Comparative analysis of analytical methods for the
quantification of sulfates in reconstituted soil matrices:
Effect of soil texture and interfering species

Mónica Gisel Arellano-Sánchez, Cynthia Abou Serhal, Christine Devouge-Boyer, Naima Ben Ghozlen, Mohamad Dhaini, Paul Honeine, Antonin van Exem, Mélanie Mignot

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Mónica Gisel Arellano-Sánchez, Cynthia Abou Serhal, Christine Devouge-Boyer, Naima Ben Ghozlen, Mohamad Dhaini, et al.. Comparative analysis of analytical methods for the quantification of sulfates in reconstituted soil matrices: Effect of soil texture and interfering species. Environmental Technology and Innovation, 2025, 38, pp.104182. 10.1016/j.eti.2025.104182. hal-05271180

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# Comparative analysis of analytical methods for the quantification of sulfates in reconstituted soil matrices: Effect of soil texture and interfering species

Mónica Gisel Arellano-Sánchez<sup>a</sup>, Cynthia Abou Serhal<sup>b</sup>, Christine Devouge-Boyer<sup>a</sup>, Naima Ben Ghozlen<sup>d</sup>, Mohamad Dhaini<sup>c,d</sup>, Paul Honeine<sup>c</sup>, Antonin Van Exem<sup>d</sup>, Mélanie Mignot<sup>a,*</sup>

## ARTICLE INFO

**Keywords:**

Soil pollution

Sulfates

Hyperspectral analysis

Ion chromatography

Turbidimetry

Machine learning

## ABSTRACT

This article studies the effect of various soil textures on sulfate determination and compares the performance of ion chromatography and the turbidimetric method for quantifying sulfates in reconstituted soil matrices. The comparison is conducted under both interference-free conditions and in the presence of interferences, such as chlorides and fluorides. These interferences caused significant overestimations of theoretical sulfate concentrations when using the standardized turbidimetric method. For instance, at a theoretical sulfate concentration of 1000 mg/kg, the result obtained through the turbidimetric method was 12085.5 mg/kg in the presence of chlorides, while the result obtained through ion chromatography was 915.5 mg/kg. An alternative method relying on hyperspectral imaging is also presented for direct sulfate analysis in soil without the need for extraction. Hyperspectral analyses proved to enable rapid analysis and accurate prediction of sulfate concentrations in soil samples, with an R² score of 0.87 in the absence of interferences and an R² score of 0.9 in the presence of chlorides.

## 1. Introduction

Soil is a mixture of gases, liquids, and solids (minerals and organic matter) that supports terrestrial life and regulates essential ecosystem services crucial for the environment and human health (Food and Agriculture Organization of the United Nations (FAO) and the United Nations Environment Programme (UNEP), 2021). However, it also has the capacity of retaining various pollutants such as heavy metals, polycyclic aromatic hydrocarbons (PAHs), volatile organic compounds (VOCs), pesticides, among others. The majority of these pollutants have anthropogenic causes, such as mining, industrial processes, ineffective waste management, unsustainable farming methods, industrial accidents, and military activity (Food and Agriculture Organization of the United Nations (FAO) and the United Nations Environment Programme (UNEP), 2021). Nowadays, soil pollution represents a major concern considering that 95 % of

<footnote><sup>a</sup> INSA Rouen, INSA Rouen Normandie, Univ Caen Normandie, ENSICAEN, CNRS, Institut CARMEN UMR 6064, Saint-Étienne-du-Rouvray F-76800, France</footnote>

<footnote><sup>b</sup> École Supérieure de Chimie Organique et Minérale, 1 allée du réseau Jean-Marie Buckmaster, Compiègne 60200, France</footnote>

<footnote><sup>c</sup> Univ Rouen Normandie, INSA Rouen Normandie, Université Le Havre Normandie, Normandie Univ, LITIS UR 4108, Rouen F-76000, France</footnote>

<footnote><sup>d</sup> TELLUX, 11 rue du moulin à poudre, Maromme 76150, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: melanie.mignot@insa-rouen.fr (M. Mignot).</footnote>
our food originates from the soil and adversely affects the environment and wildlife. Contaminants from polluted soil enter the food chain through plants consumed by animals and humans. Similarly, contaminants can transfer from soil to invertebrates, which are then eaten by birds and poultry, ultimately reaching humans (Artiola et al., 2019; Food and Agriculture Organization of the United Nations (FAO) and the United Nations Environment Programme (UNEP), 2021).

In recent decades, the intensified influx of sulfates originating from industries engaged in mining and processing ores, drilling for oil and gas, and/or burning coal, has been acknowledged as a severe global issue leading to environmental contamination (Artiola et al., 2019). In fact, sulfur stands out as a fundamental macronutrient essential for the proper growth and development of numerous plants and microorganisms (Magnucka et al., 2023). It can be found in soil in the form of organic and inorganic sulfur. Ester sulfate (C-O-S) and C-bound S (C-S) are the two most common forms of organic sulfur, while sulfate, sulfide, elemental sulfur, and sulfate precipitates are examples of inorganic sulfur (Meng et al., 2022). Nevertheless, while sulfate ions are non-toxic, they can indirectly harm the environment by forming toxic compounds with certain cations like copper, or by converting to sulfites (SO<sub>3</sub><sup>2-</sup>), which may cause breathing problems and inflammatory reactions (Anderson et al., 2005; Tavares-Dias, 2021). Furthermore, sulfates are the most well-known substances that can affect soil stabilization with lime and cements, as demonstrated by Cuisinier et al. (2011). According to their study, sulfates can alter soil stabilization processes by inducing significant volume changes in the stabilized soil, thereby reducing its mechanical performance.

Given the associated risks, the measurement of sulfates in soils is a critical aspect in environmental monitoring and regulatory inspection. Various direct and indirect analytical methods, including ion chromatography (Morales et al., 2000), turbidimetry (Kolmert et al., 2000; Melchert and Rocha, 2008), conductometric titration (Garcia and Schultz, 2016), and gravimetric methods (International Organization for Standardization (ISO), 1992), have been employed for sulfate quantification in various samples, such as groundwaters, bacterial cultures, natural waters, and solid fertilizers. However, when it comes to determining sulfates in soil samples, different methods have been explored such as the methylene blue method, ion chromatography, the turbidimetric method, and an indirect atomic absorption spectrophotometric method (Ajwa and Tabatabai, 1993; Nair et al., 2020). Additionally, a gravimetric standard method exists for determining water-soluble and acid-soluble sulfates in soil (International Organization for Standardization (ISO), 1995). Nevertheless, the turbidimetric method remains the most widely adopted due to its speed and accuracy (Ajwa and Tabatabai, 1993; Nair et al., 2020).

