Atmospheric Correction of Satellite Ocean-Color Imagery In the Presence of Semi-Transparent Clouds

Robert Frouin1*, Lucile Duforêt2, François Steinmetz3

1Scripps Institution of Oceanography, La Jolla, California, USA 2Laboratoire d'Océanologie et de Géosciences, Wimereux, France

3HYGEOS, Euratechnologies, Lille, France

ABSTRACT

An algorithm is proposed to perform atmospheric correction of ocean-color imagery in the presence of semi-transparent clouds. The atmospheric “path” reflectance, due to scattering by molecules, aerosols, and droplets, absorption by aerosols, and reflection by the surface, including coupling terms, is modeled by a polynomial with three terms, i.e., three unknown coefficients. The marine reflectance is modeled as a function of chlorophyll concentration and a backscattering coefficient that accounts for scattering by non-algal particles (or deviation from the backscattering coefficient specified for typical phytoplankton), i.e., two additional unknown variables. The cloud transmittance, assumed constant spectrally, is estimated separately from top-of-atmosphere reflectance in the near infrared. The five unknowns are retrieved by an iterative, spectral matching scheme. The methodology, including the decomposition of the top-of-atmosphere signal and the modeling of the path reflectance, is evaluated theoretically and applied to actual MODIS imagery acquired over relatively thin clouds. Chlorophyll concentration is retrieved adequately under the clouds, and continuity is good between the cloudy and adjacent clear regions. Values are similar to those obtained with the SeaDAS algorithm in clear sky conditions, but cloud coverage is increased considerably. The algorithm is applicable operationally, but needs to be further evaluated in varied cloudy situations. Keywords: Ocean-color remote sensing, Atmospheric correction, Marine reflectance, Chlorophyll concentration

1. INTRODUCTION It is generally admitted that ocean color can be observed from space only over cloud-free areas and that the presence of a cloud definitely prevents utilization of the data. Ocean color algorithms, therefore, use a cloud filter to select clear sky observations, commonly a threshold applied to the radiance or reflectance measured in the near infrared bands of the satellite sensors. The threshold is very restrictive, and typically 15-20 % of the observed pixels pass the cloud filter. As a result Level-2 daily products are very patchy, and weekly Level-3 products show many areas with no information. This limits considerably the utility of satellite ocean color observations for biological oceanography. In the open ocean, global coverage every three to five days is necessary to resolve seasonal biological phenomena such as phytoplankton blooms. In coastal waters and estuaries, where wind forcing create “events” (e.g., upwelling) that occur every two to ten days and tidal influence may be substantial, at least daily observations are needed to describe adequately temporal changes (IOCCG, 1999; 2000; 2012). These requirements are not achieved with the present satellite systems and state-of-the-art operational algorithms. Instruments onboard multiple satellites can improve the daily ocean coverage. For example, three instruments like the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), flying in a constellation on polar orbits differing by the mean anomaly, would increase the ocean coverage from 15 to 25% over one day and from 40% to 60% over four days (Gregg et al., 1998). This option is quite costly, and coverage improvement may not be sufficient. Furthermore, it may not be available. On the other hand, ocean-color sensors in geostationary orbit would provide adequate frequency of revisit (IOCCG, 2012), but a limitation, leaving aside cost, is the degraded spatial resolution and large viewing zenith angles (i.e., difficult atmospheric correction) at high latitudes.

The cloud-free observation problem is illustrated in Fig. 1(left), which displays a cumulative histogram of the “nadir” reflectance values at 865 nm, derived from POLDER-2 observations over the ocean on 02 July 2003. (POLDER views a target at the surface in up to 14 directions, and the direction closest to nadir is retained.) 20 % of the pixels can be declared cloud-free if the reflectance threshold is set at 0.03, the current situation in operational processing, where only cloud-free pixels are used. More that 50 % pixels would be validated if a cloud correction algorithm could extend the processing to thin cloud situations, with a reflectance of up to 0.2.

