1. Introduction

The marine reflectance measured just above the water surface, ρ_w(λ) (also referred to as ${\rho }_w^{0+}$(λ) or normalized water-leaving reflectance [1]), 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 ρ_w(λ). This processing includes, among others, the removal of the atmospheric contribution, the so-called atmospheric correction (AC) [1]. The top of atmosphere reflectance, ρ^TOA(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, ${\rho }_{\mathit{rc}}^{\mathit{TOA}}$(λ) [1]:

At the time of the Coastal Zone Color Scanner (CZCS) satellite, the initial AC procedure assumed zero ρ_w(λ) at 670 nm allowing to retrieve the atmospheric contributions from the total signal [2] (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 [1] suggested to apply the black pixel assumption to the NIR spectral bands allowing to estimate ${\rho }_a^{\mathit{TOA}}$(λ_NIR) and ${\rho }_{\mathit{ra}}^{\mathit{TOA}}$(λ_NIR) 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 ρ_w(λ) is not valid neither in the red nor in the NIR region of the spectrum [3, 4]. Assuming zero red or NIR ρ_w(λ) in such water masses leads to an overcorrection of the atmospheric effects and subsequently to an underestimation of ρ_w(λ) [3].

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 ρ_w(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 ρ_w(λ_NIR) 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 [9].

Another approach to extent the GW94 AC procedure to turbid waters, consists of forcing the AC process with spectral relationships estimating red or NIR ρ_w(λ) by means of ρ_w(λ) at shorter wavelengths (i.e., ρ_w(λ_j) = f (ρ_w(λ_i))). 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 ρ_w(λ) retrievals where current AC algorithms fail.

For the CZCS AC, empirical spectral relationships have been proposed to estimate ρ_w(670) from ρ_w(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. [17] 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 ρ_w(λ_NIR) for the AC of second generation ocean color satellite images (hereafter referred to as the NIR spectral relationships) [18–20]. Lee et al. [21] also suggested to correct remote sensing ρ_w(667) estimations (due, for instance, to imperfect AC) for the Quasi-Analytical Algorithm by means of spectral relationships between ρ_w(667) and ρ_w(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. [22] 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 ρ_w(λ) at shorter wavelengths. Most spectral relationships encountered in the literature were initially developed for the CZCS sensor to retrieve ρ_w(λ_red). 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. [4] and Bailey et al. [5] modeling ρ_w(λ_NIR) according to ρ_w(λ_red)).

With the arrival of SWIR ocean color bands, a similar exercise could be performed to evaluate spectral relationships allowing to estimate ρ_w(λ) in the NIR from ρ_w(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. [23] 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 [2]. 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 [15]. Therefore, red-modeling schemes have been developed based on, e.g., spectral relationships to estimate the water signal at 670 nm from ρ_w(λ) at shorter wavelengths. Smith and Wilson [10] and Austin and Petzold [11] related ρ_w(670) with the reflectance ratio ρ_w(443)/ρ_w(550) and the amplitude of reflectance at either 443 or 520 nm (Table 1). According to Austin and Petzold [11] using the reflectance at 520 nm was more appropriate to account for variations in non-algal particles while the ratio ρ_w(443)/ρ_w(550) accounts for the pigment concentrations.

Table 1. Review of the spectral relationships and their applications

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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) [24]. Hence, Sturm [13] 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). ρ_w(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 [11], turbid near coastal waters [12] and in situ measurements taken in the northern Adriatic Sea (AAOT data) [12].

Viollier and Sturm [14] observed simple linear relations between ρ_w(670) and ρ_w(550) as a function of the water type. In the turbid coastal waters of the eastern English Channel, ρ_w(670) represented 40% of ρ_w(550) while, over a coccolithophorid bloom, it represented only 15%. In order to satisfy both water types, Viollier and Sturm [14] proposed a non-linear relationship similar to Smith and Wilson [10] and Austin and Petzold [11], but including the ρ_w(520)/ρ_w(550) ratio instead of the blue-green ratio ρ_w(443)/ρ_w(550) (Table 1).