The turbidimetric method, based on the precipitation of sulfate ions as insoluble barium sulfates, is a well-established approach for sulfate quantification and is commercially available in the form of sulfate kits for on-site sulfate measurement. ISO 15923-1:2013 (International Organization for Standardization (ISO), 2013) by the International Organization for Standardization (ISO) outlines this method, in which sulfate ions react with barium ions in acidic conditions to create a turbid suspension. Turbidity is subsequently measured at 540 nm and correlated with sulfate concentration in water samples (ground, potable, surface, waste, eluates, and boiler water). Nonetheless, studies have demonstrated its limited quantification range and potential interference caused by nitrate ions in mining wastewater samples (Reisman et al., 2007). Therefore, while the turbidimetric method offers notable advantages, such as minimal sample preparation, rapid analysis, and cost-effectiveness, making it highly suitable for routine testing, it also has limitations, such as susceptibility to interferences and lower specificity and sensitivity compared to more advanced analytical techniques.

On the other hand, suppressed ion chromatography is an advantageous technique that permits to directly determine the concentration of sulfates based on the ion-exchange mechanism (Michalski, 2014; Reisman et al., 2007). Suppressed ion chromatography has shown high accuracy in determining sulfate concentrations in mining wastewater samples. Additionally, its performance has been shown to be independent of sample dilution, in contrast to the turbidimetric method (Reisman et al., 2007). Hence, this analytical method is highly sensitive, capable of detecting a wide range of ions individually, providing accurate and reproducible quantitative data, and is well-suited for analyzing complex mixtures. However, the limitations of ion chromatography in this context include high instrumentation costs and the need for meticulous sample preparation, which involves proper dilution of the sample as well as the preparation of eluents and standards.

Hyperspectral imaging is a remote sensing technology that captures a broad spectrum of light for each pixel in the scene under study. With spectra consisting of continuous and contiguous ranges of wavelengths in more than a hundred of spectral bands, hyperspectral imaging goes beyond conventional cameras that are restricted to the human eye characteristics with their three RGB channels. The resulting spectra provide insights into the physical and chemical composition of the observed materials, enabling applications that range from quality control in food and manufacturing to earth observation with airborne sensors (Jia et al., 2020; Lu et al., 2020). To explore these data, machine learning algorithms have been developed in order to address tasks such as land cover classification and mining, target/anomaly detection, and physical parameters estimation (Gewali et al., 2018). Hyperspectral imaging has been increasingly applied in soil analysis due to its ability to capture detailed characterization of soil properties, such as moisture content assessment (Oltra-Carrió et al., 2015) and petroleum hydrocarbon detection (Dhaini et al., 2021). Despite the increasing interest in hyperspectral imaging for soil characterization, significant challenges persist due to the high variability in soil composition (commonly referred to as the matrix) and the diverse types of pollutants, which present new obstacles to address. Few articles (Shi et al., 2014; Shi et al., 2014a, 2014b, 2014c) can be found on sulfate determination using hyperspectral analysis but, to the best of our knowledge, this work is the first to demonstrate the relevance of hyperspectral imaging coupled with machine learning for the characterization of sulfates in soils while simultaneously studying the influence of chloride and fluoride on such estimation.

The main goal of this research is to develop a methodology for improving soil rehabilitation through onsite, real-time pollutant analysis without extraction, enabling direct and rapid assessment. The specific objectives are the following: (i) to study the effect of diverse soil textures on sulfate extraction, (ii) to compare the performance of conventional analytical methods, namely ion chromatography, versus the turbidimetric standardized method (ISO 15923-1:2013), for the determination of extractable sulfate in reconstituted soil matrices, without interferences, (iii) to compare the performance of ion chromatography versus the turbidimetric
standardized method (ISO 15923-1:2013) for the determination of extractable sulfate in reconstituted soil matrices in the presence of potential interferences, such as chlorides and fluorides, and (iv) to test an alternative method based on hyperspectral imaging, which directly analyzes sulfate concentration in soil without the need for extraction.

## 2. Experimental

### 2.1. Methods

#### 2.1.1. Preparation of the samples

The study began by preparing various reconstituted soil matrices to investigate the impact of soil texture on sulfate quantification. A reconstituted soil is a soil whose natural structure has been broken down and remolded to achieve uniform properties for controlled testing or analysis. For this purpose, 24 types of soils were prepared by mixing specific amounts of sand and silt (Fontainebleau sand), white clay (Cokoon illite), vermicompostas organic matter (from company Veragrow), and iron oxide (Sigma Aldrich), in a way to obtain a total mass of 80 g. The reconstitution process followed the quantities specified in the ELLISTAT experimental design outlined in Table 1. Specifically, components were weighed according to the experimental plan, resulting in a total sample weight of 80 g in an aluminum dish. The mixtures were then thoroughly homogenized using a porcelain mortar. For the solid fraction, sand ranged between 7.43 % and 50.47 %, silt ranged between 9.21 % and 54.84 %, clay ranged between 9.14 % and 52.68 %, organic matter ranged between 0 % and 17.23 %, and iron oxide ranged between 0 % and 1.29 %.

Within the 80 g of each soil sample, 5 g were spiked with 3 mL of sulfate solutions. The solutions had known concentrations: 282, 526.6, 2806.1, 11227.7, and 19952.5 mg/L. To achieve this, 5 g of the sample and 3 mL of the spiking solution were thoroughly mixed using a porcelain mortar. Subsequently, these spiked samples were dried overnight at 40°C in the oven. Following the drying process, an appropriate amount of ultrapure water was added to each dried soil sample in accordance with the experimental design. This was followed by thorough homogenization using a porcelain mortar. Ultrapure water with a resistivity of 18.2 MΩ·cm, obtained from a Milli-Q system (Millipore, Bedford, MA, USA), was used for the preparation of all samples and solutions unless stated otherwise.

