1. Introduction
Soil shrinking and swelling due to expansive clays have consequences on urban planning for decision makers since they cause billions of dollars in building damages every year [
1,
2,
3]. They are also responsible for off-road vehicle mobility, the latter being impacted by the sinking and stickiness of wet soils [
4,
5,
6]. Aluminum-rich smectite (montmorillonite) has been demonstrated to be the clay mineral having the most expansive potential hazard [
7]. Thus to monitor soil shrinking and swelling, the characterization of clay mineralogy is needed, both in terms of detection and quantification. In mid-latitude regions, smectite (whose montmorillonite represents the most common variety), illite and kaolinite are the main clay minerals found in soils affected by swelling risk [
8]. For soil swell–shrinking application, Dufréchou et al. and Chassagneux et al. [
9,
10] defined four classes linking shrink–swell potential and montmorillonite content: low swelling potential (<10%), moderate swelling potential (between 10% and 50%), high swelling potential (between 50% and 70%) and very high swelling potential (>70%). Many well-used techniques, either qualitative or quantitative, can assess clay minerals characterization, but they only provide little and local information due to a low number of soil samplings along a coarse grid such as: ground geotechnical engineering techniques measuring soil swelling potential [
11] and X-ray diffraction (XRD) for mineral identification/quantification, and infrastructure damage reports for expansive clay qualitative assessment. However, the use of these methods mainly remains expensive and time-consuming.
An alternative to overcome these limitations is the use of hyperspectral imaging spectroscopy, which is able to discriminate clay minerals using their specific spectral absorption features in the short wave infrared region (SWIR) 2100–2500 nm [
12,
13,
14]. However, clay minerals are rarely pure in soils and are usually intimately mixed with other minerals, water and organic matter. Spectral preprocessings are used to overcome intraclass spectral variability, remove some non-linear illumination effects and enhance shallow absorption features [
15,
16,
17,
18,
19,
20]. For example, the identification of soil minerals using spectral similarity distance increases up to 18% using continuous wavelet transform [
20]. Using spectral preprocessings could be a first preliminary step to further discrimination/quantification methods [
16,
20,
21].
Two classes of methods exist in order to map mineral clays in soils: the first is based on spectral features and the second on unmixing. The first class includes the use of spectral indices (Dufréchou et al. [
12] obtained a root mean square error (RMSE) of 15.4% for montmorillonite, 25.2% for kaolinite and 29.8% for illite), and linear regression methods using clay spectral feature characteristics (e.g., depth, width and position close to 2200 nm; [
22,
23,
24,
25]), and decision tree methods (Mulder et al. [
26] obtained a RMSE of 9% for clay–calcite intimate mixtures). Expert systems such as Tetracorder use spectral features in order to detect and discriminate minerals, such as clays [
27], for example to map clay alteration of Hawaii volcanoes [
28]. These characteristics can also be automatically extracted using partial least square regression (Viscarra Rossel et al. [
29,
30] obtained a RMSE of 3% for illite, kaolinite and smectite in clay–quartz–organic mixtures). Neural networks have been tested for mineral sub-pixel classification [
31], on a Hyperion dataset. Compared to ground reference, fraction prediction provides a correlation coefficient r
2; value of 0.62 for illite/montmorillonite class and 0.6 for kaolinite class.
