# Using near-infrared spectroscopy to estimate soil water retention curves with the van Genuchten model

Youssef Fouad, Inès Soltani, Christophe Cudennec, Didier Michot

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## To cite this version:

Youssef Fouad, Inès Soltani, Christophe Cudennec, Didier Michot. Using near-infrared spectroscopy to estimate soil water retention curves with the van Genuchten model. Geoderma, 2025, 454, pp.117175. 10.1016/j.geoderma.2025.117175. hal-05057880

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# Using near-infrared spectroscopy to estimate soil water retention curves with the van Genuchten model

Youssef Fouad* , Inès Soltani , Christophe Cudennec , Didier Michot

Institut Agro, INRAE, SAS, 35000 Rennes, France

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## ARTICLE INFO

Handling Editor: C. Morgan

**Keywords:**

Near-infrared spectroscopy

Water absorption feature

Soil water content

Effective saturation

## ABSTRACT

Hydraulic properties of unsaturated soils are essential for understanding hydric functioning and solving flow and mass-transfer problems in the vadose zone. One of the best-known models for representing the experimental soil-water retention curve, which describes the matric potential (h) as a function of the water content (θ) of a soil horizon, is the van Genuchten (VG) model. It requires four parameters whose values vary by soil type: residual water content (θr), saturated water content (θs), the inverse of the air-entry pressure (α) and a shape parameter (n). The main objective of this study was to show the relevance of using near-infrared (NIR) spectroscopy to estimate the parameters of the VG model, based on the relation established between the soil water spectral index (SWSI) and θ (Soltani et al., 2019a). Based on this approach, the effective saturation of VG equals the effective SWSI. We applied the approach to 25 soil samples collected from topsoil and subsoil horizons in Brittany (western France), which exhibited high variability in texture and soil organic carbon content ranging from 0.07 % to 6.23 %. The results showed that i) the NIR-spectroscopy approach was relevant for estimating hydraulic parameters θs, α and n of the VG model and ii) the parameters obtained from a VG-like equation based on the relation between h and SWSI predicted values of θ of the soil-water retention curve that were similar to observed values, with a root-mean-square error of 0.031 and 0.045 cm³cm⁻³ for topsoil and subsoil horizons, respectively. The method was thus more accurate for topsoil horizons.

## 1. Introduction

Characterizing the soil-water retention (SWR) curve is an important prerequisite for assessing water flow in saturated and unsaturated soils, as frequently done in hydrological, agricultural, ecological and geotechnical studies. The SWR curve also serves as a crucial input for detailed hydrological models that are used to make water-resource management plans at various scales. The SWR curve describes the relation between the matric potential (h) and volumetric soil water content (SWC) (θ) (i.e. θ(h)), a relation that is a specific to each soil. Several empirical models have been developed to estimate the SWR curve, such as those of van Genuchten (1980) and Brooks and Corey (1964). The parameters for these models are usually estimated by adjusting observed values of θ(h). Being able to estimate the SWR curve indirectly is thus interesting, especially if it is simple and cost-effective.

In comparison, measuring SWR curves, or more specifically θ at field capacity (FC) and permanent wilting point (PWP), to estimate soil water-holding capacity (WHC) is expensive, time-consuming and often impractical for large areas. Over the past three decades, pedotransfer

functions (PTFs) have developed greatly (Vereecken et al., 2010), enabling the prediction of specific soil properties using soil properties that are more readily available (Bouma, 1989). Many PTFs have been developed to predict soil hydraulic properties (Tóth et al., 2015; Román Dobarco et al., 2019; Richard et al., 2023). Two main types of PTFs are commonly used: i) point PTFs, which predict water contents directly at specific matric potentials (Al Majou et al., 2008; Rawls et al., 2004; Contreras & Bonilla, 2018), and ii) parametric PTFs, which predict parameters of an equation that describes a SWR curve or hydraulic conductivity functions (Bruand et al., 2003; Cresswell et al., 2006). PTFs can also be categorized by the type of input data required, such as continuous PTFs or class PTFs. Continuous PTFs use soil physico-chemical properties as input variables in multivariate regression or machine-learning methods to estimate the parameters of the SWR curve model or θ at specific matric potentials (Shiri et al., 2017). Class-PTFs assign values of θ at specific matric potentials or values of SWR-curve parameters based on soil properties such as texture or texture-structural classes, sometimes defined by soil horizon type (Bruand et al., 2003; Al Majou et al., 2008). Nonetheless, a major limitation of PTFs is their

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: youssef.fouad@agrocampus-ouest.fr (Y. Fouad).</footnote>
inherent uncertainties, which can decrease the accuracy of predictions. These uncertainties come from several sources, including i) measurement error in input data, ii) a poorly representative PTF-calibration sample when applying a PTF outside its domain of validity and iii) model-related uncertainties (e.g. model structure, bias) (Minasny and McBratney, 2002; Román Dobarco et al., 2019).