Interfering species are substances present in a sample that can cause errors in the measurement or detection of a target analyte. To assess the impact of interferences on sulfate quantification, three additional matrices were prepared by mixing various amounts of sand and clay (see Table 2). Matrices were weighed in an aluminum dish and then thoroughly homogenized using a porcelain mortar. Each matrix was subsequently spiked with six different sulfate concentrations (500, 1000, 5000, 10000, 15000, and 20000 mg/kg), thoroughly mixed using a porcelain mortar, and dried overnight at 40°C in the oven. A mass equivalent of 10 g of the sulfate-spiked matrix was subsequently spiked with four different concentrations (1000, 5000, 10000, and 20000 mg/kg) of sodium chloride (NaCl, Sigma, 99%) or sodium fluoride (NaF, Sigma, 99%), thoroughly homogenized using a porcelain mortar, and dried overnight at 40°C in the oven. The matrices will be identified as Mx-Cl(y) and Mx-F(y), where (x) denotes the matrix number (1, 2 or 3), Cl and F represent chloride and fluoride, and (y) represents the concentration of the interferent.

<table><caption>**Table 1**
Experimental design for the preparation of reconstituted soil matrices.</caption><thead><tr><th rowspan="2">Soil Sample</th><th colspan="5">Components mass (g) for a total of 80 g</th><th colspan="2">Mass of water (g) for:</th><th rowspan="2">Soil classification</th></tr><tr><th>Sand</th><th>Silt</th><th>Clay</th><th>Organic matter</th><th>Iron oxide</th><th>80 g</th><th>5 g</th></tr></thead><tbody><tr><td>1</td><td>5.94</td><td>31.19</td><td>32.67</td><td>9.90</td><td>0.30</td><td>4.46</td><td>0.28</td><td>sandy clay</td></tr><tr><td>2</td><td>19.11</td><td>15.29</td><td>38.22</td><td>6.37</td><td>1.02</td><td>21.16</td><td>1.32</td><td>clay</td></tr><tr><td>3</td><td>10.55</td><td>35.15</td><td>33.39</td><td>0.59</td><td>0.32</td><td>4.12</td><td>0.26</td><td>sandy clay</td></tr><tr><td>4</td><td>11.35</td><td>21.07</td><td>42.15</td><td>5.40</td><td>0.03</td><td>9.61</td><td>0.60</td><td>clay</td></tr><tr><td>5</td><td>13.14</td><td>36.51</td><td>18.98</td><td>11.20</td><td>0.17</td><td>5.30</td><td>0.33</td><td>silt loam</td></tr><tr><td>6</td><td>18.87</td><td>30.19</td><td>28.30</td><td>1.89</td><td>0.75</td><td>2.57</td><td>0.16</td><td>clay loam</td></tr><tr><td>7</td><td>18.98</td><td>18.98</td><td>27.61</td><td>13.80</td><td>0.63</td><td>9.68</td><td>0.60</td><td>clay loam</td></tr><tr><td>8</td><td>31.93</td><td>21.29</td><td>13.30</td><td>13.30</td><td>0.18</td><td>5.27</td><td>0.33</td><td>loam</td></tr><tr><td>9</td><td>23.77</td><td>43.89</td><td>7.31</td><td>4.88</td><td>0.15</td><td>7.61</td><td>0.48</td><td>silt loam</td></tr><tr><td>10</td><td>20.85</td><td>10.43</td><td>40.21</td><td>8.44</td><td>0.07</td><td>7.63</td><td>0.48</td><td>clay</td></tr><tr><td>11</td><td>20.47</td><td>20.47</td><td>28.66</td><td>10.01</td><td>0.39</td><td>5.40</td><td>0.34</td><td>clay loam</td></tr><tr><td>12</td><td>30.79</td><td>11.55</td><td>32.72</td><td>4.49</td><td>0.45</td><td>1.98</td><td>0.12</td><td>clay</td></tr><tr><td>13</td><td>25.35</td><td>34.30</td><td>11.93</td><td>7.95</td><td>0.47</td><td>10.56</td><td>0.66</td><td>loam</td></tr><tr><td>14</td><td>32.44</td><td>21.63</td><td>12.62</td><td>12.62</td><td>0.69</td><td>1.25</td><td>0.08</td><td>loam</td></tr><tr><td>15</td><td>21.01</td><td>24.33</td><td>30.97</td><td>3.32</td><td>0.37</td><td>6.14</td><td>0.38</td><td>clay loam</td></tr><tr><td>16</td><td>25.79</td><td>23.21</td><td>23.21</td><td>7.74</td><td>0.04</td><td>0.00</td><td>0.00</td><td>clay loam</td></tr><tr><td>17</td><td>23.99</td><td>21.71</td><td>28.56</td><td>5.33</td><td>0.40</td><td>0.40</td><td>0.03</td><td>clay loam</td></tr><tr><td>18</td><td>33.68</td><td>15.31</td><td>30.62</td><td>0.00</td><td>0.38</td><td>10.39</td><td>0.65</td><td>clay loam</td></tr><tr><td>19</td><td>33.98</td><td>7.39</td><td>35.46</td><td>2.95</td><td>0.22</td><td>2.52</td><td>0.16</td><td>loam</td></tr><tr><td>20</td><td>35.63</td><td>20.79</td><td>17.82</td><td>5.44</td><td>0.32</td><td>9.30</td><td>0.58</td><td>loam</td></tr><tr><td>21</td><td>24.90</td><td>27.88</td><td>22.90</td><td>4.32</td><td>0.00</td><td>4.64</td><td>0.29</td><td>clay loam</td></tr><tr><td>22</td><td>39.39</td><td>25.76</td><td>13.64</td><td>1.01</td><td>0.20</td><td>4.06</td><td>0.25</td><td>loam</td></tr><tr><td>23</td><td>40.42</td><td>13.47</td><td>16.47</td><td>9.48</td><td>0.15</td><td>11.00</td><td>0.69</td><td>sandy clay loam</td></tr><tr><td>24</td><td>34.84</td><td>32.35</td><td>7.47</td><td>4.98</td><td>0.37</td><td>4.16</td><td>0.26</td><td>loam</td></tr></tbody></table>
<table><caption>**Table 2**

