The present study provides an extensive overview of red and near infra-red (NIR) spectral relationships found in the literature and used to constrain red or NIR-modeling schemes in current atmospheric correction (AC) algorithms with the aim to improve water-leaving reflectance retrievals, ρw(λ), in turbid waters. However, most of these spectral relationships have been developed with restricted datasets and, subsequently, may not be globally valid, explaining the need of an accurate validation exercise. Spectral relationships are validated here with turbid in situ data for ρw(λ). Functions estimating ρw(λ) in the red were only valid for moderately turbid waters (ρw(λNIR) < 3.10−3). In contrast, bounding equations used to limit ρw(667) retrievals according to the water signal at 555 nm, appeared to be valid for all turbidity ranges presented in the in situ dataset. In the NIR region of the spectrum, the constant NIR reflectance ratio suggested by Ruddick et al. (2006) (Limnol. Oceanogr. 51, 1167–1179), was valid for moderately to very turbid waters (ρw(λNIR) < 10−2) while the polynomial function, initially developed by Wang et al. (2012) (Opt. Express 20, 741–753) with remote sensing reflectances over the Western Pacific, was also valid for extremely turbid waters (ρw(λNIR) > 10−2). The results of this study suggest to use the red bounding equations and the polynomial NIR function to constrain red or NIR-modeling schemes in AC processes with the aim to improve ρw(λ) retrievals where current AC algorithms fail.
© 2013 OSA
The marine reflectance measured just above the water surface, ρw(λ) (also referred to as (λ) or normalized water-leaving reflectance ), retrieved from ocean color satellite images, allows to estimate biogeochemical parameters with a high revisit frequency and over large areas of oceans. The accuracy of these parameters depends however on the processing of the sensor-measured radiance, L(λ), at the top of the atmosphere (TOA) used to obtain ρw(λ). This processing includes, among others, the removal of the atmospheric contribution, the so-called atmospheric correction (AC) . The top of atmosphere reflectance, ρTOA(λ), is derived from the sensor-measured radiance and corrected for gas absorption, Rayleigh scattering, white-caps reflection and sun glint, to obtain the Rayleigh corrected reflectance, (λ) :Eq. (1), if the optical properties and the concentrations of the aerosols are known, the quantities (λ), (λ), tθ0(λ) and tθv(λ) can be estimated and hence ρw(λ) can be calculated.
At the time of the Coastal Zone Color Scanner (CZCS) satellite, the initial AC procedure assumed zero ρw(λ) at 670 nm allowing to retrieve the atmospheric contributions from the total signal  (hereafter referred to as the black pixel assumption). With the addition of near infrared (NIR) bands for the next generation of ocean color satellite sensors (e.g., SeaWiFS, MODIS and MERIS), the 700–900 nm spectral range was used to estimate the aerosol contributions in the AC processes. Gordon and Wang  suggested to apply the black pixel assumption to the NIR spectral bands allowing to estimate (λNIR) and (λNIR) and to select the appropriate aerosol optical models (hereafter referred to as the GW94 AC procedure). However in highly productive and turbid waters, due to absorption and backscattering of significant loads of algal and non-algal water constituents, the assumption of zero ρw(λ) is not valid neither in the red nor in the NIR region of the spectrum [3, 4]. Assuming zero red or NIR ρw(λ) in such water masses leads to an overcorrection of the atmospheric effects and subsequently to an underestimation of ρw(λ) .
To avoid the inappropriate application of the black pixel assumption, numerous red or NIR-modeling schemes have been developed to account for non-zero red or NIR ρw(λ) within the AC processes. The standard NASA AC procedure for the processing of SeaWiFS and MODIS Aqua images, for instance, is a GW94-based AC procedure which includes a NIR-modeling iterative scheme with a bio-optical model to retrieve ρw(λNIR) where the black pixel assumption is not valid [4, 5]. Other AC approaches have also been suggested, e.g., coupled ocean-atmosphere optimization methods, such as the the direct inversion approaches using artificial neural networks [6–8]. For MODIS Aqua, the black pixel assumption was successfully applied in the Short-Wave-Infra-Red (SWIR) spectral domain where even turbid seawater appears to be totally absorbent .