The second class of methods using unmixing relies on the knowledge of pure mineral spectra or endmembers [
32,
33,
34,
35]. Linear unmixing methods only consider materials at the surface that are contiguously distributed (named in the following “aeral mixture”, [
36]
Figure 1a) while non linear unmixing methods consider mixed pixels several soil elements of volumetric distribution (also called “intimate mixture”, [
32,
36]
Figure 1b). On one side, the most used linear unmixing methods considering only one spectrum per endmember class are the fully constrained least square (FCLS; [
37]) and mixture tuned matched filtering (MTMF; [
38]). On contrary, several algorithms account for the endmember spectral intraclass variability such as multiple endmember spectral mixture analysis (MESMA; [
39]), the spectral assistant, (TSA; [
40]) and the unmixing within a multi-task Gaussian process framework (UMTGP; [
41]). For example, Chabrillat and Bedini [
42,
43] used MTMF and MESMA to discriminate illite/smectite from kaolinite in soils with airborne data. On the other side, Heylen [
44] gave a review of performance of nonlinear unmixing methods, including the Hapke model [
45], generalized bilinear model (GBM; [
46]) and multi-linear model (MLM; [
34]). For example, [
34] showed with laboratory spectroscopy datasets of quartz–alunite intimate mixtures that the Hapke model delivers the best result (bias of 1–2% between estimated and measured abundances), then MLM (bias of 10–20%) and at last both GBM and FCLS have a similar performance (bias 30–40%). Robertson et al. [
47] compared a version of the Shkuratov model [
48] with the Hapke model to quantify laboratory mineral mixtures of montmorillonite–gypsum. In these samples, minerals fractions are estimated with an error less than 10% for both models. Unmixing methods can also be embedded in expert systems such as Tetracorder in order to increase the accuracy of mineral discrimination [
27].
The advantage of using unmixing methods is to be not site-dependent and they do not require a learning stage with a representative training dataset, which is the case with the first class of methods. The difficulty to choose the most appropriate unmixing method is that their performance differs from the mineral mixture composition of soils. Few studies have used unmixing methods to estimate clay minerals fraction, but unmixing is more used for mineral discrimination. Moreover, very few studies have combined spectral preprocessings with unmixing methods, but they demonstrated the ability to decrease mineral fraction estimation errors using spectral preprocessing [
16,
20,
21].
Then, by using airborne and satellite hyperspectral imaging spectroscopy, the sensor spatial resolution and the possible presence of vegetation overlaid on soil within a pixel degrade the performances of mineral estimation [
42,
43,
49]. A first step commonly practiced is to study spectroscopy data under laboratory conditions to avoid environmental factors such as atmospheric and soil water content and soil/vegetation mixtures [
12,
26,
29,
50,
51,
52].
The main objective of this study is to compare the performance of both linear and non-linear unmixing methods combined with spectral preprocessings to estimate montmorillonite abundance in mineral mixtures. For this purpose, this pioneer work is based on spectroscopic measurements of intimate mixtures composed of different mineral types (clays, calcite and quartz) and controlled abundances, manually generated in the laboratory with dry conditions and further used as proxies for soil samples. Performances of the spectral preprocessings and unmixing methods will be assessed from the spectral database deriving from them. Another scenario considering synthetic mineral aeral mixtures computed from spectral measurements of pure minerals will be also analyzed in order to compare the performances of spectral preprocessings and unmixing methods between aeral and intimate mixtures. Thus, the spectral database of intimate and aeral mixtures and the laboratory imaging spectroscopy setup are presented in
Section 2. The methodology including the spectral preprocessing and selected unmixing methods are described in
Section 3. Results are presented in
Section 4 and discussed in
Section 5, with the conclusions exposed in
Section 6.
5. Discussion
5.1. Non-Linearity of Intimate Mixtures Depending on the Mineralogical Composition
Following the increase in montmorillonite abundance, the non-linearity of intimate mixtures was put into evidence compared to aeral mixtures. For two minerals having the same granulometry (around 80 µm), the main contribution of this non-linearity was due to the mean level of reflectance if the minerals have close spectral absorption features such as illite and montmorillonite. Then, with two minerals having no overlapping spectral features such as calcite and montmorillonite, the spectral variations in the absorption features were added as a second contributor to the non-linearity. At last, in the presence of a mineral without any absorption feature such as quartz, the spectral effect of the non-linearity increased drastically. Actually, the reflectance could be decomposed into two components, the volume and the surface reflectances, whose relative contribution depended on the granulometry. First, due to the high reflectance of quartz, the volume reflectance was favored by the multiple scattering inside the mixture and as such increased the chance for a photon to interact with montmorillonite mineral. As a consequence, the non-linearity was observed in the absorption band of montmorillonite, even if its abundance was low as it had already been mentioned by Clark [
62]. Second, the surface reflectance depended on the reflective value and the abundance of each mineral. The higher the granulometry, the higher is the surface reflectance relative contribution. Thus for quartz/montmorillonite mixtures, the non-linearity contribution might be partially compensated by the quartz particle size (300 µm).
