Challenges and scale issues for predicting rare earth elements in soils using near-infrared spectroscopy

ABSTRACT

Developing strategies for monitoring concentrations of rare earth elements (REEs) in soils is an urgent issue. Using near-infrared spectroscopy (NIR) as an alternative method could optimize the assessment of REEs across large areas. This study evaluated NIR performance for predicting REEs in soils from Piauí State (about 241,755 km²), one of the largest producers of agricultural commodities in Northeast Brazil. To cover the pedological variability across the entire state, 243 composite topsoil samples were collected. Samples were ground and sieved to ≤150 µm, then analyzed for REE concentrations using inductively coupled plasma optical emission spectroscopy (ICP-OES). Spectra were obtained in the NIR range (1000–2500 nm) from soil samples with particle sizes ≤2 mm using an FT-IR/NIR spectrometer. To reveal relationships between local REE characteristics and the performance of prediction models, the samples were subdivided into three distinct regions within Piauí State: (1) North, (2) Southeast, and (3) Southwest. To provide a comprehensive view of the data, the model performance across the entire state of Piauí was also evaluated. Soil spectra were preprocessed, and models were built using partial least squares (PLS) and random forest (RF) regression algorithms. Soil samples from Piauí state showed high spatial variability in terms of REE concentrations. The overall performance of prediction models was improved by reducing the scale to smaller areas. Reasonable results were found for dysprosium (Dy), erbium (Er), and ytterbium (Yb) in the Southwest and for the average concentration of heavy rare earth elements (∑HREE) in both the Southeast and Southwest. Our findings indicated that reducing the sampling scale area could lead to better modeling results and that NIR spectroscopy is a viable alternative method for assessing REEs. We suggest future similar studies in Piauí State should focus on localized areas with more homogeneous environmental settings.

Keywords
soil pollution; potentially toxic elements; soil modeling; lanthanides

INTRODUCTION

Rare earth elements (REEs) comprise the chemical elements from the lanthanide series (La–Lu), Y, and Sc (Connelly et al., 2005), which are found in about 100 minerals (Barbieri et al., 2020). The REE geochemistry in soils varies according to the mineral type of the parent compounds, such as phosphates, carbonates, and silicates. Weathering of the parent materials causes REE dissolution in soil solutions and/or retention in solid phases, such as organic matter and clay minerals. This process results in distinct geochemical signatures of light and heavy rare earth elements (LREEs and HREEs, respectively) in soils (Silva et al., 2018; Wu et al., 2022). The concentration of REEs in soils is relevant for industrial and technological purposes (Gwenzi et al., 2018; Minganti and Drava, 2018). The REEs are also added to fertilizers for agricultural purposes (Carpenter et al., 2015; Fiket et al., 2017; Neves et al., 2018; Xueqing, 2019). Agricultural areas are advancing into the Cerrado biomes, one of the hotspots of global biodiversity (Myers et al., 2000; Mittermeier et al., 2011), and Caatinga, an exclusively Brazilian biome. Intensive fertilizer use in these areas has led to an increase in soil REE concentrations (Pereira et al., 2019; Silva et al., 2019) and resulted in adverse environmental, ecological, and health-related damage (Li et al., 2014; Meryem et al., 2016; Gwenzi et al., 2018; El Zrelli et al., 2021; Tao et al., 2022).

Information on REE levels in soil holds both environmental and economic significance. Traditionally, this information is obtained through analytical methods that quantify REE concentrations, such as acid digestion followed by optical emission spectrometry. These methods are complex, slow, expensive, pose environmental risks, and are prone to laboratory errors (Zawisza et al., 2011). Near-infrared (NIR) spectroscopy is an alternative to traditional methods and is already used to predict many soil properties (Bilgili et al., 2010; Munawar et al., 2020). The NIR can also be used to predict REEs in soil (Wang et al., 2017; Maia et al., 2020, 2022). The main advantages of this technique are its non-destructive and relatively low-cost properties (Shi et al., 2014). Furthermore, it has the potential to estimate multiple soil properties from a single analysis, provided each property is properly modeled and validated.