Another approach to extent the GW94 AC procedure to turbid waters, consists of forcing the AC process with spectral relationships estimating red or NIR ρw(λ) by means of ρw(λ) at shorter wavelengths (i.e., ρw(λj) = f (ρw(λi))). These relationships reflect thus the spectral dependence of the marine signal itself, including the spectral dependence of the total absorption and backscattering simultaneously. Hence, it does not require retrieval of inherent optical properties. Moreover, it can be easily implemented in current red or NIR-modeling schemes to improve ρw(λ) retrievals where current AC algorithms fail.
For the CZCS AC, empirical spectral relationships have been proposed to estimate ρw(670) from ρw(λ) in the blue and green region of the spectrum (hereafter referred to as red spectral relationships) [10–16]. An empirical spectral relationship was also used by Nicolas et al.  within the AC procedure of the POLarization and Directionality of the Earth’s Reflectances-2 (POLDER-2) sensor. Similarly, several studies investigated the spectral dependence of the marine reflectance in the NIR region of the spectrum to model ρw(λNIR) for the AC of second generation ocean color satellite images (hereafter referred to as the NIR spectral relationships) [18–20]. Lee et al.  also suggested to correct remote sensing ρw(667) estimations (due, for instance, to imperfect AC) for the Quasi-Analytical Algorithm by means of spectral relationships between ρw(667) and ρw(555).
Most of these spectral relationships have been developed with restricted datasets and have not been confirmed theoretically nor validated with independent in situ datasets. An overview and validation of these different red and NIR marine spectral relationships are thus essential to verify if these relationships are globally valid and if they can be used to improve AC for past, present and future ocean color sensors. In a companion paper, Goyens et al.  investigate how these spectral relationships can be implemented in current NIR-modeling schemes [5,18,19] to improve AC processes in turbid coastal waters.
In the present study, the AC literature is reviewed from the launch of the CZCS satellite till today giving a non-exhaustive list of various red and NIR spectral relationships used to estimate the water signal in the red (Section 2) and the NIR spectral region (Section 3) from ρw(λ) at shorter wavelengths. Most spectral relationships encountered in the literature were initially developed for the CZCS sensor to retrieve ρw(λred). However, since the CZCS spectral bands are relatively close to the second generation satellite sensor spectral bands (e.g., Sea-WiFS, MODIS Aqua or MERIS), these CZCS-oriented spectral relationships may eventually lead to red spectral relationships also valuable to constrain actual NIR-modeling schemes (e.g., the iterative scheme suggested by Stumpf et al.  and Bailey et al.  modeling ρw(λNIR) according to ρw(λred)).
With the arrival of SWIR ocean color bands, a similar exercise could be performed to evaluate spectral relationships allowing to estimate ρw(λ) in the NIR from ρw(λ) in the SWIR spectral domain, and inversely. However, the present study is limited by the spectral range of the in situ reflectance measurements, notably, from 400 to 900 nm, and is thus valuable for sensors with visible and NIR spectral bands (e.g., SeaWiFS, MODIS and MERIS sensors, the SEVIRI instrument on MSG, the Geostationary Ocean Color Imager (GOCI) and possibly the future GOCI-2 carried by COMS) as well as for studies covering decadal time scales including data from past and current sensors.
After reviewing the red and NIR spectral relationships, in situ reflectance spectra are described and their selection is outlined ensuring highly accurate reflectance spectra (Section 4). Next, red and NIR spectral relationships are validated (section 5). A similar exercise has been done by Doron et al.  with in situ, remote sensing and simulated data. However the authors only focussed on the constant NIR reflectance ratio suggested by Ruddick et al. [18, 19]. Here a comprehensive overview and validation of 16 spectral relationships encountered in the literature are proposed.
