We investigated the relationships between inherent and apparent optical properties (IOP and AOP, respectively) and suspended sediment concentrations (SSC) in the main Amazonian river waters. In situ measurements of SSC, remote sensing reflectance (), the diffuse light attenuation coefficient () and the total and non-algal particle (NAP) absorption coefficients ( and , respectively) were conducted during three sampling trips along different streams of the Amazon River catchment (104 stations). The size distribution and chemical characteristics of the suspended sediment were also determined for 85 stations. We show that the particle size distribution (PSD) in the river water is best described by a segmented Junge power law distribution with a smaller slope value for the smallest particles ( = 2.4) and a larger slope value ( = 4.1) for the largest particles (> 10 µm). A strong relationship was found between AOPs and IOPs and SSC when the entire data set was considered. However, for the Madeira River, the primary Amazon River tributary in terms of suspended sediment discharge, a significant dispersion was detected for the – SSC relationship but not for the – SSC relationship. This dispersion has been shown by a previous study, using MODIS data, to display a seasonal pattern, which we investigated in this study using Mie modeling calibrated with suspended sediment characteristics. In the Madeira River, suspended sediment had a finer distribution size and a different mineralogy (e.g., a greater smectite content and a lower kaolinite content) during the rising water stage. Spectral variations of the imaginary part of the refraction index also showed significant differences during the rising water stage. In contrast, other streams of the Amazon basin had very stable properties with respect to granulometry and mineralogy. Model simulations made possible to reproduce both field and satellite observations, showing that the hysteresis observed in the Madeira River in the near infrared was mainly due to seasonal variations, leading to a decrease of absorption during the rising water stage. was shown to remain stable because of its strong dependency on scattering processes. The model was used to further understand how suspended sediment size distribution and refraction index drive the IOPs in large rivers: variations were shown to control primarily the reflectance variability; (850) presented limited variations as a function of PSD in the range typical of large rivers ( < 3) although it remained sensitive to particle mineralogical composition; (670) showed the opposite behavior with a higher sensitivity to PSD variation for coarser PSD. Finally, we demonstrate that the use of the ratio between the red and infrared channels allowed a reduction of the sensitivity in all cases, by an average of 50% with respect to changes in the mineral composition or size distribution of suspended sediment. In particular, the ratio varied by less than 5% for PSD representative of surface river waters.
© 2017 Optical Society of America
The monitoring of erosion, sediment transport and deposition processes in a catchment is crucial for addressing a large variety of topics such as geomorphology , the dissemination of nutrients and contaminants in the environment , river navigability and river bank and coastal erosion in the context of land use and climate change . In large river basins, the issue of sediment transport is of particular relevance both at a regional and global scale because these systems represent the major source of most of lithogenic and anthropogenic elements in the ocean [4,5]. Paradoxically, these basins are often poorly equipped with hydrological stations in comparison with their surface of drainage . Overcoming this problem could be accomplished by in an increase in the use of spaceborne remote sensing. In recent years, an increasing number of studies have mapped suspended sediment concentrations (SSC – see the acronyms in Table 1) using satellite ‘water color’ data [7–15]. Although some works investigated water quality in lakes [16–19], wetlands  or estuaries [21–24], most applications of remote sensing have been dedicated to coastal waters (i.e., case 2 waters ). Retrieval algorithms for SSC, the diffuse attenuation coefficient and the Secchi disk depth from reflectance data have been developed and applied in studies of the inherent optical properties of waters, mainly for case 2 waters, either experimentally or via modeling [26–31].
Conversely, there is an important lack of knowledge on the optical properties of river waters. More specifically, little is known about how the physical characteristics of the suspended sediment in continental waters drive their optical properties. Thus, concurrent measurements of suspended sediment optical properties and physical characteristics including particle size distribution (PSD) and mineralogy are needed. However, experimental data acquired in river waters are scarce and previous modeling efforts have been based upon parameters suited to oceanic conditions, such as the fine particle distribution (e.g., considering a Junge size distribution of slope 4) and have used a generic suspended sediment mineral composition that was not representative of any specific catchments. There is a need to measure and jointly interpret suspended sediment optical properties and their physical characteristics, including PSD and mineralogy, to understand how remote sensing reflectance can be robustly linked to suspended sediment concentration in rivers. Such a full characterization would support realistic modeling studies and pave the way for the development of robust retrieval algorithms for river sediment discharge monitoring.
In this study, we present a detailed water color study for river waters that encompasses field measurements of the apparent optical properties (AOPs) and inherent optical properties (IOPs), and a characterization of both the mineralogy and PSD of the suspended particles. The study was performed in the Amazon River basin and focused on the Madeira River, benefitting from previous studies that showed the relative stability of optical properties of the Amazon Basin river waters, except for the Madeira River. In this sub-catchment, Villar et al.  used field spectroradiometry and MODIS images to show that reflectance had a hysteretic relationship with SSC during the annual hydrological cycle. They showed that the seasonal variability of the reflectance could be efficiently accounted for by using a band ratio between the red and infra-red wavelengths. New data were collected along the Madeira River to support the detailed modeling of the seasonal variation of the IOPs and to understand how the physical and chemical characteristics control the optical properties. Optical modeling was further used to understand the contribution of the different particle size classes and the sensitivity of the IOPs/AOPs to the sediment type and size distribution. Finally, the use of the band ratio to reduce the impact of the characteristics of the suspended sediment on the reflectance was investigated to understand its advantages when using satellite data to map the SSC over rivers.