Various multivariate regression models are used for spectral modeling. Partial Least Squares (PLS) regression is likely the most used regression model and is frequently mentioned as relatively easy to understand (Soriano-Disla et al., 2014). However, one alternative for modeling is the Random Forest (RF) machine learning algorithm developed by Breiman (2001). The RF has been applied to resolve regression problems (Cipullo et al., 2019; Cunha et al., 2020) and classification (Denisko and Hoffman, 2018; Benedet et al., 2020). Researchers demonstrated greater soil-predictive capacity via NIR spectroscopy using non-linear RF modeling compared to traditional PLS modeling (Knox et al., 2015; Zhang et al., 2017; Santana et al., 2018).

Scientific discussions regarding the geographic scale at which infrared spectroscopy can serve as an effective predictive method are ongoing (Nawar and Mouazen, 2017). Many studies apply this technique on the farm or field scale (Wetterlind et al., 2008; Kuang and Mouazen, 2011; Seidel et al., 2019; Oliveira et al., 2022) while others test the capacity for applying models calibrated on larger scales to local scale scenarios (Gogé et al., 2014). Similar investigations at regional scales are ongoing (Chen et al., 2015; Nyarko et al., 2022) and, in addition, include studies comparing performance across different scales (Carvalho et al., 2022).

This study hypothesizes that predicting REE concentrations across large areas using NIR reflectance spectroscopy combined with RF and PLS modeling can provide valuable insights into soil REE levels. To further enrich this broader research topic and to explore the regional characteristics of our study area, our research aimed to apply NIR reflectance spectroscopy to predict REE concentrations at different scales in soils from Piauí State, Northeastern Brazil, using PLS and RF modeling. These findings may help improve the REE monitoring in large territories.

MATERIALS AND METHODS

Study area

Piauí State is subdivided into mesoregions based on geographic characteristics (Boechat et al., 2020). These areas are officially divided into four regions: (1) Southeast, (2) Southwest, (3) North, and (4) Center-North. In this study, mesoregions were used as spatial units to examine relationships between REE predictions and the inherent soil characteristics of these areas. North and Center-North mesoregions were grouped together as “North” and summed with “Southwest” and “Southeast” to compose three distinct regions within the total area of Piauí State (Figure 1).

Figure 1
Soil classes and spatial distribution of soil samples collected at the North, Southwest, and Southeast regions of Piauí State, Brazil.

Besides the prevalent influence of the Cerrado biome, there is also a transition area between Cerrado and Caatinga. The Caatinga biome is an exclusive Brazilian biome, occupying 11 % of Brazil and harboring endemic flora and fauna (Monteiro et al., 2015). Piauí State predominantly features the typical vegetation of Cerrado and Caatinga, and has an agricultural aptitude for planted pasture (54.57 %) and intensive crop use (26.74 %), presenting high pedological diversity (Almeida et al., 2019). The main soil classes found in the state are Ferralsols (Latossolos), Leptsols (Neossolos Litólicos), Plinthosols (Plintossolos), Acrisols (Argissolos), Luvisols (Luvissolos), and Arenosols (Neossolos Quartzarênicos), with small areas of Vertisols (Vertissolos), Fluvisols (Neossolos Flúvicos), Chernozems (Chernossolos), and Gleysols (Gleissolos) (Figure 2).

Figure 2
Geological map of the Piauí State, Brazil, and soil sampling points.