Similarly to Sturm [13], Bricaud and Morel [15] 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 (Chl_a) absorption bands ratio ρ_w(443)/ρ_w(670) and the blue-green ratio ρ_w(443)/ρ_w(550) (Table 1). When the water type could not be defined as turbid or clear, Bricaud and Morel [15] used an intermediate relationship similar to the model of Smith and Wilson [10] (Table 1).

The OCEAN code, developed to process the level-2 European CZCS historical data [16], used both the relations of Viollier and Sturm [14] and Bricaud and Morel [15] within the red-modeling scheme to correct CZCS images for atmospheric contribution in turbid waters. According to a first guess for ρ_w(443) (based on the Black Pixel Assumption), the algorithm iterates with either the reflectance function of Viollier and Sturm [14] (ρ_w(443) < 3.10⁻⁵) or the function of Bricaud and Morel [15] (ρ_w(443) > 3.10⁻⁵) to account for non-zero ρ_w(670).

Inspired by the CZCS red-modeling scheme proposed by Viollier and Sturm [14], Nicolas et al. [17] 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 ρ_a(670) as the difference between the observed and modeled ρ_w(λ). According to Nicolas et al. [17], this approach was satisfactory for most cases except for waters with high yellow substance absorption.

The Quasi Analytical Algorithm (QAA v.5) [21], used to derive the inherent optical properties from satellite ρ_w(λ) estimations, includes three spectral relationships to correct erroneous satellite retrieved ρ_w(667). ρ_w(667) values are constrained within an upper and lower range defined by two spectral functions relating ρ_w(λ) at 667 and 555 nm (Table 1). When the retrieved ρ_w(667) is missing or out of limit, ρ_w(667) is estimated from ρ_w(555) and the ratio ρ_w(490)/ρ_w(555) (Table 1).

As observed in Table 1, some spectral relationships are written in terms of sub-surface radiance, L_ss(λ) or remote sensing reflectance, R_rs(λ). For data analysis all functions are expressed here in terms of ρ_w(λ). L_ss(λ) and R_rs(λ) are converted into ρ_w(λ) following Morel and Gentili, [26] and considering the approximation for the ratio (1−r_F)/n_w (with r_F being the Fresnel reflectance and n_w the water refractive index) suggested by, e.g., Bricaud and Morel [15], Morel and Gentili [26], and Mobley [27].

3. NIR spectral relationships

Constant reflectance ratios in the NIR region of the spectrum were suggested by Ruddick et al. [18]. With assumptions on the backscattering and absorption in the NIR, the authors approximated ρ_w(λ₁)/ρ_w(λ₂) by the water absorption ratio a_w(λ₂)/a_w(λ₁) (with λ₁ and λ₂ being two wavelengths in the NIR). Ruddick et al. [19] 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. [19] also suggested theoretical values for α (λ₁,λ₂) based on the pure water absorption spectrum of Kou et al. [28] 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 [19]. A similar conclusion was made by Shi and Wang [29] who observed a quasi linear relationship between ρ_w(645) and ρ_w(859) for ρ_w(859) values below 0.03. For waters with ρ_w(859) above this threshold, ρ_w(λ) at 645 nm saturated and remained almost constant (∼ 0.012). Doron et al. [23] also observed some deviations from the constant reflectance ratio with both in situ and satellite derived data. According to that study, for ρ_w(865) between 10⁻⁴ and 10⁻², α (765,865) varied little between 1.73 and 1.84 as suggested by Ruddick et al. [19], but decreased with an increase in turbidity.

Wang et al. [20] 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, ρ_w(λ) is retrieved with the GW94 AC algorithm allowing to calculate the water diffuse attenuation coefficient at 490 nm, K_d(490) [30]. Next, polynomial relations are used to estimate ρ_w(748) from K_d(490) and ρ_w(869) from ρ_w(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 [9]. Although the GOCI NIR-modeling scheme provided satisfying results in the western Pacific region [20, 31], the polynomial relationship between ρ_w(748) and ρ_w(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 [32], 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. [19].