McBratney et al. (2006) developed an original approach that combined spectroscopy and PTFs to estimate functional soil properties such as WHC. It first estimates basic soil physico-chemical properties (i.e., clay, silt, sand and soil organic carbon (SOC) contents) from the information in mid-infrared spectra of soils using partial least squares (PLS) regression and then uses them as inputs to PTFs to predict bulk density (BD), $\theta$ at FC and at PWP, and thus WHC. Diffuse reflectance spectroscopy can also be used to quantify SWR properties directly. In the past few years, several studies have investigated the potential of visible-near-infrared (vis-NIR) spectroscopy, which is usually applied as a laboratory method, to provide predictors for estimating a wide range of soil properties, including $\theta$ (Dalal and Henry, 1986; Lobell and Asner, 2002; Whiting et al., 2004; Mouazen et al., 2006; Knadel et al., 2014; Babaeian et al., 2015). Most of these studies found that soil reflectance decreased non-linearly as $\theta$ increased. Soil vis-NIR spectra show absorptions of hydroxyl bonds in water that vibrate at specific wavelengths. Absorptions used to estimate $\theta$ in the vis-NIR lie near 450, 600, 1200, 1400, 1920, 2100 and 2400 nm. Recently, Soltani et al. (2019a, 2019b) defined a “soil water spectral index” (SWSI), based on the full width at half maximum (FWHM) of the absorption band near 1920 nm. The SWSI decreases linearly as $\theta$ increases, and the slope and intercept of this linear relation were significantly correlated with soil texture, SOC content and the WHC, which provides a way to assess effects of agricultural practices on SWR properties and soil structural quality. Other studies referred directly to models that predict WHC components, such as $\theta$ at FC and at PWP (Arslan et al., 2014; Viscarra Rossel and Webster, 2012; Blaschek et al., 2019). For example, Blaschek et al. (2019) showed that vis-NIR spectroscopic modeling using PLS regression and support vector machines with latent PLS variables can predict $\theta$ at FC and at PWP with root-mean-square errors (RMSE) of less than $7 \text{ cm}^3 \text{ cm}^{-3}$ and $5 \text{ cm}^3 \text{ cm}^{-3}$, respectively. However, few studies have investigated the utility of this approach for studying soil hydraulic properties by developing transfer functions using spectral reflectance data, rather than estimating only $\theta$. Santra et al. (2009) defined spectrotransfer functions (STFs) using multiple linear regressions between hydraulic properties and soil spectral measurements in the 350–2500 nm range. Using these STFs, they estimated the parameters of the SWR curve defined in van Genuchten’s (1980) model and found promising results only for the parameter related to the pore-size distribution (n). Because they used disturbed soil samples, however, they could not consider soil structural properties completely. Babaeian et al. (2015) also developed STFs to predict the hydraulic parameters of the van Genuchten (1980) model. These STFs were more accurate at low and medium $\theta$ than were PTFs, which were more accurate near saturation. Pittaki-Chrysodonta et al. (2018) tested the ability of vis-NIR spectra to predict the Campbell SWR function and compared their results to those of traditional PTFs. They concluded that vis-NIR spectroscopy predicted well the SWC at –100 kPa (pF 3) and the pore-size distribution index of the Campbell function at pF 3 (b). However, they used a narrow range of Danish soil samples with sandy to loamy texture (according to the USDA system) that had a clay content of only 3.6–25.6 %. More recently, Baumann et al. (2022) tested different approaches to model the SWR curve and WHC of a diverse set of Australian agricultural soils using their vis-NIR spectra and the Cubist learning method. They also modeled the parameters of the Kosugi (1994) and van Genuchten (1980) models to reconstruct the SWR curve to estimate WHC. They found that direct estimates of WHC using vis-NIR spectra were the most accurate (i.e. had the smallest RMSE) and that direct estimates of WHC were more accurate than indirect estimates using curves reconstructed from spectroscopic estimates of the parameters of the SWR models. Although the Cubist models predicted the

saturated $\theta$ ($\theta_s$) and residual $\theta$ ($\theta_r$) for the van Genuchten model well ($R^2 = 0.74$ and $0.71$, respectively), predictions of $\alpha$ and $n$ parameters were inaccurate ($R^2 = 0.28$ and $0.08$, respectively).

It is well known that increasing SWC affects the shape of spectra due to the presence of well-defined water absorption bands near the wavelengths of 1440 nm and 1920 nm. These absorption features can be further emphasized using continuum removal transformation of spectra. As shown by Soltani et al. (2019a) the 1920 nm absorption feature is more sensitive to changes in SWC. Moreover, some authors (Stenberg et al., 2010; Zhu et al., 2010) have found this band to be more effective for estimating SWC compared to the band near 1440 nm. Thus, the objectives of the present study are twofold:

* To assess the relevance of NIR spectroscopy, with particular focus on the absorption band near 1920 nm, for characterizing the SWR curve and estimating the parameters of the van Genuchten (VG) model based on the relation established between SWSI and $\theta$, following the approach of Soltani et al. (2019a), and assuming that the effective saturation ($S_e$) of the VG model was equal to both the effective SWSI (SWSI$_e$) and the effective FWHM (FWHM$_e$).

* To compare the NIR-predicted SWC with observed values for soil samples collected from both topsoil and subsoil under different soil moisture conditions, in order to evaluate the accuracy of these predictions.

## 2. Materials and methods

### 2.1. Study area and soil dataset

The study was conducted in Brittany (western France), a part of the Armorican Massif that has a heterogeneous landscape and a complex geology, with sedimentary rocks, rocks metamorphosed to differing degrees (sandstone, schist), metamorphic rocks (gneiss), igneous rocks (granite) and loess deposits. This high geological diversity generates a wide range of soils. According to the World Reference Base of Soil Resources (IUSS Working Group WRB, 2014), the main soils include Cambisols, Stagnic Fluvisols, Histosols, Podzols, Luvisols and Leptosols. Soil data came from the latest 2014–2015 soil survey (228 sampled horizons from 64 soil profiles) of the ‘Sols de Bretagne’ project across the whole of Brittany, which assessed a wide variety of soil conditions. In each horizon, a soil sample was collected for analysis of physicochemical properties, and an undisturbed block of soil was extracted for analysis of SWR properties and spectral measurements. The particle-size distribution was measured using the Robinson pipette method according to the NF X31–107 standard (AFNOR, 2003), and five classes were determined: clay (0–2 µm), fine silt (2–20 µm), coarse silt (20–50 µm), fine sand (50–200 µm) and coarse sand (200–2000 µm). The soil organic carbon (SOC) content was measured by dry combustion with a CHN analyzer (Thermo Finnigan EA 1112, Milan, Italy) according to the NF ISO 10694 standard (AFNOR, 1995). Undisturbed soil blocks were stored in a cold room at 4 °C until physical, chemical and spectral analysis.