Soil sampling, particle size determination, and chemical analyses

A total of 243 composite soil samples were collected at a layer of 0.00-0.20 m. Each soil sample comprised five subsamples collected within a 3–4 meter radius of the georeferenced point. Sampling points correspond to areas of minimal anthropic influence, that is, areas with characteristics more similar to native conditions without any form of land use or occupation. Composite samples were air-dried, ground, and then passed through stainless steel sieves with openings <2 mm. Soil pH was determined in water (1:2.5). Determination of Ca²⁺, Mg²⁺, and Al³⁺ was performed by titration with 1 mol L^-1 KCl (Donagema et al., 2011). Potassium (K) was extracted using the Mehlich-1 solution, and its concentration was measured with a flame photometer. Phosphorus (P) was extracted using Mehlich-1 method, and its concentration was determined using a UV-Vis spectrophotometer. Soil organic carbon (SOC) was obtained by the Walkley-Black method (Walkley and Black, 1934). Calcium acetate at pH 7.0 was used to extract H+Al. Particle size analysis was carried out according to Donagema et al. (2011) using the pipette method.

REE determination in soils

Samples were ground in an agate mortar and passed through a ≤150-µm (0.150 mm) sieve and were digested in Teflon tubes with 9 mL of HNO₃ and 3 mL of HCl and then taken for closed-system digestion in a microwave oven (Mars Xpress). Digestion was conducted following the 3051A EPA method (USEPA, 1998). Afterward, the obtained extracts were filtered through paper filters and transferred to certified 25 mL flasks (NBR ISSO/IEC), which were then filled with ultrapure water (Millipore Direct-Q System). Analyses were executed in duplicates. The REEs were determined using Optical Emission Spectrometry with Inductively Coupled Plasma (ICP-OES/Optima 7000, PerkinElmer). To enhance the sensitivity to REE contents, a cyclonic chamber/nebulizer was coupled to the ICP-OES. Blanks and certified material SRM 2709 San Joaquin Soil (NIST, 2002) were used to ensure the analytical quality of the procedures. The recovery rates ranged from 83 to 105 %.

Near-infrared reflectance measurement

The 243 soil samples were scanned using a Near-Infrared Fourier-Transform spectrometer (FT-IR/NIR, Frontier/PerkinElmer). The spectra were obtained using the following parameters: a spectral range of 1000 to 2500 nm, a scanning speed of 300 nm min^-1, and a spectral resolution of 0.5 nm. Sensor calibration was performed using the equipment’s reference material, Spectralon, which has a reflectance standard of approximately 100 %, and was repeated once every 20 samples.

Spectral modeling and descriptive statistical analysis

The full dataset consisted of 243 observations with a spectral range from 1000 to 2500 nm in 0.5 nm increments. Beforehand, the dataset was resampled to a 1-nm window size using the ‘prospectr’ R package with the resample function (Stevens and Ramirez-Lopez, 2022). Three more datasets were then created by filtering by the predefined region ranges for a total of four datasets: (1) Piauí (243 observations), (2) North (87 observations), (3) Southeast (55 observations), and (4) Southwest (101 observations). For each dataset, the conditioned Latin hypercube sampling (cLHS) method was used to split the data into 80 and 20 % for model calibration and validation, respectively. The cLHS allowed us to cover the optimal variability of the environmental variables (Minasny and McBratney, 2006), which were the soil spectra in our case. The ‘clhs’ R package was used to perform the cLHS. Absorption in the near-infrared (NIR) region is a type of vibrational spectroscopy that utilizes photon energy (Pasquini, 2003). However, noise in the spectra can interfere with the accurate measurement of the target attributes (Munawar et al., 2020). Preprocessing techniques help reduce this noise, correct spectral distortions, and improve prediction accuracy (Munawar et al., 2020).

Afterward, the calibration and validation data were preprocessed using the same R package for resampling. The Savitzky-Golay 1st derivative using a 1st order polynomial and 9-nm search window (Savitzky and Golay, 1964), Standard normal variate (Barnes et al., 1989), detrend normalization 2nd order polynomial (Barnes et al., 1989), multiplicative scatter correction (Dhanoa et al., 1994), and continuum removal (Clark and Roush, 1984) were the preprocessing procedures performed in this study. The RF (Breiman, 2001) and PLS regression algorithms were used to construct the models for REE quantification. Both methods were performed using the “caret” R package (Kuhn, 2008) with 10-fold cross-validation based on a grid search. The datasets consisted of of the 15 target variables (La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Er, Yb, Lu, and ∑REE, ∑LREE, and ∑HREE), raw spectra, and all preprocessed spectra, resulting six models for each variable for both algorithms and for each sample set, which yielded 48 models per variable and a total of 720 models.