2. Materials and methods
2.1 Study area
The Amazon River basin encompasses 6.1 x 106 km2 , representing the largest watershed in the world with respect to water discharge (on average, 208 x 103 m3 s−1 ), and is a major contributor of sediments input to the ocean, with a mean inter-annual sediment discharge of 800 x 106 t yr−1 as assessed at the Óbidos gauging station . Most of the Amazon River basin experiences a dry season from April to September and a rainy season from November to March. Accordingly, the main Amazonian rivers draining the Andes have a unique low-flow period from September to December, a rising water period from December to March, and a flood peak from February to June, depending on their position within the catchment [36–39]. Among the dense and complex network of streams and lakes that form the Amazon basin, the Solimões and the Madeira Rivers each contribute almost 50% to the total Amazon River sediment discharge to the ocean . The Solimões River is the main stream of the upper Amazon River flowing from the Central Andes in Peru and Ecuador [Fig. 1]. The Madeira River drains the southern Andes, mainly in Bolivia. The confluence of the Madeira River with the Amazon River occurs approximately 1000 km upstream from the Atlantic Ocean. The Madeira River drains an area of more than 1.4 x 106 km2 and has a mean annual water discharge of 32,000 m3 s−1 . The sediments transported by the Madeira River mainly originate from erosion in the Andes and are principally composed of clays .
Three different sampling trips were organized to collect data along the Solimões, Madeira and Amazon Rivers and their main tributaries in March 2013, April 2014 and December 2014. During all these sampling trips, the optical, physical and bio-geochemical variables were measured and the contrasting water types exhibited a large variability in the different parameters sampled (Table 2).
Water samples were collected at each station from a boat on the river water surface [0-30 cm] and at different depths. At the water surface, the parameters measured included SSC, POC, PSD, mineralogy,,,, and . Within the water column, the parameters measured included SSC, POC, PSD, mineralogy, , and .
PSDs were determined at the Brazilian Geological Service (CPRM) with a Malvern Mastersizer 2000 Laser Diffraction grain size meter for materials ranging in size from 0.95 µm to 500 µm. The general shape of the PSD is often described by a power-law function, also called a Junge size distribution [43,44], as follows:
where corresponds to the number of particles of diameter, K is the concentration of particles and J is the slope of the distribution, also called Junge’s exponent. For oceanic waters, J is often considered to vary around a mean value of 4  and may also vary in coastal waters . However, for continental waters, J values around 4 may be inappropriate to describe the full PSD [47,48], and other values must be used depending on the aggregation state, in particular towards larger size particles, thus requiring lower values of J. Following a proposal by Mobley  and Martinez et al. , we also considered two distinct Junge coefficients ( and) in two different particle size ranges to better fit the observed PSDs.
Water samples were filtered using a 0.45 µm cellulose acetate filter (Millipore) that had been previously dried for 24 h at 60°C and weighed. After filtration, the filters were dried for 24 h at 60°C and weighed again to determine the SSC. The POC values were assessed from water samples that were filtered under low vacuum on a 0.7 µm Millipore membrane using an all-glass filtering device. The POC was analyzed in the laboratory according to the protocol described in Moreira-Turcq et al. .
Suspended sediment results from the mineralogical assemblage driven by the catchment pedology, erosion processes and hydraulic transport within the stream channel. As determined by the refraction index, the mineralogy is the principal determinant of the sediment optical properties, along with their size distribution . For a suspended sediment mineralogical determination, at some stations, a volume of water was sampled (from 1 ml for highly turbid waters up to 10 ml for clearest waters), deposited on a 0.4 µm polycarbonate membrane, then analyzed using Scanning Electron Microscopy (SEM) in the backscattered imaging mode coupled with Energy-Dispersive X-ray Spectroscopy. SEM generates a beam of electrons that scans the filter sample surface allowing each individual particles to be resolved, and the emitted X-ray spectra depend on the chemical nature of the sample, making it possible to determine each chemical element present on a particle surface . For the mineralogical determination, the elementary contents in sodium (Na), magnesium (Mg), aluminum (Al), silicon (Si), potassium (K), calcium (Ca), titanium (Ti), and iron (Fe) were computed and analyzed by the use of an unsupervised classification known as Partitioning Around Medoids (PAM) . The PAM method partitions a data set into k clusters around medoids, where k is specified in advance. The group classification was also investigated in order to obtain the best coherence for each group while maintaining a reasonable number of groups. To obtain a statistically robust classification, we also used the supervised learning Random Forest classification algorithm  and compared the results of the two methods. These classification processes allowed us to estimate the mineralogical assemblage of a test sample, and to test the robustness of the classification by comparing the two techniques . The confusion matrix showed an error rate lower than 4% between the two classifications schemes for every tests (>20 times). The POC and SPM concentration values are means of 2 and 3 replicates, respectively.
The PSD measurements are means of 5 replicates for each particle size class. The protocol of mineralogical determination involves an analysis of 15 000 individual particles on average per station using Scanning Electron Microscopy.
2.3 Radiometric data
AOPs measurements were made at each station with TriOS RAMSES hyperspectral radiance and irradiance sensors (TriOS Mess- und Datentechnik GmbH, Rastede, Germany), allowing measurements ranging from 320 nm up to 950 nm with a 2.5 nm spectral resolution.