For this study, we selected 25 horizons from the 174 well-drained horizons (i.e., those with no redoximorphic features) in the 228-horizon database of the ‘Sols de Bretagne’ project (https://geosas.fr/solsdebretagne/). We used a conditioned Latin hypercube sampling (cLHS) procedure to select the samples. This method is a stratified random procedure that samples variables efficiently based on their multivariate distributions (Minasny & McBratney, 2006). The cLHS procedure allows for the selection of samples that represent the regional soil diversity, based on environmental covariates. The covariates used were the textural classes of soil parent material according to the French GEPPA (1963) 17-class texture system, SOC content, and the fine silt:coarse silt ratio. Two independent draws were made using the cLHS procedure. The first draw selected 13 topsoil organo-mineral samples (A) from 62 organo-mineral samples, and the second draw selected 12 subsoil samples (S) from 112 subsoil samples in the database. The thirteen topsoil
samples are the same as those used in Soltani et al. (2019a). The basic soil properties varied among horizons (Table 1), which belonged to five texture classes according to the USDA system (Soil Survey Division Staff, 1993) (in decreasing order): silty loam, loam, sandy loam, clay loam and clay (Fig. 1). The clay, silt and sand contents of the horizons ranged from 6.00-45.36 %, 12.73-75.69 % and 9.50-68.70 %, respectively. The SOC content ranged from 0.07-6.23 % overall (0.81-6.23 % and 0.07-5.03 % for the topsoil and subsoil horizons, respectively). Among subsoil horizons, the highest SOC contents were observed in spodic Bh horizons from Podzols. The ratio of SOC content to clay content (SOC:Clay) was 0.05-0.81 and 0.01-0.13 in topsoil and subsoil horizons, respectively. According to Johannes et al. (2017), the quality of soil structure decreases as the SOC:Clay ratio decreases; thus, they defined three SOC: Clay ratios (i.e. 0.125, 0.100 and 0.077) as the boundaries between “very good” and “good”, “good” and “moderate”, and “moderate” and “degraded” levels of structural quality, respectively. Structural quality was thus very good for 11 samples (A1, A3, A5, A6, A8, A10, A11, A12, A13, S4 and S10), good for one sample (S6), moderate for three samples (A2, A7 and S9) and degraded for 10 samples (A4, A9, S1, S2, S3, S5, S7, S8, S11 and S12).

## 2.2. Soil-water retention

In the laboratory, each soil block was broken down at FC into aggregates ca. 3-4 cm wide and 5-6 cm long. Four aggregates were collected in quadruplicate for measurements. Once saturated with deionized water, all aggregates were placed on a suction table and then in a pressure cell to be gradually dried. Aggregates were brought successively to matric potentials of -1.0 and -3.2 kPa (i.e. pF 1.0 and 1.5, respectively) on the suction table. Then, they were brought to matric potentials of -10, -20, -31.6, -63, -100, -316, -1000 and -1585 kPa (i.e. pF 2.0, 2.3, 2.5, 2.8, 3.0, 3.5, 4.0 and 4.2, respectively) using a pressure cell following the ISO 11274 standard (AFNOR, 1998). At each matric potential, the soil aggregates were weighed. Finally, the aggregates were oven-dried at 105 °C for 48 h, after which their dry mass was weighed to determine their gravimetric water content at each matric

<table><caption>**Table 1**
Soil characteristics for 25 samples including topsoil (A) and subsoil (S) horizons.</caption><thead><tr><th>Soil sample</th><th>Horizon</th><th>USDA texture class<sup>a</sup></th><th>% Clay</th><th>% Silt</th><th>% Sand</th><th>% SOC</th><th>SOC: Clay ratio</th></tr></thead><tbody><tr><td>A1</td><td>A</td><td>SaLo</td><td>10.88</td><td>31.50</td><td>57.62</td><td>2.64</td><td>0.24</td></tr><tr><td>A2</td><td>A</td><td>Lo</td><td>19.84</td><td>27.97</td><td>52.18</td><td>1.71</td><td>0.09</td></tr><tr><td>A3</td><td>A</td><td>SiLo</td><td>6.00</td><td>51.93</td><td>42.07</td><td>4.87</td><td>0.81</td></tr><tr><td>A4</td><td>AB</td><td>Lo</td><td>17.89</td><td>37.38</td><td>44.73</td><td>0.81</td><td>0.05</td></tr><tr><td>A5</td><td>A</td><td>Lo</td><td>13.26</td><td>44.46</td><td>42.28</td><td>2.63</td><td>0.20</td></tr><tr><td>A6</td><td>A</td><td>SiLo</td><td>14.66</td><td>52.90</td><td>32.43</td><td>2.36</td><td>0.16</td></tr><tr><td>A7</td><td>AB</td><td>SiLo</td><td>11.38</td><td>58.92</td><td>29.71</td><td>1.05</td><td>0.09</td></tr><tr><td>A8</td><td>A</td><td>SiLo</td><td>17.80</td><td>61.85</td><td>20.35</td><td>3.98</td><td>0.23</td></tr><tr><td>A9</td><td>A</td><td>CiLo</td><td>28.22</td><td>44.44</td><td>27.33</td><td>1.97</td><td>0.07</td></tr><tr><td>A10</td><td>A</td><td>SiLo</td><td>23.05</td><td>54.49</td><td>22.47</td><td>5.09</td><td>0.22</td></tr><tr><td>A11</td><td>A</td><td>SiLo</td><td>19.65</td><td>58.32</td><td>22.03</td><td>2.48</td><td>0.13</td></tr><tr><td>A12</td><td>A</td><td>SiLo</td><td>14.81</td><td>75.69</td><td>9.50</td><td>3.07</td><td>0.21</td></tr><tr><td>A13</td><td>A</td><td>SiLo</td><td>20.67</td><td>65.70</td><td>13.63</td><td>6.23</td><td>0.30</td></tr><tr><td>S1</td><td>C</td><td>Lo</td><td>8.96</td><td>41.36</td><td>49.68</td><td>0.27</td><td>0.03</td></tr><tr><td>S2</td><td>B</td><td>SaLo</td><td>13.56</td><td>28.53</td><td>57.91</td><td>0.72</td><td>0.05</td></tr><tr><td>S3</td><td>C</td><td>SaLo</td><td>18.57</td><td>12.73</td><td>68.70</td><td>0.07</td><td>&lt; 0.01</td></tr><tr><td>S4</td><td>B</td><td>SiLo</td><td>9.56</td><td>61.20</td><td>29.24</td><td>1.26</td><td>0.13</td></tr><tr><td>S5</td><td>B</td><td>SiLo</td><td>12.44</td><td>54.80</td><td>32.77</td><td>0.37</td><td>0.03</td></tr><tr><td>S6</td><td>Bh</td><td>SiLo</td><td>18.20</td><td>54.75</td><td>27.05</td><td>1.94</td><td>0.11</td></tr><tr><td>S7</td><td>B</td><td>Lo</td><td>26.07</td><td>37.01</td><td>36.92</td><td>1.48</td><td>0.06</td></tr><tr><td>S8</td><td>B</td><td>Lo</td><td>24.69</td><td>45.45</td><td>29.85</td><td>0.67</td><td>0.03</td></tr><tr><td>S9</td><td>E</td><td>SiLo</td><td>11.26</td><td>75.94</td><td>12.80</td><td>0.89</td><td>0.08</td></tr><tr><td>S10</td><td>Bh</td><td>CiLo</td><td>39.93</td><td>25.91</td><td>34.15</td><td>5.03</td><td>0.13</td></tr><tr><td>S11</td><td>C</td><td>CiLo</td><td>34.22</td><td>42.64</td><td>23.14</td><td>0.83</td><td>0.02</td></tr><tr><td>S12</td><td>C</td><td>Cl</td><td>45.36</td><td>37.07</td><td>17.58</td><td>0.63</td><td>0.01</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Texture classes of the 25 selected soil samples from topsoil organo-mineral A horizons (filled circles) and subsoil horizons (open circles) according to the USDA texture triangle. The circle size is proportional to the soil organic carbon (SOC) content.</figcaption></figure>