Composition of matrices used in the study of interferences.</caption><thead><tr><td>Matrix</td><td>Sand (%)</td><td>Clay (%)</td></tr></thead><tbody><tr><td>M1</td><td>90</td><td>10</td></tr><tr><td>M2</td><td>75</td><td>25</td></tr><tr><td>M3</td><td>67</td><td>33</td></tr></tbody></table>

### 2.1.2. Sulfate extraction

For all samples, sulfate ions were extracted according to the standard NF EN 12457-2 (French Standardization Association (AFNOR), 2002). A volume of 20 mL of ultrapure water was added as extractant solvent to 2 g of spiked soil. The samples were shaken for 24 hours using a Fisherbrand Multi-Purpose Tube Rotator (France) and the two phases were separated by centrifugation at 4000 rpm for 20 minutes with an Eppendorf Centrifuge 5702 (Germany). Finally, all samples were filtered using 0.45 µm PTFE filters prior to analysis. The obtained solutions were then diluted. In order to obtain a blank value for each soil, a non-spiked sample was extracted following the same protocol.

### 2.1.3. Calibration curve

All standard solutions were prepared by dissolving magnesium sulfate heptahydrate (MgSO₄·7 H₂O, VWR, purity 99 %) in ultrapure water. For the turbidimetric method, the calibration curve was constructed at 6 concentration levels ranging from 5 to 200 mg/L of sulfate, following the guidelines outlined in ISO 15923-1:2013 (International Organization for Standardization (ISO), 2013). In contrast, the ion chromatography instrument was calibrated using 8 sulfate standards with concentrations ranging from 0.5 to 50 mg/L.

## 2.2. Analysis

### 2.2.1. Turbidimetric method

The analysis of sulfate ions through the turbidimetric method followed the procedures outlined in ISO 15923-1:2013 (International Organization for Standardization (ISO), 2013). The turbidimetric reagent was prepared by mixing barium chloride dihydrate (BaCl₂·2 H₂O, ACROS, 99 %), sodium chloride (NaCl, ACROS Organics, 99 %), and hydrochloric acid (HCl, VWR, 37 %), with a heated aqueous solution of gelatin (ACROS Organics). Subsequently, 1.5 mL of the extract was combined with 1.5 mL of the turbidimetric reagent in a test tube and incubated for 4 minutes. Absorbance was measured at 540 nm using a Varian Cary 50 UV-Vis spectrophotometer (USA). Each sample was analyzed in triplicate, and the average value was used to quantify sulfate concentration based on a previously established calibration curve. All concentration values were converted to milligrams of sulfates per kilogram of dry soil sample.

<table><caption>**Table 3**

Operating conditions for the turbidimetric method and ion chromatography.</caption><tbody><tr><th colspan="2">Turbidimetric method</th></tr><tr><td>Equipment</td><td>Varian Cary 50 UV-Vis spectrophotometer</td></tr><tr><td>Spectrophotometer cell</td><td>Quartz glass</td></tr><tr><td>Wavelength</td><td>540 nm</td></tr><tr><td>Reagent</td><td>Turbidimetric reagent</td></tr><tr><td>Sample volume</td><td>1.5 mL</td></tr><tr><td>Incubation time</td><td>4 min</td></tr><tr><td>Software</td><td>Cary WinUV</td></tr><tr><th colspan="2">Ion chromatography</th></tr><tr><td>Equipment</td><td>Thermo Scientific Dionex ICS-5000 + ICS-5000 + Dual Pump (DP)</td></tr><tr><td>Pump</td><td>1 mL/min</td></tr><tr><td>Flow rate</td><td>1 mL/min</td></tr><tr><td>Guard column</td><td>IonPac AG23</td></tr><tr><td>Analytical column</td><td>IonPac AS23</td></tr><tr><td>Column temperature</td><td>30°C</td></tr><tr><td>Suppressor type</td><td>AERS_4mm</td></tr><tr><td>Suppressor current</td><td>32 mA</td></tr><tr><td>Eluent</td><td>4.5 mM Na₂CO₃/0.8 mM NaHCO₃</td></tr><tr><td>Elution mode</td><td>Isocratic</td></tr><tr><td>Autosampler</td><td>AS-AP</td></tr><tr><td>Injection volume</td><td>25 µL</td></tr><tr><td>Run time</td><td>25 min</td></tr><tr><td>Detector</td><td>ICS-5000 + DC (conductivity detector)</td></tr><tr><td>Detector temperature</td><td>30°C</td></tr><tr><td>Software</td><td>Chromleon 7</td></tr></tbody></table>
### 2.2.2. Ion chromatography

Chromatographic analysis was performed using a Dionex ICS-5000 + System (Thermo Fisher Scientific, France). A Dionex AERS 500 Anion Electrolytically Regenerated Suppressor (4 mm) (Thermo Fisher Scientific, France) was operated in the autosuppression recycle mode. A Dionex IonPac AG23 (4 × 50 mm, particle size: 4 µm) guard column was placed before the analytical column and ions were separated with a Dionex IonPac AS23 analytical column (4 × 250 mm, particle size: 4 µm). The ICS-5000 + ion chromatography system was stabilized for 1 hour before analysis in order to attain a stable conductivity baseline. Each sample was injected after proper dilution and filtration. Separation of the ions was achieved using 4.5 mM Na₂CO₃/0.8 mM NaHCO₃ as mobile phase, and the analyses were conducted on isocratic mode at a mobile phase flow rate of 1 mL/min. The column and detector temperatures were set at 30°C. Sulfate concentrations were calculated based on a previously established calibration curve and converted to milligrams of sulfates per kilogram of dry soil sample.

The optimized operating conditions for the turbidimetric method and ion chromatography are given in Table 3.