For each model, performance was assessed using root mean square error (RMSE), adjusted coefficient of determination (R²_adj), ratio of performance to interquartile distance (RPIQ), and ratio of prediction to deviation (RPD) for both cross-validation and validation. The classification criteria for selecting the best model were based on the lowest RMSE, the highest R²_adj, and the highest RPIQ. The adjusted coefficient of determination (R²_adj), coupled with RMSE and RPD, forms a classic evaluation suite for prediction models of this nature. However, the use of RPIQ as a more trustworthy metric has recently increased (Bellon-Maurel et al., 2010). The RPIQ considers the distribution of the target variable and lowers the performance indicator when a given variable presents low variability.

Results of the laboratory analyses, including REEs, were subjected to descriptive analysis, after which the mean, median, coefficient of variation (CV), minimum and maximum, asymmetry, and kurtosis were obtained. Also, Spearman correlation analyses were performed between REE content and soil properties.

RESULTS AND DISCUSSION

Soil chemical characteristics and REE contents

Soil characterization is important for understanding the REE adsorption (Dinali et al., 2019). In general, the soils presented elevated acidity (pH <5) (Table 1). Souza et al. (2019) reported similar pH values in soils from Piauí State. The average soil organic carbon (SOC) content was 0.86 dag kg^-1. According to the classification of Mendes et al. (2020), this content is considered low (<1 dag kg^-1). Average contents of clay (172.1 g kg^-1), sand (725.0 g kg^-1), and silt (102.9 g kg^-1) indicated a prevalence of sandy soils (Table 1). Norouzi et al. (2021) studied the relationship between particle size and soil reflectance. This study pointed out that soils with higher sand content and primary minerals, such as feldspar and quartz, may yield more information in the optical domain. All soil properties showed high variability and revealed the diverse pedological patterns in the study area. This study included a considerable number of samples from Ferralsols (Latossolos), namely oxidic and kaolinitic soils, which showed lower adsorption values due to their characteristics (Dinali et al., 2019). Soil texture and SOC content influence the spectral response (Salazar et al., 2020). For example, the clay content exerts a potential effect on the spectral characteristics of REEs in soil (Wang et al., 2017).

Table 1
Descriptive analysis of the soil properties from the 243 soil samples of Piauí State

Variable	Mean	Minimum	Median	Maximum	Asymmetry	Kurtosis	CV
	–––––––––––––––––– mg kg-1 ––––––––––––––––––
pH(H2O)	4.71	3.11	4.54	8.57	0.84	0.42	0.23
Sand (g kg-1)	725.0	188.9	758.5	989.7	-0.94	0.63	0.21
Clay (g kg-1)	172.1	1.0	164.0	508.0	0.89	1.39	0.53
Silt (g kg-1)	102.9	0.3	48.5	608.6	1.76	2.76	1.18
SOC (dag kg-1)	0.86	0.01	0.63	2.50	0.89	-0.26	0.80
Ca2+ (cmolc dm -3)	1.37	< DL	0.42	10.83	2.25	4.94	1.53
Mg2+ (cmolc dm -3)	0.75	< DL	0.28	12.44	4.20	24.78	1.83
P (mg dm-3)	5.81	0.97	3.50	194.03	9.62	97.51	2.91
K+ (cmolc dm-3)	0.18	0.01	0.12	1.26	2.60	10.42	0.96
Al3+ (cmolc dm-3)	0.87	< DL	0.75	6.00	1.90	9.11	0.86
H+Al (cmolc dm-3)	3.67	0.40	2.77	17.50	1.73	3.76	0.86
SB (cmolc dm-3)	2.30	0.03	0.88	17.88	2.25	5.08	1.42
CEC (cmolc dm-3)	5.96	0.57	4.73	24.09	1.28	1.54	0.76
V (%)	33.49	0.39	25.24	97.36	2.26	-0.93	0.97
m (%)	44.61	0.00	43.49	96.56	0.04	-1.58	0.80