Out of the 860 stations, 105 in situ reflectance spectra satisfy the selection criteria and were not used by Ruddick et al. [19] 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 ρ_w(λ_NIR) values above 10⁻⁴, which is approximately the limit of validity for the black pixel assumption [3]. Out of the 105 spectra, 53% presents moderate turbidity with ρ_w(869) ranging from 10⁻⁴ to 3.10⁻³ and 47% of the data presented very turbid waters with ρ_w(869) exceeding 3.10⁻³. This latter value corresponds to the threshold used by Wang et al. [9] to switch for the SWIR algorithm in the combined NIR-SWIR GW94-based AC algorithm.

Table 2. Statistics of the 105 ρ_w(λ) (dimensionless) spectra for the ocean color bands of MODIS Aqua in the 412–869 nm range.

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Figure 1 shows the spectra in the 400–900 nm range and the red-NIR reflectance spectra normalized at 780 nm (ρ_wn780(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.

 

Fig. 1 Selected ρ_w(λ) spectra between 400 and 900 nm and reflectance spectra normalized at 780 nm, ρ_wn780(λ), in the 600–900 nm range.

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According to Doxaran et al. [35], 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 ρ_wn780(λ) spectra [Fig. 1(b)]. As observed by Ruddick et al. [19], 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 ρ_wn780(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 ρ_w(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 ρ_w(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 ρ_w(670) are given in Table 3. Most functions tend to underestimate ρ_w(670) (negative bias ranging from −3 to −63%). Two functions indicate a positive bias, notably, the function of Sturm [12] 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 ρ_w(670) values below 0.05 but largely underestimate ρ_w(670) values above this threshold. The relations from Smith and Wilson [10], Austin and Petzold [11], Bricaud and Morel [15] for the Case 2 waters, Nicolas et al. [17], and Viollier and Sturm [14] 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 ρ_w(670) retrievals (Table 1). Indeed the relation of Viollier and Sturm [14] 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 [14] over a coccolithophorid bloom (multiplication factor of 0.15) and Nicolas et al. [17] (multiplication factor of 0.2) (Table 1).

Table 3. Statistical performance of spectral relationships in the red (av. RE: average Relative Error, av. Bias: average Bias and RMSE: Root Mean Square Error)

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As mentioned in Section 2, the algorithm described in the OCEAN code for the CZCS AC over turbid coastal waters [16] used the function of Viollier and Sturm [14] to model ρ_w(670) when the retrieved ρ_w(443) was below 3.10⁻⁵ and the Case 1 and 2 spectral relationships of Bricaud and Morel [15] otherwise. Although none of our in situ ρ_w(443) values are below 3.10⁻⁵, the reflectance function of Viollier and Sturm [14] yields better ρ_w(670) retrievals (Table 3).

Similarly to the other spectral relationships, the relation suggested by Lee et al. [21] to estimate ρ_w(667) when it is missing or erroneously retrieved (i.e, outside the bounding equations, Table 1), tends to underestimate larger ρ_w(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 ρ_w(667) according to ρ_w(555) correspond to the limit of our in situ data [Fig. 2(a)].

 

Fig. 2 (a) In situ ρ_w(667) versus ρ_w(555) including the upper and lower bounds to constrain ρ_w(667) as suggested by Lee et al. (2009), and observed versus modeled ρ_w(670) according to the spectral relationships suggested by (b) Austin and Petzold (1980) in Sturm (1983), (c) Sturm (1981, used for the CZCS AC over turbid waters) in Sturm (1983) and (d) Sturm (1981, developed with AAOT data) in Sturm (1983).

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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 [11] and the two spectral relationships of Sturm [12] in [13]. 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 [14]. The maximum validity range in Table 3 and the plots in Figs. 2(b)–2(d) indicate that these functions largely underestimate ρ_w(670) when the marine signal is greater than 0.03, which corresponds to very turbid waters (ρ_w(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 [19], ρ_w(λ₁) versus ρ_w(λ₂) for the NIR bands of the SeaWiFS, MERIS and MODIS sensors are plotted in Figs. 3(a)–3(c). Ruddick et al. [19] suggested empirical and theoretical α (λ₁,λ₂) parameters derived from in situ measurements and from a_w(λ) [28] (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 ρ_w(λ_NIR) 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 (ρ_w(λ_NIR) > 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 ρ_w(λ_NIR) above 3.10⁻². ρ_w(λ_NIR) 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, b_b(λ), compared to the absorption a(λ) in the NIR region of the spectrum. However, in extremely turbid waters, b_b(λ) may largely exceed a(λ) resulting in an asymptote for b_b(λ)/(b_b(λ)+a(λ)) and subsequently in ρ_w(λ). Since pure water absorption decreases with wavelength, the asymptote in b_b(λ)/(b_b(λ)+a_w(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. [36], who showed a flattening of the reflectance ratios ρ_w(850)/ρ_w(550) and ρ_w(850)/ρ_w(650) with increasing TSM concentrations, and with the conclusions of Shi and Wang [29], who observed a maxima in ρ_w(675) for ρ_w(859) values greater than 0.03.

