Tales Tiecher

Jean M Moura-Bueno

Laurent Caner

Jean Pg Minella

Olivier Evrard

Rafael Ramon

Gabriela Naibo

Cláudia Ap Barros

Yuri Jab

Fábio F Amorim

Danilo S Rheinheimer

Keywords: soil erosion, alternative fingerprints, machine learning, Vis-NIR-MIR database, spectral preprocessing

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Improving the quantification of sediment source contributions using different mathematical models and spectral preprocessing techniques for individual or combined spectra of ultraviolet-visible, near-and middle-infrared spectroscopy

To cite this version:

Tales Tiecher, Jean M Moura-Bueno, Laurent Caner, Jean P.G. Minella, Olivier Evrard, et al.. Improving the quantification of sediment source contributions using different mathematical models and spectral preprocessing techniques for individual or combined spectra of ultraviolet-visible, near-and middle-infrared spectroscopy. Geoderma, 2021Geoderma, , 384, pp.114815. 10.1016Geoderma, /j.geoderma.2020.114815.114815. cea-03007858

Introduction

The sustainable production of food, fiber and biofuel remains limited by soil erosion [START_REF] Comino | Rainfall and human activity impacts on soil losses and rill erosion in vineyards (Ruwer Valley, Germany)[END_REF][START_REF] Erkossa | Linking soil erosion to on-site financial cost: Lessons from watersheds in the Blue Nile basin[END_REF][START_REF] Seutloali | Understanding the factors influencing rill erosion on roadcuts in the south eastern region of South Africa[END_REF][START_REF] Taguas | Characteristics and importance of rill and gully erosion: a case study in a small catchment of a marginal olive grove[END_REF]. The inadequate management of soils and the lack of runoff control exposes the soil to erosive agents, accelerating the processes of mobilization and transfer of sediments to the drainage network [START_REF] Minella | Establishing a sediment budget for a small agricultural catchment in southern Brazil, to support the development of effective sediment management strategies[END_REF], along with the transportation of contaminants like pesticides [START_REF] Magnusson | Pesticide contamination and phytotoxicity of sediment interstitial water to tropical benthic microalgae[END_REF][START_REF] Yahia | Multi pesticide and PCB residues in Nile tilapia and catfish in Assiut city, Egypt[END_REF] and phosphorus [START_REF] Dodd | Is tillage an effective method to decrease phosphorus loss from phosphorus enriched pastoral soils?[END_REF][START_REF] Dodd | Recognizing the role of soil organic phosphorus in soil fertility and water quality[END_REF][START_REF] Poulenard | Analytical Electron-Microscopy Fractionation of Fine and Colloidal Particulate-Phosphorus in Riverbed and Suspended Sediments[END_REF]. Erosion control and conservation of soil hydrological functionalities are essential to meet the demand in food production as well as to maintain the quality of water resources [START_REF] Didoné | Quantifying soil erosion and sediment yield in a catchment in southern Brazil and implications for land conservation[END_REF][START_REF] Merten | No-till surface runoff and soil losses in southern Brazil[END_REF]. To better understand the occurrence of erosion processes at the catchment scale and to mitigate the problems arising from river overflow and excessive sediment production, it is first necessary to have quantitative information on the sources delivering sediment to the river systems.

To this end, the use of the sediment fingerprinting approach quantifies the contribution of non-point based sediment sources through the use of a variety of tracers, including geochemical properties and radionuclides [START_REF] D'haen | Fingerprinting historical fluvial sediment fluxes[END_REF][START_REF] Davis | Sediment Fingerprinting: Review of the Method and Future Improvements for Allocating Nonpoint Source Pollution[END_REF][START_REF] Haddadchi | Sediment fingerprinting in fluvial systems: review of tracers, sediment sources and mixing models[END_REF][START_REF] Koiter | The behavioural characteristics of sediment properties and their implications for sediment fingerprinting as an approach for identifying sediment sources in river basins[END_REF][START_REF] Walling | Tracing sources of suspended sediment in river basins: a case study of the River Culm, Devon, UK[END_REF]. However, the large-scale application of the sediment fingerprinting technique requires a large number of chemical analyses, which have a significant cost and which are relatively time consuming.

However, the use of other soil and sediment characteristics may complement or provide a powerful alternative information in source identification, such as reflectance spectroscopy [START_REF] Cooper | Combining two filter paper-based analytical methods to monitor temporal variations in the geochemical properties of fluvial suspended particulate matter[END_REF].

Reflectance spectroscopy in the visible and infrared ranges provides an efficient, low-cost, fast and non-destructive method easily applicable to soil and sediment samples to quantify various physical, chemical and biological properties [START_REF] Mcbratney | Spectral soil analysis and inference systems: A powerful combination for solving the soil data crisis[END_REF][START_REF] Viscarra Rossel | Visible, near infrared, mid infrared or combined diffuse reflectance spectroscopy for simultaneous assessment of various soil properties[END_REF]. [START_REF] Poulenard | Infrared spectroscopy tracing of sediment sources in a small rural watershed (French Alps)[END_REF] were pioneers in the use of diffuse infrared spectroscopy (Diffuse Reflectance Infrared Fourier Transform Spectroscopy -DRIFTS) to trace the origin of sediments in river catchments. The method was successfully used to discriminate and predict the respective contribution of surface and subsurface sources to sediment, as well as to discriminate soils developed on different lithology [START_REF] Poulenard | Tracing sediment sources during floods using Diffuse Reflectance Infrared Fourier Transform Spectrometry (DRIFTS): A case study in a highly erosive mountainous catchment (Southern French Alps)[END_REF]. Since then, several studies have been developed using the spectroscopic method to trace sediment sources (Table 1). Only 28 scientific articles had been published around the world after that of [START_REF] Poulenard | Infrared spectroscopy tracing of sediment sources in a small rural watershed (French Alps)[END_REF] by early 2020, representing an average of about 2.5 scientific publications per year (Fig. 1). They include studies in the ultraviolet-visible (UV-Vis) and near-infrared (NIR) ranges in the French Alps [START_REF] Legout | Quantifying suspended sediment sources during runoff events in headwater catchments using spectrocolorimetry[END_REF] and the Southern France [START_REF] Uber | Comparing alternative tracing measurements and mixing models to fingerprint suspended sediment sources in a mesoscale Mediterranean catchment[END_REF], Luxemburg (Martínez-Carreras et al., 2010c, 2010b, 2010a), Spain (Brosinsky et al., 2014a(Brosinsky et al., , 2014b)), Ethiopia [START_REF] Verheyen | The use of visible and near-infrared reflectance measurements for identifying the source of suspended sediment in rivers and comparison with geochemical fingerprinting[END_REF], South Africa [START_REF] Pulley | Colour as reliable tracer to identify the sources of historically deposited flood bench sediment in the Transkei, South Africa: A comparison with mineral magnetic tracers before and after hydrogen peroxide pre-treatment[END_REF][START_REF] Pulley | The use of an ordinary colour scanner to fingerprint sediment sources in the South African Karoo[END_REF], Argentina [START_REF] Batistelli | Development of a fast and inexpensive method for detecting the main sediment sources in a river basin[END_REF], the United Kingdom [START_REF] Collins | Sources of sediment-bound organic matter infiltrating spawning gravels during the incubation and emergence life stages of salmonids[END_REF], Canada [START_REF] Barthod | Selecting Color-based Tracers and Classifying Sediment Sources in the Assessment of Sediment Dynamics Using Sediment Source Fingerprinting[END_REF][START_REF] Boudreault | Using colour, shape and radionuclide fingerprints to identify sources of sediment in an agricultural watershed in Atlantic Canada[END_REF][START_REF] Liu | Determining sources of fine-grained sediment for a reach of the Lower Little Bow River, Alberta, using a colour-based sediment fingerprinting approach[END_REF], Brazil [START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF][START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF][START_REF] Valente | Quantification of sediment source contributions in two paired catchments of the Brazilian Pampa using conventional and alternative fingerprinting approaches[END_REF] and Iran [START_REF] Nosrati | Storm dust source fingerprinting for different particle size fractions using colour and magnetic susceptibility and a Bayesian un-mixing model[END_REF]. In the middle infrared region (MIR), sediment fingerprinting studies were carried out in France [START_REF] Poulenard | Tracing sediment sources during floods using Diffuse Reflectance Infrared Fourier Transform Spectrometry (DRIFTS): A case study in a highly erosive mountainous catchment (Southern French Alps)[END_REF][START_REF] Poulenard | Infrared spectroscopy tracing of sediment sources in a small rural watershed (French Alps)[END_REF], Mexico [START_REF] Evrard | Tracing sediment sources in a tropical highland catchment of central Mexico by using conventional and alternative fingerprinting methods[END_REF], the United Kingdom [START_REF] Vercruysse | Using source-specific models to test the impact of sediment source classification on sediment fingerprinting[END_REF], China [START_REF] Liu | Chemical characterization and source identification of organic matter in eroded sediments: Role of land use and erosion intensity[END_REF], Brazil [START_REF] Tiecher | Tracing Sediment Sources Using Mid-infrared Spectroscopy in Arvorezinha Catchment, Southern Brazil[END_REF] and in a transnational river catchment covering part of Switzerland, France and Germany [START_REF] Chapkanski | Provenance discrimination of fine sediments by mid-infrared spectroscopy: Calibration and application to fluvial palaeo-environmental reconstruction[END_REF]. Many of these studies have shown a good agreement between the results obtained with the spectroscopic method and those provided by the conventional approach based on geochemical and / or radionuclide properties (Evrard et al., 2013;[START_REF] Legout | Quantifying suspended sediment sources during runoff events in headwater catchments using spectrocolorimetry[END_REF]Martínez-Carreras et al., 2010c;[START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF][START_REF] Tiecher | Tracing Sediment Sources Using Mid-infrared Spectroscopy in Arvorezinha Catchment, Southern Brazil[END_REF][START_REF] Verheyen | The use of visible and near-infrared reflectance measurements for identifying the source of suspended sediment in rivers and comparison with geochemical fingerprinting[END_REF].