2. Red spectral relationships
Initially the CZCS AC algorithm used the spectral band at 670 nm to estimate the aerosol contribution . However, at 670 nm, both atmospheric and marine turbidity affect the TOA signal making it difficult to estimate either the aerosol content or the water reflectance with this single band . Therefore, red-modeling schemes have been developed based on, e.g., spectral relationships to estimate the water signal at 670 nm from ρw(λ) at shorter wavelengths. Smith and Wilson  and Austin and Petzold  related ρw(670) with the reflectance ratio ρw(443)/ρw(550) and the amplitude of reflectance at either 443 or 520 nm (Table 1). According to Austin and Petzold  using the reflectance at 520 nm was more appropriate to account for variations in non-algal particles while the ratio ρw(443)/ρw(550) accounts for the pigment concentrations.
In the open ocean, the optical properties are essentially dominated by phytoplankton (often referred to as Case 1 waters) while in optically complex waters, the optical properties are dominated by other constituents such as dissolved organic matter and suspended sediments (often referred to as Case 2 waters) . Hence, Sturm  proposed an iterative approach to solve the AC suggesting three equations according to the water type. The three equations are of the same type (Table 1). ρw(670) is estimated from the water reflectance at 550 nm and an average blue-green ratio function β related to the total suspended matter (TSM) [14, 25]. The empirically defined constant terms of the equations were based on previous works and differed for clear waters , turbid near coastal waters  and in situ measurements taken in the northern Adriatic Sea (AAOT data) .
Viollier and Sturm  observed simple linear relations between ρw(670) and ρw(550) as a function of the water type. In the turbid coastal waters of the eastern English Channel, ρw(670) represented 40% of ρw(550) while, over a coccolithophorid bloom, it represented only 15%. In order to satisfy both water types, Viollier and Sturm  proposed a non-linear relationship similar to Smith and Wilson  and Austin and Petzold , but including the ρw(520)/ρw(550) ratio instead of the blue-green ratio ρw(443)/ρw(550) (Table 1).
Similarly to Sturm , Bricaud and Morel  demonstrated that AC could be improved by discriminating between Case 1 and Case 2 waters in the red-modeling scheme. They suggested several functions according to the water type, relating the Chlorophyll-a (Chla) absorption bands ratio ρw(443)/ρw(670) and the blue-green ratio ρw(443)/ρw(550) (Table 1). When the water type could not be defined as turbid or clear, Bricaud and Morel  used an intermediate relationship similar to the model of Smith and Wilson  (Table 1).
The OCEAN code, developed to process the level-2 European CZCS historical data , used both the relations of Viollier and Sturm  and Bricaud and Morel  within the red-modeling scheme to correct CZCS images for atmospheric contribution in turbid waters. According to a first guess for ρw(443) (based on the Black Pixel Assumption), the algorithm iterates with either the reflectance function of Viollier and Sturm  (ρw(443) < 3.10−5) or the function of Bricaud and Morel  (ρw(443) > 3.10−5) to account for non-zero ρw(670).
Inspired by the CZCS red-modeling scheme proposed by Viollier and Sturm , Nicolas et al.  proposed an operational AC algorithm for POLDER-2 including a linear relationship between the marine signal at 565 and 670 nm (Table 1). The authors estimated ρa(670) as the difference between the observed and modeled ρw(λ). According to Nicolas et al. , this approach was satisfactory for most cases except for waters with high yellow substance absorption.
The Quasi Analytical Algorithm (QAA v.5) , used to derive the inherent optical properties from satellite ρw(λ) estimations, includes three spectral relationships to correct erroneous satellite retrieved ρw(667). ρw(667) values are constrained within an upper and lower range defined by two spectral functions relating ρw(λ) at 667 and 555 nm (Table 1). When the retrieved ρw(667) is missing or out of limit, ρw(667) is estimated from ρw(555) and the ratio ρw(490)/ρw(555) (Table 1).
As observed in Table 1, some spectral relationships are written in terms of sub-surface radiance, Lss(λ) or remote sensing reflectance, Rrs(λ). For data analysis all functions are expressed here in terms of ρw(λ). Lss(λ) and Rrs(λ) are converted into ρw(λ) following Morel and Gentili,  and considering the approximation for the ratio (1−rF)/nw (with rF being the Fresnel reflectance and nw the water refractive index) suggested by, e.g., Bricaud and Morel , Morel and Gentili , and Mobley .