The above-water surface remote sensing reflectance, , is defined as the ratio between the water-leaving radiance and the downwelling irradiance :
where indicates above water; and define the polar and azimuthal directions, respectively; and is the wavelength. Hereafter, for simplification, the dependence of radiometric parameters to , and has been omitted. Because the upwelling radiance,, is the sum of the leaving-water radiance and of the sky-reflected radiance at the water surface, is evaluated using the following equation:
where the proportionality coefficient is the skyglint correction factor. A value of = 0.028 is commonly used for surfaces presenting low rugosity . The radiance sensors were pointing the sky and the water surface for and , respectively, with an angle from the nadir and with an azimuth angle 135° relatively to the sun, while the irradiance sensor was fixed vertically, as suggested by Mobley . The measurements were taken for a minimum of 10 minutes when the sky conditions were as clear as possible, then the median spectrum was selected to avoid the influence of possible passing clouds.
A series of in-water downwelling irradiances vertical profiles were acquired at discrete depths in rapid succession within the euphotic layer at the river surface, usually after the measurement. The diffuse attenuation coefficients for the downward irradiance were calculated from the slope of the semi-log plot of the downwelling irradiance versus depth. The depth over which the attenuation coefficient is calculated has been defined as the lowest depth where downwelling irradiance in the blue and NIR wavelengths (e.g., the region of the spectrum where light absorption is the strongest) show significant values. Thus, the was always assessed over layer depths varying between 50 cm (strongest SPM level) and 3 m. Log was then found to vary linearly with depth.
The Online hyperSpectral integrating Cavity Absorption meteR (OSCAR) spectrophotometer was used to determine the dissolved and the total absorption coefficients ( and , respectively) from 360 to 750 nm. This spectrophotometer includes a system based on the principle of a Point Source Integrating Cavity Absorption Meter (PSICAM) [58–64], with a spherical cavity of 8 cm diameter. The OSCAR sensor is equipped with inlets and outlets, allowing a water flow in the sensor cavity. The sensor corresponds to a miniature spectrometer, as it has been used by Wollschläger et al. [62,63]. During the field sampling campaigns, OSCAR calibration was performed daily using a reference solution of nigrosine. The spectral absorption coefficient of the nigrosine solution was previously measured in laboratory against purified water as a reference using a spectrophotometer (Secoman Uvi light XT5, 10 cm pathlength). The water sample was first passed through the sensor cavity using a peristaltic pump and was calculated by averaging absorption spectra recorded during 5 minutes. The Oscar sensor was rinsed after each measurement with Milli-Q water. For , 500 ml of the water sample were filtered through 0.7 µm Millipore glass-fiber filter. Sensitivity of to membrane porosity have been tested using filters from 0.2 to 0.7 µm, showing that the results varies less than 5% on average at all wavelengths. Most of the organic matter in river water is in the finest fraction range, which is much smaller than the 0.45 µm filter porosity [65,66]. For both and, after the suppression of every air bubbles in the sensor, we launched the acquisition for 5 mn (about 20 measurements). Results were then post-treated: the median spectrum was kept as the final value of the sample absorption.
Because the phytoplankton concentration is weak in relation to the mineral particle concentration in the Amazonian rivers , the Non-Algal Particle (NAP) absorption coefficients () were simply calculated as follows:
The absorption spectra and originally incremented with a 1.7 nm step were interpolated linearly at a 1 nm wavelength resolution. The shape and intensity of the absorption spectra are absolutely unchanged. Then, we extrapolated the absorption spectra up to 850 nm using regressions following an exponential relationship and calculated on the range [400-700 nm].
2.4.1 Theoretical background
The inherent and apparent optical properties of turbid waters were computed using the Meerhoff Mie Program (MMP) , based on the Mie scattering theory developed for homogenous spherical particles (usually called Mie scattering) . Despite the natural diversity of particle shapes, the permanent turbulence of the riverine waters during the sampling campaigns leads to randomly oriented particles in the water and allowed us to accept the hypothesis of spherical particles, assuming that gains and losses compensate for each other. The MMP was used to calculate the optical properties either for single particles of radius r or for populations of particles with log-normal or power-law PSDs. We first computed the optical properties for single particles with a diameter corresponding to all size classes considered by the grain size meter. We then calculated the optical properties for the entire population with the corresponding PSD using the following formulations [68,69]:
where is the scattering efficiency factor of the population of particles, the average scattering cross section and G is the average geometrical cross section. These efficiency factors enabled us to retrieve the mass-specific scattering, backscattering and absorption coefficients (, and respectively, in m2 g−1) :
where is the density of the mineral particles and specific , , are equal to the ratio between , , , respectively and SSC.
where is a factor that depends on the light conditions and the water type, and is typically equal to 0.33 ; is a coefficient that has been shown to vary from 0.233 to 0.264 and that can be defined as the relative contribution of the scattering to the vertical attenuation of the irradiance ; the ratio is equal to 0.546 and stands for the air-water Fresnel reflection and refraction effects ; the ratio can be estimated to be equal to 0.13 in turbid waters, Q representing the anisotropy factor ; the , and coefficients represent the total scattering, absorption and backscattering coefficients, respectively, defined as follows:
where subscripts W stands for water and PHY for phytoplankton.