Figure 1 (right) displays, as a function of latitude, the percentage of pixels that pass a cloud threshold of 0.03 and 0.20 on 02 July 2003. The percent of valid pixels is increased from 40 % to 80 % in the inter-tropical zone, and tripled at southern mid-latitudes, when using the higher cloud threshold. The percent increase in valid pixels is still very significant at northern mid-latitudes, which are stormy at that time of the year. In some cloudy situations, even in the presence of an extended cloud layer, a significant amount of photons do interact with the ocean. For a cloud albedo of 0.2, 80 % of the photons incident upon the top of the cloud layer may reach the surface, and 80% of the photons reflected by the ocean are transmitted back through the cloud layer. The transmittance along the double optical path through the cloud layer, 64%, is large. In other words, for such a cloud layer, the signal measured at satellite altitude will be sensitive to interactions with, and therefore to the characteristics of the water body. The main challenge, however, is to calculate the rather large cloud scattering and subtract it from the measurements at ocean color wavelengths. The situation is far from being desperate. Cloud scattering is due to particles of water and ice, which have a scattering cross section and a phase function nearly independent of wavelength in the visible (except in the rainbow region), because they are large and the refractive index of water and ice is nearly constant. As a result, whatever the geometry of a cloud, its scattering is practically independent of wavelength, except its interaction with molecules, an important process that needs to be considered, but whose spectral dependence is well known, aerosols, and the surface. In any case, the perturbing atmospheric signal varies smoothly with wavelength, making it possible to describe it by a simple polynomial or a few principal components. This provides the basis of the method we propose and describe in the following to estimate marine reflectance and chlorophyll concentration in the presence of a thin or broken cloud layer and, therefore, improve the spatial coverage of satellite ocean color products. In Section 2 we present a theoretical analysis of the signal measured at the top of the atmosphere in the presence of clouds and justify its modeling from accurate radiative transfer calculations. In Section 3, we describe the atmospheric correction algorithm, which includes estimating the perturbing signal, i.e., the component of the top-of-atmosphere (TOA) measurements that contains no information about the water body, and the cloud transmittance. We also evaluate theoretically the algorithm performance using an ensemble of realistic simulations. In Section 4, we apply the atmospheric correction algorithm to actual imagery from the MODerate resolution Imaging Spectrometer (MODIS) onboard Aqua, compare retrievals with those from the standard SeaDAS algorithm, and quantify the gain in spatial coverage. In Section 5, we summarize the results of the study, discuss the general applicability of the method, and provide a perspective for future work.

Figure 1: (Left) Cumulative histogram of the TOA reflectance at “nadir” observed by POLDER-2 over the global ocean on 02 July 2003. Here “nadir” refers to the direction of observation closest to nadir. (Right) Percentage of POLDER-2 pixels (observations of 02 July 2003) selected by a threshold of 0.03 and 0.2 for the “nadir” reflectance at 865 nm.

2. RADIATIVE TRANSFER MODELING 2.1 Decomposition of the TOA signal In a clear sky situation, when the influence of direct sun glint, whitecaps, and gaseous absorption is neglected, the apparent TOA reflectance of a scattering atmosphere can be expressed as (Tanré et al., 1979): ρ(θs,θv,ϕ,λ) = ρpath(θs,θv,ϕ,λ) + tma(θs,λ)tma(θv,λ)ρw(l)/[1 - ρw(λ)(Sm(λ) + Sa(λ))] (1) where θs, and θv are the sun and view zenith angles, ϕ is the relative azimuth angle between Sun and view directions, λ is the wavelength, ρpath is the atmospheric “path” reflectance defined as the reflectance generated along the optical path by scattering in the atmosphere and specular reflection of atmospherically scattered light, tma is the diffuse atmospheric transmittance along the path Sun to surface of surface to sensor, ρw is the water-body reflectance above the air-sea interface (assumed Lambertian), Sm is the spherical albedo of molecules, and Sa is the spherical albedo of aerosols. In this expression, ρ and ρpath are defined from the TOA radiance L and path radiance Lpath as ρ = πL/[Escos(θs)] and ρpath = πLpath/[Escos(θs), and ρw from the water-leaving radiance Lw as ρw = πLw/[Estma(θs)tma(θv)cos(θs)]. The atmospheric “path” reflectance is equal to: ρpath(θs,θv,ϕ,λ) = ρm(θs,θv,ϕ,λ) + ρa(θs,θv,ϕ,λ) + ρma(θs,θv,ϕ,λ) (2) where ρm is the pure-Rayleigh scattering contribution, ρa the pure-aerosol contribution, ρma the contribution due to the interaction effects between molecules and aerosols. Note that ρm, ρa, and ρma include the specular (Fresnel) reflection of atmospherically scattered light from the wavy ocean surface.

