Guillaume Lassalle
email: guillaume.lassalle@onera.fr

Anthony Crédoz

Rémy Hédacq

Georges Bertoni

Dominique Dubucq

Sophie Fabre

Arnaud Elger

Anthony Credoz

Estimating persistent oil contamination in tropical region using vegetation indices and random forest regression

Keywords: reflectance spectroscopy, soil contamination, Total Petroleum Hydrocarbons, vegetation indices, Random Forest

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Introduction

Along with its development during the last century, oil and gas industry has become a major source of contamination in the environment [START_REF] Barraza | Distribution, contents and health risk assessment of metal(loid)s in small-scale farms in the Ecuadorian Amazon: An insight into impacts of oil activities[END_REF][START_REF] Durango-Cordero | Spatial Analysis of Accidental Oil Spills Using Heterogeneous Data: A Case Study from the North-Eastern Ecuadorian Amazon[END_REF][START_REF] Ogri | A review of the Nigerian petroleum industry and the associated environmental problems[END_REF][START_REF] Romero | Large-scale deposition of weathered oil in the Gulf of Mexico following a deep-water oil spill[END_REF]. Crude oil and by-products (e.g. petroleum products, wastewater, oil sludge) are frequently released in soils, following accidental facility failures, bad practices and, more rarely, storm events [START_REF] Ahmadun | Review of technologies for oil and gas produced water treatment[END_REF][START_REF] Chang | A study of storage tank accidents[END_REF][START_REF] Correa Pabón | Reflectance and imaging spectroscopy applied to detection of petroleum hydrocarbon pollution in bare soils[END_REF][START_REF] Hu | Recent development in the treatment of oily sludge from petroleum industry: A review[END_REF]. They cause important ecological disturbances, because oil contaminants -especially Total Petroleum Hydrocarbons (TPH) -are highly toxic toward organisms [START_REF] Bejarano | Oil spills and their impacts on sand beach invertebrate communities: A literature review[END_REF][START_REF] Finer | Oil and gas projects in the Western Amazon: Threats to wilderness, biodiversity, and indigenous peoples[END_REF][START_REF] Merkl | Phytoremediation in the tropics-the effect of crude oil on the growth of tropical plants[END_REF]. The contamination of soil may persist in brownfields and mud pits after cessation of the oil production activity and affect ecosystems on the long term (Lassalle et al., 2019b(Lassalle et al., , 2019a)). The monitoring of oil activities has therefore become a critical environmental issue, and gave rise to an increasing need in reliable and cost-effective methods for assessing soil contamination. For this purpose, reflectance spectroscopy provided promising results when applied to bare soils [START_REF] Correa Pabón | Spectroscopic characterization of red latosols contaminated by petroleum-hydrocarbon and empirical model to estimate pollutant content and type[END_REF][START_REF] Scafutto | Quantitative characterization of crude oils and fuels in mineral substrates using reflectance spectroscopy: Implications for remote sensing[END_REF]. Its application to multi-and hyperspectral remote sensing imagery makes possible to detect and quantify soil TPH content at large scale using airborne sensors [START_REF] Correa Pabón | Reflectance and imaging spectroscopy applied to detection of petroleum hydrocarbon pollution in bare soils[END_REF][START_REF] Scafutto | Hyperspectral remote sensing detection of petroleum hydrocarbons in mixtures with mineral substrates: Implications for onshore exploration and monitoring[END_REF]. More recently, a new approach has been proposed to extend its use to vegetated areas, where oil cannot be detected directly at the soil surface [START_REF] Lassalle | Assessing Soil Contamination Due to Oil and Gas Production Using Vegetation Hyperspectral Reflectance[END_REF][START_REF] Rosso | Reflectance properties and physiological responses of Salicornia virginica to heavy metal and petroleum contamination[END_REF]Sanches et al., 2013a). This approach shows great interest in tropical regions, where vegetation is particularly dense [START_REF] Achard | Direct or indirect on-shore hydrocarbon detection methods applied to hyperspectral data in tropical area[END_REF][START_REF] Adamu | Remote sensing for detection and monitoring of vegetation affected by oil spills[END_REF][START_REF] Arellano | Detecting the effects of hydrocarbon pollution in the Amazon forest using hyperspectral satellite images[END_REF].

TPH affect vegetation health -especially pigment and water contents -and optical properties in the reflective domain (400 -2500 nm) [START_REF] Balliana | Development of Canavalia ensiformis in soil contaminated with diesel oil[END_REF]Emengini et al., 2013a;[START_REF] Rosso | Reflectance properties and physiological responses of Salicornia virginica to heavy metal and petroleum contamination[END_REF][START_REF] Tran | Germination , physiological and biochemical responses of acacia seedlings ( Acacia raddiana and Acacia tortilis ) to petroleum contaminated soils *[END_REF]. By exploiting the reflectance of leaves and canopies at particular wavelengths, it is possible to detect the changes induced by TPH in leaf biochemistry [START_REF] Gürtler | Determination of changes in leaf and canopy spectra of plants grown in soils contaminated with petroleum hydrocarbons[END_REF][START_REF] Lassalle | Assessing Soil Contamination Due to Oil and Gas Production Using Vegetation Hyperspectral Reflectance[END_REF]Sanches et al., 2013a). This approach is however still under development and needs further improvements in order to be used operationally. Methods based on vegetation indices (VI) (i.e. reflectance ratios) have succeeded in distinguishing healthy and oil-exposed vegetation and in discriminating among various types of oil contamination, under controlled and natural conditions (Emengini et al., 2013a;Lassalle et al., 2019b). In recent studies, TPH were accurately detected from satellite images [START_REF] Arellano | Detecting the effects of hydrocarbon pollution in the Amazon forest using hyperspectral satellite images[END_REF], but their quantification remains rarely considered, although it is of great interest for assessing the environmental risks deriving from the contamination.