It is possible to reduce these expressions for the turbid waters of the Amazonian basin because of the low concentrations of phytoplankton , and the spectral domination of scattering by terrigenous particles and backscattering coefficients compared to those for water and CDOM. Thus, we obtain the following:
2.4.2 Model parametrization
Optical modeling was used to understand the seasonal variability of the AOPs and IOPs as a function of the SSC on the Madeira River (Fig. 2). Inputs were determined from field measurements or from realistic ranges of values for continental waters. At each station, the real part of the refraction index was calculated as the integration of the percentage of each mineral with the corresponding refraction indices given by Kerr  and of the POC with a typical mean value of n = 1.05 for organic matter [30,48,77]. For the imaginary part of the refraction index, very little data are available in the literature. In this study, we calculated such that the modeled fits to the measured following the methodology proposed by Kobayashi et al. . At every wavelength, values of ranging from 0 to 0.05 by steps of 5 x 10−5 were tested and the associated errors between the measured and simulated were calculated to assess the best parameterization. We then performed a series of simulations with n ranges that encompassed the values measured in the field. The spectral variations of the imaginary part of the refraction index , strongly related to , were estimated at visible and infra-red wavelengths by scanning a large range of values. The retained value was the one that produced the smallest difference between the simulated and measured . The Malvern grain size meter provided the total volume distribution of the particles, allowing us to calculate a relative number of particles for each size class between 0.27 µm and 240 µm (i.e., Dmin and Dmax, respectively), then to generate Junge’s exponent () for each station.
3.1 Grain size distribution
Figure 3 shows the 85 PSDs measured during our three surveys in the Solimões River, Madeira River, Amazon River and their main tributaries (Table 3). Power-law regressions were fitted to the entire particle size range measured [0.95 – 500 µm] and for all of the samples. The residuals between the regressions and the measurements were the highest between 10 µm and 15 µm, exposing a gap between the field data and the power-law regressions for these size classes. We then calculated the Junge coefficients for particles smaller and larger than 10 µm to better fit the observed PSDs. The determination coefficients (r2) used to derive the segmented linear regressions were higher than 0.99, demonstrating a good fit of the observed PSDs for all size classes.
Considering the entire data set, the average slope of the fine grain size range (from 1 to 10 µm) was 2.180 ± 0.056 and the average slope for the coarse range ( from 10 to 104 µm) was 3.856 ± 3 x 10−4, instead of J = 3.006 ± 0.455 representing a single regression. These results are in agreement with Martinez et al.  who found a slope of 2.22 for the fine material (from 1 to 15 µm) and of 4.56 for the coarser material (from 15 to 104 µm) for 39 water surface samples from different rivers across the Amazon River watershed.
Separately considering the PSDs for each river (Table 3), the Madeira River had average slopes of 2.443 and 4.054, respectively, for the finer and coarser size ranges ( = 0.093) and a median diameter of the suspended sediment (D50 = 6.68 µm) significantly lower than in other tributaries. Furthermore, D50 showed strong annual variation in the Madeira River, with a mean value of 8.16 µm during the high water stage (March 2013) and a value of 5.57 µm during the rising water period (December 2014), indicating a shift towards smaller sizes during the rising stage. These values are consistent with those estimated by Villar et al.  on a limited set of samples, who found D50 values close to 5m for rising waters (November 2009) and 7-9 µm at flood peak (April 2010) in the Madeira River.
SEM analyses were conducted on 17 water samples from the Solimões, Amazon and Madeira Rivers, and were based on 306 SEM images and more than 25,000 individually analyzed particles. A PAM classification was completed for 6366 particles from the field campaign of March 2013, resulting in the differentiation of 15 groups. Each of these groups was associated with a mineralogy based on the proportion of the main chemical elements. The mean correlation coefficient was greater than 92% for samples collected at the Solimões River stations taken two by two, and greater than 96% for samples collected at the Amazon River stations with a 1-year interval, demonstrating the stability of the mineralogical composition of the suspended sediment in those two rivers. For the Madeira River stations, the mineralogy retrieved from the SEM analysis of the samples collected in December 2014 had a correlation coefficient of 97%, but the samples were poorly correlated with those collected in March 2013 on the same river (55%). We detected a much higher kaolinite content in March 2013 (18%) than in all other stations analyzed by SEM (7% on average), while the smectite content was up to 24% for the Madeira River stations sampled in December 2014 (11% on average for other stations) [Fig. 4]. In all cases, iron oxides did not contribute over 2.5%.
Figure 5 shows the variation of (850), the ratio R(850)/R(670), (670) and (550) as a function of the SSC at the 104 sampled stations. The measured AOPs and IOPs generally show good correlations with the SSC, with showing the highest correlation, exhibiting a linear relationship [Fig. 5(c)]. For the Madeira River stations, a significant dispersion was detected for (850) [Fig. 5(a)] that did not appear with (670) or (550) [Fig. 5(c), 5(d)]. Such a high dispersion between the surface reflectance (850) and the SSC on the Madeira River was described by Villar et al.  based on field radiometric measurements and MODIS data [Fig. 6]. This dispersion resulted from a seasonal dependence that led to high (850) values during the rising water period (November to January) despite medium SSCs. For the rest of the hydrological cycle, a near linear trend was found between (850) and the SSCs. Villar et al.  showed that this seasonal hysteresis could be attenuated by the use of a band ratio between the infra-red and red band channels. For our data set, we found that the (850)/(670) band ratio significantly improved the regression accuracy (r2 = 0.89 vs. 0.79) [Fig. 5(b) vs. Fig. 5(a)]. and do not show seasonal dependence, however the mean specific absorption coefficients for non-algal particles, , calculated from OSCAR measurements show differences between the rising water stage and the rest of the year on the Madeira River.