• Extractable acidity (H+Al); Exchangeable Cation (SB: Ca²⁺ + Mg²⁺ + K⁺); CEC cation exchange capacity; SB+Al³⁺+H⁺; Effective CEC (t) SB+Al³⁺; Base saturation (V%); Aluminum saturation (m%); < DL = below detection limit.

The average REE concentrations indicated that elements with even atomic numbers are more abundant than those with uneven atomic numbers, a situation known as the Oddo–Harkins rule (Silva et al., 2018; Gwenzi et al., 2018). The complete descriptive statistics of REEs across the four regions are available in the Supplementary Material. Considering all samples from Piauí State, the average concentrations for light and heavy REEs (ƩLREEs and ƩHREEs, respectively) were 100.88 and 7.46 mg kg^-1, respectively. The average concentration for the sum of REEs (ƩREEs) was 108.34 mg kg^-1. This value was higher than those reported for the Uruçuí watershed (Pereira et al., 2019) and the Gurguéia River basin (Silva et al., 2021), both located in the southwestern portion of the state of Piauí, which were 10.06 and 32.94 mg kg^-1, respectively. These two catchments are large areas within Piauí State, suggesting that other areas are enriched in REEs.

The REE contents exhibit an asymmetrical distribution across all considered regions (Figure 3). However, this pattern is less evident in the Southeast region, where elemental concentrations have shown overall higher values, especially for the LREEs. Likewise, the Southwest region presents a unique pattern in terms of REE elemental concentrations, as most of the elements were within the low-value range. The North region showed REE contents in intermediate ranges between the Southwest and Southeast patterns, except for Lu, which showed lower values in most samples from the North region compared with the other regions.

Figure 3
Box plots of the concentrations from all target variables for the four sample sets

Spearman correlation analysis of soil properties and REEs revealed distinct patterns (Figure 4). Soil pH showed positive correlations with most elements, except Gd, Tb, Yb, and Lu, for which no significant correlations were observed. Sand content typically correlates inversely with REEs, a pattern observed in our study, though less so with Gd. Clay content generally exhibited weak correlations, except for LU, which showed a stronger correlation. Organic carbon (OC) was mostly negatively correlated with the REEs, except for a weak positive correlation with Lu. Unlike the other REEs, Lu shows lower correlations with common cations and exhibits the weakest correlations with soil properties, followed by Gd and Tb. These findings suggest varying degrees of interaction between different soil components and REEs and emphasize the complexity of these relationships within the Piauí State.

Figure 4
Spearman correlation analysis between the soil properties and the elemental concentrations of all target variables

Rare earth elements prediction

The spectra for all samples are shown in figure 5, along with the mean spectra for the four regions. It can be observed that the North samples exhibited higher overall reflectance, while the Southeast samples showed the opposite, especially between 1400 and 2200 mm. The Southwest samples were closer to the average spectra of the whole Piauí State area but showed the lowest reflectance peaks near 1400 and 2200 nm. This difference can be attributed to the intrinsic pedological characteristics of each area. Soil class distribution for each area (Figure 1) showed a high presence of Plinthosols (Plintossolos), Leptosols (Neossolos Litólicos), Arenosols (Neossolos Quartzarênicos), and Ferralsols (Latossolos) in the North region, while the Southwest and Southeast regions consisted mostly of Ferralsols (Latossolos), Leptosols (Neossolos Litólicos), and Acrisols (Argissolos), with smaller areas of Luvisols (Luvissolos). These differences are reflected in REE contents (Figure 3), spectral features (Figure 5), and soil properties from each area. Therefore, variable performance of the prediction models across the four geographic scenarios was expected.