The quantification of TPH remains a major challenge, as it implies tracking little variations in leaf biochemistry from its reflectance. This might be particularly difficult on contaminated brownfields and mud pits, because the established species are particularly tolerant to oil exposure [START_REF] Credoz | Experimental study of hyperspectral responses of plants grown on mud pit soil[END_REF]Lassalle et al., 2019b). This difficulty is moreover enhanced when dealing with low TPH concentrations, for two main reasons. In most cases, the lower the concentration, the lower the effects on vegetation health and reflectance (Emengini et al., 2013a;Sanches et al., 2013a). These effects become more difficult to detect below a certain concentration (Lassalle et al., 2019b). Moreover, some species undergo a stimulation of growth under exposure to low oil contamination [START_REF] Kirk | Phytotoxicity assay to assess plant species for phytoremediation of petroleum-contaminated soil[END_REF][START_REF] Lin | The dose-response relationship between No. 2 fuel oil and the growth of the salt marsh grass, Spartina alterniflora[END_REF]. It is particularly frequent for tropical species.

These phenomena make the quantification of TPH very challenging using vegetation reflectance.

Previous studies focusing on heavy metals -which is a very different context of soil contamination -achieved accurate quantification of these compounds by exploiting reflectance data in empirical univariate regression models and in Partial Least Square Regression (PLSR) (Shi et al., 2014b(Shi et al., , 2014a)). Similar approaches proved efficient for quantifying high levels of TPH contamination (up to 77 g.kg -1 ) in our previous study (Lassalle et al., 2019a), but became ineffective below a certain concentration (~ 20 g.kg -1 ). So, to date, there is still no evidence that low levels of TPH can be quantified using vegetation reflectance, especially in tropical region.

To achieve this, alternative methods are necessary. Emerging machine learning methods, which proved efficient for solving complex regression problems, could help quantifying low TPH concentrations [START_REF] Hastie | The Elements of Statistical Learning The Elements of Statistical Learning[END_REF][START_REF] Breiman | Random forests[END_REF].

This study aims to assess the potential and limits of vegetation reflectance for quantifying low TPH concentrations in soils, under controlled conditions. The proposed approach relies on the combination of VI and a machine learning method -namely Random Forest (RF) regression.

This method was tested on reflectance measurements performed at various acquisition scales, under realistic tropical conditions.

Materials and Methods

Study site and greenhouse experiment

An experiment was carried out for 42 days, for which a realistic case of oil contamination was reproduced under controlled tropical conditions. An industrial vegetated mud pit located in tropical region was identified for this purpose. Residues of oil production have been accumulated on this site resulted in persistent oil contamination in soils. After cessation of the activity, the site has been colonized by herbaceous vegetation, mainly Cenchrus alopecuroides (L.). The experiment focused on this species, which proved good indicator of oil contamination in previous studies (Emengini et al., 2013c;[START_REF] Lassalle | Assessing Soil Contamination Due to Oil and Gas Production Using Vegetation Hyperspectral Reflectance[END_REF]. To reproduce as faithfully as possible the conditions of the mud pit, the soil was sampled on two locations of the site and used in the experiment. Soil analyses revealed low concentrations of BTEX and Polycyclic Aromatic Hydrocarbons (PAHs) in both samples, and C 5 -C 40 TPH concentrations of 5 and 21 g.kg -1 , respectively. The lower (C 5 -C 10 ) and intermediate (C 10 -C 21 ) hydrocarbon fractions have been partially degraded, so the remaining contamination mostly came from the dense ones (C 21 -C 40 hydrocarbons), which are poorly degradable and whose uptake by roots is very limited (Lassalle et al., 2019b). Detailed soil analyses can be found in the Supporting Information section. No substantial change in TPH concentrations was observed for the different treatments at the end of the experiment (data not shown). In addition, an uncontaminated soil with similar texture was sampled on another site and used in the experiment. All the soils were homogenized manually and sieved to 10 mm to remove coarse root residuals.

Five treatments were applied to C. alopecuroides for the greenhouse experiment, with TPH concentrations ranging from 0 to 19 g.kg -1 . For this purpose, the soils sampled on the mud pit and the control site were mixed in varying proportions to obtain five levels of contamination, respectively 0 (control), 1, 5, 13 and 19 g.kg -1 TPH (see Supporting Information). Cultivated young plants were acclimated for 15 days in greenhouse and reached 15-cm height before being transplanted in individual pots filled with a 3-cm layer of clay balls and 3 L of the corresponding treatment soil. For each treatment, 11 replicates were grown for 42 days in May and June at 27° C and 70% hygrometry, with a 12:12 light:dark photoperiod provided by natural and artificial light. N-P-K (6-6-6) fertilization was applied weekly to the plants, which were irrigated to field capacity every day. At the end of the experiment, plant shoots were harvested, oven-dried for 48 h at 60° C and then weighed.

Biochemical analyses and reflectance acquisitions

The biochemical and spectral responses of C. alopecuroides to the treatments were measured during the study. For this purpose, we followed the procedure described in Lassalle et al. (2019b). Young leaves were sampled on five different replicates per treatment and served for determining leaf water (LWC) and pigment contents [START_REF] Arellano | Detecting the effects of hydrocarbon pollution in the Amazon forest using hyperspectral satellite images[END_REF][START_REF] Diepens | Toxicity effects of an environmental realistic herbicide mixture on the seagrass Zostera noltei[END_REF].

Leaf pigment content was quantified by High Pressure Liquid Chromatography (HPLC), and included chlorophylls a and b and various carotenoids, such as β-carotene, lutein, antheraxanthin, violaxanthin and zeaxanthin [START_REF] Barlow | Improved resolution of mono-and divinyl chlorophylls a and b and zeaxanthin and lutein in phytoplankton extracts using reverse phase C-8 HPLC[END_REF]. Differences among the treatments were analyzed through ANOVA and Tukey post-hoc tests. In addition, the spectral reflectance of the same sampled leaves was measured following the protocol described below, and linked to biochemical analyses (see section 2.3). This procedure was carried out after 21 and 42 day of experiment. No leaf was sampled before in order to avoid influencing plant growth during early stages.