### 2.2.3. Hyperspectral imaging

Hyperspectral scanners measure the intensity of the electromagnetic spectrum, often categorized by their spectral ranges: visible and near-infrared (VNIR) from 400 to 1000 nm, near-infrared (NIR or SWIR, short wavelength infrared) from 1000 to 2500 nm, and mid-infrared (MIR) from 2700 to 5000 nm. A hyperspectral image consists of pixels, each containing a spectrum of 100–300 continuous and contiguous spectral bands, depending on the imager. The spectral resolution averages 5 nm. The signal is calibrated against two reference recordings: firstly, the camera's electronic noise, which remains constant over time due to the sensor's thermal regulation, and secondly, a reference signal recorded from a material with assumed perfectly reflectance (99 % reflectance). The calibration process applied to hyperspectral imaging for soil studies has been patented by Tellux (Van Exem et al., 2022).

### 2.2.4. Lasso regression

To provide powerful results in identifying and quantifying the scene under study, hyperspectral imaging needs to be combined with machine learning algorithms. To this end, we explore the estimation of sulfate concentrations using Lasso. Lasso, or Least Absolute Shrinkage and Selection Operator, is a type of linear regression that incorporates regularization to enhance the prediction accuracy and interpretability of the statistical model it produces. The regularization process involves adding a penalty equivalent to the absolute value of the magnitude of coefficients to the loss function. This penalty term causes some coefficients to be exactly zero, thus performing variable selection and yielding simpler, more interpretable models. This methodology was used to analyze hyperspectral data and predict sulfate concentrations.

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Comparative curves of theoretical versus experimental sulfate concentrations obtained through: a) the turbidimetric method and b) ion chromatography, for samples with a balanced texture (loam and sandy clay loam, see Table 1).</figcaption></figure>
# 3. Results and discussion

## 3.1. Calibration

A calibration curve was constructed each day a sample was analyzed. The linearity values obtained were above 0.9940 for turbidimetric analyses, and above 0.9990 for ion chromatography analyses. An example of the calibration curves obtained through both methods is available as *Supplementary Information* in Figure S1. The limit of detection and the limit of quantification of the turbidimetric method were 12 mg/kg and 500 mg/kg (milligrams of sulfates per kilogram of dry soil sample), respectively. For ion chromatography, the limit of detection and the limit of quantification were 3 mg/kg and 13 mg/kg (milligrams of sulfates per kilogram of dry soil sample), respectively. Limits of detection and quantification were calculated based on the calibration curves.

## 3.2. Influence of soil texture

The texture triangle established by the United States Department of Agriculture (USDA), shown as *Supplementary Information* as Figure S2, is widely recognized as one of the principal soil classification systems (Moreno-Maroto and Alonso-Azcárate, 2022). It categorizes soil textures into 12 major classifications, including sand, loamy sand, sandy loam, loam, silt loam, silt, sandy clay loam, clay loam, silty clay loam, sandy clay, silty clay, and clay. A loam soil is a balanced mixture of sand, silt, and clay, and it is considered the ideal soil texture due to its balanced characteristics. This texture triangle permitted the classification of our 24 reconstituted soil matrices, as it can be seen in Table 1.

The sulfate concentration values obtained by both techniques were generally similar regardless of the sample classification. Fig. 1 exemplifies a comparison of theoretical versus experimental sulfate concentrations obtained through ion chromatography and the turbidimetric method in samples with a balanced texture (loam and sandy clay loam). It is evident from these figures that both techniques generate comparable results. In other words, the performance of both techniques appears not to be affected by potential variations in soil texture. This consistent pattern was observed across other soil classifications as well.

## 3.3. Comparative analysis: turbidimetric method versus ion chromatography for sulfate quantification

### 3.3.1. In the absence of interferences

The performance of the turbidimetric method and ion chromatography were compared for sulfate quantification using three matrices (M1, M2, and M3). These matrices were spiked with various sulfate concentrations (0, 500, 1000, 5000, 10000, 15000 and 20000 mg/kg), as described in Section 2.1.1.

Regarding the turbidimetric method, as shown in Table 4, the sulfate recovery percentage ranged from 120.3 % to 159.8 % for M1, from 61.3 % to 94.1 % for M2, and from 70.4 % to 92.4 % for M3. Regarding ion chromatography, the sulfate recovery percentage ranged from 81.2 % to 97.3 % for M1, from 81.9 % to 98.8 % for M2, and from 83.6 % to 97.6 % for M3.

Based on these data, it is evident that the turbidimetric method tends to overestimate theoretical sulfate concentrations in matrix M1. Regarding matrices M2 and M3, both ion chromatography and turbidimetric methods have proved to be effective in measuring

<caption>**Table 4**</caption>

Recovery percentages of sulfate-spiked soil matrices (without interferent) via ion chromatography and the turbidimetric method.

<table><thead><tr><th rowspan="2">Matrix</th><th rowspan="2">Theoretical sulfate concentration [mg/kg]</th><th colspan="2">Experimental sulfate concentration [mg/kg]</th><th colspan="2">Recovery [%]</th></tr><tr><th>Ion chromatography</th><th>Turbidimetric method</th><th>Ion chromatography</th><th>Turbidimetric method</th></tr></thead><tbody><tr><td rowspan="6">M1</td><td>0</td><td>11.9</td><td>93.9</td><td>-</td><td>-</td></tr><tr><td>500</td><td>406.2</td><td>601.6</td><td>81.2</td><td>120.3</td></tr><tr><td>1000</td><td>869.6</td><td>1219.9</td><td>87.0</td><td>122.0</td></tr><tr><td>5000</td><td>4606.4</td><td>6271.4</td><td>92.1</td><td>125.4</td></tr><tr><td>10000</td><td>9729.8</td><td>13626.0</td><td>97.3</td><td>136.3</td></tr><tr><td>15000</td><td>13902.3</td><td>23967.2</td><td>92.7</td><td>159.8</td></tr><tr><td rowspan="6">M2</td><td>20000</td><td>17875.2</td><td>25392.1</td><td>89.4</td><td>127.0</td></tr><tr><td>0</td><td>22.6</td><td>53.5</td><td>-</td><td>-</td></tr><tr><td>500</td><td>414.0</td><td>320.9</td><td>82.8</td><td>64.2</td></tr><tr><td>1000</td><td>818.7</td><td>613.0</td><td>81.9</td><td>61.3</td></tr><tr><td>5000</td><td>4941.4</td><td>4704.3</td><td>98.8</td><td>94.1</td></tr><tr><td>10000</td><td>8324.7</td><td>7684.6</td><td>83.2</td><td>76.8</td></tr><tr><td rowspan="6">M3</td><td>15000</td><td>12861.6</td><td>11797.3</td><td>85.7</td><td>78.6</td></tr><tr><td>20000</td><td>17668.1</td><td>15015.6</td><td>88.3</td><td>75.1</td></tr><tr><td>0</td><td>27.0</td><td>170.1</td><td>-</td><td>-</td></tr><tr><td>500</td><td>418.5</td><td>447.9</td><td>83.7</td><td>89.6</td></tr><tr><td>1000</td><td>903.4</td><td>704.0</td><td>90.3</td><td>70.4</td></tr><tr><td>5000</td><td>4177.8</td><td>3896.1</td><td>83.6</td><td>77.9</td></tr><tr><td rowspan="6">M3</td><td>10000</td><td>8916.2</td><td>7853.2</td><td>89.2</td><td>78.5</td></tr><tr><td>15000</td><td>14635.2</td><td>13866.6</td><td>97.6</td><td>92.4</td></tr><tr><td>20000</td><td>16884.8</td><td>16462.2</td><td>84.4</td><td>82.3</td></tr></tbody></table>
sulfate concentrations. However, selecting the most efficient method depends on various factors, including the specific requirements of the study, cost considerations, and the desired level of accuracy.