If we add a cloud layer, Eq. (1) becomes:

ρ(θs,θv,ϕ,λ) = ρpath(θs,θv,ϕ,λ) + tma(θs,λ)tma(θv,λ) tc(θs,λ)tc(θv,λ)ρw(λ)/{1 - [ρw(λ) + Ss](Sm(λ) + Sa(λ) + Sc)} (3) with ρpath(θs,θv,ϕ,λ) = ρm(θs,θv,ϕ,λ) + ρa(θs,θv,ϕ,λ) + ρma(θs,θv,ϕ,λ) + ρc(θs,θv,ϕ,λ) + ρcm(θs,θv,ϕ,λ) + ρca(θs,θv,ϕ,λ) + ρcma(θs,θv,ϕ,λ) (4) where ρc is the cloud reflectance, ρcm is the interaction term between molecules and cloud droplets, ρca is the interaction term between aerosols and cloud droplets, ρcma is the interaction term between molecules, aerosols, and cloud droplets, tc is the diffuse transmittance of the cloud layer, and Ss and Sc are the spherical albedos of the surface and cloud layer, respectively. Note, in this formulation, that ρm, ρa, ρma, Sm and Sa are the same as in the clear sky situation. Like ρm, ρa, and ρma in Eq. (2), the atmospheric terms ρc, ρca, and ρcma in Eq. (3) take into account the specular reflection of the diffuse skylight. The term [ρw + Ss](Sm + Sa + Sc) is generally much smaller than unity and therefore can be neglected, leading to the following expression for ρ(θs,θv,ϕ,λ) in the presence of a cloud layer: ρ(θs,θv,ϕ,λ) ≈ ρpath(θs,θv,ϕ,λ) + tma(θs,λ)tma(θv,λ) tc(θs,λ)tc(θv,λ)ρw(λ) (5) 2.2 Numerical simulations A synthetic database, hereafter referred to as DTB, was generated to estimate theoretically the validity of the different assumptions used in the decomposition of the TOA signal (Section 2.1) and the retrieval algorithm (described in Section 3). The calculations were performed using an accurate radiative transfer model, GAME-AD (Duforêt et al., 2007). This model accounts for scattering and absorption by air molecules, aerosols, and cloud droplets, and interactions between scattering and absorption. It is based on the plane-parallel approximation and the radiative transfer equation is solved by

means of the Adding-Doubling method (De Haan et al., 1987). Since the upward radiance is sensitive to the lower boundary conditions, reflection of the atmospheric radiation field on the sea surface is considered. A wavy sea-surface description based on Fresnel equations and the Cox-Munk wave slope probability density distribution was included in the GAME-AD code. The radiance backscattered by the water column is assumed to be diffuse after the crossing of the air-sea interface. Consequently, the ocean-atmosphere system may be described as an atmosphere above a diffusely reflecting boundary. The diffuse marine reflectance (Case 1 waters only) is modeled as a function of chlorophyll concentration according to Morel and Maritorena (2002).

The synthetic database is made up of 54, 432 000 numerical simulations carried out for a wide range of geometrical and geophysical conditions. The TOA reflectance was computed at ten wavelengths, i.e., 400, 410, 440, 490, 510, 550, 670, 765, 865 and 910 nm, for three aerosol models, namely the World Meteorological Organization (WMO) maritime (MAR), continental (CONT), and urban (URB) models. Maritime aerosols are weakly absorbing, continental aerosols are moderately absorbing, and urban aerosols are strongly absorbing, with a single-scattering albedo ω0 of 0.99, 0.89, and 0.64 at 550 nm, respectively. The computations were conducted for seven total aerosol optical thickness (ta) values of 0.05, 0.10, 0.15, 0.2, 0.3, 0.4, and 0.6 at 550 nm, and five different mixtures of continental/urban, maritime/continental, or urban/maritime aerosols. The aerosol concentration decreases with altitude according to an exponential law with a typical scale height H0 of 1, 2 or 3 km. Cloud optical properties are computed from Mie theory assuming a certain type of cloud water droplet. We considered liquid water droplets with an effective radius of 10 µm and an effective variance of 0.15. The cloud is located between 1 km and 2 km and its optical thickness at 550 nm is 2.0 (which gives a cloud albedo Ac of about 0.2). Simulations were carried out for 16 values of equally spaced sun zenith angles ranging from 0° to 75°, 18 equally spaced view zenith angle from 5° to 80°, and 5 values of relative azimuth angles, i.e., 0°, 45°, 90°, 180°, 270°. The wind speed was 3, 5, or 10 m.s-1. The diffuse boundary marine reflectance was specified for chlorophyll concentrations of 0.03, 0.3, 3, and 30 mg m-3. 2.3 Results Spectral dependency of atmospheric terms Figure 2 gives ρpath and its various components (right-hand side of Eq. 4) as a function of the wavelength for nine study cases (DTB9). The sun zenith angle is 5°, 30°, and 60°, the view zenith angle is 10°, 40°, and 75°, and the relative azimuth angle is 45°. The aerosol mixture is composed of 60% moderately absorbing aerosols and 40% weakly absorbing aerosols. The aerosol scale height is of 2 km and the total aerosol optical thickness at 550 nm, ta