Reflectance measurements were also performed directly on the plants (i.e. without picking leaves) at day 0, 21 and 42, using an ASD FieldSpec 4 Hi-Res spectroradiometer (Malvern Panalytical, Malvern, UK). Data were acquired in radiance in the reflective domain (400 -2400 nm) and converted to reflectance using a white reference calibration panel (Spectralon, Labsphere Inc., North Sutton, USA) [START_REF] Milton | Principles of field spectroscopy[END_REF]. For each treatment, three leaves per replicate were measured at random (n = 165 spectra per date) using a leaf-clip with an internal light source (10 measurements averaged per leaf). Additional measurements were conducted at plant scale, by placing a 10°-FOV fore-optic above the pots to obtain a 5-cm wide acquisition footprint (10 measurements averaged per plant). These measurements were performed on each replicate (n = 55 spectra per date) under natural light between 11.30 am and 1.30 pm, under clear sky. The reflectance data from the 1350 -1450 and 1800 -1950 nm ranges were not conserved, because of low atmospheric transmission at plant scale. A Savitzky-Golay smoothing filter was then applied at the remaining wavelengths, improving the signal-to-noise ratio [START_REF] Savitzky | Smoothing and Differentiation of Data by Simplified Least Squares Procedures[END_REF].

Vegetation indices

In this study, 33 VI were computed and used in two ways. They are listed in the Supporting Information section. These indices have been specifically exploited for detecting oil-induced changes in leaf biochemistry in our previous study, so here they were tested for quantifying TPH (Lassalle et al. 2019b). Most of them exploited reflectance in the visible (VIS) region (450 -700 nm), which is the most important spectrum region for assessing oil contamination. It has been shown that under exposure to oil, changes in the values of a single vegetation index result from the alteration of several inter-correlated pigments that share common light absorption features (e.g. chlorophylls and carotenoids). Consequently, the pigments to which an index has been initially linked in the literature may differ from those involved in the response to oil exposure. So, it is necessary to identify which pigments contribute the most to index changes, in order to understand how vegetation reflectance is affected by oil. For this purpose, the 33 indices were first computed from the reflectance data of leaves sampled for biochemical analyses, and each of them was linked to leaf pigment and water contents using Elastic net (ENET) multiple regression [START_REF] Zou | Regression and variable selection via the elastic net[END_REF], as described in Lassalle et al. (2019b). ENET is a penalized least squared regression method that allows selecting predictors under multicollinearity.

Multicollinearity appears when predictors -in our case, leaf pigment contents -are linear combination of each other, and results in confusions when selecting those contributing the most to the target variable (i.e. VI) [START_REF] Belsley | Detecting and Assessing Collinearity[END_REF][START_REF] Dormann | Collinearity: a review of methods to deal with it and a simulation study evaluating their performance[END_REF]. ENET regression prevents from such consequences and has already proved efficient for identifying biochemical parameters involved in reflectance changes under exposure to contaminants (Lassalle et al., 2019b). For each VI, the best predictors were retained and the R 2 of the model was calculated.

In a second time, the same 33 indices were computed from the reflectance data acquired at leaf and plant scales and used for predicting TPH concentrations using RF regression [START_REF] Breiman | Random forests[END_REF]. RF is an ensemble method that builds and average a lot of independent decision trees to model the relationship between predictors (i.e. the 33 VI) and a response variable -here, TPH concentration [START_REF] Hastie | The Elements of Statistical Learning The Elements of Statistical Learning[END_REF][START_REF] Hutengs | Downscaling land surface temperatures at regional scales with random forest regression[END_REF][START_REF] Mutanga | High density biomass estimation for wetland vegetation using worldview-2 imagery and random forest regression algorithm[END_REF]. Each tree is constructed from a set of decision rules that results from the recursive fragmentation of the original space into successively smaller sub-regions. To define these sub-regions, binary splits are applied independently to each vegetation index. A simple model is then adjusted between VI and TPH concentrations with respect to the splits, and those minimizing the mean squared error between the measured and predicted concentrations are retained. The succession of the selected index splits represents the branches of the decision tree, in such a way that each set of decision rules leads to an estimation of TPH concentration (see [START_REF] Hutengs | Downscaling land surface temperatures at regional scales with random forest regression[END_REF] for a complete description). RF accounts for non-linear relationships between the predictors and the response variable -which can occur for low concentrations of contaminants, so it was of great interest in our case. Moreover, RF informs on the relative contribution of VI to the quantification of TPH [START_REF] Breiman | Random forests[END_REF][START_REF] Grömping | Variable importance assessment in regression: Linear regression versus random forest[END_REF], which is essential for operational applications of the method.

The RF regression was fitted to half of the data (50% training set) and tested on the remaining part (50% test set), at leaf and plant scales separately (Lassalle et al., 2019b(Lassalle et al., , 2019a)). For this purpose, we used the data from day 42, because no difference among the treatments was observed on the previous dates, so no quantification of TPH was possible (see section 3.1). The predictions of TPH made on the test set were compared to those from initial soil analyses based on the R 2 , the Root Mean Squared Error (RMSE) and the Residual Predictive Deviation (RPD) (Shi et al., 2014). The RPD denotes the ratio of the standard deviation of the measured TPH concentrations to the RMSE calculated between the measured and predicted concentrations.