At 620 nm, was slightly higher in March 2013 (0.0081 m2 g−1) than in December 2014 (0.0072 m2 g−1). At 850 nm, the differences were greater: at the high water stage reached 1.81 x 10−3 m2 g−1, while its mean value for the rising water period was 7.8 x 10−4 m2 g−1. Variations of at 440 nm, from 0.021 m2 g−1 (Solimões River) to 0.031 m2 g−1 (Madeira river during rising stage) are towards the lower end of the range documented by Babin et al.  for non-algal particles in European coastal waters (0.033 – 0.067) or by Peng & Effler  (0.04 – 0.13). Our values are all also close to the one reported over various turbid waters such as in an alpine lake  with (440) = 0.08 m2 g−1 or for the Gironde River estuary  with (440) = 0.042 ± 0.017 m2 g−1. Ma et al.  reported for highly turbid inland waters of a tropical lake in China that (440) shows decreasing values with increasing SSC within the [0-150] g m−3 range, from 0.169 down to 0.043 m2 g−1. At 700 nm, varied from 0.0046 to 0.006 m2 g−1, which is also in the range reported by Doxaran et al.  (0.008 ± 0.004 m2 g−1). The spectral variations of fitted the pattern observed by Babin & Stramski , highlighting that at near infra-red (NIR) is less than 10% of (400).
3.4.1 IOP variability during the hydrological cycle
Despite the differences in the mineralogy observed for the Madeira River between the rising water stage and the high water stage, the real part (n) of the refraction index varied within a very limited range, from 1.167 to 1.183. Spectral variations of were retrieved for the Madeira River at the high water stage (N = 4) and the rising water stage (N = 3) and for the Solimões River (N = 11), and compared to those obtained by Kobayashi et al.  in the Bangpankong River estuary [Fig. 7].
Overall, the spectral variations of showed a negative exponential pattern, as found by Babin et al. , Kobayashi et al. , and Peng & Effler . The values were very similar for the Madeira River at the high water stage ((440) = 0.0022) and for the Solimões River for all hydrological periods ((440) = 0.0021), with a spectral slope of −0.004 ± 0.0005 nm−1 [Fig. 7]. However, the values ((440) = 0.0028) and the spectral slope were higher for the Madeira River at the rising water stage of the flood (−0.0075 ± 0.0007 nm−1). Kobayashi et al.  reported values ((440) = 0.0034) and a spectral slope (0.007 nm−1) in the Gulf of Thailand close to our results, in particular for the Madeira River during rising water. Stramski et al.  reported for various minerals assessing a large variability from 0.002 to 0.023 at 440 nm. Studying Lake Erie, Peng & Effler  assessed a significant variability on 14 samples (0.0012 – 0.0055 at 400 nm). Our results showed that displays a seasonal variability during the hydrological cycle on the Madeira River but in a much more limited range (0.0026 – 0.0038 at 400 nm) than the work presented by Stramski et al. , or Peng & Effler  for other environments / mineralogical assemblages although our samples points represent locations separated by more than 2000 km. As registered for the real part of the refraction index, this is consistent with the hydrology of large river catchments that integrate a large variety of sedimentary sources converging to an average mineralogical composition in the suspended sediment that does not vary much across the hydrological cycle. Our results show that (700) varies between 4.7 x 10−4 and 7.1 x 10−4, which is slightly lower than the values of 2.2 x 10−3 reported by Stramski et al. (2007) and of 1.3 x 10−3 reported by Dubovik et al.  on desert dust samples. At 850 nm, varies from 1.6 10−4 to 3.7 10−4, showing a relative percent change much stronger in relation to the values retrieved in the visible part of the spectrum. Based on these results, we considered two different values in the numerical simulations of the IOPs and AOPs for the Madeira River for the rising stage and for the other periods.
To assess the variability in the IOP during the Madeira River hydrological cycle, we computed the mass-specific absorption, the scattering and the backscattering coefficients (, and ) for each month of the year. The average monthly SSC values at the Porto Velho station from 12 years of MODIS data (2000 – 2013), as calculated by Villar et al. , were considered in the simulations. For the period from March to October, the refraction indices (both the real and imaginary parts) and the PSD were determined from the flood peak measurements (n = 1.173, = 0.015λ-0.004, = 2.25, = 4.23). For the period between November and January, the refraction index and the grain size distribution were determined from the rising stage measurements (n = 1.175, = 0.063λ-0.007, = 2.65, = 4.72). Finally, for the transition regime in February, the refraction index and the grain size distribution were calculated as averaged values between both the high water and the rising stages.
The scattering and backscattering coefficients exhibited less contrasted spectral dependence than [Fig. 8], and and showed strong linear variations with the SSCs, with their values slightly increasing with increasing wavelengths. The variability of on a monthly scale was different: from November to February, the values were much lower than during the period from March to October at equivalent SSCs, thus introducing a hysteresis effect in the – SSC monthly variation. This hysteresis was extremely low at 440 nm and low at 550 nm, and the effect increased with the wavelengths and was the highest at 850 nm [Fig. 8]. As expected, the values decreased with an increase in λ (e.g., from 27.43 m−1 at 440 nm to 0.99 m−1 at 850 nm in January) and differed from the behavior of and, which varied little with wavelength. Both the and values showed relatively low values at all wavelengths in comparison to , (e.g., with mean values of 1.18 ± 0.82 m−1, 2.85 ± 1.82 m−1, and 115.90 ± 74.60 m−1 at 850 nm, respectively).