3. NIR spectral relationships
Constant reflectance ratios in the NIR region of the spectrum were suggested by Ruddick et al. . With assumptions on the backscattering and absorption in the NIR, the authors approximated ρw(λ1)/ρw(λ2) by the water absorption ratio aw(λ2)/aw(λ1) (with λ1 and λ2 being two wavelengths in the NIR). Ruddick et al.  further investigated these assumptions with radiative transfer simulations as well as above-water in situ measurements. The authors concluded that the NIR reflectance spectral shape is almost invariant for moderate turbidity and observed, as a function of λ1 and λ2, a constant reflectance ratio α (λ1, λ2) (Table 1). Accordingly, normalizing the reflectance spectra to the reflectance at a single wavelength in the NIR (referred by the authors to as the similarity NIR reflectance spectrum) allows to determine, at any wavelength, the water leaving reflectance shape in the NIR. This assumption is used to extent the GW94 AC process to turbid waters (hereafter referred to as the MUMM NIR-modeling scheme) [18, 19].
Ruddick et al.  also suggested theoretical values for α (λ1,λ2) based on the pure water absorption spectrum of Kou et al.  for the MUMM NIR-modeling scheme of MODIS, MERIS and SeaWiFS. However, the similarity NIR reflectance spectrum assumption appeared to be only valid for a certain range of turbidity. Indeed, variations in α (λ1,λ2) were observed when the NIR reflectance values were outside the 10−4 - 10−1 range . A similar conclusion was made by Shi and Wang  who observed a quasi linear relationship between ρw(645) and ρw(859) for ρw(859) values below 0.03. For waters with ρw(859) above this threshold, ρw(λ) at 645 nm saturated and remained almost constant (∼ 0.012). Doron et al.  also observed some deviations from the constant reflectance ratio with both in situ and satellite derived data. According to that study, for ρw(865) between 10−4 and 10−2, α (765,865) varied little between 1.73 and 1.84 as suggested by Ruddick et al. , but decreased with an increase in turbidity.
Wang et al.  proposed an NIR-modeling scheme for the AC of the Korean Ocean Satellite GOCI including a polynomial relationship between the water signal at 748 and 869 nm (Table 1, hereafter referred to as the GOCI NIR-modeling scheme). Initially, ρw(λ) is retrieved with the GW94 AC algorithm allowing to calculate the water diffuse attenuation coefficient at 490 nm, Kd(490) . Next, polynomial relations are used to estimate ρw(748) from Kd(490) and ρw(869) from ρw(748). These empirical relations were developed based on long term MODIS Aqua images over the turbid western Pacific region and processed with the NIR-SWIR GW94-based AC algorithm . Although the GOCI NIR-modeling scheme provided satisfying results in the western Pacific region [20, 31], the polynomial relationship between ρw(748) and ρw(869) has not yet been validated with in situ data and applied to other coastal regions.
4. In situ data
Above-water reflectance measurements were made using TriOS-RAMSES hyperspectral radiometers during 63 sea campaigns undertaken between 2001 and 2012 (860 stations). Data were collected in coastal waters located in the southern North Sea and English Channel , the Celtic Sea, the Ligurian Sea, the Adriatic Sea and in the Atlantic Ocean along the coasts of Portugal and French Guyana [33, 34]. This dataset is particularly suitable for the validation of the spectral relationships as it includes measurements over contrasted and optically complex coastal waters. In situ data processing, averaging and selection are described in Ruddick et al. .
Out of the 860 stations, 105 in situ reflectance spectra satisfy the selection criteria and were not used by Ruddick et al.  for the calibration of the NIR similarity spectrum. Table 2 provides an overview of the minimum, maximum, average and standard deviation for the selected spectra for the ocean color MODIS Aqua visible and NIR bands. The largest standard deviations in marine reflectance are encountered in the green and red region (Table 2). Around 869 nm the marine signal ranges from near zero to approximately 0.1, confirming the non-valid zero water-leaving reflectance assumption in the NIR. All spectra present ρw(λNIR) values above 10−4, which is approximately the limit of validity for the black pixel assumption . Out of the 105 spectra, 53% presents moderate turbidity with ρw(869) ranging from 10−4 to 3.10−3 and 47% of the data presented very turbid waters with ρw(869) exceeding 3.10−3. This latter value corresponds to the threshold used by Wang et al.  to switch for the SWIR algorithm in the combined NIR-SWIR GW94-based AC algorithm.