Results and discussion

Biochemical and spectral responses to oil contamination

As expected, C. alopecuroides was highly tolerant to oil, as none of the plants from the contaminated treatments died during the experiment. This observation is consistent with previous studies carried out on the same species with various types of oil contamination (engine oil and oil and gas waste mud) (Emengini et al., 2013c;[START_REF] Lassalle | Assessing Soil Contamination Due to Oil and Gas Production Using Vegetation Hyperspectral Reflectance[END_REF]. No visible stress symptom was observed on any of the replicates before the last stages of the experiment (35 -42 days), so no difference in leaf pigment contents and in leaf and plant reflectance was observed among the treatments on the previous dates (0 and 21 days, data not shown). On day 42, leaf discoloration was observed for the individuals exposed to 5 g.kg -1 TPH or more, expressing a significant decrease in leaf chlorophyll and carotenoid contents when compared to the control (p < 0.05) (Fig. 1). Plant growth was also significantly affected on this date. The alterations in pigment contents induced an increase of reflectance by 5 to 10% in the VIS region, especially around 550 and 700 nm (Fig. 2). Other regions of the spectrum were also affected in the same way by contamination. This response was more pronounced at leaf scale, because plant reflectance is also influenced by plant architecture, background soil and illuminating and viewing geometry [START_REF] Asner | Biophysical and Biochemical Sources of Variability in Canopy Reflectance[END_REF]Sanches et al., 2013a). As suggested in previous works (Emengini et al., 2013c;[START_REF] Lassalle | Assessing Soil Contamination Due to Oil and Gas Production Using Vegetation Hyperspectral Reflectance[END_REF], the late response of C. alopecuroides to oil highlights its interest for monitoring long-term contaminated sites, especially brownfields and mud pits remaining after cessation of oil and gas activities. Alterations in leaf biochemistry and optical properties are very common for vegetation exposed to contaminants [START_REF] Balliana | Development of Canavalia ensiformis in soil contaminated with diesel oil[END_REF]Lassalle et al., 2019b;[START_REF] Rosso | Reflectance properties and physiological responses of Salicornia virginica to heavy metal and petroleum contamination[END_REF]Sanches et al., 2013a). They depend on multiple factors, especially the species, the contamination type and concentration and the time of exposure, and have been previously observed on C. alopecuroides and other tropical species (Arellano et al., 2017b;Emengini et al., 2013c;[START_REF] Lassalle | Hyperspectral signature analysis of three plant species to long-term hydrocarbon and heavy metal exposure[END_REF]. In the case of oil, these alterations result from the reduction of water and nutrient availability in soils and uptake capacities of roots [START_REF] Athar | Influence of sub-lethal crude oil concentration on growth, water relations and photosynthetic capacity of maize (Zea mays L.) plants[END_REF][START_REF] Balasubramaniyam | Scanning electron microscopic investigations of root structural modifications arising from growth in crude oil-contaminated sand[END_REF][START_REF] Nie | Plants ' use of different nitrogen forms in response to crude oil[END_REF]. Additional effects may come from the accumulation of hydrocarbons in tissues [START_REF] Baruah | Effect of crude oil contamination on the chlorophyll content and morpho-anatomy of Cyperus brevifolius (Rottb.) Hassk[END_REF], but they mostly involve low-carbon TPH, so they are unlikely to explain the responses observed in our experiment. The amplitude of these biochemical and spectral responses was determined by the level of contamination, which confirmed previous results obtained for higher levels of oil (Emengini et al., 2013c;Sanches et al., 2013a). The more the TPH, the lower the leaf pigment contents and the higher the reflectance (Fig. 2). Consequently, leaf chlorophyll content felt to 17.7 (± 3.0) µg.cm -2 under exposure to 19 g.kg -1 TPH, while it reached 51.7 (± 3.5) µg.cm -2 for control at the end of the experiment (Fig. 1). A similar trend was observed on carotenoids, and suggested being able to discriminate among the different levels of contamination using reflectance data. In contrast to the other treatments, a stimulating effect was observed for plants exposed to 1 g.kg -1 TPH. Shoot dry weight and leaf chlorophyll and carotenoid contents were significantly higher for this treatment than those of the control (p < 0.05), and reflectance was slightly lower at leaf and plant scales. This particular response -called hormesis -has already been observed on the growth of other oil-exposed species in previous studies [START_REF] Kirk | Phytotoxicity assay to assess plant species for phytoremediation of petroleum-contaminated soil[END_REF][START_REF] Lin | The dose-response relationship between No. 2 fuel oil and the growth of the salt marsh grass, Spartina alterniflora[END_REF][START_REF] Salanitro | Crude oil hydrocarbon bioromediation and soil ecotoxicity assessment[END_REF]. However, its causes remain poorly documented. To our knowledge, this study is the first to bring evidence of this phenomenon using reflectance measurements. Previous experiments aimed to simulate accidental oil spills (e.g. pipeline leakage), by applying high doses of oil -mainly diesel or engine oil -to crop species, which are particularly sensitive to such contamination (Emengini et al., 2013a;[START_REF] Gürtler | Determination of changes in leaf and canopy spectra of plants grown in soils contaminated with petroleum hydrocarbons[END_REF]Sanches et al., 2013a).

Consequently, strong alterations in leaf biochemistry and reflectance have been observed regardless of the contamination level, so no hormesis has been noticed. The responses of C. alopecuroides observed in our study substantially differed, because we focused on a totally different context. When oil contamination persists in industrial brownfield and mud pit soilssuch as that reproduced in our experiment, the most phytotoxic fractions of petroleum hydrocarbons (e.g. BTEX, PAH) are almost absent from the mixture. The effects on oil-tolerant established vegetation are therefore much less pronounced than those observed for other types of oil contamination with high proportion of these compounds (e.g. crude oil, diesel, gasoline), especially at low concentration (Lassalle et al., 2019b). Here, PAHs and BTEX were found below the detection limits (0.02 and 0.05 mg.kg -1 , respectively) at 1 g.kg -1 of TPH and in the control soil, so they did not affect the plants negatively. Conversely, these compounds are likely to induce positive effects at very low concentration [START_REF] Maliszewska-Kordybach | Ecotoxicological Activity of Soils Polluted with Polycyclic Aromatic Hydrocarbons (PAHs) -Effect on Plants[END_REF], but they cannot be the only contaminants responsible for the differences observed between the two treatments. Some other hydrocarbon fractions -which were absent from the control soil -enhance the availability of nutrients and organic matter for plants by stimulating microorganisms [START_REF] Li | Chronic Low Level Hydrocarbon Amendments Stimulate Plant Growth and Microbial Activity in Salt-Marsh Microcosms[END_REF]. Therefore, the very low concentrations of PAHs and BTEX combined to those of other hydrocarbon fractions might have induced the hormetic effect observed in this study.