Figure 5
Soil spectral signatures considering: (a) all samples from Piauí state; and (b) mean spectra for the four sample sets.

The best model for each element in the four regions was selected based on the lowest RMSE (Table 2). Thus, a collective visualization for the RPIQ values was devised to provide a clearer understanding of the results (Figure 6). We used the following threshold values for considering the model performance as reasonable: (1) R²_adj >0.50 and (2) RPIQ >1.4 (Wang et al., 2017; Dotto et al., 2018).

Table 2
Results of the fittest models (lowest RMSE) for all variables and the four regions from Piauí State

Variables	Piauí				North				Southwest				Southeast
	Model	R2adj	RMSE	RPD	Model	R2adj	RMSE	RPD	Model	R2adj	RMSE	RPD	Model	R2adj	RMSE	RPD
La	RF-SG	0.22	25.81	1.09	PLS-CR	0.30	8.74	1.17	PLS-MSC	0.39	5.35	1.24	PLS-SNV	0.42	48.26	1.28
Ce	RF-SG	0.21	52.14	1.05	PLS-SNV	0.19	19.04	1.17	PLS-CR	0.38	11.27	1.25	RF-DET	0.45	54.13	1.37
Pr	PLS-SG	0.24	6.65	1.10	RF-DET	0.44	2.22	1.37	RF-CR	0.42	2.44	1.24	RF-DET	0.47	7.97	1.33
Nd	RF-SG	0.26	21.33	1.12	PLS-SNV	0.34	6.31	1.23	RF-CR	0.43	5.45	1.29	RF-DET	0.52	23.90	1.40
Sm	RF-SG	0.23	4.44	1.15	PLS-SNV	0.34	1.16	1.02	PLS-CR	0.40	1.11	1.29	RF-DET	0.42	4.68	1.31
Eu	RF-SG	0.35	0.94	1.25	PLS-MSC	0.31	0.28	0.83	RF-SG	0.59	0.16	1.62	RF-SNV	0.57	1.14	1.28
Gd	RF-SNV	0.16	2.64	1.09	RF-SG	0.48	0.70	1.18	PLS-MSC	0.53	0.63	1.48	RF-DET	0.23	3.48	1.15
Tb	RF-SG	0.32	0.70	1.21	RF-DET	0.30	0.30	1.08	RF-DET	0.33	0.18	1.15	RF-MSC	0.15	0.88	1.17
Dy	RF-DET	0.24	4.92	1.17	PLS-MSC	0.11	1.77	0.50	RF-SG	0.57	0.44	1.50	RF-MSC	0.35	5.54	1.18
Er	RF-SG	0.39	1.58	1.28	PLS-DET	0.41	0.62	0.54	RF-SG	0.55	0.24	1.47	RF-MSC	0.24	1.86	1.24
Yb	RF-SG	0.36	1.32	1.25	PLS-MSC	0.29	0.53	0.53	RF-SG	0.53	0.20	1.47	PLS-SNV	0.29	1.76	1.06
Lu	PLS-DET	0.44	0.38	1.24	RF-RAW	0.79	0.20	2.23	RF-SNV	0.39	0.18	1.31	RF-MSC	0.06	0.53	1.09
∑REE	RF-SG	0.25	117.56	1.09	PLS-SNV	0.26	37.30	1.20	RF-CR	0.44	27.66	1.25	RF-DET	0.52	139.23	1.37
∑LREE	RF-SG	0.20	108.85	1.08	PLS-SNV	0.24	36.11	1.19	PLS-CR	0.39	25.42	1.27	RF-DET	0.46	135.45	1.34
∑HREE	RF-SG	0.37	9.56	1.27	PLS-DET	0.26	3.33	0.69	RF-SG	0.53	1.77	1.37	PLS-DET	0.15	11.37	1.19

• R²_adj: Adjusted coefficient of determination; RMSE: Root mean squared error; RPD: Ratio of prediction to deviation; RF: Random forest; PLS: Partial least squares; RAW: Raw spectra; SG: Savitzky-golay; CR: Continuum removal; DET: Detrend normalization; SNV: Standard normal variate; MSC: Multiplicative scatter correction.