3.4.1 Seasonal variations in the AOP
The monthly values of and in the Madeira River were calculated using the simulated IOPs and Eq. (14) and Eq. (15). Figure 9 shows the monthly variations of (850), (670) and (850)/(670). The simulated (850) shows a seasonal dependence with a higher reflectance during the rising water stage than for the rest of the year [Fig. 9(a)]. The simulated (670) varied almost linearly with the SSC, although slightly lower values were found during the rising water stage than for the rest of the year at equivalent SSC values [Fig. 9(b)]. The use of the ratio (850)/(670) tended to reduce the dispersion in the reflectance – SSC relationship, and showed a near linear trend compared to a one-band relationship [Fig. 9(c) and Fig. 6]. The simulations thus made it possible to reproduce the different behaviors observed for, and, and IOPs simulations, which implied a seasonal dependence of.
R and [Eq. (13) and Eq. (15)] are controlled by and and depend on, whose value is more sensitive to seasonal variations with increasing wavelength [Fig. 8]. During the early rising water stage (from November to February), lower values [Fig. 8] caused a higher reflectance than during the rest of the year. Unlike for reflectance, the model predicted a very limited seasonal effect on, as this AOP is controlled by [Eq. (13)], which varied linearly with the SSCs throughout the year [Fig. 8], causing a monotonic increase of values with an increasing SSC.
showed very small spectral differences from 670 nm to 850 nm [Fig. 8]. In contrast, (670) had much higher values than(850), especially during the rising water stage. The former was responsible for a partial correction in the seasonal disparity in the reflectance – SSC relationship when using the band ratio (850)/(670) [Fig. 9], thus showing a more linear trend in the relationship than if a single band such as (850) was considered. Comparing these simulations to the seasonal hysteresis determined by remote sensing revealed an agreement between the physically based simulations and the satellite estimations [Fig. 10]. Despite a general underestimation of the observed (23% on average), bio-optical modeling allowed us to reproduce the seasonal variation of (850), especially for the rising water and the high water stages. The lack of measurements and determinations during the low water stage (from July to October) may explain the higher deviation observed between simulations and remote sensing estimates for this period. Furthermore, the ratio used to calculate (850) may vary spectrally around the value of 0.13, increasing jointly with the ratio /( .
In situ measurements of particle size characteristics of fluvial suspended sediment, unlike bed sediments, are scarce for many environments upstream the estuarine zone . Existing information on suspended sediment shows significant variability in the grain size distribution at the global scale , but some common features can be identified. Most large rivers (Amazon, Nile, Mississippi, Brahmaputra, Parana etc.) have been shown to display reduced grain size range in the bed load and suspended sediment mainly because they flow across vast plains for a major part of their course with very low topographic gradient (lower than 10 cm km−1, on average) causing strong sedimentation in the foothills and floodplains . Furthermore, sediment transport dynamics in a turbulent flow system implies a relatively constant distribution of the fine-grain size fraction in the water column in which the coarse-grain size fraction increases from the surface to the river bottom , resulting in an almost pure fine sediment composition at the river surface. In oceanic waters, the slope of the PSD are mostly centered on 4 with a suspension mostly composed by fine planktonic cells . In coastal waters, lower slope values are registered, down to 3.4, owing to the presence of particles of terrestrial origin and larger planktonic species [30,90], or even less around coral reefs . In continental waters dominated by non-living particles such as in river waters, values are centered towards lower values. Peng et al.  reported values of ranging from 2.5 to 3.2 for different lakes and rivers presenting a suspension dominated by inorganic particles in New York State. Boller & Kaegi  reported values up to 2.7 for some alpine waters, while Buffle & Leppard  showed that colloidal submicron fraction in rivers usually present a value of about 3. In our data set, values of varied between 2.7 and 3.3, when considering a single power law function over the whole grain size range, confirming the fact that inland inorganic suspensions present lower Junge exponent than in oceanic waters. As observed by Peng et al.  and Reynolds et al. , the use of a single Junge function fitting PSD over the whole grain size range may be inappropriate, especially for sediment-laden waters, as it may result in an overestimation of the smaller and larger particles. In this article, we proposed to use two Junge distributions for fine and coarse fraction, allowing to reduce the overestimation problems pointed out by Peng et al. . Our slope estimates for Amazonian river waters vary within a rather narrow range for the fine size fraction [1.8-2.4] as well as for the largest fraction [3.5-4.0].
4.2 Hysteresis of the – SSC relationship
The seasonal dependence in the (850) – SSC relationship first described by Villar et al.  was deeply investigated using optical modeling and field measurements [Fig. 5]. We showed that hysteresis was mainly driven by changes in the specific absorption from red to near-infrared which in turn was caused by variations in . Our interpretation is that PSD seasonal variability are responsible for the imaginary part of the refraction index variation. The mineralogy of particles from the Madeira River indicated a greater amount of smectite and a lower percentage of kaolinite during the early rising water period, which extends from November to February. These significant seasonal changes in the clays composition did not result in a large variation in the real part n of the refraction index because clays have a limited n range [94,95]. Furthermore, the organic particulate fraction remained very low in these sediment-laden waters, from 0.5 to 4% , leading to a negligible contribution of organic matter to the resulting n. The particle size distributions was segmented in two parts as proposed by Martinez et al.  to better fit the observed distribution. The measured PSDs indicated that particles smaller than 10 µm were more abundant during the rising water stage in the Madeira River. Such a variation of the PSD is consistent with Chipera & Bish , who showed that the finest fraction in a mixture of clays was mostly pure smectite. Combined variations of PSD towards finer range and clay composition in the Madeira River seemed to have affected more significantly the imaginary part of the refraction index than the real part. However, it remains important to assess which parameter (n, , PSD) is the determinant that drives the reflectance in the Amazon River basin and how is this relevant for large rivers around the world.