Vegetation indices

Elastic net regressions

The VI succeeded in linking the biochemical and spectral responses of C. alopecuroides to oil contamination. 20 out of the 33 indices tested were strongly correlated to leaf pigment or water content (R 2 ≥ 0.7) (Tab. 1). For most of them, at least three contributing pigments were identified, the others having not being retained by the ENET regression. Chlorophylls and βcarotene were often the most contributing ones, and provided some of the best models (R 2 ≥ 0.8) when used together (i.e. without addition of other carotenoids). Therefore, these pigments explained most of the modifications in reflectance observed among the treatments in the VIS region. Other carotenoid pigments -especially lutein and violaxanthin -were frequently retained in the models (e.g. GM2 and PSSRb indices), thus confirming previous results obtained on another oil-tolerant species (Lassalle et al., 2019b). These pigment are usually of less contribution to leaf optical properties, because of the masking effect of chlorophylls, which are present at higher concentrations in leaves and share common light absorption features [START_REF] Feret | PROSPECT-4 and 5: Advances in the leaf optical properties model separating photosynthetic pigments[END_REF][START_REF] Zhang | An extended PROSPECT : Advance in the leaf optical properties model separating total chlorophylls into chlorophyll a and b[END_REF]. Our study shows that they also contribute to the spectral response of vegetation to oil contamination.

Table 1. Results of the elastic net regressions performed on the 33 vegetation indices. For each index, the R 2 of the model is presented, along with the contributing set of biochemical parameters (in order of importance). (Chl a: Chlorophyll a, Chl b: Chlorophyll b, B-car: βcarotene, Lut: Lutein, Ant: Antheraxanthin, Vio: Violaxanthin, Zea: Zeaxanthin, LWC: Leaf Water Content.) The close relationship between some indices and contributing pigments are illustrated in Figure 3. As observed, these indices exhibited strong link with single pigment content. ENET regression allowed identifying those contributing the most to index changes, in order of importance. These results confirmed the interest of combining pigment contents into multiple models for better understanding the effects induced by oil contamination on vegetation reflectance (Lassalle et al., 2019b). Most of the indices exploited reflectance around 550 and 700 nm, which was particularly affected by oil (Fig. 2), so they were particularly adapted to our context of study. The same wavelengths also proved efficient for assessing soil contaminated by oil and by-products in other situations (oil extraction, pipeline leakages, etc.). Zhu et al. ( 2014) exploited reflectance at 700 nm for distinguishing among various levels of alteration in pigment contents induced by phenanthrene contamination on Suaeda salsa. Likewise, Sanches et al. (Sanches et al., 2013b) used the same spectrum region for assessing the effects of oil leakages on crops species. One of the main advantages of VI relies on their robustness. Some of them remain only little affected by bare soil and plant architecture, so they can be applied for tracking subtle alterations in leaf pigment contents induced by oil at different acquisition scales (e.g. leaf, plant and canopy) [START_REF] Blackburn | Quantifying chlorophylls and carotenoids at leaf and canopy scales: An evaluation of some hyperspectral approaches[END_REF][START_REF] Dash | Evaluation of the MERIS terrestrial chlorophyll index (MTCI)[END_REF]. For example, the same 33 indices succeeded in discriminating among various types of oil contamination from leaf to canopy scales in previous study (Lassalle et al., 2019b). Here, they were suitable for estimating TPH concentrations in soils. was the most difficult to predict, as it was almost systematically underestimated (Fig. 4). This may be caused by saturation in the spectral response of C. alopecuroides to this type of oil contamination, as described for other species in previous study. Confusions also arose at the lowest concentrations (0 -1 g.kg -1 ). They highlighted the difficulty to detect the hormesis phenomenon using reflectance data, for which only little differences were observed among the two treatments (Fig. 2). These results thus helped identifying the detection limit of our approach. The relative contribution of VI to the RF models was consistent from leaf to plant scales. Four out of the 33 indices contributed the most to TPH predictions (> 75%, Fig. 5). These indices were among those closely linked to leaf pigment contents (R 2 > 0.7, Tab. 1), and more precisely chlorophylls and β-carotene. They exploit reflectance around 550 and 700 nm, but also 670 -680 and 750 nm, which helped enhancing the differences among the treatments. Only few wavelengths are therefore necessary for estimating TPH accurately using reflectance spectroscopy. Conversely, the other indices remained of little contribution to the models (< 5% each), especially those linked to additional carotenoids (e.g. lutein, violaxanthin), because they brought redundant information.

Index
The consistence of the results between acquisition scales opens up promising perspectives for operational applications of our approach under natural conditions. Some of the main indicesespecially the MTCI and TCARI / OSAVI -have been originally designed for imagery application purposes [START_REF] Dash | Evaluation of the MERIS terrestrial chlorophyll index (MTCI)[END_REF][START_REF] Haboudane | Integrated narrow-band vegetation indices for prediction of crop chlorophyll content for application to precision agriculture[END_REF], and proved efficient for detecting -but not for quantifying -oil contamination in tropical regions. For example, [START_REF] Arellano | Detecting the effects of hydrocarbon pollution in the Amazon forest using hyperspectral satellite images[END_REF] used the MTCI index to discriminate among control and oil-contaminated sites in the Amazon forest using hyperspectral satellite images. However, the application of these indices for estimating the level of contamination remained unexplored until now. This study was a first attempt in that direction, but further researches are needed to assess the reliability of our approach under natural conditions, using field measurements, and in the long term using multiand hyperspectral imagery. High to very high spatial resolution might help achieving this, because the contamination can occur on a few square meters and be therefore difficult to detect using medium to low spatial resolution imagery [START_REF] Adamu | Remote sensing for detection and monitoring of vegetation affected by oil spills[END_REF][START_REF] Arellano | Detecting the effects of hydrocarbon pollution in the Amazon forest using hyperspectral satellite images[END_REF]. As discussed in section 3.1, the case of persistent low contamination in brownfields and mud pits makes the estimation of TPH very challenging, because of the composition of the contamination and the tolerance of the species. Under natural conditions, additional difficulties should be considered before application of our approach. Vegetation established on brownfields and mud pits is exposed to a multitude of environmental factors that affect its health and reflectance (e.g. drought, waterlogging), especially in the tropical regions with marked seasonality [START_REF] Adamu | An investigation into the factors influencing the detectability of oil spills using spectral indices in an oil-polluted environment[END_REF][START_REF] Smith | Use of hyperspectral derivative ratios in the red-edge region to identify plant stress responses to gas leaks[END_REF]. These factors might overlap with the effects induced by TPH, making their estimation more difficult. Thanks to recent advances, it seems however possible to discriminate among oil and other stressors using reflectance spectroscopy (Emengini et al., 2013b;Lassalle et al., 2019b[START_REF] Lassalle | Assessing Soil Contamination Due to Oil and Gas Production Using Vegetation Hyperspectral Reflectance[END_REF]. Because of the selective growing conditions imposed, only few species are generally established on soils with oil [START_REF] Noomen | Spectral and spatial indicators of botanical changes caused by long-term hydrocarbon seepage[END_REF], as observed on our study site. This makes the estimation of TPH feasible, provided that these species are oilsensitive. Species richness is however very high in some tropical regions subject to oil contamination (Arellano et al., 2017a(Arellano et al., , 2017b)). Such diversity in plant species means important differences in sensitivity to oil among them. Some species are totally tolerant to oil, whereas others are affected even at very low concentration. This makes the estimation of TPH more difficult, so it is necessary to identify the most suitable species before, as we did under controlled conditions.