Figure 6
The RPIQ values for all elements in the four regions.

Considering all samples from Piauí State, the best models for all variables achieved poor results overall (Table 2). This result is likely due to the large pedological and environmental variability of the entire state, which may not have been fully captured by the prediction models. In contrast, the three regions within Piauí State showed reasonable results for the following variables: (1) the North Region for Lu; (2) the Southwest Region for Eu, Gd, Dy, Er, Yb, and HREE; and (3) the Southeast Region for Nd, Eu, and ΣREE (Table 2). However, analyzing the RPIQ values (Figure 6) revealed whether a given prediction model truly achieved good results. The Lu (in the North region) performed well according to classical metrics (R²_adj, RMSE, and RPD) and showed the lowest RPIQ among all variables for both PLS and RF models, indicating a poor prediction outcome. This result could have been a consequence of the extreme positive skewness of the Lu distribution in the North region, which led to a decrease in the RPIQ due to the low interquartile range. This instance underscores the utility of RPIQ in evaluating such models. For the Southwest and Southeast regions, both the RPIQ values and classical metrics were consistent in their assessments of the models, with higher RPIQ values for variables that also yielded decent R²_adj and RPD values.

The RPIQ results indicate that the performance of the PLS and RF models did not differ (Figure 6). Overall, the Southeast region displayed the highest RPIQ values, while Piauí State as a whole showed the lowest. In the North region, RPIQ values were near or above 1.4 for Pr and Gd, based on RF, and for La and Gd, based on PLS. In the Southwest Region, RPIQ values were near or above 1.4 for Dy, Er, Yb, and ∑HREE based on both RF and PLS. In the Southeast region, RPIQ values were near or above 1.4 for Ce, Pr, Nd, Sm, Tb, Dy, Er, Yb, Lu, and ∑HREE based on both RF and PLS. For Piauí State, RPIQ values were below 1.4 for all variables, with higher values for La, Ce, Pr, Nd, ∑REE, and ∑LREE, and the lowest for all HREEs and ∑HREE. This finding indicated that better results could be obtained by reducing the scale from a larger to a smaller area, which specifically achieved better predictions for HREEs in the Southwest region and for LREEs in the Southeast region.

The Southeast region showed the highest concentrations of all REEs among the three regions in Piauí State (Figure 3). These higher concentrations may have enhanced the models' capacity to extract spectral features related to elemental content, especially for the LREEs, which exhibit the highest concentrations. It is also worth noting that the Southeast region is the smallest of the three regions, further supporting the conclusion that reducing the sampling scale could lead to better modeling results.

Furthermore, the Southeast region is geologically distinct from the rest of Piauí State (Figure 2) because it exhibits a high proportion of metamorphic and igneous rocks, whereas the Piauí State as a whole shows a clear predominance of sedimentary rocks. Traditionally, high concentrations of REEs are found in igneous rocks (Chakhmouradian and Wall, 2012). The climate is also different, with semiarid areas (400–600 mm average yearly rainfall) in the Southeast, while sub-humid areas (800–1600 mm average yearly rainfall) are present in the North and Southwest regions (Andrade Júnior et al., 2005). Such contrasting features are probably directly responsible for the distinct aptitude for REE predictions for the Southeast Region. According to Brilhante et al. (2024), pedogenesis significantly influences the distribution of REEs in soils. In a study on the establishment of quality reference values (QRVs) for REEs in soils from the state of Piauí, Landim et al. (2022) noted that high levels of REEs in the Southeast region are associated with lithological enrichment. In addition, they indicated that such enrichment is a consequence of environmental factors, such as soil pH near neutrality and a semiarid climate, both of which favor REE adsorption and leaching avoidance.