5.2. Spectral Variability Reduction with Spectral Preprocessings
Application of spectral preprocessings on intimate mixtures spectra showed that 1st SGD, CWT, SNV and CR significantly reduced the intrasample spectral variability while Log(1/R) and Hapke gave an intrasample spectral variability with the same order of magnitude as with reflectance spectra, but sometimes much worse.
Actually, two classes of spectral preprocessings could be distinguished based on their spectral transformation: quasi-linear (1st SGD, CWT) and non-linear (SNV, CR, Log(1/R), Hapke). These two spectral preprocessing classes led to different spectra and introduced some artifacts. CWT decomposes the spectrum into a sum of linear signals and preserves additive properties of the spectra [
20] while the 1st SGD is only sensitive to the local spectral variations. SNV is based on a centered-reduced spectrum normalization [
17,
19] corresponding to a multiplicative correction causing a loss of any additive contribution. Clark et al. [
60,
62] showed that CR correctly identifies the location of spectral absorption features with spectra having a steep slope continuum but to the detriment of the deformation of the spectral feature [
20,
62]. Log(1/R) transforms data into the logarithmic space, which, in relationship with Lambert–Beer’s law increases linearity between spectral data and constituent abundance [
17,
19]. However, additive and multiplicative properties of the spectrum are not suppressed, so that the variability is not reduced. Hapke transforms the data into the albedo space, leading to the same conclusions as Log(1/R).
As a result, the weak intrasample spectral variability of spectra deduced from quasi-linear and non-linear spectral preprocessings 1st SGD, CWT, SNV and CR, was explained by their low sensitivity to the reflectance mean level. On the contrary, the non-linear Hapke and Log(1/R) preserved the intrasample spectral variability of the reflectance. However, the reduction of the latter did not lead to a better discrimination between the different mixture spectra because our samples were homogeneous and thus had low intraclass variability.
5.3. Performance of Linear Unmixing Methods with Spectral Preprocessings
For clay binary aeral mixtures (IM and MK) and reflectance spectra, MESMA is expected to have better performances than FCLS, as it takes into account the intrasample variability of endmember [
39]. Improved estimation results were particularly noticeable with reflectance spectra and Log(1/R) having a large intrasample spectral variability, but improvements were very small with the other spectral preprocessings already having a reduced intrasample spectral variability. Overall, FCLS and MESMA had comparable performances with SNV, CR, CWT and 1st SGD. However, SNV and CR carried higher biases in montmorillonite abundance estimation. For calcite and quartz aeral mixtures (MC and MQ), the same conclusions as before could be done in the main lines, with the best results achieved with 1st SGD, CWT and CR.
For clay binary intimate mixtures, the best spectral preprocessings were SNV, CR, CWT and 1st SGD for FCLS whereas for MESMA, Hapke and reflectance spectra were added. MK mixtures had larger montmorillonite estimation errors than for IM ones, oppositely to the clay aeral mixtures. Possible reasons might be that bias values were more important for intimate mixtures than aeral ones. Then for the latter, since there was a strong spectral overlapping of IM mixtures within the range of the intrasample spectral variability (
Figure 6a), confusions might occur in finding the best unmixing solution, whereas, confusions might be added due to the non-linear effects for intimate mixtures (more important for MK than IM mixtures). Among the best couples spectral preprocessing/unmixing method, CWT or 1st SGD/FCLS or MESMA were selected. By comparing their results between the aeral and intimate mixtures, the main source of error based on the RMSE came from the non-linearity of the intimate mixtures with an increase by a factor of 2–6. For calcite/montmorillonite intimate mixtures, the best couples spectral preprocessing/unmixing method were REF/FCLS or MESMA. Performances were similar with IM intimate mixtures but better than MK ones. The impact of the non-linearity within the intimate mixtures compared to the aeral mixtures increased by a factor of 2–4. For quartz/montmorillonite intimate mixtures, the non-linearity effect due to the presence of quartz was too strong to be taken into account by the linear unmixing methods and the performances were very low. For ternary clay intimate mixtures, CR or CWT/FCLS or /MESMA were the best couples and their performance had the same order of magnitude as those of clay binary mixtures.