Conclusion

This study aimed to quantify low TPH concentrations in soils using C. alopecuroides reflectance under controlled tropical conditions. Modifications in leaf biochemistry appeared after a long-term exposure, depending on the level of contamination. Pigment contents were reduced for TPH concentrations of 5 g.kg -1 and above, whereas they increased at lower concentration when compared to control. These modifications were linked to the reflectance data through VI, which brought evidence of the implication of chlorophylls and various carotenoids in the spectral response of the species to oil. The same indices succeeded in predicting TPH concentrations with good accuracy using RF regressions, at leaf and plant scales. Four out of the 33 indices tested were almost sufficient to achieve these predictions. This study emphasizes the potential of reflectance spectroscopy for quantifying oil contamination in tropical regions with dense vegetation. More specifically, the long-term response of C. alopecuroides to oil highlights its interest for assessing persistent contamination, for example after cessation of the oil production activity. Although our approach is at early stage and needs further improvements, we are convinced that it could soon result in imagery applications. The emergence of new satelliteand UAV-embedded hyperspectral sensors is sparking a growing interest by oil and gas companies, because they could help assessing oil contamination locally or at large scale. Our study under controlled conditions was the first necessary step prior to such applications. In its continuity, our upcoming research will focus on the adaptation of the approach to hyperspectral imagery with high spatial resolution, and its assessment in tropical region with heavy past oil and gas production activities.

Figure 1 .

 1 Figure 1. Shoot dry weight and leaf chlorophyll and carotenoid contents (mean ± SD; n = 11 and 5 samples per treatment, respectively) of C. alopecuroides after 42 days of exposure to various levels of Total Petroleum Hydrocarbons (TPH). Significant differences among the treatments are denoted by different lowercase letters (ANOVA and Tukey post-hoc tests, p < 0.05). (VAZ: Violaxanthin + Antheraxanthin + Zeaxanthin.)

Figure 2 .

 2 Figure 2. Mean reflectance of C. alopecuroides in the reflective domain after 42 days of exposure to various levels of Total Petroleum Hydrocarbons (TPH), at leaf and plant scales. Reflectance data from the 1350-1450 and 1800-1950 intervals were removed, because of low atmospheric transmission at plant scale. (The legend is common to both figures.)

Figure 3 .

 3 Figure 3. Relationship between vegetation indices and leaf pigment contents. Figures include data from leaves sampled on all the treatments, after 21 and 42 days of experiment (n = 50).

Figure 4 .

 4 Figure 4. Comparison between the measured and predicted concentrations of Total Petroleum Hydrocarbons (TPH) using the 33 vegetation indices and the random forest regression on the test set, at leaf and plant scales (top figures), and residuals of the predictions (bottom figures).

Figure 5 .

 5 Figure 5. Relative contribution of the vegetation indices to the estimation of Total Petroleum Hydrocarbons (TPH) using random forest regression, at leaf and plant scales. Only indices with non-zero contribution are displayed.

Acknowledgements

This interdisciplinary work was achieved in the frame of the NAOMI R&D project between TOTAL and the ONERA, with the support of Ecolab and Dynafor research units of Toulouse.

The authors gratefully acknowledge E. Buffan-Dubau, D. Lambrigot and O. Berseille for their assistance in pigment analysis.

Declarations of interest: None.

Funding: Financial support of this work was provided by TOTAL.


Eslam El Shamy

Julien Jaeck

Riad Haïdar

Patrick Bouchon

Light scattering by correlated disordered assemblies of nanoantennas

Optical nanoantennas are widely used to build absorbing meta-surfaces with applications in photo-detection, solar cells and sensing. Most of the time, the nanoantennas are assembled as a periodic distribution, but there have been various works where disordered arrays are used, either to get rid of diffraction orders or due to a fabrication process that prevents any determined distribution. Here, we investigate both theoretically and experimentally, the unavoidable scattering introduced by such disorders. By introducing a perturbation on the positions of 1D arrays of metal-insulator-metal (MIM) nanoantennas, the light is scattered rather than increasingly absorbed. The scattering is occurring only in the plane of incidence and on a given spectral range. We show how this scattering can be manipulated from 0 to 55 % of the incoming light.