In addition to the more qualitative attempts that combine the use of discriminant analysis with spectroscopy [START_REF] Chapkanski | Provenance discrimination of fine sediments by mid-infrared spectroscopy: Calibration and application to fluvial palaeo-environmental reconstruction[END_REF], previous studies conducted to trace sediment source contributions using spectroscopy (Table 1) can be divided into three main groups, according to the way they used the spectroscopic information. The first group uses color parameters extracted from the visible range [START_REF] Barthod | Selecting Color-based Tracers and Classifying Sediment Sources in the Assessment of Sediment Dynamics Using Sediment Source Fingerprinting[END_REF]Martínez-Carreras et al., 2010c, 2010b, 2010a;[START_REF] Pulley | Colour as reliable tracer to identify the sources of historically deposited flood bench sediment in the Transkei, South Africa: A comparison with mineral magnetic tracers before and after hydrogen peroxide pre-treatment[END_REF][START_REF] Pulley | The use of an ordinary colour scanner to fingerprint sediment sources in the South African Karoo[END_REF] and other spectral characteristics (spectral features and overtones) (Brosinsky et al., 2014b(Brosinsky et al., , 2014a;;[START_REF] Collins | Catchment source contributions to the sediment-bound organic matter degrading salmonid spawning gravels in a lowland river, southern England[END_REF][START_REF] Collins | Sources of sediment-bound organic matter infiltrating spawning gravels during the incubation and emergence life stages of salmonids[END_REF] in an optimized mixed linear model, separately or in combination with conventional geochemical tracers [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF]. The second group of studies uses spectroscopic information to generate mathematical models using the least squares method (PLSR) to estimate the concentrations of geochemical tracers, which in turn are introduced in a mixed linear model optimized to estimate the contribution of sediment sources (Vis-NIR-SWIR - Martínez-Carreras et al., 2010b).

The third group of studies directly uses the entire spectrum [START_REF] Batistelli | Development of a fast and inexpensive method for detecting the main sediment sources in a river basin[END_REF]Evrard et al., 2013;[START_REF] Poulenard | Tracing sediment sources during floods using Diffuse Reflectance Infrared Fourier Transform Spectrometry (DRIFTS): A case study in a highly erosive mountainous catchment (Southern French Alps)[END_REF][START_REF] Poulenard | Infrared spectroscopy tracing of sediment sources in a small rural watershed (French Alps)[END_REF][START_REF] Tiecher | Tracing Sediment Sources Using Mid-infrared Spectroscopy in Arvorezinha Catchment, Southern Brazil[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF][START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF][START_REF] Verheyen | The use of visible and near-infrared reflectance measurements for identifying the source of suspended sediment in rivers and comparison with geochemical fingerprinting[END_REF] or the spectrum combined with color parameters extracted from the visible range [START_REF] Legout | Quantifying suspended sediment sources during runoff events in headwater catchments using spectrocolorimetry[END_REF]. They estimate the source contributions in sediment samples after generating a model (Partial Last Squares Regression -PLSR) calibrated using artificial mixtures combining potential sediment sources in variable proportions. To date, no study has been conducted combining the bands of UV-Vis, NIR and / or MIR, although it may be expected that predictions of soil properties may be improved using the combined range of these regions of the electromagnetic spectrum [START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF][START_REF] Reeves | Near-versus mid-infrared diffuse reflectance spectroscopy for soil analysis emphasizing carbon and laboratory versus on-site analysis: Where are we and what needs to be done?[END_REF][START_REF] Soriano-Disla | The performance of visible, near-, and mid-infrared reflectance spectroscopy for prediction of soil physical, chemical, and biological properties[END_REF] due to the sum of distinct information that is added to the models [START_REF] Viscarra Rossel | Visible, near infrared, mid infrared or combined diffuse reflectance spectroscopy for simultaneous assessment of various soil properties[END_REF].

This third approach has the advantage of using all the spectral information directly in a mathematical model calibrated using artificial mixtures. To achieve this goal, all the previous studies used the Partial Least Squares Regression method (PLSR) (Table 1).

However, more robust and non-parametric models, such as Support Vector Machine (SVM), could usefully be tested be tested for this type of application, as they were successfully used to derive soil properties, including clay and organic carbon content [START_REF] Dotto | Two preprocessing techniques to reduce model covariables in soil property predictions by Vis-NIR spectroscopy[END_REF][START_REF] Lucà | Effect of calibration set size on prediction at local scale of soil carbon by Vis-NIR spectroscopy[END_REF][START_REF] Stevens | Prediction of Soil Organic Carbon at the European Scale by Visible and Near InfraRed Reflectance Spectroscopy[END_REF][START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]. This multivariate method seeks to identify an interpolation function using the kernel function, adjusting the calibration data until simultaneously minimizing the size of the coefficients and the prediction errors, in which data with non-linear patterns can be better represented by the calibrated model [START_REF] Ivanciuc | Applications of Support Vector Machines in Chemistry[END_REF].