As a first conclusion, when two minerals present overlapped absorption features (clay mixtures), the best spectral preprocessings were those enhancing the slight spectral local changes, such as SNV, CR, CWT and 1st SGD. However, SNV was not recommended since it might bring higher errors on mineral abundance estimation in some cases. Oppositely, when no overlap occurred (mixtures with calcite), Hapke, and reflectance spectra performed the best because they rely on the global variation of the spectrum (i.e., continuum), which varied linearly with the addition of minerals.
5.4. Performance of Allunmixing Methods with Spectral Preprocessings
For clay binary intimate mixtures and whatever linear or non-linear unmixing method, results of montmorillonite abundance estimation were in the range 10.8–25.4% (RMSE) for MK mixtures and 7.0–29.5% for IM ones. MESMA, FCLS and GBM had comparable performances when using SNV, CR, CWT and 1st SGD, the same as MLM combined with whatever spectral preprocessing. MLM algorithm might compensate the higher intrasample spectral variability with the P non-linear parameter, because this spectral variability had a larger amplitude than the non-linearity of the intimate mixture for similar grain size in clay mixtures [
34]. Revel et al. [
63] have also observed the prevalence of intraclass variability over non-linear effects on the performance of unmixing methods in another context.
For calcite/montmorillonite intimate mixtures, RMSE ranged between 8.2% and 38.6%. GBM had a very close performance with reflectance and Log(1/R) compared to FLCS and MESMA with reflectance, while MLM performed the worst. Compared to clay binary intimate mixtures, this last case may be explained because the P parameter of MLM had negative values. Heylen et al. [
34] mentioned that the use of MLM could lead to errors in the case of high reflective materials, like calcite.
For quartz/montmorillonite intimate mixtures, results of montmorillonite abundance estimation were very poor with RMSE around 50.4–65.3%. The difficulties raised in this study with mixtures containing quartz are also noticed by Asadzadeh et al., Viscarra Rossel et al. and Mulder et al. [
15,
26,
29] since detecting and quantifying quartz are still major limitations for soil mineralogy spectroscopy in the range 400–2500 nm. Indeed, some studies chose to neglect the impact of quartz abundance [
26]. However, Debba et al. [
16] demonstrated that taking into account quartz abundance as an endmember for unmixing produces more accurate results.
For clay ternary intimate mixtures, besides the increasing impact of non-linear effects from clay binary to clay ternary intimate mixtures, the performance was globally similar whatever the unmixing method with montmorillonite abundance estimation in the range 7.5–24.3% (RMSE). The best performance was obtained for CWT or 1st SGD/FCLS or MESMA or GBM or MLM.
Globally several trends could be deduced, except for the quartz/montmorillonite mixtures:
For clay intimate mixtures either binary or ternary and whatever unmixing methods, the best spectral preprocessings were CWT and 1st SGD while for calcite/montmorillonite intimate mixtures, the best results were obtained without the use of spectral preprocessing. Consequently, it was recommended to use quasi-linear spectral preprocessings (CWT or 1st SGD) when the absorption bands of minerals overlap and keep the reflectance in the other cases (calcite). Attention should be paid with the use of SNV leading to higher biases in montmorillonite abundance estimations, and Log(1/R)/Hapke leading to non robust results dependent on the mixture type and the unmixing method. The only best results for Hapke were obtained with MESMA for clay intimate mixtures (IM: RMSE of 6.6%, MK: RMSE of 12.1% and IMK: RMSE of 7.1%) with minerals of similar granulometry (80 µm), which is in agreement with Heylen and Scheunders [
31] (RMSE less than 2% for alunite–quartz mixtures having similar grain size). However, with minerals of different granulometry (calcite: 70 µm, quartz: 300 µm), performance was poor because it violated the main assumption of the Hapke algorithm used in this paper [
44].