Optical nanoantennas is a very common building block of metasurfaces. Most of the time, the nanoantennas are assembled as a periodic distribution. However, there have been various works where disordered arrays are used with a large variety of motivations 1 . Among the most obvious reasons, suppressing the periodicity allows getting rid of diffraction orders 2,3 . It can also allow various bottom-up fabrication techniques that are scalable, but prevents any determined distribution, which is very appealing for applications where large areas are needed [4][5][6][7] . Analytical models have been developed to describe disordered nanoparticles scattered on a transparent substrate 8,9 . Disorder has also been used to improve performances of optical components [10][11][12] or of light extraction 13 , as well as to enhance physical effects such as plasmons localization 14,15 or surface enhanced Raman spectroscopy 16,17 . The influence of disorder to reduce the scattered fields have been previously reported in the microwaves region, using randomly distributed unit cells 18,19 . Quantifying the diffuse reflection energy is rather challenging, both numerically because it results in huge electromagnetic problems for a given computation accuracy, and experimentally because the diffuse reflection throws in 2π steradian and cannot be detected without a high signal to noise ratio experiment. This challenge can be simplified by studying nanoantennas infinite along one direction. Indeed, it results in less-demanding computations while keeping a good numerical accuracy. Besides, a 1D grating scatters light in the plane of incidence increasing the signal, thus reducing the experimental challenge.

Here, we investigate both theoretically and experimentally, the scattering introduced by a correlated disorder in arrays of 1D metal-insulator-metal (MIM) nanoantennas, which are used to build absorbing metasurfaces [20][21][22][23][24] . MIM nanoantennas have previously been used as local absorber or emitter [25][26][27] , but here, as the disorder is increased, we show that the diffractive orders are progressively disappearing, and the energy is redirected exclua) Electronic mail: patrick.bouchon@onera.fr sively into scattering. The introduction of diffractive orders in the response of MIM nanoantennas results in a strong coupling between the localized resonance and the diffracted order 28,29 and it could have been expected that the suppression of the diffraction behavior would bring back the MIM to their original behavior of local absorber with a given absorption effective cross-section. We also show how such metasurfaces can be used to manipulate the amount of scattering on the spectral band of resonance of the antenna.

The geometry of the MIM resonator array studied in the following is shown in Fig. 1(a), it consists of an array of gold ribbons (width w mim = 1.35 µm, period p = 7.5 µm) of 100 nm thickness defined by an e-beam lithography and deposited on a continuous layer of silicon dioxide (thickness 300 nm) and an optically opaque gold layer (thickness 200 nm). A 5-nm adhesion chromium layer is used at both interfaces between silicon dioxide and gold. Disorder is introduced by moving each metallic ribbon from a displacement that is sampled from a uniform probability law with a deviation δX max , which is refered hereafter as the disorder parameter. This disorder parameter gives the maximum possible displacement, and is chosen in the manuscript so as to prevent any overlap between two ribbons. In order to reduce the computation burden, disorder was introduced on a subset of 50 ribbons, which was repeated periodically. A top-view scanning electron microscope image of the periodic and disordered array of MIM ribbons is shown in Fig. 1(b). The samples are experimentally studied with a Fourier transform infrared spectroscope (Bruker Vertex 70v) with a configuration depicted in Fig. 1(a). The incoming light is TM-polarized and focused by a mirror on the sample with an incoming angle θ in , and the beam collected by a second mirror at an angle θ out is detected by a DTGS detector. Both focused beams have a numerical aperture dθ, which value slightly depends on the angle of incidence, and is typically 10 • .

The measured specular reflectivity diagram of the periodic MIM array as a function of the incidence angle is shown in Fig. 1(c). This structure exhibits a fundamental resonance at λ r = 5.15 µm, with several characteristic properties: a high absorption of light, a low quality factor of the resonance Q 10, an independence of the resonance wavelength to the angle of incidence. Since the period of the array is not subwavelength, the reflectivity diagram also shows the various Rayleigh-Wood anomalies (RWA), due to the appearance/disappearance of diffraction orders. The RWA can be suppressed with the introduction of a disorder (δX max = 2.7 µm), restoring the intrinsic response of the MIM resonator, thus freed of the coupling with diffraction orders (see Fig. 1(d)). This is very appealing since the presence of RWA is known to be detrimental to the absorption efficiency. However, the energy can be either redirected towards absorption or towards the scattering that stems from the disorder arangement. Both samples responses were simulated with an exact Maxwell solver 30,31 . The optical properties of gold are modeled by a Drude model that fits Palik data 32 , and the silicon dioxide is modeled by a Brendel-Bormann model [START_REF] Kischkat | [END_REF] . The theoretical (red line) and experimental (blue line) specular reflectivity spectra are compared in Fig. 2 for an incident angle of θ in = 50 • . There is a good agreement on the spectral position of the RWA and on the fundamental resonance, but overall, the amplitudes of the RWA are pretty different. In order to get a better agreement, the optical beam numerical aperture has to be taken into account in the simulation with a dθ = 10 • . In that case, a very good agreement between experiment and simulation (gray curve) is obtained. The various RWA peaks observed in Fig. 2(a) are vanishing when considering the disordered array (Fig. 2(b)), and there are two minima of reflectivities corresponding to the fundamental resonance of the MIM and its second harmonic at λ harmonic 2.6 µm. At the resonance wavelength, nearly 70% of the light is diffracted by the periodic array. With the introduction of disorder, the diffracted energy can be redirected into either radiative (diffuse reflection) or nonradiative (absorption) losses since the specular reflectivity R spec is almost unchanged. There is still a reminiscent diffraction behavior in disordered systems, and in the following, the value of scattering R scatt does not include the energy scattered in direction similar to diffraction angles R diffracted .