In spectroscopic fingerprinting studies, there is also a knowledge gap regarding the use of spectrum pre-processing techniques in spectroscopic modeling (Table 1), despite the fact that several soil studies demonstrated that this step is extremely important when calibrating the models [START_REF] Buddenbaum | The effects of spectral pretreatments on chemometric analyses of soil profiles using laboratory imaging spectroscopy[END_REF][START_REF] Dotto | Two preprocessing techniques to reduce model covariables in soil property predictions by Vis-NIR spectroscopy[END_REF][START_REF] Nawar | Estimating the soil clay content and organic matter by means of different calibration methods of vis-NIR diffuse reflectance spectroscopy[END_REF]. Several spectrum pre-processing techniques can be used for this purpose, such as smoothing, Savitzky-Golay with 1st or 2nd derivative using a first or second order polynomial, standard normal variate, multiplicative scatter correction and normalization.

However, so far, very few fingerprinting sediment tracing studies have reported whether they used any type of spectral pre-processing. Most of them used only pre-processing (Brosinsky et al., 2014b(Brosinsky et al., , 2014a;;[START_REF] Chapkanski | Provenance discrimination of fine sediments by mid-infrared spectroscopy: Calibration and application to fluvial palaeo-environmental reconstruction[END_REF][START_REF] Tiecher | Tracing Sediment Sources Using Mid-infrared Spectroscopy in Arvorezinha Catchment, Southern Brazil[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF][START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF], except for [START_REF] Ni | Mid-infrared spectroscopy tracing of channel erosion in highly erosive catchments on the Chinese Loess Plateau[END_REF], who used four pre-processing techniques, although they did not compare them to each other.

In this context, the current research provides, to the best of our knowledge, the first attempt to compare the outputs of different multivariate mathematical models (both parametric and non-parametric) and preprocessing techniques of reflectance in UV-Vis, NIR and MIR spectral bands used in combination or in isolation to predict the contribution of sediment sources at the catchment scale. Accordingly, the objectives of the study were (i)

to evaluate the accuracy of two multivariate methods for sediment source apportionment (PLSR and SVM), (ii) to evaluate the effect of eight spectra preprocessing techniques, and

(iii) to evaluate the effect of using the information contained in the UV-Vis, NIR and MIR regions either separately or in combination. For this purpose, the estimated contribution for each source using the spectroscopic models was also compared against the values obtained by the conventional fingerprinting approach based on geochemical tracers

Materials and methods

Study site

The horizon favor the formation of runoff that controls erosion dynamics in cropland. In addition to erosion processes in cropland, the inadequate location and maintenance of unpaved roads generate preferential pathways for runoff concentration accelerating erosion, and converting these roads into significant potential sources of sediment. The catchment also shows signs of channel banks erosion due to the high flow energy observed during the events (flash flood) associated with the absence of riparian forest along several river sections. Further details on the catchment can be found in [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF].

Soil samples were collected from the three main potential sources of sediment, including (i) cropland surface, (ii) unpaved roads and (iii) stream channels. Cropland (n=20) and unpaved road (n=10) samples were taken using a non-metallic trowel from the uppermost layer (0-0.05 m). Stream channels (n=10) were sampled on exposed bank sites located along the main river channel network. Each sample was composed of at least 10 subsamples collected in the vicinity of the sampling point (within a radius of approximately 10 m). Source sampling sites were selected based on visible signs of soil erosion and hydrological connectivity as well as taking into account pedological variability. In order to characterize the sediments transported in the drainage network, 29 suspended sediment samples were collected during nine rainfall events from October 2009 to July 2011 at the catchment outlet, where the flow and sediment concentration are also continuously monitored, which allows the calculation of liquid and solid discharges, as well as the catchment sediments yields. The sampled events cover the seasonal variability of land cover in the drainage area, as well as the variations of river flow conditions. For high magnitude events, several samples were collected to characterize the intra-event variability (rise, peak and recession of the hydrograph). Sediment concentrations during monitored events ranged from 300 to 2000 mg L -1 . To obtain a sufficient mass of suspended sediment for conducting all analyses, samples were collected using a portable continuous flow centrifuge (Alfie-500 Alfa Laval). All the source material and sediment samples were oven-dried at 50 °C, gently disaggregated using a pestle and mortar, and passed through a 63-μm mesh prior to laboratory analyses to investigate similar particle size-fractions for all the samples (suspended sediments and sediment sources).

Artificial mixtures of sediment sources

The samples of each potential sediment source were mixed in equal proportions in the laboratory to constitute a unique reference sample for the corresponding source. Then, those reference samples were mixed in 48 different weight proportions as presented in Fig.

2. These artificial mixtures containing different proportions of the three sources were then used to calibrate the multivariate mathematical models used to estimate the source contributions to the suspended sediment samples.

Spectral analyses

UV-Vis diffuse reflectance spectra of samples were recorded at room temperature from 200 to 800 nm with a 1-nm step using a Cary 5000 UV-Vis-NIR spectrophotometer (Varian, Palo Alto, CA, USA). Samples were ground and loaded into a Harrick Praying Mantis diffuse reflectance accessory that uses elliptical mirrors. BaSO4 was used as a 100% reflectance standard. Care was taken when adding the samples into the sample holder to avoid differences in sample packing and surface smoothness.

Near infrared (NIR) spectra were recorded in the range 10000-4000 cm -1 (1000-2500 nm) using a Nicolet 26700 FTIR spectrometer (Waltham, Massachusetts, USA) in diffuse reflectance mode with an integrating sphere and a InGaAs detector with a resolution of 4 cm -1 and 100 readings per spectrum.

Mid infrared (MIR) spectra were obtained in the range 400-4000 cm -1 (2500-25000 nm) using a Nicolet 510-FTIR (Thermo Electron Scientific, Madison, WI, USA) spectrometer in diffuse reflectance mode with a resolution of 4 cm -1 and 100 readings per spectrum. A direct current of air was used (dry and without CO2) to eliminate CO2 and water from the spectrometer in order not to interfere with scanning and obtaining the spectra.

UV-Vis, NIR and MIR spectral data were subjected to spectral pre-processing to remove physical variability due to light dispersion and to remove systematic variations of instrumental and environmental conditions in order to emphasize the characteristics of interest along the spectrum. Spectra without pre-processing constitute the "control treatment" (RAW). Eight spectral processing techniques commonly employed in chemometric studies [START_REF] Rinnan | Review of the most common preprocessing techniques for near-infrared spectra[END_REF] were tested to evaluate its effect on the calibration of spectroscopic models.

Pre-processing includes: (i) smoothing (SMO) from a convolution function using a 25 nm mobile window, after initial testing to define the best search window; (ii) Savitzky-Golay

Spectroscopic model development: calibration and validation

The spectroscopic models were calibrated from the spectral signature of the 48 mixtures with different proportions of each sediment source (Figure 2). Spectral data were generated from the following regions of the electromagnetic spectrum: UV-Vis, NIR, MIR, UV-Vis+NIR, UV-Vis+MIR, NIR+MIR and UV-Vis+NIR-MIR. Two multivariate calibration methods were used to adjust the models, where the effect of the eight spectral preprocesses plus the raw spectrum (RAW) was tested. This totaled 126 spectroscopic models for each source, totaling 378 models (Figure 4).

Two multivariate methods with different approaches were selected to calibrate the spectroscopic models: (i) Partial Least Squares Regression (PLSR) (R pls package [START_REF] Mevik | Partial Least Squares and Principal Component Regression[END_REF]) parametric technique widely used in spectroscopic modeling [START_REF] Angelopoulou | From Laboratory to Proximal Sensing Spectroscopy for Soil Organic Carbon Estimation-A Review[END_REF][START_REF] Dotto | A systematic study on the application of scatter-corrective and spectral-derivative preprocessing for multivariate prediction of soil organic carbon by Vis-NIR spectra[END_REF] and (ii) Support Vector Machines (SVM) (R e1071 package [START_REF] Meyer | Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071)[END_REF]), non-parametric technique. Methods with different approaches were selected due to the occurrence of linear and non-linear correlations between the organomineral components of soil/sediment and the spectral variables [START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]. The PLSR model handles data sets containing many independent and highly correlated variables, such as UV-Vis-NIR-MIR spectral data. PLSR analysis reduces large data sets to a small number of uncorrelated orthogonal factors to minimize the sum of the squares of the predicted value errors [START_REF] Varmuza | Introduction to Multivariate Statistical Analysis in Chemometrics[END_REF]. The SVM model was used with the kernel function, which separates the calibration data into hyperplanes and seeks to establish correlations between the dependent and independent variables when these have non-linear behavior [START_REF] Ivanciuc | Applications of Support Vector Machines in Chemistry[END_REF].

