wavenumbers reporting both accuracy (R²_cv/RMSE_cv) and uncertainty relative to reference−method precision. For properties that remain challenging (P₂O₅, CEC), it is also recommended to prioritize targeted sample augmentation, moisture/particle size stress tests, and robust models.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

RM: Investigation, Software, Validation, Conceptualization, Writing – review & editing, Writing – original draft, Formal analysis, Methodology, Visualization. MG: Methodology, Investigation, Conceptualization, Writing – review & editing, Validation, Software. IB: Formal analysis, Project administration, Visualization, Data curation, Resources, Validation, Software, Methodology, Supervision, Funding acquisition, Writing – review & editing, Investigation, Conceptualization.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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