 

Fig. 3 Reflectance ratio in the red and the NIR for (a) SeaWiFS: ρ_w(865) versus ρ_w(670) and ρ_w(765), (b) MODIS: ρ_w(869) versus ρ_w(678) and ρ_w(748), and (c) MERIS: ρ_w(865) versus ρ_w(705) and ρ_w(775). The constant α (λ₁,λ₂) suggested by Ruddick et al. (2006) based on in situ measurements and on a_w(λ) (Kou et al., 1993) are represented for each reflectance ratio by a plain and dashed line, respectively. Horizontal grey lines indicate the limit between moderately turbid and very turbid waters (3.0⁻³).

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Our results also confirm the observations of Doron et al. [23] who observed deviations from the constant ratios of ρ_w(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. [19] reported for this band ratio a constant α (765,865) of 1.61 based on the pure water absorption model of Kou et al. [28]. Similarly to Doron et al. [23], we observe a larger NIR reflectance ratio in moderately turbid waters (α(765,865) ∼ 1.84) and a ratio closer to 1.61 for ρ_w(865) values up to 10⁻² [Fig. 4(b)]. For extremely turbid waters (ρ_w(865) > 10⁻²), α (765,865) is below 1.5 as noticed by Doron et al. [23].

 

Fig. 4 ρ_w(765) versus ρ_w(865) according to Ruddick et al. (2006) (R, dashed line) and Doron et al. (2011) (D, grey bands) for (a) moderately turbid and (b) very turbid waters and ρ_w(748) versus ρ_w(869) for (c) moderately turbid and (d) very turbid waters with the polynomial function proposed by Wang et al. (2012) (W, plain grey line) and the constant ratio proposed by Ruddick et al. (2006) (R, dashed line). Spectra from extremely turbid coastal waters of French Guiana described in Section 4 are indicated by a triangle.

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Since the parameter α (λ₁,λ₂) appeared to vary with turbidity, the polynomial relationship suggested by Wang et al. [20], between ρ_w(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 ρ_w(869). About 65% of the estimated ρ_w(869) ranges within ± 10% of the corresponding observations. For moderately turbid waters, the constant NIR reflectance ratio of Ruddick et al. [19] and the polynomial function of Wang et al. [20] 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 ρ_w(λ_NIR) (see triangles in Fig. 4(d)).

6. Conclusion

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 ρ_w(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 ρ_w(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. [21] to estimate ρ_w(667) from the water signal in the green and the blue-green reflectance ratio, tends to underestimate higher ρ_w(667) values. In contrast, the bounding equations used in the latest version of the QAA, to evaluate maximum and minimum ρ_w(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 ρ_w(865 – 869) values below 10⁻², while the polynomial function of Wang et al. [20] was also valid for extremely turbid water masses. However, the latter slightly underestimated ρ_w(869) for water masses with ρ_w(λ_NIR) 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. [21], 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 [20], 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 ρ_w(670) from inherent optical properties at 555 nm and Chl_a concentration estimations [4, 37–40]. Hence, in turbid waters where ρ_w(670) is not solely determined by algal particles, CZCS ρ_w(λ) retrievals may be improved by forcing the iteration scheme with the red bounding equations suggested by Lee et al. [21]. 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 [5] and the MUMM NIR-modeling scheme [18, 19]). How these spectral relationships may lead to improved ρ_w(λ) retrievals, is investigated in the companion paper of this study by Goyens et al. [22].