The parameterization in the calibration of the PLSR method was: method = 'pls', resampling method = 'cross-validation 10 k-fold', and number of components = '.ncomp = seq(1, 20, 1)'. For SVM the parameters were: method = 'svmLinear', resampling method = 'crossvalidation 10 k-fold', and Kernel parameters = 'Support Vector Machine with Linear Kernel'.

Each model was calibrated with 70% of the samples (n= 34) and validated with 30% of the samples (n = 14). Both sets were randomly generated. To evaluate the accuracy of the models the following parameters were calculated: coefficient of determination (R 2 ) (Equation 1), bias (Equation 2) and mean square root of the prediction error (RMSE) (Equation 3).

where: ŷ = predicted value of each source; ȳ = observed mean value of each source in the mixture; y = observed values of each source in the mixture; n = number of samples with i = 1, 2,..., n.

Estimation of sediment source contributions by spectroscopic models and independent validation comparing with the contribution results obtained with the conventional geochemical approach

The contribution of sediment sources was estimated by spectroscopic models from an independent set of spectral reflectance data, which were obtained from 29 suspended sediment samples. The predicted values were then compared with those obtained with the geochemical tracers [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF] and the biassp error statistics (Equation 2) and RMSEsp (Equation 3) of the proportion of sediment estimated for each source were calculated. This approach used the total concentration in various elements (Ag, As, Cr, Fe, Mo, and P) estimated by ICP-OES after microwave assisted digestion with concentrated HCl and HNO3 in the 3:1 ratio (aqua regia). Detailed information regarding sediment sampling and the statistical procedure used in the conventional geochemical approach can be found in [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF].

Finally, data of quality of the models based on validation with artificial mixtures of sediment (RMSEv), and compared with the sediment contribution values obtained with geochemical tracers (RMSEsp) were entered in a conditional inference regression tree procedure to highlight the factors that most influenced the quality of the models.

Results and discussion

Model calibration performance

The results of the validation of the 378 models are presented in Figure 5. In general, there is variation in the predictive behavior of the models depending on the type of spectral preprocessing, spectral range, multivariate method and sediment source considered (Figure 5). One the one hand, the calibrated models with SGD1, NOR+SGD1 and NOR preprocessing achieved a greater accuracy in predictions, differing significantly from that obtained with other techniques (Figure 6a). Studies on organic carbon and soil clay content predictions have also shown that it is possible to increase the accuracy of spectroscopic models calibrated with SGD1 and NOR pre-processing [START_REF] Dotto | A systematic study on the application of scatter-corrective and spectral-derivative preprocessing for multivariate prediction of soil organic carbon by Vis-NIR spectra[END_REF][START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF][START_REF] Moura-Bueno | Stratification of a local VIS-NIR-SWIR spectral library by homogeneity criteria yields more accurate soil organic carbon predictions[END_REF][START_REF] Pinheiro | Prediction of Soil Physical and Chemical Properties by Visible and Near-Infrared Diffuse Reflectance Spectroscopy in the Central Amazon[END_REF][START_REF] Vasques | Comparison of multivariate methods for inferential modeling of soil carbon using visible/near-infrared spectra[END_REF]. On the other hand, the models calibrated with preprocessed spectra using the SGD2, MSC, MSC+SGD1, SMO and SNV techniques presented the lowest performance among all spectral ranges and their combinations in the three sediment sources (Figure 6a). These results agree with the studies of [START_REF] Dotto | A systematic study on the application of scatter-corrective and spectral-derivative preprocessing for multivariate prediction of soil organic carbon by Vis-NIR spectra[END_REF] and Moura-Bueno et al. ( 2019) that showed a lower accuracy in organic carbon predictions of subtropical soils in southern Brazil when the SVM and PLSR models are calibrated with Vis-NIR spectra submitted to the MSC and SNV techniques, respectively.

The SDG2 technique stands out with a higher value of RMSEv observed in the predictions of the three sources, differing from the other pre-processes (Figure 6a). Moreover, the SDG2 technique was the only pre-processing that resulted in a RMSEv value higher than 15% and was also the only method with a RMSEv higher than that obtained for the spectra without any type of pre-processing (RAW). Possibly, the SGD2 technique may be eliminating features (predictor variables) of the spectra that are important for the prediction of sediment sources. Nevertheless, several studies have used the 2nd derivative technique to treat UV-Vis, NIR and MIR spectra [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF][START_REF] Tiecher | Tracing Sediment Sources Using Mid-infrared Spectroscopy in Arvorezinha Catchment, Southern Brazil[END_REF] and MSC [START_REF] Ni | Mid-infrared spectroscopy tracing of channel erosion in highly erosive catchments on the Chinese Loess Plateau[END_REF] and SNV [START_REF] Chapkanski | Provenance discrimination of fine sediments by mid-infrared spectroscopy: Calibration and application to fluvial palaeo-environmental reconstruction[END_REF] techniques to treat MIR spectra, with the objective to derive the characteristics of interest along the spectrum and to improve the predictions of the models of sediment source contributions. However, as observed in the current research, these pre-processing methods do not appear to be the most promising.

There is still no consensus on how to define a priori the pre-processing techniques that will produce predictive models with a greater accuracy. Each pre-processing method will behave differently [START_REF] Rinnan | Review of the most common preprocessing techniques for near-infrared spectra[END_REF] depending on the set of soil samples considered, or as in the current research, on the intra-source spectral variation. Thus, ideally, it remains necessary to perform preliminary tests with different pre-processing methods, especially in river catchments with contrasted geologies and soil types, and when considering greater number of potential sediment sources and in larger basins, where the complexity is greater. The content in organic matter, clay and iron oxides strongly influence the spectral behavior of soils [START_REF] Moura-Bueno | Stratification of a local VIS-NIR-SWIR spectral library by homogeneity criteria yields more accurate soil organic carbon predictions[END_REF][START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]) and sediments (Figure 3) [START_REF] Tiecher | Tracing Sediment Sources Using Mid-infrared Spectroscopy in Arvorezinha Catchment, Southern Brazil[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF][START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF]. Therefore, in a context of great variability between sources, as when comparing sources with different geology and mineralogy [START_REF] Poulenard | Infrared spectroscopy tracing of sediment sources in a small rural watershed (French Alps)[END_REF], or surface and subsurface sources with contrasting carbon contents [START_REF] Evrard | Tracing sediment sources in a tropical highland catchment of central Mexico by using conventional and alternative fingerprinting methods[END_REF], pre-processing techniques may result in limited improvement of predictive models. However, they may have a greater potential to improve models in larger basins and in study areas characterized by sources showing homogeneous carbon contents and mineralogical compositions.