4.3 On the relative importance of n and PSD over the IOPs
In this section, we used a parameterization of the PSD and mineralogy representative to large river waters to analyze the sensitivity of reflectance to changes in the suspended sediment characteristics. Red and NIR wavelengths have been shown to be strongly correlated with SSC in inland and coastal waters although reflectance in the red spectrum may saturate with increasing SSC [13,50]. We focus on 670 and 850 nm wavelengths as most current spaceborne sensors suited for the study of inland waters (LANDSAT 8, SENTINEL-2) offer spectral bands at those wavelengths. We paid special attention to the sensitivity of the resulting spectral ratio that several studies have indicated as an efficient method to limit the reflectance sensitivity to the suspended sediment characteristics [21,50,97]. We also evaluated the contributions of the particle size classes on the IOPs values by following the modeling protocol described in Stramski & Kiefer  for different PSDs, and by including absorption processes using values retrieved from Kobayashi et al. .
Figure 11 shows the relative contributions of 10 suspended sediment size classes [0-100 µm] for two refraction index values and two PSDs to absorption, scattering and backscattering. As expected, smaller particles have a higher contribution to the IOPs with increasing values of (i.e., with more fine material). Small particles (D < 8 µm) were responsible for the majority of the scattering and backscattering processes from 60% to 63% with = 3 and from 67% to 78% with = 3.5 for , and from 83% to 86% with = 3 and from 86% to 92% with = 3.5 for. These estimates are consistent with the results by Peng et al.  who assessed that 50% of the total scattering and backscattering processes where resulting from particles with diameter less than 5 µm in suspension from inland waters dominated by inorganic matter. Variations in the n values between 1.15 and 1.20 had a very small effect on the absorption coefficient but strongly impacted the scattering and backscattering coefficients: an increasing n value increased the importance of the smallest fraction in the particles population on the scattering and backscattering effect. These results are of special significance for large rivers where fine particles are predicted to dominate the inorganic suspension at the river surface as coarser suspension sediments increase in concentration toward the bottom of the water column. Walling and Moorehead  compared particle size distribution in the water column, in terms of mass, for several rivers across the world showing that suspended sediment smaller than 20 µm represent 50 to 100% of the total mass in all cases. More recent results acquired either on the Amazon River , the Parana River  or on temperate rivers  confirm the fact that water samples acquired at river surface usually display a unique size mode centered on fine sizes (e.g., < 20 µm). Suspended sediment loads of rivers can be transported in composite particles but it is far from straightforward to quantify the relative importance of discrete and composite particles in river suspended sediment loads . The importance of fine particles on the scattering and backscattering processes suggests that knowledges of their size distribution need to be improved, and particularly in composites particles, to better characterize the optical properties of inland waters.
4.4 On the relative importance of , and PSD over the AOPs
We analyzed the theoretical sensitivity of to PSD and mineralogy using modeling. For PSD, we stepped the values between 1.5 and 3.0 by increments of 0.5 while setting to 4. For mineralogy, the values were stepped between 0 and 0.001 by increments of 0.0005 and n varied from 1.165 to 1.185 [Fig. 12]. Each of these new simulations corresponded to a single combination of these parameters at 670 nm and 850 nm. (850) showed moderated sensitivity to, with a relative variation of 20% when varies from 0 to 10−3. (850) showed also moderated sensitivity to n, with a relative variation of 25% when varies from 1.165 to 1.185. (670) showed much stronger sensitivity to with a relative variation of 50% when varies from 0 to 10−3. On the contrary, (670) showed little variability as a function of n with a relative variation of 5%. At both wavelengths, showed low to moderate sensitivity (7 to 17%) to the PSD (when varied from 1.5 to 3) with a relative variation increasing with increasing and n. Therefore, it appears on Fig. 12 that variations play a major role in sensitivity to suspended sediment characteristics and that this variability is stronger at red wavelength where is stronger. However, is itself a function of suspended sediment mineralogy and grain size distribution in a complex way. We further analyzed the role of PSD and mineralogy by setting to a constant value.
Figure 13 shows the variation in (850), (670) and (850)/(670) as a function of and n, with n values typical of most clay particles. For PSD, we tested increasing values with the value set to 4. For distribution towards coarser particles (i.e., with lower slopes), the reflectance varied smoothly as a function of PSD. When varied from 2 to 3, reflectance varied by 18% at infra-red wavelength [Fig. 13(a)] and by 24% in the red [Fig. 13(b)]. For the same size distribution variation, the (850)/(670) ratio varied by only 5% [Fig. 13(c)]. For finer distributions (i.e., those with higher slopes), the reflectance varied rapidly as a function of . As varied from 3.75 to 4.5, the reflectance varied by 70% in the infra-red [Fig. 13(a)] and by 55% in the red [Fig. 13(b)]. For the same size distribution variation, the (850)/(670) ratio varied by 33% [Fig. 13(c)]. The reflectance showed maximum value for varying from 3.5 to 3.75 probably under the influence of backscattering processes that has been shown to increase from = 3 to 4  and then to decrease from 4 to 5 (considering a unique slope parameter). The impact of the mineralogical variations changed according to the particle size distribution and wavelength. (850) variations as a function of mineralogical variations were rather stable, from 24 to 28% when n varied from 1.165 to 1.185, and for any value of . For a high value of , n appeared to have moderated effect on reflectance at red wavelength (e.g., when n varied from 1.165 to 1.185 and for = 4.25, (670) varied by 17%). In contrast, for low values of , (670) variations were small as a function of the n values (e.g., for = 2.5, when n varied from 1.165 to 1.185, (670) varied by 9%). Accordingly, (850)/(670) showed limited sensitivity to mineralogical variations from 8 to 18% when n varied from 1.165 to 1.185.