Figure 1 shows the spectra in the 400–900 nm range and the red-NIR reflectance spectra normalized at 780 nm (ρwn780(λ)) as suggested by Ruddick et al. [18,19]. Most spectra exhibit an increasing signal from the blue to the green region of the spectrum followed by a large peak between 550 and 600 nm [Fig. 1(a)]. A second peak is observed around 800 nm. Out of the 105 spectra, three spectra, taken in the Ligurian Sea, show a shape similar to clear ocean waters (peak in the blue followed by a decreasing signal with an increase in wavelength). In contrast, seven spectra present a lower peak around 550 and 600 nm and a higher peak around 690 nm followed by a relatively large signal at 800 nm and beyond.
According to Doxaran et al. , water masses with a reflectance spectrum showing a larger peak at 550–600 nm are characterised by lower SPM values (< 100 mg l−1), while water masses with a large reflectance peak around 700 and 800 nm present larger concentrations of SPM (> 100 mg l−1). Indeed, these seven spectra are from the coastal waters of French Guiana known as being influenced by important river-discharge resulting in extremely turbid waters [33, 34]. These in situ measurements also exhibit distinctive ρwn780(λ) spectra [Fig. 1(b)]. As observed by Ruddick et al. , most spectra present similar spectral shapes between 710 and 900 nm with a peak at 805–812 nm [Fig. 1 (b)]. The extremely turbid spectra from French Guiana instead show relatively lower ρwn780(λ) values around 710 nm and often higher values at 850 nm and beyond.
5. Validation experiment
Spectral relationships are validated by comparing modeled and measured ρw(λ) values qualitatively and quantitatively. The average percent relative error (RE), percent bias, root mean square error (RMSE), and R-squared coefficient (R2) are calculated for each spectral relationship.
The percentage of data for which the RE does not exceed 10% of the observed value is also calculated as well as the validity ranges of each function in the visible. Validity ranges are determined by fitting a non-linear regression line through the observed and modeled ρw(λ). The reflectance range for which the spectral relationship is satisfactory is defined by a difference between the regression and 1:1 line less than 10%.
5.1. Validation of spectral relationships in the visible
The statistical parameters comparing modeled and observed ρw(670) are given in Table 3. Most functions tend to underestimate ρw(670) (negative bias ranging from −3 to −63%). Two functions indicate a positive bias, notably, the function of Sturm  developed with AAOT data and the function of Viollier and Sturm developed with data from the English Channel (18 and 31%, respectively). However these spectral relationships overestimate ρw(670) values below 0.05 but largely underestimate ρw(670) values above this threshold. The relations from Smith and Wilson , Austin and Petzold , Bricaud and Morel  for the Case 2 waters, Nicolas et al. , and Viollier and Sturm  for the Coccolithophorid blooms show the lowest statistical performances. Statistics in Table 2 indicate that linear functions including a larger multiplication factor between the water signal in the red and the green spectral region result in better ρw(670) retrievals (Table 1). Indeed the relation of Viollier and Sturm  developed with in situ data from the English Channel (multiplication factor of 0.4) provides more satisfying results (see Table 2; lower bias, larger percentage of data with less than 10% RE and larger validity range) compared to the relations of Viollier and Sturm  over a coccolithophorid bloom (multiplication factor of 0.15) and Nicolas et al.  (multiplication factor of 0.2) (Table 1).
As mentioned in Section 2, the algorithm described in the OCEAN code for the CZCS AC over turbid coastal waters  used the function of Viollier and Sturm  to model ρw(670) when the retrieved ρw(443) was below 3.10−5 and the Case 1 and 2 spectral relationships of Bricaud and Morel  otherwise. Although none of our in situ ρw(443) values are below 3.10−5, the reflectance function of Viollier and Sturm  yields better ρw(670) retrievals (Table 3).