potential. Dry BD was measured for whole aggregates using the kerosene-displacement method according to the X31-505 standard (AFNOR, 1992). For each soil aggregate, gravimetric water content was converted to volumetric water content $\theta$, and total porosity was calculated assuming a particle density of $2.65 \text{ g cm}^{-3}$. The dry BD and $\theta$ of the four aggregates were averaged at different matric potentials for all soil horizons studied.

## 2.3. NIR spectroscopy

Once the desired matric potential had been reached and also after soil aggregates had been oven dried, reflectance spectra of soil samples were recorded using a full-range vis-NIR spectrometer (ASDFieldspec® 3, Malvern Panalytical Ltd, UK) at wavelengths from 350-2500 nm, with a sampling interval of 1 nm. All spectra were recorded using a standard contact probe with a 10 mm spot size and an integrated light source featuring a halogen bulb with a color temperature of ca. 2901 K. This setup reduces errors associated with stray light and atmospheric water content during measurements. Before spectral measurement of each soil sample, the spectrometer was optimized on a dark current followed by a white reference panel (Spectralon®). Spectral measurements were taken in the laboratory in a dark room. For each soil aggregate, reflectance spectra were measured in triplicate at each matric potential by slightly modifying the position of the contact probe. As a result, the single spectrum for a given soil aggregate was a mean of 30 scans, and the final spectrum used in the treatment was a mean of the three replicates. The total time spent measuring the spectra was standardized to 6 s per aggregate to avoid heating and drying the samples. Each spectrum was corrected with a splice correction, and the continuum-removal technique (Clark and Roush, 1984) was applied to all spectral data to ease interpretation of the absorption features in a diffuse reflectance spectrum by normalizing spectra to a common convex hull.

## 2.4. VG parameterization

The VG model is often used to predict soil hydraulic properties (van Genuchten, 1980). It was developed by combining an empirically based power-law equation describing the relation between $h$ and volumetric $\theta$ with Mualem's (1976) pore-size distribution model for predicting unsaturated hydraulic conductivity. In the VG model as derived by van Genuchten (1980), effective saturation ($S_e$) is calculated as follows:

<footnote>* Texture classes of the USDA system: Cl, Clay; CILO, Clay Loam; SiLo, Silty Loam; Lo, Loam; SaLo, Sandy Loam; SOC, soil organic carbon content.</footnote>
$$S_e = \frac{\theta - \theta_r}{\theta_s - \theta_r} = \left[ \frac{1}{1 + (\alpha|h|)^n} \right]^m \quad (1)$$

where h is the matric potential (cm), considered here under unsaturated conditions, $\theta_r$ is residual $\theta$ (dimensionless), $\theta_s$ is $\theta$ at saturation (dimensionless), $\alpha$ corresponds approximately to the inverse of the air-entry pressure (cm$^{-1}$), n and m are shape parameters, and m is related to n as follows:

$$m = 1 - \frac{1}{n} \qquad (2)$$

Following the approach proposed in this study, the three hydraulic parameters $\theta_s$, $\alpha$ and n are derived from the variation of the FWHM of the water absorption band near 1920 nm as a function of soil moisture status. $\theta_s$ is obtained from the relation between $\theta$ and SWSI, while the parameters $\alpha$ and n are determined by fitting the VG model to the SWR-like curve, as defined in Section 2.5 below.

## 2.5. NIR-spectroscopy parametrization

Soltani et al. (2019a) proposed a new soil water spectral index, SWSI, which is calculated based on the FWHM of the water absorption band near 1920 nm as shown by equation (3) hereafter:

$$SWSI_i = 1 - \frac{FWHM_i}{FWHM_s} \qquad (3)$$

where i is a matric potential, and FWHM$_s$ is FWHM at saturation. Their results showed that $\theta$ decreases linearly as SWSI increases (Fig. 2), and the slope and intercept of this linear relation were significantly correlated with soil texture and SOC content. Their results also indicated that the slope is directly related to SWR, while the intercept, which is obtained when SWSI equals zero, corresponds to the theoretical value of SWC at saturation, $\theta_s$.

Using spectral data, FWHM was first measured at saturation and then at 10 matric potentials to calculate SWSI$_i$ at each of these potentials: -1.0, -3.2, -10, -20, -31.6, -63, -100, -316, -1000 and -1585 kPa. As in Soltani et al. (2019a), the linear relation between SWSI and $\theta$ was fitted for each soil sample to obtain the slope (i.e. rate of water release from soil pores) and intercept, which is the predicted $\theta_s$. To illustrate this linear relation, two soil samples were selected: one from the topsoil and

the other from subsoil. For both samples $\theta$ decreased linearly as SWSI increased (Fig. 2).