The lowest variation and value in the RMSEv for the unpaved roads source in all spectral ranges and combinations (Figure 6c) compared to the other potential sediment sources are likely associated with the spectral behavior of this source. Among the three sources considered, unpaved roads are the most depleted in organic matter and the coarsest grainsized [START_REF] Tiecher | Potential of phosphorus fractions to trace sediment sources in a rural catchment of Southern Brazil: Comparison with the conventional approach based on elemental geochemistry[END_REF]. Furthemore, it is composed of subsoil material that is richer in 2:1 clay mineral [START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF]. In addition, qualitatively, organic matter from unpaved roads contains a higher proportion of alkyl-benzene, and a lower proportion of polysaccharides and amino acids, compared to cropland and stream channels, which in turn are sources that show organic matter of similar quality [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF]. The lower organic matter content of the unpaved roads strongly limits masking effects on spectral features related to iron oxides between 450-850 nm. The influence of organic matter on the shape and albedo of the spectral curve along the entire UV-Vis+NIR spectrum, with an emphasis on specific regions of Fe oxides, was reported in studies conducted in Brazil [START_REF] Dalmolin | Relação entre os constituintes do solo e seu comportamento espectral[END_REF][START_REF] Galvao | Role of organic matter in obliterating the effects of iron on spectral reflectance and colour of Brazilian tropical soils[END_REF][START_REF] Moura-Bueno | Stratification of a local VIS-NIR-SWIR spectral library by homogeneity criteria yields more accurate soil organic carbon predictions[END_REF] and worldwide [START_REF] Ben-Dor | The reflectance spectra of organic matter in the visible near-infrared and short wave infrared region (400-2500 nm) during a controlled decomposition process[END_REF]. This results in lower spectral variation (Viscarra Rossel and Behrens, 2010) compared with samples with higher organic matter content, such as cropland and stream channels. This explains the higher RMSEv variation in the UV-Vis range among different pre-processing methods observed for these two sources compared to the unpaved road source (Figure 5a). Consequently, the calibrated models for unpaved roads achieve a greater accuracy in estimates. In addition, the unpaved road source is also richer in hematite oxides of Fe, with prominent features compared to crop fields and stream channels [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF]. This shows that the composition of each source affects the spectral behavior of sediment differently in each spectral range (Figure 3) and, consequently, this affects in turn the predictive models calibrated for each source [START_REF] Batistelli | Development of a fast and inexpensive method for detecting the main sediment sources in a river basin[END_REF]. These results are also in line with those observed in soil spectroscopic modeling, in which variations in the organo-mineral composition of the soil were shown to strongly influence the performance of predictive models [START_REF] Araújo | Improving the prediction performance of a large tropical vis-NIR spectroscopic soil library from Brazil by clustering into smaller subsets or use of data mining calibration techniques[END_REF][START_REF] Moura-Bueno | Stratification of a local VIS-NIR-SWIR spectral library by homogeneity criteria yields more accurate soil organic carbon predictions[END_REF][START_REF] Wijewardane | Prediction of Soil Carbon in the Conterminous United States: Visible and Near Infrared Reflectance Spectroscopy Analysis of the Rapid Carbon Assessment Project[END_REF] with an emphasis on parametric multivariate methods [START_REF] Lucà | Effect of calibration set size on prediction at local scale of soil carbon by Vis-NIR spectroscopy[END_REF][START_REF] Ramirez-Lopez | The spectrum-based learner: A new local approach for modeling soil vis-NIR spectra of complex datasets[END_REF].

By comparing the spectral ranges, it is possible to note that the RMSEv has decreased in the following order: UV-Vis > NIR > MIR (Fig. 6b). Good calibration results using MIR were also observed in previous sediment tracing studies [START_REF] Collins | Sources of sediment-bound organic matter infiltrating spawning gravels during the incubation and emergence life stages of salmonids[END_REF][START_REF] Evrard | Tracing sediment sources in a tropical highland catchment of central Mexico by using conventional and alternative fingerprinting methods[END_REF][START_REF] Ni | Mid-infrared spectroscopy tracing of channel erosion in highly erosive catchments on the Chinese Loess Plateau[END_REF][START_REF] Poulenard | Tracing sediment sources during floods using Diffuse Reflectance Infrared Fourier Transform Spectrometry (DRIFTS): A case study in a highly erosive mountainous catchment (Southern French Alps)[END_REF]. This may be related to an increased sensitivity and an improved identification of functional groups of organic matter by MIR compared to UV-Vis and NIR (Viscarra Rossel and Behrens, 2010). Studies show that spectroscopic models calibrated with MIR region spectra have the potential to discriminate different fractions of organic matter [START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF] and sediment sources [START_REF] Evrard | Tracing sediment sources in a tropical highland catchment of central Mexico by using conventional and alternative fingerprinting methods[END_REF][START_REF] Ni | Mid-infrared spectroscopy tracing of channel erosion in highly erosive catchments on the Chinese Loess Plateau[END_REF]. This also explains why, in the current research, the models calibrated with MIR spectra and their combinations presented the lowest variation in the RMSEv of predictions among all pre-processing techniques (Figures 5c, 5e, 5f and g), in particular for the models calibrated with the SVM method.

Our results show that there was no significant gain in terms of RMSEv when combining the UV-Vis+NIR, UV-Vis+MIR and NIR+MIR bands, but that RMSEv decreases significantly when the three bands of the electromagnetic spectrum were combined in a single model (UV-Vis+NIR+MIR) (Figure 6b). The same result has been observed in studies performed to estimate the concentration of elements in soil samples [START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF][START_REF] Reeves | Near-versus mid-infrared diffuse reflectance spectroscopy for soil analysis emphasizing carbon and laboratory versus on-site analysis: Where are we and what needs to be done?[END_REF][START_REF] Soriano-Disla | The performance of visible, near-, and mid-infrared reflectance spectroscopy for prediction of soil physical, chemical, and biological properties[END_REF]. The increase observed in RMSEv for models calibrated with UV-Vis range (Figure 6b) is a consequence of the lower UV-Vis spectral range (200-800 nm), which does not allow distinguishing organic matter components (Viscarra Rossel and Behrens, 2010), associated with the absence of NIR range, which is more sensitive to detect clay minerals. This implies a reduction in the predictive capacity of models calibrated with UV-Vis only or with the absence of the NIR band. This behavior is observed for models calibrated with UV-Vis+MIR range, where the absence of NIR range increased the prediction error (RMSEv) of the estimates (Figure 6b). Although the RMSEv of the models combining Vis-UV+MIR are intermediate to the RMSEv of the models calibrated using these spectral ranges separately (i.e. Vis-UV and MIR alone), it was expected that the errors would be smaller when combining them. A possible explanation for this result may be the overfitting caused by the high number of parameters and a relatively low number of artificial mixture samples used for calibrating the models (48 in total). Therefore, the low number of artificial mixture samples used to calibrate the models can be a limitation of this study, especially when combining different spectral ranges. Further efforts in future studies should evaluate the effect of the number of artificial mixture samples on the overfitting of spectroscopic models.

In summary, the explanation for this difference is associated with the interaction of UV-Vis, NIR and MIR wavelength bands, which are bands basically related to color, particle size, type of minerals and organic matter, their chemical bonds and functional groups [START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF], resulting in gain of explanatory information of the spectral variation of the data [START_REF] Viscarra Rossel | Visible, near infrared, mid infrared or combined diffuse reflectance spectroscopy for simultaneous assessment of various soil properties[END_REF]. Therefore, as sediment often consists of a heterogeneous mixture, there is a greater variation of these factors, resulting in a larger amount of functional groups detected on their surface and, therefore, the combination of several wavelengths, for example, UV-Vis+NIR+MIR, enhances the performance of spectroscopic models to discriminate between contrasted sediment sources.