Similarly to the other spectral relationships, the relation suggested by Lee et al.  to estimate ρw(667) when it is missing or erroneously retrieved (i.e, outside the bounding equations, Table 1), tends to underestimate larger ρw(667) values. According to the R2 this spectral relationship shows a relatively good fit with our in situ data (Table 3). However, the average bias and RE remain large (43% and −43%, respectively) and the percentage of values within 10% of the 1:1 line remains small (4%). In contrast, the bounding equations used by the authors to evaluate ρw(667) according to ρw(555) correspond to the limit of our in situ data [Fig. 2(a)].
Functions showing the best fit with the observed data are shown in Figs. 2(b)–2(d). These are the relations proposed by Austin and Petzold  and the two spectral relationships of Sturm  in . The three relationships are of the same type (Table 1). They include the average blue green ratio β and the magnitude reflectance at 550 nm which can be related to the total absorption and the backscattering coefficient, respectively . The maximum validity range in Table 3 and the plots in Figs. 2(b)–2(d) indicate that these functions largely underestimate ρw(670) when the marine signal is greater than 0.03, which corresponds to very turbid waters (ρw(869) ≥ 3.10−3).
5.2. Validation of NIR spectral relationships
To evaluate the validity of the constant NIR reflectance ratios used in the MUMM NIR-modeling scheme , ρw(λ1) versus ρw(λ2) for the NIR bands of the SeaWiFS, MERIS and MODIS sensors are plotted in Figs. 3(a)–3(c). Ruddick et al.  suggested empirical and theoretical α (λ1,λ2) parameters derived from in situ measurements and from aw(λ)  (considering wavelength independent backscattering), respectively. With λ1 taken in the red region of the spectrum (600–700 nm range), constant reflectance ratios are valid for moderately/very turbid water with ρw(λNIR) below 10−2. With λ1 taken in the NIR region of the spectrum (700–800 nm range) the constant ratios are also valid for extremely turbid waters (ρw(λNIR) > 10−2) [Figs. 3(a)–3(c)]. Accordingly, α (λ1,λ2) has a wider validity range when λ1 is taken at longer wave-lengths (> 750 nm). However, the constant α (λ1,λ2) values are not valid for ρw(λNIR) above 3.10−2. ρw(λNIR) is systematically underestimated for these water masses [Figs. 3(a)–3(c)]. This suggests that one or more assumptions made by Ruddick et al. [18, 19] are not verified with the present dataset and result in variations of the reflectance ratio α (λ1,λ2) with turbidity. Indeed, Ruddick et al. [18, 19] assumed a negligible backscattering coefficient, bb(λ), compared to the absorption a(λ) in the NIR region of the spectrum. However, in extremely turbid waters, bb(λ) may largely exceed a(λ) resulting in an asymptote for bb(λ)/(bb(λ)+a(λ)) and subsequently in ρw(λ). Since pure water absorption decreases with wavelength, the asymptote in bb(λ)/(bb(λ)+aw(λ)) is reached earlier at shorter wavelengths, explaining the flattening of the ratios with turbidity as shown in Figs. 3(a)–3(c). This is in agreement with the observations of Doxaran et al. , who showed a flattening of the reflectance ratios ρw(850)/ρw(550) and ρw(850)/ρw(650) with increasing TSM concentrations, and with the conclusions of Shi and Wang , who observed a maxima in ρw(675) for ρw(859) values greater than 0.03.
Our results also confirm the observations of Doron et al.  who observed deviations from the constant ratios of ρw(λ) in the NIR with variations in turbidity and mineral particle types. Figures 4(a–b) show the NIR reflectance ratio for the SeaWiFS bands for moderately turbid and very turbid waters, respectively. Ruddick et al.  reported for this band ratio a constant α (765,865) of 1.61 based on the pure water absorption model of Kou et al. . Similarly to Doron et al. , we observe a larger NIR reflectance ratio in moderately turbid waters (α(765,865) ∼ 1.84) and a ratio closer to 1.61 for ρw(865) values up to 10−2 [Fig. 4(b)]. For extremely turbid waters (ρw(865) > 10−2), α (765,865) is below 1.5 as noticed by Doron et al. .