Similar performances in terms of RMSE were noticed between the use of linear and non-linear unmixing methods. As a result, the use of the simplest linear unmixing method, FCLS, was advised, coupled with the simplest spectral preprocessing, 1st SGD, for clay intimate mixtures and without the use of spectral preprocessing with calcite/montmorillonite.
The error in montmorillonite abundance estimation achieved for the best couple mentioned in
Section 2, a RMSE of 9.2% for IM mixtures, 13.9% in MK mixtures, 10.8% in clay ternary mixtures and 8.8% for MC mixtures. These results were better than those obtained by [
12] using a geometrical analysis for montmorillonite–illite–kaolinite mixtures (RMSE 15.5%). For more complex mixtures, the performance gave an RMSE of around 8% using a regression tree for smectite–kaolinite–muscovite–calcite–quartz mixtures [
26] and an RMSE of around 3.4% using a multivariate analysis for smectite–illlite–kaolinite–carbonate–quartz mixtures [
29].
6. Conclusions
A comparative study was carried out in order to assess the performance of combining unmixing methods (two linear and two non-linear methods, FCLS and MESMA, GBM and MLM, respectively), with and without the use of six spectral preprocessings (SNV, CR, CWT, Hapke, 1st SGD and Log(1/R)), for the estimation of montmorillonite abundance. The objective of this work was to analyze the sources of non-linearities as a function of the mixture type (aeral versus intimate), the number of minerals (binary and ternary) and their nature (clay, calcite and quartz).
The major results included the following: (i) spectral preprocessing SNV, CR, CWT and 1st SGD reduced the spectral intrasample variability, (ii) the benefit of the spectral preprocessings CWT and 1st SGD occurred when spectral absorption features of minerals overlapped, whereas the reflectance spectra without spectral preprocessing performed the best when no overlap occurred, (iii) SNV carried non-linear effects, which led to biases for montmorillonite estimation and the use of Log(1/R) and Hapke sometimes led to non robust results, (iv) unmixing on mixtures with quartz achieved the worst performance with RMSE higher than 50%, (v) linear and non-linear unmixing methods had similar performance and so the use of FCLS, the simplest method, might be recommended and (vi) the most robust couple of spectral preprocessing and unmixing method was 1st SGD and FCLS for the clay binary mixtures and reflectance and FCLS for the mixtures with calcite, with RMSE ranging between 8.8% and 13.9%. For soil swell–shrinking application, our results with ternary and binary clay and clay–calcite mixtures gave an RMSE less than 15%, the use of unmixing methods could be of interest in order to improve the classification of expansive soils.
This study was only carried out with mineral mixtures manually generated in laboratory conditions, in order to study non-linear interactions due to mineralogy alone. However, these mixtures did not represent real soil composition, mainly because they did not include the presence of soil organic matter and water content and because of the homogeneous mineral content (little variability in a mixture, with a controlled grain size). Thus, future work will be to carry out the same comparative study applied on real soils with very high resolution hyperspectral imaging in order to take into account the impact of soil composition like mineralogy and, water content and organic matter content [
7,
29], as well as environmental factors like soil surface roughness [
64] and shadow effects [
64,
65,
66,
67] and the presence of either sparse green or dry vegetation with soil within a pixel [
49,
68,
69,
70]. As quartz and carbonates minerals possess distinct features in long wave infrared (LWIR, 7.5–14 µm) [
56,
71], we propose in a further perspective to use the combination of SWIR and LWIR spectral domains in order to improve clay estimation in soil.