Then, the study aimed to evaluate the performance of both methods in the presence of interferences, such as chlorides and fluorides.

### 3.3.2. *In the presence of interferences*

In the final part of the experimental work outlined in this research article, the impact of interferences on sulfate quantification was studied. As mentioned before, different matrices (M1, M2, and M3) were spiked with various sulfate concentrations. Then, portions of each sulfate-spiked matrix were further spiked with varying concentrations of NaCl or NaF. Sulfate concentrations were then determined in all samples using both the turbidimetric method and ion chromatography.

The comparative curves of theoretical versus experimental sulfate concentrations obtained through the turbidimetric method and ion chromatography, are shown in Fig. 2. There curves represent matrices spiked with 10000 mg/kg of NaCl and matrices spiked with 10000 mg/kg of NaF. As it can be straightforwardly appreciated in Fig. 2a) and c), the turbidimetric method shows no consistency for sulfate determination in the presence of chlorides and fluorides. As an example, for a theoretical sulfate concentration of 1000 mg/kg, the result obtained through the turbidimetric method was 12085.5 mg/kg in the presence of chlorides (M1-Cl(10000)), while the result obtained in the presence of fluorides was 19042.5 mg/kg (M3-F(10000)). These results represent a recovery of 1208.6 % and 1904.3 % respectively.

On the other hand, ion chromatography shows a more consistent behavior for sulfate determination in the presence of chlorides and fluorides. This is shown in Fig. 2b) and d). As it can be seen, the comparative curves are more linear and similar for the three matrices (M1, M2, and M3). Moreover, for a theoretical sulfate concentration of 1000 mg/kg, the result obtained through ion chromatography was 915.5 mg/kg in the presence of chlorides (M1-Cl(10000)), while the result obtained in the presence of fluorides was 842.1 mg/kg (M3-F(10000)). These results represent a recovery of 91.6 % and 84.2 %, respectively. The graphs obtained for matrices spiked with 1000, 5000, and 20000 mg/kg of NaCl and NaF are available as *supplementary information* in Figure S3, S4, and S5, respectively.

The results show that chloride and fluoride interferences significantly affect sulfate measurements using the turbidimetric method. These interferences result in an overestimation of sulfate concentrations, likely due to additional turbidity caused by unintended precipitation reactions. In a related study, carbonate ions were also found to interfere with sulfate quantification by forming barium carbonate (BaCO₃) precipitate, leading to a 5 % variation in turbidity at concentrations as low as 7.21 mg/L after the addition of the BaCl₂ reagent (Anechiţei et al., 2019). A similar mechanism may be at play with chloride and fluoride ions. Fluoride ions may react

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Comparative curves of theoretical versus experimental sulfate concentrations obtained through: a) the turbidimetric method for samples spiked with 10000 mg/kg of NaCl, b) ion chromatography for samples spiked with 10000 mg/kg of NaCl, c) the turbidimetric method for samples spiked with 10000 mg/kg of NaF, and d) ion chromatography for samples spiked with 10000 mg/kg of NaF. All matrices (M1, M2, and M3) were previously spiked with different sulfate concentrations (0, 500, 1000, 5000, 10000, 15000 and 20000 mg/kg).</figcaption></figure>
with Ba²⁺ to form barium fluoride (BaF₂), contributing to turbidity. Similarly, high chloride concentrations may promote BaCl₂ crystallization or co-precipitation with sulfate, further increasing measured turbidity. Ion chromatography permits to directly determine the concentration of sulfates, based on the different retention times of the ions involved (F⁻, Cl⁻ and SO₄²⁻). Therefore, ion chromatography is a more specific technique than the standardized turbidimetric method and is more reliable in the presence of interferences.

## 3.4. Hyperspectral imaging for sulfate quantification

### 3.4.1. In the absence of interferences

The reconstituted soils (M1, M2, M3 in Table 2) were first doped with sulfate concentrations ranging from 500 to 20000 mg/kg. The first part of the analysis of hyperspectral data consisted of normalizing raw data between 0 and 1 to unify the reflectance level among samples with different sulfate doping. This helped the model to focus more on the spectral features rather than the reflectance level. Figure S6 a) shows the raw data, and Figure S6 b) shows the data after normalization. These figures can be found as Supplementary Information.

As previously mentioned, Lasso regression was employed to enhance the prediction accuracy and interpretability of the different models produced. The first model, referred to as Model 1, was trained using samples doped with sulfates, with no interferences added. A total of twenty samples were analyzed: nine were used to fit the Lasso Model (Fig. 3a)), and eleven were used for validation (Fig. 3b)). An R² score of 0.93 was achieved on the training data, and an R² score of 0.87 was obtained on the validation data. The selected wavelengths by Lasso Model 1 are represented in Figure S7 a) (see Supplementary Information). For sulfate quantification (without interferences) through the hyperspectral method, the model delivers reliable performance at concentrations exceeding 500 mg/kg.