The scattering spectra of the specular reflectivity, the diffracted reflectivity and the diffuse reflection are plotted in Figure 3(a-c) for both the periodic array and the disordered array. The diffraction spectra confirm the vanishing of the RWA, even if around 10% of the energy is still reflected in the same direction as the diffracted orders. Eventually, a large part of the energy which is no longer diffracted is in fact scattered with a resonance behavior at λ r = 5.15 µm. Below λ r , there is still an important diffuse reflection > 30%, which could be attributed to the various resonances. On the contrary, there is no longer diffuse reflection for wavelengths above 6.5 µm, when there is no resonances anymore. Figure 3(d) shows the influence of the disorder parameter δX max on the balance of energy between specular reflection, diffraction, diffuse reflection and absorption, which is deduced from the conservation of energy: A = 1 -R spec -R diffracted -R scatt , at the fundamental resonance wavelength of the MIM λ r = 5.15 µm and for an angle of incidence θ in = 50 • . The increase of disorder has nearly no influence on the value of absorption and of the specular reflectivity, whereas the diffracted reflectivity decreases monotonously as δX max grows, and the energy is redistributed almost exclusively in diffuse reflection. In the highest case of disorder, the proportion of diffused reflectivity can reach more than 50% of total incoming energy. Disorder changes thereby the initially highly diffractive structure (60%) into a strongly scattering one. It must be emphasized that even if the absorbed power does not depend on the disorder, each antenna of a given disordered subset absorbs a different amount of the incoming light due to interactions with its neighbors. A given disorder parameter can produce pretty different structures, and for each value of the disorder parameter 10 draws were computed. Errorbars on the Fig. 3(d) represent the data range and the mean value for each data range is given by the marker. The dispersion is higher for intermediate values of the disorder parameter, and could be used to optimize a metasurface with a given scattering behavior.

Measured asymmetric angle resolved reflectivity diagram is presented on Fig. 4(a) for the periodic case for an incidence angle of θ in = 50 • . The various bands shown on this diagram are the diffraction orders, each of which is following the classic law of grating diffraction θ out = arcsin(sin θ inc -mλ d ). The width of each band is directly linked to the beam numerical aperture dθ generated by the mirror. As expected, the localized resonance occurring at λ = 5.15 µm does not depend on the angle of incidence. The dark stripes on each diffraction band are due to the redistribution of energy associated to the appearance or disappearance of a diffracted order (RWA). A similar measured diagram for the highest disordered (δX max = 2.7 µm) sample is plotted in Fig. 4(b).

The specular reflectivity band is nearly unchanged, apart from the vanishing of the RWA features. But for values of θ out below 40 • , the diffracted orders bands have been replaced by diffuse reflection occurring for every angle. Here, we take advantage of the high numerical aperture dθ and of the fact that scattering can only occur in the xz-plane to obtain a good signal to noise ratio in the measurement. Noteworthily, no scattering is measured above θ out > 55 • , as well as above λ > 6 µm.

In order to validate the experimental measurement of diffuse reflection, the measured and computed reflectivity as a function of the scattering angle θ out is plotted for an incident angle θ in = 50 • at a λ = 5.15 µm wavelength for the periodic grating (red line and crosses) and the disordered array (blue line and crosses). As in Fig. 2(b), the numerical simulation is done for a focused beam (dθ = 10 • ), which leads to a pretty good agreement for both samples. There are three peaks for the periodic grating corresponding to the zeroth order (θ out = 50 • ), the first order (θ out = 0 • ) and the second order (θ out = -40 • ) of diffraction. Away from these angles, there is no scattered energy. In contrast, the disordered array scatters energy on each angle in the range θ out between -90 • and 40 • , and with higher values near θ out = 0 • , which is consistent with the single nanoantenna behavior. The absence of scattering for θ out > 60 • is confirmed by the computation, and is also not observed for scattering of a single nanoantenna. This intriguing behavior is present for other incident angles, and could be attributed to the disorder itself. It could open some interesting prospective such as producing diffusion only on a given range of angles. Diffractive arrays of 1D-MIM nanoantennas have been studied both theoretically and experimentally. Theoretical predictions show that introducing disorder involves redistribution of the energy from diffraction mainly to diffuse reflection. Therefore, it is possible to change a highly diffractive periodic structure into a highly diffusive one only by changing the spatial distribution, these changes have nearly no influence on the absorption and zero-order reflectivity efficiencies. Our study highlights the importance of taking into account scattering of light as soon as random assemblies of random assemblies of plasmonic resonators are at stake, and this, even if localized resonances are involved. These results also pave the way to the design of metasurfaces for manipulating the scattering of light on a limited spectral range.

FIG. 1 .

 1 FIG. 1. (a) Experimental configuration used for the angular characterization of the sample. The inset shows the scheme of the two kinds of samples studied: periodic and disordered. In both cases, the geometrical parameters are wmim = 1.35 µm, hAu = 0.1 µm, hSiO2 = 0.3 µm and hCr = 5 nm. (b) SEM images of a periodic sample (period p = 7.5 µm) and a disordered sample (disorder parameter δXmax = 0.6 µm). Measured specular reflectivity diagram as a function of the incident angle for (c) a periodic array (period p = 7.5 µm) and (d) a disordered array (disorder parameter δXmax = 2.7 µm).

FIG. 2 .

 2 FIG. 2. Theoretical (red dashed line) and experimental (blue continuous line) reflectivity spectra for a TM wave incident with an angle θin = 50 • for (a) the periodic grating and (b) a disordered array (disorder parameter δXmax = 2.7 µm).

FIG. 3 .

 3 FIG. 3. Computed reflectivity spectra for the periodic array (continuous line) and the disordered array with a disorder parameter δXmax = 2.7 µm (dashed line) divided into three parts: (a) the specular reflectivity, (b) the diffracted reflectivity and (c) the scattering, for an angle θin = 50 • . (d) Specular reflectivity, diffuse reflection, diffraction and absorption efficiency as a function of the disorder parameter δXmax at λ = 5.15 µm and θin = 50 • . Errorbars represent the data range for the 10 draws and markers indicate the mean values for each data range.

FIG. 4 .

 4 FIG. 4. Measured reflectivity diagram as a function of the scattering angle θout (incidence angle θin = 50 • ) for (a) the periodic grating and (b) the disordered array (δXmax = 2.7 µm).

FIG. 5 .

 5 FIG. 5. Measured (continuous lines) and computed (crosses) reflectivity efficiency as a function of the scattering angle θout for an incidence angle θin = 50 • at a λ = 5.15 µm wavelength for the periodic grating (red line and crosses) and the disordered array (blue line and crosses).

ACKNOWLEDGEMENT

This work has been supported by a DGA-MRIS scholarship.