Taking into account the linear relation between $\theta$ and SWSI, and by substituting $\theta$ in Eq. (1), we derive the following equation:

$$S_e = \frac{\theta - \theta_r}{\theta_s - \theta_r} = \frac{SWSI - SWSI_r}{SWSI_s - SWSI_r} = SWSI_e = \left[ \frac{1}{1 + (\alpha|h|)^n} \right]^m \quad (4)$$

where SWSI$_e$ is the effective SWSI, the spectral equivalent of the effective saturation Se. Here, SWSI$_s$ represents the index calculated at saturation, and SWSI$_r$ denotes the residual index determined from the residual FWHM (FWHM$_r$) obtained after oven-drying the soil sample at 105 °C for 48 h. Thus, if one considers the VG model, Eq. (4) suggests that SWSI$_e$ should behave similarly to S$_e$ with similar parameters $\alpha$ and n. Furthermore, given the relation between SWSI and FWHM in Eq. (3), Eq. (4) can also be expressed in terms of FWHM as follows:

$$FWHM_e = \frac{FWHM - FWHM_r}{FWHM_s - FWHM_r} = \left[ \frac{1}{1 + (\alpha|h|)^n} \right]^m \quad (5)$$

where FWHM$_e$ is the effective FWHM.

Eq. (5) indicates that the parameters $\alpha$ and n can be straightforwardly and directly inferred by fitting the VG model to the geometric parameter FWHM, obtained from the water absorption band near 1920 nm under different matric potentials.

## 2.6. Statistical analysis

Statistical analyses were performed using R software (v. 3.6.3) (R Core Team, 2020). Least squares regression was performed on each soil sample to relate $\theta$ to SWSI across the 10 matric potentials considered, and the assumptions of linear regression (linearity of the relation, homoscedasticity, and normality of residuals) were verified. A Pearson correlation matrix was calculated to explore correlations between soil properties and the parameters of the VG model. Before Pearson correlation analysis, the statistical distribution of these variables was examined. To assess the accuracy of the VG model, the root-mean-square error (RMSE) was calculated (Eq. (6)):

$$RMSE = \sqrt{\sum_{i=1}^{n} \frac{(\hat{y}_i - y_i)^2}{n}} \qquad (6)$$

<figure><img src="image_5.png" /><figcaption>Fig. 2. Volumetric soil water content as a function of the soil water spectral index (SWSI) for selected soil samples from the topsoil and subsoil.</figcaption></figure>
where *n* is the number of observations, ŷᵢ is the ith predicted θ(*h*) value and yᵢ is the ith observed θ(*h*) value.

# 3. Results and discussion

## 3.1. Soil-water retention curves

The relation between the matric potential (log |*h*|) and θ was used to define the SWR curves, which depended on a horizon's soil type, texture, and SOC content and thus differed among horizons with sandy loam (A1), silty loam (A12), loamy (S1) and clay loam (S11) textures (Fig. 3a). In addition, θ varied greatly among horizons at each matric potential. In the wet part of the SWR curve, especially for matric potentials of -10 to -1 kPa, topsoils A1 and A12 had higher θ than subsoils S1 and S11. Moreover, A12, which had the highest SOC content, had the highest θ. At lower matric potentials (i.e. *h* < -31.6 kPa), the trend was reversed, since both subsoil samples (S1 and S11) had higher θ than the topsoil samples (A1 and A12). In this case, the soil sample with the finest texture (S11, CILO) had the highest θ due to its high clay content and its clay structure, which was related to the larger surface area of the clay particles and the electrical charge density on it (Bruand and Tessier, 2000). In the capillary region, where the matric potential was most negative (i.e. *h* from -316 to -10 kPa), curves for A1 and A12 changed over a wide range of θ, while those for S1 and S11 changed over a narrow range (Fig. 3a). Since the shape of the SWR curve reflects the pore-size distribution, the subsoil samples (S1 and S11) had a different pore-size distribution (i.e. mainly micropores and mesopores) than the topsoil samples (A1 and A12) (i.e. more macropores). This result was consistent with the SOC:

Clay ratio of the soil samples, which indicated good structural quality for the topsoil samples (A1 and A12) and degraded structural quality for the subsoil horizons (S1 and S11). Examining the SWR-like curve (Eq. (5), FWHM generally increased in the same way that θ did as *h* increased (Fig. 3b). In the wet part of the SWR-like curve, topsoil sample A12 had the highest FWHM, while in the driest part, the subsoil sample S11 did. In the capillary region (i.e. *h* from -316 to -10 kPa), the curves of the topsoils (A1 and A12), changed over a wide range of FWHM, while those of the subsoils (S1 and S11) changed over a narrow range. The similarity of these ranges to those of θ were thus related to the pore-size distributions of the soil samples selected, but there were some differences: for *h* from -1 kPa to -10 kPa, the soil samples A1 and S11 had the same FWHM, while for *h* < -63 kPa, A1 had a higher FWHM than A12.

## 3.2. Parameters of the VG model

The parameters of the VG model fit to the θ measured at 10 matric potentials varied among soil samples (Table 2). The VG model fit the observed data well for topsoil and subsoil samples (RMSE = 0.006–0.022 and 0.007–0.081 cm³cm⁻³, respectively). The RMSE was highest for loamy subsoil sample S7 (0.081 cm³cm⁻³) and less than or equal to 0.022 cm³cm⁻³ for all other samples. For all soil samples, θₛ_VG ranged from 0.379 cm³cm⁻³ (S7) to 0.712 cm³cm⁻³ (A10). Parameter θₛ_VG ranged from 0.49 to 0.712 cm³cm⁻³ for topsoil samples and from 0.379 cm³cm⁻³ (S7) to 0.609 cm³cm⁻³ (S4) for subsoil samples. Most of these θₛ_VG values were higher than those of Carsel and Parrish (1988) (i.e. from 0.38 to 0.46 for clayey and silty samples, respectively), although they predicted SWR curves from BD using a PTF of Rawls and

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) Water-retention curves and (b) curves of the full width at half maximum of the absorption band near 1920 nm as a function of the absolute value of matric potential for four soil samples.</figcaption></figure>
<caption>**Table 2**</caption>

Values of van Genuchten (VG) model parameters adjusted for the relation between the matric potential (h) and soil water content (θ) for topsoil (A) and subsoil (S) samples. Values in parentheses are standard deviations.