These simulations confirmed that the use of the band ratio makes the reduction of the reflectance sensitivity to suspended sediment characteristics possible in most cases. The impact of the variability in the particle size distribution and the mineralogy on reflectance showed a rather complex pattern with a significant sensitivity of the reflectance ratio on mineralogy for a coarser distribution. When varied from 1.5 to 3, the reflectance ratio was almost unaffected by PSD variations (e.g., relative variation lower than 5%) showing much greater stability in relation to reflectance. For the same size distribution variation, (850) and (670) varied by 22% and 29%, respectively. In contrast, mineralogy has little effect on the reflectance ratio for distributions of finer size. For the PSD corresponding to sediment-laden waters in large river basins ( < 3), (850) and reflectance ratio vary weakly. However, for < 3.5, at red and infrared appears to be significantly sensitive to changes in sediment mineralogy, either through n or . It is expected that for a river catchment showing rather stable sediment sources during the hydrological cycle, the – SSC relationship may be robust as PSD variations induce limited impact on (850) and (850)/(670). On the contrary, (670) shows stronger sensitivity to PSD and may experience significant changes as a function of PSD and thus local hydraulic conditions from foothills to the estuary.
We investigated the AOPs and the IOPs of the river waters of the Amazon basin catchment using field measurements and modeling. The field campaigns provided a large data set of radiometric, physico-chemical, sedimentological (PSD and mineralogy) parameters for the two main tributaries of the Amazon catchment (the Solimões and Madeira Rivers) with respect to sediment discharge. This experimental database allowed us to improve our knowledge of the relationships between the inherent or apparent optical properties and the suspended sediment concentrations. The optical properties of the Madeira River were shown to be significantly different from the rest of the catchment. Indeed, its geographical origin, drainage area, and hydrological cycle confer a seasonal behavior different from that of the Solimões River on this large tributary.
The presence of a seasonal hysteresis in the (850) – SSC relationship for the Madeira River was caused by seasonal changes in the mineralogy and PSD, showing that variability of the AOPs and IOPS in response to changes in the suspended load characteristics during the hydrological cycle may limit the accuracy of the SSC retrieval based on remote sensing data.
Our results showed that the imaginary part of the refraction index was the main origin of the hysteresis in the (850) – SSC relationship of the sediment-laden Madeira River via a strong effect on the absorption by the suspended particles in the infra-red wavelengths. The spectral slope of from the blue region of the visible spectrum to the infra-red region decisively drove the different absorption levels during the annual hydrological cycle. The dispersion of the (850) – SSC relationship could be overcome to some extent using of a ratio between the infra-red and the red spectral bands (850)/(670). Temporal changes in the mineralogy had less effects on the scattering and backscattering coefficients for increasing wavelengths. Those properties were very sensitive to changes in the PSD and particularly to the number of particles with diameter of less than 10 µm. Backscattering was extremely dependent on the percentage of small particle size classes. This high sensitivity caused maximum reflectance values for average PSD and minimum reflectance values for sediment mixtures dominated by fine or large particles. Finally, the real part of the refraction index played a slight role in the development of the hysteresis, which was the lowest for the PSD dominated by fine particles. However, through an accentuation of the previously cited relationships between the optical properties and the characteristics of the optically active components, the role of the real part of the refraction index remained non-negligible. Therefore, particular attention must be paid to the characterization of these properties in continental waters to retrieve the SSC from water color measurements.
Finally, extending the data set to other large river basins and applying the combined use of measured, simulated and remotely sensed data seems to be a way to overcome uncertainties and to provide concrete solutions for water management agencies, especially for large basins with sediment-laden waters.
Institut de Recherche pour le Développement (IRD, France); Agência Nacional de Águas (ANA, Brésil); Centre National d’Etudes Spatiales (CNES, France); Noveltis (France). This work has been supported by the French Institut de Recherche pour le Développement (IRD) as a major partner of the Service National d’Observations HYBAM since 2003, the Brazilian Agência Nacional de Águas (ANA) for funding the sampling trips, and the French Centre National d’Etudes Spatiales (CNES) and Noveltis that cofinanced the first author PhD thesis.
The authors thank Elisa Armijos, Pascal Fraizy, Thierry Aigouy and Sophie Gouy for the technical support. The authors are also grateful to the Universidade Federal Fluminense (UFF), the Geological Survey of Brazil (CPRM) for their help during measurements. We notably thank Lucile Duforêt-Gaurier and William Moutier of the French Laboratoire d’Océanologie et de Géosciences for their support in the modeling processes, and Frédéric Julien of the French laboratoire d’Ecologie Fonctionnelle et Environnement Ecolab for his help with the absorption meter calibration.
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