In general, most spectroscopic models had RMSEv values below 15% for the validation, and in some cases, values below 5% were found (Figure 5). The models calibrated to MIR, UV-Vis+NIR, UV-Vis+MIR and NIR+MIR spectra achieved RMSEv values lower than 10% in the three sediment sources (Figure 6b), and those calibrated for the UV-Vis+NIR+MIR spectral range, presented values lower than 7% for crop fields and stream channels and equal to 5% for unpaved roads. These values are lower than the error of 15%, which is often considered to provide the acceptable level for sediment fingerprinting studies [START_REF] Collins | Selecting fingerprint properties for discriminating potential suspended sediment sources in river basins[END_REF]. This shows that the use of the spectroscopy technique employing the most appropriate spectral processing approaches, spectral bands and multivariate methods has a great potential for discriminating the contribution of sediment sources.

The lowest RMSEv values in the predictions for both multivariate methods (PLSR and SVM)

were observed for unpaved roads, which differed significantly from the other potential sources (Figure 6c). The models calibrated with the SVM method had a better performance compared to the PLSR, especially for the crop fields source (Figure 6c). This is explained by the greater ability of the SVM method to model non-linear relationships [START_REF] Ivanciuc | Applications of Support Vector Machines in Chemistry[END_REF][START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF] compared to the PLSR method. In this case, the crop fields source presents a heterogeneous organo-mineral composition, mainly regarding the quality of organic matter. In this scenario, non-linear relationships between the organomineral components and the spectral variables of the crop fields source predominate. In this case, SVM method is able to establish explanatory correlations of data variance, resulting in more accurate estimates. This also explains why the lowest variations in predictions are observed for the SVM method, which is shown to provide a more stable method for the modeling of sediment sources, with an emphasis on sources with greater variations in organo-mineral composition.

Comparing sediment source predictions by spectroscopy models with those obtained with the conventional geochemical approach

The estimated sediment contribution of each source obtained from the best calibrated models for the UV-Vis, NIR, MIR spectral ranges and their combinations is shown in Figure 7. In general, the PLSR and SVM models calibrated with spectra of the three spectral bands and their combinations submitted to SGD1, NOR, and NOR+SGD1 pre-processing have achieved a greater accuracy in predicting sediment sources when compared to estimates derived from the geochemical method tested by [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF] (Appendix 1). The models calibrated with spectra processed by the SGD2 technique showed the lowest predictive performance among all approaches (Appendix 1). These results corroborate those observed during the calibration and validation of the models (Figs. 5 and6).

In all modeling approaches, estimates of PLSR and SVM models clearly indicate that the main contribution of sediment is supplied by the crop fields source, followed by stream channels and unpaved roads (Figure 7), corroborating the results estimated by the geochemical method [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF]. Good agreement is observed between the contribution of the sources obtained with the geochemical tracer approach and that estimated by the PLSR and SVM models when combining the UV-Vis+NIR+MIR spectral ranges, with the crop fields source contributions amounting to 57%, 62% and 55%, respectively, followed by the unpaved roads sources, with 23%, 24% and 19%, and stream channel 20%, 20% and 21%, respectively (Figure 7g).

In general, the highest RMSEsp values were observed for crop fields and stream channel source estimates and the lowest for unpaved roads (Appendix 1). The predictions of crop fields and stream channel sources by the models generated with the SVM method were better than with PLSR. For the unpaved roads source, the SVM and PLSR methods presented very close RMSEsp values. For example, for the SVM method, the model with the most accurate estimates was SVM-SGD1-UV-Vis+NIR+MIR, with RMSEsp of 17.7, 16.4 and 13.9%, and biassp of 2.0, -0.7 and -2.7% for crop fields, stream channel and unpaved roads, respectively (Figure 8; Appendix 1). Accordingly, an overestimation of the crop fields contribution to sediment was found, such as an underestimation of the stream channel and thee unpaved roads source contributions. Despite the good accuracy of the models calibrated and validated with the mixtures of proportions of each source of sediment (Figure 8), there is still a considerable error compared to predictions made with fingerprinting based on geochemical tracers. This can be partly attributed to the low number of sediment samples evaluated (n = 29). Future studies should use a larger number of sediment samples in order to better understand this relationship. Nevertheless, the magnitude of the contributions calculated by spectroscopy and geochemical approach is very similar for each source (Figure 8).

For the PLSR method, the PLSR-NOR-UV-Vis+NIR+MIR model was more accurate, with higher RMSEsp for the crop fields (20.0%) and stream channel (18.7%) sources and also larger under-(biassp = -4.5%) and overestimations (biassp = 3.6%), respectively, and the lower RMSEsp (14.5%) and biassp (-0.1%) were observed for unpaved roads source. The highest prediction errors observed for crop fields and stream channel sources are in accordance with the findings of [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF], who used the PLSR method and NIR spectral range to estimate sediment sources in the same study area. According to the authors, the three sources is enriched in 1:1 kaolinite type minerals. However, an increase in the abundance of 2:1 clay minerals may be observed in the following order: crop fields > stream channel >> unpaved roads, and an increase in the abundance of quartz may be found in reverse order. In addition, crop fields and stream channels also have a higher organic matter content than unpaved roads [START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF]. Therefore, the closer mineral composition and higher organic matter content of the crop fields and stream channels provide higher spectral variations, resulting in higher prediction errors (20.0 and 15.8% for crop fields and stream channel, respectively) than those obtained for the unpaved roads (15.5%) for the PLSR-NOR-UV-Vis+NIR+MIR model (Appendix 1).

Furthermore, this variation in the organo-mineral composition of the sources has a greater effect on the prediction errors when looking at the estimates of the calibrated PLSR models for the separate spectral ranges such as UV-Vis which showed RMSEsp of 23. 7, 26.6 and 15.7% for crop fields, stream channel and unpaved roads, respectively, for the PLSR-NOR-SGD1 model; and MIR with RMSEsp 25.8, 25.7 and 18.6% for crop fields, stream channel and unpaved roads, respectively, for the PLSR-SGD1 model. This is because the UV-Vis and MIR bands are less sensitive to clay mineral types (Viscarra Rossel and Behrens, 2010) than the NIR spectral band, which identifies these constituents more clearly. Therefore, for the PLSR-SGD1-NIR model, no major differences in RMSEsp values (23.8, 16.2 and 15.8% for crop fields, stream channel and unpaved roads, respectively) were observed with respect to the PLSR-UV-Vis+NIR+MIR.

The difference between the multivariate methods is related to the statistical approach followed in each method (PLSR -parametric and SVM -non-parametric). In this case, the estimate of the contribution of the crop fields source obtained by the SVM-UV-Vis+NIR+MIR model presented a value very similar to that observed by the geochemical method (Figure 7g), indicating that this non-parametric model is more robust for the spectroscopic modeling of this sediment source. Among the three sources considered, crop fields had greater spectral variation [START_REF] Tiecher | Combining visible-based-color parameters and geochemical tracers to improve sediment source discrimination and apportionment[END_REF] and, therefore, concomitant occurrence of linear and nonlinear correlations between spectral variables and sediment.

In this scenario, non-parametric methods present better adjustments in the models, especially SVM, which uses the kernel mathematical function to establish relationships between the dependent and independent variables, in which the model seeks to identify an interpolation function between the variables and creates support vectors [START_REF] Ivanciuc | Applications of Support Vector Machines in Chemistry[END_REF]. Studies have observed a similar behavior for the spectroscopic modeling of organic carbon content [START_REF] Lucà | Effect of calibration set size on prediction at local scale of soil carbon by Vis-NIR spectroscopy[END_REF][START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF], and also that of exchangeable clay and calcium [START_REF] Ramirez-Lopez | The spectrum-based learner: A new local approach for modeling soil vis-NIR spectra of complex datasets[END_REF] in soil samples with high spectral variations.