<table><thead><tr><th>Soil sample</th><th>θ<sub>s</sub>_VG</th><th>α_VG (cm<sup>-1</sup>)</th><th>n_VG</th><th>RMSE_θ</th></tr></thead><tbody><tr><td>A1</td><td>0.517 (0.008)</td><td>0.018 (0.003)</td><td>1.261 (0.012)</td><td>0.006</td></tr><tr><td>A2</td><td>0.497 (0.012)</td><td>0.021 (0.006)</td><td>1.203 (0.013)</td><td>0.009</td></tr><tr><td>A3</td><td>0.702 (0.021)</td><td>0.041 (0.011)</td><td>1.251 (0.013)</td><td>0.010</td></tr><tr><td>A4</td><td>0.555 (0.031)</td><td>0.069 (0.042)</td><td>1.165 (0.013)</td><td>0.011</td></tr><tr><td>A5</td><td>0.490 (0.013)</td><td>0.010 (0.003)</td><td>1.244 (0.022)</td><td>0.012</td></tr><tr><td>A6</td><td>0.556 (0.026)</td><td>0.022 (0.012)</td><td>1.204 (0.026)</td><td>0.019</td></tr><tr><td>A7</td><td>0.577 (0.007)</td><td>0.033 (0.004)</td><td>1.234 (0.006)</td><td>0.004</td></tr><tr><td>A8</td><td>0.625 (0.018)</td><td>0.020 (0.007)</td><td>1.221 (0.018)</td><td>0.013</td></tr><tr><td>A9</td><td>0.498 (0.020)</td><td>0.004 (0.002)</td><td>1.210 (0.038)</td><td>0.022</td></tr><tr><td>A10</td><td>0.712 (0.020)</td><td>0.017 (0.005)</td><td>1.248 (0.019)</td><td>0.015</td></tr><tr><td>A11</td><td>0.539 (0.017)</td><td>0.009 (0.003)</td><td>1.240 (0.026)</td><td>0.016</td></tr><tr><td>A12</td><td>0.622 (0.017)</td><td>0.026 (0.007)</td><td>1.238 (0.015)</td><td>0.011</td></tr><tr><td>A13</td><td>0.602 (0.015)</td><td>0.013 (0.003)</td><td>1.280 (0.021)</td><td>0.013</td></tr><tr><td>S1</td><td>0.396 (0.007)</td><td>0.002 (0.001)</td><td>1.251 (0.027)</td><td>0.009</td></tr><tr><td>S2</td><td>0.417 (0.008)</td><td>0.010 (0.003)</td><td>1.161 (0.011)</td><td>0.007</td></tr><tr><td>S3</td><td>0.478 (0.011)</td><td>0.027 (0.013)</td><td>1.097 (0.008)</td><td>0.008</td></tr><tr><td>S4</td><td>0.609 (0.011)</td><td>0.012 (0.002)</td><td>1.250 (0.015)</td><td>0.010</td></tr><tr><td>S5</td><td>0.432 (0.009)</td><td>0.005 (0.001)</td><td>1.298 (0.024)</td><td>0.010</td></tr><tr><td>S6</td><td>0.672 (0.015)</td><td>0.027 (0.008)</td><td>1.148 (0.008)</td><td>0.010</td></tr><tr><td>S7</td><td>0.379 (0.041)</td><td>0.029 (0.007)</td><td>1.019 (0.024)</td><td>0.081</td></tr><tr><td>S8</td><td>0.388 (0.012)</td><td>0.004 (0.002)</td><td>1.211 (0.024)</td><td>0.010</td></tr><tr><td>S9</td><td>0.546 (0.012)</td><td>0.006 (0.001)</td><td>1.296 (0.024)</td><td>0.013</td></tr><tr><td>S10</td><td>0.562 (0.010)</td><td>0.022 (0.005)</td><td>1.129 (0.008)</td><td>0.015</td></tr><tr><td>S11</td><td>0.412 (0.011)</td><td>0.002 (0.001)</td><td>1.185 (0.023)</td><td>0.022</td></tr><tr><td>S12</td><td>0.514 (0.008)</td><td>0.016 (0.007)</td><td>1.076 (0.006)</td><td>0.012</td></tr></tbody></table>

Brakensiek (1982). Nonetheless, most subsoil samples in the present study had lower θs_VG values than topsoil samples did, due mainly to their lower SOC contents and higher clay contents and BDs (Carsel and Parrish, 1988). This is also consistent with Fukumasu et al. (2022), who found positive correlations between SOC content and porosities in the 0.2–720 µm diameter classes in topsoil from an arable field, and with several studies that found negative correlations between SOC content and BD (Kätterer et al., 2006; Ruehlmann and Körschens, 2009; Meurer et al., 2020), which suggests that higher SOC content induces higher soil total porosity and thus higher θs.

Parameter α_VG ranged from 0.002 (S1) to 0.069 cm⁻¹ (A4) overall, and specifically from 0.009 (A11) to 0.069 cm⁻¹ (A4) for topsoil samples and 0.002 (S1) to 0.029 cm⁻¹ (S7) for subsoil samples (Table 2). Overall, the α_VG values in this study were consistent with those of previous studies, particularly with the mean values per texture class estimated by Carsel and Parrish (1988) (i.e. 0.005 to 0.075 cm⁻¹ for silty clay to sandy loam soils, respectively). They were also consistent with recently estimated α parameters for sandy-loam topsoil samples under conventional tillage or no-tillage: 0.0145–0.0296 cm⁻¹ (Jabro and Stevens, 2022).

Finally, n_VG ranged from 1.019 (S7) to 1.298 (S5) overall and had a

smaller range for the topsoil samples (i.e. 1.165 (A4) to 1.280 (A13)) than subsoil samples (Table 2). These n_VG values were consistent with the mean values per texture class estimated by Carsel and Parrish (1988) (i.e. from 1.090 to 1.410 for clay to silty loam soils, respectively). However, the n_VG values estimated for the three horizons with sandy-loam texture in the present study were slightly lower than those reported by Carsel and Parrish (1988) (≤1.890) or Jabro and Stevens (2022) (> 1.526).