### 3.4.2. In the presence of interferences

To evaluate the robustness of the techniques, chloride was added to the soil samples. Each matrix (M1, M2, and M3) was doped with 7 sulfate concentrations ranging from 0 to 20000 mg/kg and 4 chloride concentrations ranging from 0 to 20000 mg/kg. This represented 84 samples (3 matrices × 7 sulfate concentrations × 4 chloride concentrations), plus 12 additional samples for the 4 chloride concentrations without sulfate in M1, M2, and M3, leading to a total of 96 samples. Then, Model 1, which had been previously trained using sulfate-doped samples, was tested with samples doped with sulfates and containing chlorides as interferences. As shown in Supplementary Information as Figure S8, there is a correlation between the predicted concentration of the model and the actual doping concentration. Each point is colored based on the chloride doping. There are four main classes (1000 mg/kg, 5000 mg/kg, 10000 mg/kg, and 20000 mg/kg). The R² score obtained for the validation of Model 1 on samples containing both sulfates and chlorides was 0.81.

A second model, referred to as Model 2, was developed specifically to be trained with samples containing both sulfates and chlorides. Out of the 84 samples, 42 were used to fit the Lasso Model, and 42 samples were used for validation. Model 2 achieved an R² score of 0.89 on the training data (Fig. 4a)) and 0.9 on the validation data (Fig. 4b)). Therefore, a better correlation was obtained for Model 2 when the sulfate-doped samples contained chlorides as interferences. The selected wavelengths by Lasso Model 2 are represented in Figure S7 b). Figure S7 c) depicts the selected wavelengths of Lasso Model 1 and Lasso Model 2 on the same plot. It is evident that a distinct wavelength band centered around 1900 nm appears in Model 1 but is absent in Model 2. The spectral region around 1900 nm is well-known for its strong absorption of water, as corroborated by Figure S9 (see Supplementary Information) a). Chlorides introduce additional water content to the sample or alter its hydration state compared to pure sulfate, resulting in notable differences in the spectral signature near 1900 nm.

In the same way as chloride, fluoride was added to the sulfate-spiked samples to evaluate the robustness of the technique. The first observation was a significant change in reflectance, as shown in Figure S9 b).

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Lasso Model 1, trained using sulfate-doped samples (no interferences), shown for the: a) training and b) validation data. M1 (90 % sand, 10 % clay), M2 (75 % sand, 25 % clay), and M3 (67 % sand, 33 % clay).</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Lasso Model 2, trained using sulfate-doped samples with chlorides as interferences, shown for the: a) training and b) validation data. M1 (90 % sand, 10 % clay), M2 (75 % sand, 25 % clay), and M3 (67 % sand, 33 % clay).</figcaption></figure>

Model 1, trained using sulfate-doped samples, was tested with sulfate-doped samples containing fluorides as interferences. The model yielded a very low R² score of 0.08. Notably, samples with higher fluoride concentrations exhibited greater errors as shown in **Supplementary Information** as Figure S10 a). Figure S10 b) shows the trace of R² as a function of fluoride concentration. This figure confirms that as fluoride concentration increases, the R² score drops. Therefore, Model 1 is not suitable for sulfate-doped samples that contain fluorides as interferences.

A third model, referred to as Model 3, was developed specifically to be trained with samples containing both sulfates and fluorides. For the training step, 42 soil samples were used, and another 42 samples were used for the validation step. Fig. 5a) shows the low R² score of 0.56, obtained from the validation step of Model 3. This poor predictive performance of Model 3 in the presence of fluorides may be due to a non-linear relationship between sulfate and fluoride interactions, which linear regression methods like Lasso fail to capture effectively. A potential way to improve predictive accuracy is to explore the use of non-linear machine learning methods like neural networks, which can capture complex relationships. In Fig. 5b), which plots R² as a function of fluoride concentration, it can be noticed that as fluoride concentration increases, the R² score drops. High fluoride concentrations can interfere with sulfate estimation in hyperspectral analysis due to spectral overlapping and ion-specific absorption effects, which can distort sulfate signal detection at higher wavelengths. Additionally, high ionic strength solutions alter sensor response and baseline noise, affecting sulfate quantification (Arancibia et al., 2004). The results of the training step of Model 3, as well as the selected wavelengths for this model, can be found as **supplementary information** in Figures S11 and S12, respectively. Therefore, Model 3 is not suitable for sulfate-doped samples that contain fluorides as interferences either.

It can be concluded from this section that chlorides have a low influence on the spectral domain, while fluorides have a greater influence. This can be verified in Figure S13, which illustrates the effect of chlorides and fluorides on the first order derivative of the reflectance spectrum of soil samples. Reflectance spectra of these soil samples are shown in Figure S14. Both Figures are provided as **supplementary information**. This behavior can explain the results obtained when testing Model 1, which was initially trained with pure sulfate, on sulfate-spiked samples with fluorides as interferences.

Fig. 6 shows a summary of the experimental results of this research work. It provides a comparative of the performance of the analytical methods across the different experimental conditions.

<figure><img src="image_8.png" /><figcaption>Fig. 5. a) Lasso Model 3 validated using sulfate-doped samples with fluorides as interferences, and b) R² value on validation data versus fluorides concentration. M1 (90 % sand, 10 % clay), M2 (75 % sand, 25 % clay), and M3 (67 % sand, 33 % clay).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. Summary of the experimental results.</figcaption></figure>

## 4. Limitations of this study

Indeed, the present study also has some limitations. It is important to keep in mind that the main objective is to develop a methodology for improving soil rehabilitation, as mentioned before.

Currently, soil pollution is typically assessed by sampling a small portion of the soil and sending it to a certified laboratory, where pollutants are extracted and analyzed according to specific guidelines (for example, the turbidimetric method for sulfate determination). While ion chromatography offers better specificity for sulfate determination, even in the presence of interferents such as chloride or fluoride, it still requires sampling a small portion of the soil. This may not be representative of a larger surface area.

In contrast, the hyperspectral method proposed in this study allows the averaging of results by scanning a wider surface area of the sample, rather than being limited to a 1–10 g sample. However, the interferences examined in this study do not cover all possible interferences that may be encountered in real-world conditions. A comparative study with other common interferents should be conducted to evaluate their impact on sulfate determination. This includes assessing the influence of water content, the presence of other pollutants, and a broader range of soil types. Although the present study has been carried out using various soil compositions representative of many commonly encountered types, further investigation is needed to ensure larger applicability.