The results show that there is a difference in the performance of the calibrated spectroscopic models with each spectral range and their combinations. For example, models calibrated only with spectrum in the UV-Vis range have the highest error for both PLSR and SVM, with RMSEsp values > 22% for crop fields; RMSEsp > 26% for stream channels and RMSEsp > 20% for unpaved roads (Appendix 1). By contrast, the lowest errors were achieved in the UV-Vis+NIR+MIR ranges, where RMSEsp values were ~18% for crop fields and ~16% for stream channels and unpaved roads. This shows that when using narrower spectrum bands there is a loss of information and consequently a loss of discriminating power of the models. However, the models that combined the three UV-Vis+NIR+MIR spectral bands (Figure 7g) achieved a greater accuracy due to the better discrimination of the inherent compositional characteristics of each source, as all major components that may influence the spectral behavior (organic matter, clays and oxides) are taken into account in the spectra [START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF][START_REF] Reeves | Near-versus mid-infrared diffuse reflectance spectroscopy for soil analysis emphasizing carbon and laboratory versus on-site analysis: Where are we and what needs to be done?[END_REF][START_REF] Viscarra Rossel | Visible, near infrared, mid infrared or combined diffuse reflectance spectroscopy for simultaneous assessment of various soil properties[END_REF].

Other differences in error metrics with respect to spectral ranges are observed by the higher predictive capability of UV-Vis+NIR+MIR (Appendix 1) compared to models using only UV-Vis+NIR range. This is in accordance with the findings of [START_REF] Reeves | Near-versus mid-infrared diffuse reflectance spectroscopy for soil analysis emphasizing carbon and laboratory versus on-site analysis: Where are we and what needs to be done?[END_REF] and [START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF] for soil organic carbon estimation. Furthermore, a study conducted by [START_REF] Bellon-Maurel | Near-infrared (NIR) and mid-infrared (MIR) spectroscopic techniques for assessing the amount of carbon stock in soils -Critical review and research perspectives[END_REF] and [START_REF] Knox | Modelling soil carbon fractions with visible near-infrared (VNIR) and mid-infrared (MIR) spectroscopy[END_REF] showed that models developed to quantify organic carbon content using MIR region data only produce slightly better results than the UV-Vis+NIR region. However, this was not observed in the current research, where models using only MIR showed a lower performance compared to that obtained with UV-Vis+NIR (Appendix 1). It should be noted that in this study we are modeling sediment source contributions, which is very different from obtaining spectroscopic estimates of elemental concentrations. Sediments consist of a mixture of particles with different contents and types of clays, Fe oxides and organic matter. In this case, UV-Vis and NIR spectral ranges have potential to discriminate between contrasted contents and types of clays and Fe oxides [START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]. They are therefore important for discriminating between contrasted sediment sources, as already reported in the literature [START_REF] Collins | Sources of sediment-bound organic matter infiltrating spawning gravels during the incubation and emergence life stages of salmonids[END_REF][START_REF] Legout | Quantifying suspended sediment sources during runoff events in headwater catchments using spectrocolorimetry[END_REF][START_REF] Pulley | The use of an ordinary colour scanner to fingerprint sediment sources in the South African Karoo[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF].

Moreover, the estimates obtained by the models in the UV-Vis and MIR spectral ranges (Figure 7a, 7c, respectively) showed a greater dispersion between the PLSR and SVM models and the three sediment sources. The same behavior is observed for the combination UV-Vis+MIR (Figure 7e), particularly for crop fields. This may be attributed to the interaction of UV-Vis and MIR wavelengths, which are bands related to the content and type of Fe oxides, and functional groups of organic matter, respectively [START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]. As sediment is a rather heterogeneous mixture, mainly supplied by crop fields, there is a greater compositional variation in these samples, which in this case, the UV-Vis and MIR spectra are unable to capture. This observation interferes in the correlations between sediment and spectral bands and, therefore, in the predictive power of models. By contrast, the NIR spectral band resulted in estimates very close to those obtained by the geochemical method, with emphasis on the crop fields and unpaved roads sources (Figure 7b). The explanation for this is due to the wavelengths corresponding to the NIR region being able to jointly identify particle size, type of minerals and organic matter, and supertons of chemical bonds and functional groups [START_REF] Viscarra Rossel | Using data mining to model and interpret soil diffuse reflectance spectra[END_REF]. Furthermore, the combinations of spectral bands with NIR (such as NIR+MIR and UV-Vis+NIR+MIR) present the same tendency as that observed for NIR, i.e., lower amplitude in estimates (Figure 7f,7g). This shows that the NIR spectral range is the most important region of the electromagnetic spectrum for building spectroscopic models for estimating sediment source contributions. This confirms previous findings obtained in studies conducted at different locations around the world, which showed the good performance of models that use data derived from the NIR spectral range to estimate sediment source contributions [START_REF] Collins | Sources of sediment-bound organic matter infiltrating spawning gravels during the incubation and emergence life stages of salmonids[END_REF][START_REF] Tiecher | Tracing sediment sources in a subtropical rural catchment of southern Brazil by using geochemical tracers and nearinfrared spectroscopy[END_REF].

Assessing the quality of the models

It is important to note that in all models tested here, the contribution of each source is estimated independently, i.e. each model estimates the proportion of a source independently of the other two sources. Therefore, the sum of the estimates generated for each source can provide a good indicator of model quality. In this case, it is understood that models with the sum of contributions from sediment sources closer to 100% are better [START_REF] Legout | Quantifying suspended sediment sources during runoff events in headwater catchments using spectrocolorimetry[END_REF]. Figure 8 shows this comparison, where it is observed that under and overestimation (ranging from 90 to 132% -Figure 9a) of the sum of the sources for some approaches occur. Regarding the spectral pre-processing techniques, overestimation occurs for the models calibrated for both multivariate methods (PLSR and SVM) with raw spectra (RAW) and submitted to SMO, SGD2, SNV, MSC and NOR techniques (Figure 9a). Moreover, a slight underestimation is observed for MSC+SGD1. It is noted that RAW and SMO spectra presented the highest overestimates and showed significant differences compared to the others, indicating that the absence of preprocessing of spectral data and/or only the smoothing provided less accurate estimates of source proportions. It is also possible to note that the NOR+SGD1 and SGD1 techniques presented the lowest variations in the sum of the sediment source contributions (Figure 8a). This corroborates the best performance observed for these models during the validation step (Figure 6a). The models that reached values closer to 100% were PLSR-SGD1 (100.6%) and SVM-SGD1 (100.1%) (Figure 9a).

Regarding the spectral ranges, it is noted that the models calibrated with the combinations NIR+MIR and UV-Vis+NIR+MIR presented the values closest to 100%, differing significantly from the others (Figure 8b). The model calibrated with the SVM method and the combination of UV-Vis+NIR+MIR presented the values closest to 100% (100.1%) (Figure 8b). Therefore, the results observed in Figure 8 corroborate those discussed in the section dealing with the accuracy of the model validation and in the estimates of the sediment source contributions. In addition, future studies should address the use of spectral variable selection algorithms. This strategy has shown the potential to improve spectroscopic estimates (Xiaobo et al., 2010;Gomes et al., 2013;Hong et al., 2020). Additionally, research employing the use of two-dimensional correlation (Hong et al., 2018) to identify regions or bands most correlated with different sediment sources can be a promising approach.

Finally, the decision tree analysis shows that the quality of calibration of spectroscopic models depends primarily on the spectral preprocessing technique, and secondarily on the spectral band, and that the sediment source has little or no influence (Figure 10b). It is evident that pre-processing with SGD2 and UV-Vis spectral band always result in higher RMSEv values. However, when comparing the quality of the models based on the estimates of sediment sources obtained with geochemical tracers (RMSEsp, Figure 10b), the spectral band and sediment source is of greater importance, and NIR range or its combination with the other spectral ranges result in contributions that are more similar to those obtained with the geochemical approach.