### 3.3. Pearson correlations

Correlations between the VG model parameters (i.e. θs_VG, α_VG and n_VG), the absolute value of the slope (AvS) and the intercept (b) of the linear relation between θ and SWSI, the soil-fraction contents (i.e. sand, silt and clay) and SOC content varied (Table 3). Correlations between θs_VG and soil-fraction contents were consistent. Specifically, correlations between θs_VG and the silt (r = 0.540, p < 0.01) and sand (r = -0.455, p < 0.05) contents were significant. Increasing the sand content increased BD and thus decreased total porosity, which decreased θs. There was also a strong correlation between θs_VG and SOC (r = 0.676, p < 0.01) or the SOC:Clay ratio (r = 0.732, p < 0.001), which were consistent with results of the meta-analysis of Minasny & McBratney (2018), who investigated relations between SOC and θs, FC, PWP and available water capacity. They found that the increase in θ as SOC increased depended on the texture, being much larger for coarse soils, followed by medium-textured soils and then fine soils. More specifically, their meta-analysis found that θ generally increased the most at saturation, followed by FC and then PWP. In the present study, b, which represents θs, was strongly correlated with θs_VG (r = 0.931, p < 0.001) and had similar correlations as θs_VG did, except with α_VG. The only significant correlation for α_VG was that with θs_VG (r = 0.487, p < 0.05). A large θs means high total porosity which, in a highly structured soil, means that the maximum pore size can be large, resulting in a low air-entry pressure and thus a high α. Because the shape parameter n is related to pore-size distribution and determines the steepness of the SWR curve, it is assumed to be influenced by soil texture, and the results showed that n was correlated negatively with the clay content (r = -0.635, p < 0.01) and positively with the silt content (r = 0.607, p < 0.01). Generally, n is larger for soils with narrow pore-size distribution, and the negative correlation observed with the clay fraction was consistent with this general trend. Parameter n also had a positive correlation with the SOC:Clay ratio (r = 0.487, p < 0.05). AvS was significantly correlated with both parameters for volumetric SWC at saturation (i.e. θs_VG (r = 0.535, p < 0.01) and b (r = 0.578, p < 0.01)) and with the silt content (r = 0.408, p < 0.05).

<caption>**Table 3**</caption>

Pearson correlation matrix of van Genuchten model parameters (θs_VG, α_VG and n_VG), the absolute value of the slope (AvS) and the intercept (b) of the relation between soil water content and the soil water spectral index, and soil physico-chemical properties; Clay content (Clay), Silt content (Silt), Sand content (Sand), soil organic carbon content (SOC) and the ratio of soil organic carbon content to clay content (SOC:Clay).

<table><thead><tr><th></th><th>θ<sub>s</sub>_VG</th><th>α_VG</th><th>n_VG</th><th>AvS</th><th>b</th><th>Clay</th><th>Silt</th><th>Sand</th><th>SOC</th><th>SOC:Clay</th></tr></thead><tbody><tr><td>θ<sub>s</sub>_VG</td><td>1.000</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>α_VG</td><td>0.487<sup>*</sup></td><td>1.000</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>n_VG</td><td>0.248</td><td>-0.365</td><td>1.000</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AvS</td><td>0.535<sup>**</sup></td><td>0.108</td><td>0.367</td><td>1.000</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>b</td><td>0.931<sup>***</sup></td><td>0.376</td><td>0.336</td><td>0.578<sup>*</sup></td><td>1.000</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Clay</td><td>-0.190</td><td>-0.055</td><td>-0.635<sup>**</sup></td><td>-0.273</td><td>-0.145</td><td>1.000</td><td></td><td></td><td></td><td></td></tr><tr><td>Silt</td><td>0.540<sup>**</sup></td><td>-0.116</td><td>0.607<sup>**</sup></td><td>0.408<sup>*</sup></td><td>0.650<sup>*</sup></td><td>-0.322</td><td>1.000</td><td></td><td></td><td></td></tr><tr><td>Sand</td><td>-0.455<sup>*</sup></td><td>0.183</td><td>-0.205</td><td>-0.187</td><td>-0.572<sup>*</sup></td><td>-0.270</td><td>-0.762<sup>***</sup></td><td>1.000</td><td></td><td></td></tr><tr><td>SOC</td><td>0.676<sup>*</sup></td><td>0.273</td><td>0.253</td><td>0.278</td><td>0.762<sup>**</sup></td><td>0.065</td><td>0.308</td><td>-0.325</td><td>1.000</td><td></td></tr><tr><td>SOC:Clay</td><td>0.732<sup>***</sup></td><td>0.293</td><td>0.487<sup>*</sup></td><td>0.380</td><td>0.798<sup>**</sup></td><td>-0.325</td><td>0.455<sup>*</sup></td><td>-0.234</td><td>0.907<sup>***</sup></td><td>1.000</td></tr></tbody></table>

<footnote>*** p < 0.001.</footnote>

<footnote>** p < 0.01.</footnote>

<footnote>* p < 0.05.</footnote>
## 3.4. Relevance of SWSI for parametrizing the VG model

### 3.4.1. Relevance for estimating θs

Parameter θs is important for the VG model and as a physical parameter of soil since it provides information about total porosity (i.e. BD) and the maximum SWC at saturation. It is one of the main soil hydraulic parameters, along with θr, α and n, that can be estimated from the SWR curve. In the NIR-spectroscopy approach, soil samples were scanned from saturation to oven-dried conditions, which allowed a linear relation to be established between θ and SWSI, whose intercept (b) was used to estimate θs. Thus, the approach provided a new way to estimate θs. Comparing b to θs_VG showed that the two estimates agreed well for topsoil and subsoil horizons, despite some scatter (Fig. 4). For all horizons combined, the Pearson correlation coefficient between θs_VG and the b-intercept was strong (r = 0.931, *p* < 0.001) (Table 3), but θs estimates from the b-intercept were generally larger than those obtained from fitting the VG model to the SWR curve. In the air-entry region near *h* = 0, θ was large and nearly constant and tended towards θs. Thus, the assumption of a linear relation between θ and SWSI, even in this range, was likely why b tended to be larger than θs_VG. However, the accuracy was higher for topsoil than subsoil horizons (RMSE = 0.053 and 0.067 cm³/cm⁻³, respectively).

#### 3.4.1.1. Relevance for estimating α and n.
Given the linear relation between θ and SWSI, S<sub>e</sub> was equivalent to its spectral counterparts SWSI<sub>e</sub> (according to Eq. (4)) and FWHM<sub>e</sub> (according to Eq. (5)), which suggests that parameters α and n of Eq. (1), 4 and 5 were identical. Based on Eq. (4), which establishes the relation between the VG model, SWSI and subsequently FWHM (Eq. (5)), we calculated values of α and n that provided the best fit for the relation between *h* and SWSI. These derived parameters were then compared to those estimated for the SWR curve based on Eq. (1).