## 5. Practical applications and future research prospects

As discussed earlier, ion chromatography and the turbidimetric method have advantages and limitations. Ion chromatography has proven to be a more specific and reliable technique, whereas the turbidimetric method requires minimal sample preparation and provides rapid results, making it well-suited for routine analysis. However, this study has revealed that the standardized turbidimetric method for sulfate determination can result in overestimated sulfate concentrations when certain interferences, such as chloride and fluoride, are present. Such inaccuracies could misclassify soils, leading to improper redirection to reprocessing channels. In France, there are inert waste, non-hazardous waste, and hazardous waste storage facilities. Decision 2003/33/EC (European Union, 2002) of December 19, 2002, establishing criteria and procedures for the acceptance of waste at landfills pursuant to Article 16 and Annex II of Directive 1999/31/EC, sets a sulfate limit value of 20000 mg/kg for soil stored in a non-hazardous waste facility. Above this value, the soil must be stored in a hazardous waste storage facility, and below 1000 mg/kg, it can be stored in an inert waste storage facility. The incorrect quantification of pollutant concentration can lead to additional costs for site developers, given the different storage costs depending on the storage facility type. Future research could focus on studying the impact of other substances that may interfere with the determination of sulfates in soils. If additional interfering ions are found to significantly affect the performance of the turbidimetric method, the adoption of ion chromatography would be even more justified than it already is, despite the associated increase in instrumentation costs and extended analysis times due to the preparation of samples, eluents, and standards.

Regarding hyperspectral data, Model 1, designed for samples containing sulfates, and Model 2, designed for samples containing
both sulfates and chlorides, demonstrated acceptable performance. However, Model 3 still requires significant improvement for the prediction of sulfate concentration in the presence of fluorides. Future studies should focus on better understanding the conditions that need to be considered to enhance the predictive accuracy of this model. Machine learning, particularly regression models like Lasso, play an important role in leveraging hyperspectral data for sulfate concentration estimation. Hyperspectral imaging captures reflection spectra across hundreds of contiguous wavelength bands, providing detailed spectral signatures of materials. By applying machine learning to these high-dimensional features, key correlations between specific wavelengths and sulfate concentration can be extracted. Lasso regression enhances this process by enforcing sparsity, selecting the most relevant spectral bands, reducing overfitting, and improving model interpretability. Compared to traditional laboratory methods such as ion chromatography, hyperspectral-based machine learning offers several advantages. It enables rapid sulfate estimation with minimal sample preparation, significantly reducing analysis time. Once trained, the model efficiently processes large datasets, making it ideal for high-throughput applications. Additionally, it provides spatially resolved sulfate concentration maps, which conventional point-based techniques cannot achieve. This combination of speed, efficiency, and spatial insight makes machine learning with hyperspectral data a powerful tool for sulfate monitoring in environmental, agricultural, and industrial applications. However, one limitation of the hyperspectral method is its higher quantification limit and potential issues with interferences, which may need the development of enhanced machine learning models to improve accuracy and reliability. In particular, the presence of fluoride significantly deteriorates model performance, likely due to signal masking that alters the spectral characteristics of sulfates. To address these challenges, further studies are needed to refine the model and improve its ability to predict sulfate concentrations in complex environments with multiple contaminants.

## 6. Conclusions

The performance of ion chromatography and the turbidimetric method was unaffected by soil texture differences. In the interference-free scenario, the turbidimetric method overestimated theoretical sulfate concentrations in matrix M1. For the other matrices, results were acceptable. Under interference conditions, the presence of chlorides and fluorides caused significant overestimations when using the turbidimetric method. As an example, for a theoretical sulfate concentration of 1000 mg/kg, the result obtained through the turbidimetric method was 12085.5 mg/kg in the presence of chlorides, whereas the result obtained through ion chromatography was 915.5 mg/kg. Regarding hyperspectral data, Model 2, designed for samples containing both sulfates and chlorides, provided an R² score of 0.9. In the presence of fluorides, Model 3, designed for samples containing both sulfates and fluorides, yielded an R² score of 0.56. This suggests that fluorides have a greater influence on the spectral domain compared to chlorides.

## Funding sources

This work was partially supported by University of Rouen Normandy, INSA Rouen Normandy, Institute of Analytical Science (Labex iMust, University of Lyon) the Centre National de la Recherche Scientifique (CNRS), European Regional Development Fund (ERDF) No. HN0001343, Labex SynOrg (ANR-11LABX-0029), Carnot Institute I2C, the graduate school for research XL-Chem (ANR-18-EURE-0020 XL CHEM), Region Normandie. The IC instrument was funded by RIN LabEx Milliflux No 19E00566.

## CRediT authorship contribution statement

**Mignot Mélanie:** Writing – review & editing, Supervision, Project administration, Conceptualization. **Arellano-Sánchez Mónica Gisel:** Writing – original draft, Data curation. **Abou Serhal Cynthia:** Writing – original draft, Supervision, Methodology, Investigation. **Devouge-Boyer Christine:** Writing – review & editing, Supervision, Resources. **Van Exem Antonin:** Project administration, Funding acquisition. **Honeine Paul:** Validation, Methodology, Formal analysis. **Ben Ghozlen Naima:** Supervision, Project administration, Conceptualization. **Dhaini Mohamad:** Software, Formal analysis, Data curation.

## Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Melanie Mignot reports financial support was provided by Tellux. Melanie Mignot has patent #WO2022069827 licensed to WO2022069827. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors would like to thank Valentin Grisel for his contribution to the experimental work during his three-month Master's internship.

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.eti.2025.104182.
# Data availability

Data will be made available on request.

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Glossary

**Turbidity:** reduction in water clarity as a consequence of suspended matter.

**Suppressed ion chromatography:** A technique where analyte ions (are first separated on a column. They then move to a suppressor where the conductivity of the eluent is reduced. This lowers the background noise and increases the sensitivity of the detection.

**RGB channels:** RGB (red, green, and blue) is a system used to represent colors on a digital display screen.