Conclusions

The current research demonstrated the great potential to improve the estimation of the sediment source contributions using spectroscopy when using adequate spectral preprocessing technique, multivariate method, and spectral range. In general, the nonparametric support vector machine (SVM) model was more robust than the partial last square regression (PLSR), especially to estimate the contribution of sediment sources with high organo-mineral variations, such as the crop fields source. For both models tested (PLSR and SVM), a better performance was obtained using Savitzky-Golay spectral preprocessing techniques with 1 st derivative (SGD1), normalization (NOR) and combining NOR+SGD1. Furthermore, it was verified that the combination of the three spectral ranges of the electromagnetic spectrum tested (UV-Vis, NIR and MIR) enhanced the performance of the spectroscopic models, resulting in lower errors in the predictions of the sediment source contributions. This is due to the sum of different information contained in each spectral range related to the organic and mineral composition of each sediment source.

Despite the good accuracy of the models calibrated and validated with the mixtures, significant errors remain when comparing sediment source contributions c to the results obtained with the conventional sediment fingerprinting method based on geochemical tracers. Nevertheless, the magnitude of the contributions calculated by spectroscopy and geochemical approaches remains very similar for all sources. Efforts should be done in future studies to validate these findings in larger catchments as well as in sites where more potential sediment sources may supply material to the river systems.

  Improving the quantification of sediment source contributions using different mathematical models and spectral preprocessing techniques for individual or combined spectra of ultraviolet-visible, near-and middle-infrared spectroscopy Tales Tiecher, Jean M Moura-Bueno, Laurent Caner, Jean P.G. Minella, Olivier Evrard, Rafael Ramon, Gabriela Naibo, Cláudia A.P. Barros, Yuri J.A.B. Silva, Fábio F Amorim, et al.

(

  Savitzky and Golay, 1964) with 1st derivative using a first order polynomial (SGD1), with 25 nm search window, after initial testing to define the best search window; (iii) Savitzky-Golay(Savitzky and Golay, 1964) with 2nd derivative using a second order polynomial (SGD2), with 25 nm search window. The 1st and 2nd derivates calculate the change of reflectance in wavelength variation rate. This technique is widely used to remove baseline shifts and highlight spectral features of interest; (iv) varied normal standard deviation (SNV) is used to remove spectral data dispersion caused by noise and different particle sizes and consists of subtracting the mean and dividing it by the standard deviation (spectrum -mean/standard deviation) of each spectrum individually; (v) multiplicative scatter correction (MSC) is effective in minimizing baseline compensations and multiplicative effects; (vi) normalization (NOR) is the ratio of spectrum bands measured by standard deviation (NOR); (vii) combination of NOR+SGD1; (viii) combination of MSC+SGD1. These eight techniques can be divided into three groups according to the objective and the mathematical approach employed. The first group includes only the smoothing of the spectra, represented by the SMO. The second group is defined by the use of derivatives to remove baseline shifts and enhance spectral features, represented by SGD1 and SGD2. The third group corresponds to techniques for spectral data normalizationand dispersion corrections such as SNV, MSC and NOR. All pre-processing was performed using the prospectr and clusterSim packages[START_REF] Stevens | An introduction to the prospectr package[END_REF][START_REF] Walesiak | The Choice of Variable Normalization Method in Cluster Analysis[END_REF]) R software (R Core Team, 2020).

FigureFigure 2 .

 2 Figure 1. Number of published scientific articles per year and cumulative number of published articles using spectroscopy to trace sediment sources for the period 2009-2020 (a), relative distribution of spectroscopic fingerprinting studies by country (b) and spectral range (c). *Until 15 th June 2020. UV, ultraviolet. Vis, visible. NIR, near infrared. SWIR, short-wave infrared. MIR, mid infrared.

Figure 3 .

 3 Figure 3. Characterization of the main spectral features found in the UV-Vis, NIR and MIR ranges for the suspended sediment and potential sediment sources in the Arvorezinha catchment.

Figure 4 .

 4 Figure 4. Schematic construction of predictive models of the spectral signature of sediment sources.

Figure 5 .

 5 Figure 5.Performance in validating Partial Last Square Regression (PLSR) and Support Vector Machine (SVM) prediction models from raw spectral data and combined with the eight spectral preprocessing techniques for the sediment sources including stream channels (SC), unpaved roads (UR) and surface of crop fields (CF). RAW -raw spectral; SMO -smoothing; SGD1 -Savitzky-Golay with 1 st derivative; SGD2 -Savitzky-Golay with 2 nd derivative; SNV -varied standard deviation correction; MSC -multiplicative scatter correction; NOR -normalization by standard deviation.

Figure 6 .

 6 Figure 6. Mean values of the RMSEv error statistic of the validation of the prediction models of the three sediment sources in relation to (a) eight spectral pre-processing techniques; (b) spectral bands and their combinations; (c) Partial Last Square Regression -PLSR and Support Vector Machine -SVM. Means followed by the same letter do not differ by the Tukey's test at p<0.05.

Figure 7 .

 7 Figure 7. Boxplot of the contribution of sediment sources estimated by the different approaches for the 29 sediment samples. The estimates are derived from the models that presented the highest accuracy among all processing and spectral range combinations for the PLSR and SVM methods (UV-Vis = SGD1, NIR = NOR+SGD1, MIR = SGD1, UV-Vis+NIR = NOR+SGD1, UV-Vis+MIR = SGD1, NIR+MIR = NOR+SGD1, UV-Vis+NIR+MIR = SGD1).

Figure 8 .

 8 Figure 8. Scatter plot of the validation and calibration of the best model (SVM-SGD1-UV-Vis + NIR + MIR) for mixtures the three sediment sources and the predicted contribution values by the spectra and observed by the geochemical method.

Figure 9 .

 9 Figure 9. Sum of sediment source contributions comparing Partial Last Square Regression -PLSR and Support Vector Machine -SVM multivariate methods for each pre-processing technique (a) and for each spectral range and their respective combinations (b). Means followed by the same letter do not differ according to the Tukey's test at p<0.05. The dotted line represents 100%.

Figure 10 .

 10 Figure 10. Conditional inference tree analysis evaluating the factors that most affect the quality of the models based on validation with artificial mixtures of sediment (RMSEv -a), and compared with the sediment contribution values obtained with geochemical tracers (RMSEsp -b).

  Arvorezinha catchment is located in the northeastern part of the Rio Grande do Sul

	climate is classified as Cfb (subtropical super-humid with no dry season and warm summer)
	according to Köppen (Alvares et al., 2013). The mean annual precipitation for the last 15
	years (2002-2016) is 1938 mm with a mean erosivity of 9344 MJ mm ha -1 h -1 yr -1 (Ramon,
	2017). The main crop is tobacco grown in small farms. Corn, soybean, eucalyptus and
	native forests are also found in the catchment. The landscape is characterized by short,
	steep slopes with a strong hydrological connectivity between hillslopes and the drainage
	network. The soil classes found in the catchment are Acrisols, Cambisols and Leptosols
	(IUSS Working Group WRB, 2015). Inadequate soil management under agricultural land
	associated with limited water infiltration due absence of subsurface horizon or clayey B
	State, southern Brazil. Igneous rocks (basalts and rhyodacite) characterize the geology and
	the altitude varies from 580 to 730 meters. The upper third of the catchment has an
	undulating plateau relief with slopes up to 7%, and the middle and lower thirds of the
	catchment have a much steeper topography with slope gradients often exceeding 15%. The

Acknowledgements

The first author thanks the National Council for Scientific and Technological Development (CNPq) for the research grant 311788/2019-0.