In their investigation of soil samples from a smaller (about 3,430 km²) and less heterogeneous area, Maia et al. (2022) presented results that outperform the best models of this study for La, Ce, Pr, and Sm, presenting R²_adj values ranging from 0.48 to 0.60 and RPIQs ranging from 1.2 to 1.48. The high spatial variability resulting from the wide sampling area of Piauí State was a limiting factor for model construction, as models depend on the correlation between REE concentrations and detectable spectral characteristics to be accurate. The low precision achieved by the models was most likely due to these limitations. This observation is supported by better results in the Southeast, Southwest, and North regions of Piauí State (Figure 6). For these regions, it was possible to develop viable predictive models for some REEs, such as Dy, Er, and Yb in the Southwest, and ∑HREE in both the Southeast and Southwest. Thus, it appears possible to generate robust, accurate models for predicting REE concentrations by reducing the sampling area to more homogeneous settings.

CONCLUSION

Concentrations of rare earth elements (REEs) in soils across the state of Piauí exhibit significant variability, influenced by the region’s pedological and geological diversity. The Southeast region, characterized by higher concentrations of all REEs and distinct geological features—including the presence of metamorphic and igneous rocks—generally showed a higher ratio of performance to interquartile distance (RPIQ) values than the other regions, particularly for light REEs. This finding suggests that localized geological enrichment significantly impacts REE detectability. Our findings underscore the influence of scale on the predictive accuracy. The overall performance of prediction models improved after reducing the scale from Piauí State area to smaller regions. This finding indicates that this enhancement results from decreased variability in sampling areas.

Additionally, it was observed that RF and PLS regression techniques did not differ significantly in modeling REE concentrations, with RF generally providing slightly better accuracy and robustness. However, both models faced challenges due to the inherent complexity and variability of the soils within Piauí State. Despite these challenges, promising results were achieved in specific regional contexts with better outcomes for Dy, Er, and Yb in the Southwest and for ∑HREE in both the Southeast and Southwest. This study strengthens the case for NIR spectroscopy as a viable alternative for assessing REE concentrations in soils. Future similar studies in Piauí State should prioritize localized analyses, as the current approach suggests a limitation in large, heterogeneous regions. Focusing on specific local contexts can improve predictive accuracy and yield more reliable insights for sustainable soil resource management and exploration.

ACKNOWLEDGMENTS

We gratefully acknowledge the Federal University of Piauí (UFPI/CPCE) and the Programa de Pós-Graduação em Ciências Agrárias (PPGCA) for their support and for making the research facilities available.

• How to cite:
  Maia AJ, Almeida TS, Barbosa RS, Boechat CL, Nascimento CWA, Saraiva PC, Silva CMCAC, Silva YJAB, Morais PGC, Nascimento RC, Sena AFS, Mendes WS, Silva YJAB. Challenges and scale issues for predicting rare earth elements in soils using near-infrared spectroscopy. Rev Bras Cienc Solo. 2026;50:e0240243. https://doi.org/10.36783/18069657rbcs20240243
• FUNDING
  Yuri J.A.B. da Silva gratefully acknowledges the support of the National Council for Scientific and Technological Development (CNPq) through a Research Productivity Scholarship (Process No. 303323/2022-1) as well as the Universal Project (Process No. 402841/2023-9). Additional support was provided by the Federal University of Piauí (PPGCA/CPCE/UFPI), which made available the necessary research infrastructure.

SUPPLEMENTARY DATA

Supplementary data to this article can be found online at https://www.rbcsjournal.org/wp-content/uploads/articles_xml/1806-9657-rbcs-50-e0240243/1806-9657-rbcs-50-e0240243-suppl01.pdf

DATA AVAILABILITY

The data will be provided upon request.

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Edited by

• Editors:
  José Miguel Reichert https://orcid.org/0000-0001-9943-2898 and Ricardo Simão Diniz Dalmolin https://orcid.org/0000-0002-8834-9869

Publication Dates

• Publication in this collection
  23 Mar 2026
• Date of issue
  2026

History

• Received
  27 Dec 2024
• Accepted
  21 Aug 2025