Estimates of *n* were similar for both equations, especially for the topsoil samples (RMSE = 0.031) (Fig. 5). For the subsoil samples, estimates of *n* were generally similar, but they had slightly more scatter and lower accuracy (RMSE = 0.070). Estimates of α for the spectral SWR-like curve (SWSI(*h*)) (Eq. (4)) and the SWR curve (Eq. (1)) were widely scattered around the 1:1 line for both topsoil and subsoil horizons (Fig. 6) (RMSE = 0.024 and 0.012, respectively).

The present study yielded consistent and even more accurate estimates for α and n than those estimated by Santra et al. (2009), who estimated properties such as saturated hydraulic conductivity and parameters α and n for surface-soil samples (0–10 cm) using both PTFs and

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** The intercept (b) of the relation between the volumetric soil water content (θ) and the soil water spectral index (SWSI) vs. θ at saturation estimated using the van Genuchten (VG) model for topsoil organo-mineral A horizons (filled circles) and subsoil horizons (open circles). The dashed line is the 1:1 line.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Scatterplots of the shape parameter (n) of the van Genuchten (VG) model: predicted SWSI(h) vs. observed θ(h) fitting for topsoil organo-mineral A horizons (filled circles) and subsoil horizons (open circles). The dashed line is the 1:1 line.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Scatterplots of air-entry pressure (α) for the van Genuchten (VG) model: predicted SWSI(h) vs. observed θ(h) for soil samples from topsoil organo-mineral A horizons (filled circles) and subsoil horizons (open circles). The dashed line is the 1:1 line.</figcaption></figure>

STFs, and then compared results of the two approaches. The STFs allowed them to develop multiple linear regressions between α or *n* and attributes of measured spectral reflectance over the vis-NIR spectral range. They found that the STFs generally performed similar to the PTFs and worked best when they considered specific spectral features related to water (1414 and 1913 nm) and clay minerals (2207 nm).

In the present study, *n* had less variability and higher accuracy than that of Santra et al. (2009) (RMSE = 0.031 vs. ca. 0.074, respectively), especially for topsoil samples, although RMSE could not be compared directly because Santra et al. (2009) estimated ln(α) rather than α. Nonetheless, the general trend in both studies showed variability around the 1:1 line. Finally, the results for α agreed with those of Santra et al. (2009), who found that, of the three hydraulic parameters, ln(α) was not estimated accurately by PTF or STF.

Using Eq. (4), α and *n* were subsequently incorporated into Eq. (1), the original VG model, which was used to predict θ after setting θs and θr to *b* and 0, respectively. When comparing predicted θ to observed θ, the predicted θ for topsoil samples were scattered less around the 1:1 line than those for subsoil samples and were thus more accurate (RMSE = 0.031 and 0.045 cm³.cm⁻³, respectively) (Fig. 7). Nonetheless, the predicted θ for subsoil samples were generally accurate, with only a few values being greatly underestimated. These results confirm the
<figure><img src="image_10.png" /><figcaption>Fig. 7. Predicted vs. observed soil water contents ($\theta$) at the ten matric potentials considered for all soil samples: thirteen from topsoil organo-mineral A horizons (filled circles), and twelve from subsoil horizons (open circles). The dashed line is the 1:1 line.</figcaption></figure>

similarity of Eq. (1), 4 and 5, which supports the assertion that the hydraulic parameters $\alpha$ and $n$ are indeed identical among the equations.

## 4. Conclusions

We introduced a new approach that uses NIR-spectroscopy measurements to estimate the SWR curve, a fundamental hydraulic property of soils. The method applies the SWSI, which is based on the FWHM of the absorption band near 1920 nm (Soltani et al., 2019a). The existence of a linear relation between $\theta$ and SWSI prompted us to explore the behavior of the FWHM of the absorption band near 1920 nm in relation to $h$.

The curves of the relation between $h$ and FWHM were similar to the SWR curves for the soil samples investigated, which allowed parameters of the VG model to be estimated to predict the SWR curve, by capitalizing on the linear relation established between $\theta$ and SWSI. This estimate was based on two crucial assumptions: i) the $S_e$ of the VG model is equal to $SWSI_e$ and therefore to FWHMe, and ii) $\theta_s$ corresponds to the intercept in the relation between $\theta$ and SWSI. This result is fundamental as it implies that fitting the VG model can be achieved simply using an easily accessible geometric parameter, namely the FWHM of the water absorption band near 1920 nm. It follows that implementing our approach requires only a low-cost spectrometer, as only a reduced spectral range, including the absorption band near 1920 nm, is needed.

Our study was conducted on 25 samples from topsoil and subsoil, with highly variable textures and OC contents. We assume that our approach can be generalized to other soils, while acknowledging that exceptions may exist. This hypothesis needs to be validated by increasing the sample size and considering soil samples collected from different pedoclimatic contexts.

In summary, results of the NIR-spectroscopy approach highlight its ability to estimate hydraulic parameters such as $\theta_s$, $\alpha$, and $n$ of the VG model. The parameters estimated from the VG-like equation based on the relation between $h$ and SWSI yielded predicted $\theta$ for the SWR curve that were similar to observed $\theta$ (RMSE = 0.031 and 0.045 cm$^3$·cm$^{-3}$ for topsoil and subsoil horizons, respectively). This spectroscopic method opens promising avenues for future applications, particularly in the field of estimating topsoil SWR properties under various agricultural practices.

### CRediT authorship contribution statement

**Youssef Fouad:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Investigation, Formal analysis, Data

curation, Conceptualization. **Inès Soltani:** Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Christophe Cudennec:** Writing – review & editing, Methodology, Investigation, Formal analysis. **Didier Michot:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This research was conducted as part of the “Sols de Bretagne 2” program, which received financial support from the Regional Council of Brittany and Institut Agro Rennes Angers. The authors sincerely thank the soil surveyors who helped collect soil samples, as well as B. Lemercier and C. Walter. We also thank P. Breger and R. Dubois for their invaluable support and assistance in acquiring laboratory data.

### Data availability

Data will be made available on request.

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