Since the parameter α (λ1,λ2) appeared to vary with turbidity, the polynomial relationship suggested by Wang et al. , between ρw(λ) at 748 and 869 nm (Table 1), may be more appropriate. Their function, developed with satellite data over the western Pacific region, is validated with our in situ data for moderately turbid and very turbid waters [Figs. 4(c) and 4(d)]. A RE of 10%, a small bias (−7%) and a R2 of 99% are calculated between estimated and modeled ρw(869). About 65% of the estimated ρw(869) ranges within ± 10% of the corresponding observations. For moderately turbid waters, the constant NIR reflectance ratio of Ruddick et al.  and the polynomial function of Wang et al.  are close [Fig. 4(c)]. For very turbid waters, the function performs better than the constant NIR reflectance ratio [Fig. 4(d)]. However, the polynomial function could be further refined in order to enclose the most turbid data points where it underestimates ρw(λNIR) (see triangles in Fig. 4(d)).
The present study aimed to review spectral relationships in order to select appropriate functions which could be used as constraints to improve red or NIR-modeling schemes in current AC processes. Spectral relationships found in the literature were developed with restricted or regional datasets explaining the need of an accurate validation.
Sixteen published spectral relationships, estimating ρw(λ) in the visible or NIR spectral region, were validated using 105 highly accurate in situ above-water reflectance measurements taken in diverse coastal water types. Functions used to model ρw(λ) at 670 nm for CZCS AC processes [10–12, 15], systematically underestimated the water signal for very turbid waters. Similarly, the function suggested by Lee et al.  to estimate ρw(667) from the water signal in the green and the blue-green reflectance ratio, tends to underestimate higher ρw(667) values. In contrast, the bounding equations used in the latest version of the QAA, to evaluate maximum and minimum ρw(667) estimations according to the water signal in the green, appear to be valid for the entire range of turbidity encountered in the in situ dataset.
In the NIR spectral region, the constant reflectance ratio α (λ1,λ2), suggested by Ruddick et al. [18, 19] to extend the GW94 AC algorithm to turbid waters, was valid for moderately to very turbid waters with ρw(865 – 869) values below 10−2, while the polynomial function of Wang et al.  was also valid for extremely turbid water masses. However, the latter slightly underestimated ρw(869) for water masses with ρw(λNIR) exceeding 0.05.
From this study we can conclude that the red spectral relationships are not appropriate for the entire range of coastal turbidity encountered in our in situ dataset suggesting that either the red spectral functions need to be updated or that the functions should differ according to the optical water type and/or the turbidity range. In contrast, bounding equations, as suggested by Lee et al. , allow some variability and may thus be more appropriate to force red or NIR-modeling schemes within AC processes when a priori informations on the water type or turbidity levels are not available or when the AC procedure is expected to perform globally. The polynomial NIR function, initially developed with remote sensing reflectances over the Western Pacific , presented a satisfying fit with our in situ data.
The actual standard NASA CZCS AC procedure assumes a fixed aerosol type and includes an iteration scheme to estimate ρw(670) from inherent optical properties at 555 nm and Chla concentration estimations [4, 37–40]. Hence, in turbid waters where ρw(670) is not solely determined by algal particles, CZCS ρw(λ) retrievals may be improved by forcing the iteration scheme with the red bounding equations suggested by Lee et al. . However, to further improve red-modeling schemes, more work into developing globally valid red spectral relationships is required.
For the second generation ocean color satellite images, bounding red and NIR polynomial spectral relationships may be used to improve NIR-modeling schemes in current AC algorithms (e.g., the iteration scheme in the standard NASA AC algorithm for MODIS Aqua  and the MUMM NIR-modeling scheme [18, 19]). How these spectral relationships may lead to improved ρw(λ) retrievals, is investigated in the companion paper of this study by Goyens et al. .
Most of the in situ measurements used here were collected in the framework of the BELCOLOUR-1 and BELCOLOUR-2 projects funded by the Belgian Science Policy Office STEREO programme. Griet Neukermans and Barbara Van Mol are acknowledged for data acquisition. This work has been supported by the French Spatial Agency (CNES) through the TOSCA program and the ”Ministère de l’Enseignement et de la Recherche Française” which provided a PhD scholarship.
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