550, is 0.3. The cloud optical thickness at 550 nm, tc

550, is 2.0, and the cloud is located between 1 and 2 km. The wind speed is equal to 5 m s-1. Red, blue and green curves correspond to (θs = 5°, θv =10°), (θs = 60°, θv =74°), and (θs = 60°, θv =10°), respectively. The wavelength dependence of the molecular reflectance ρm follows an λ-n law with the exponent n between 0 and 4. At small sun and view zenith angle, i.e., θs = 5° and θv =10°, ρm is quite independent of the wavelength (Fig. 2b, red curve). At large sun and view zenith angle, i.e., θs = 60° and θv =74°, ρm rather follows an λ-4 law (Fig. 2b, blue curve). Changes in n values depend on the influence of the specular reflection of the skylight onto the wavy-sea surface. At the small sun and view zenith angles of θs = 5° and θv =10°, the molecular reflectance is greatly impacted by reflections at the sea surface, which are rather wavelength independent in the visible. Indeed, the surface reflectance, ρs(λ), defined as the ratio of the reflected irradiance [(πLs(λ)] to the incoming solar irradiance [Escos(θs)] in the absence of the atmosphere, is about 0.53 at 440 nm for this geometry (Fig. 3, black solid line). At the large sun and view zenith angles of θs = 60° and θv =74°, ρs(λ) is rather weak, i.e., about 0.002 (Fig. 3, black dotted line), but multiple scattering effects are important, consequently the exponent n is close to 4, the value predicted by the Rayleigh theory. The wavelength dependence of the aerosol reflectance ρa follows an λ-n law with the exponent n between 0 (Fig. 4c red curve) and 0.8 (Fig. 4c blue curve). It is quite consistent as the aerosol content is a mixture of WMO continental and maritime aerosol, whose Angström coefficients are 0.2 and 1.2, respectively. As for the molecular reflectance, reflection on the wavy-sea surface tends to decrease the exponent n, for small view and sun zenith angles (Fig. 2c, red curve). The cloud reflectance ρc varies slightly with wavelength as the refractive index of water also varies slightly with wavelength. For a large air mass of 5.6 (θs = 60° and θv =74°), multiple scattering increases the value of ρχ, which is 4 to 8 times larger than for other θs and θv values (see the blue curve on Fig. 2d as compared with the black, green, or red ones).

The coupling terms ρma, ρmc, and ρca, are negative, whereas the coupling term ρcma is positive (Fig. 3). Comparison of Fig. 2a and Fig. 3a-e shows that in most cases, these coupling terms and their sum cannot be negligible as they are the same order of magnitude as ρpath. In the following, for clarity, we will discuss Fig. 3a-c in terms of ρma, ρmc, and ρca absolute values. For a large air mass of 5.6 (θs = 60° and θv =74°), the coupling terms are large (Fig. 3a-d, blue curves) as multiple scattering events increase on the optical path. For (θs = 5° and θv =10°), the coupling terms are still large in spite of a smaller air mass (2.0), because the surface reflectance ρs is important (0.53 at 440 nm). In this case, the multiple reflections between the sea-surface and the skylight increase the probability for a photon to be scattered many times. The coupling terms are small for (θs = 60° and θv =10°) (green curves on Fig. 3a-d) because the sea surface reflectance is small (ρs(440) = 0.002, Fig. 4 black dotted line), increasing the probability for a photon to be absorbed by the surface, and multiple scattering events in the atmosphere are less important as for (θs = 60° and θv =74°). Reflection on the rough sea surface impacts the spectral dependency of the coupling terms in the same way as for the molecular, aerosol, and cloud reflectance. Indeed, for (θs = 5° and θv =10°) (Fig. 3, red curves), they are rather wavelength-independent. For other geometries, ρcma and the absolute values of ρma ρcm, and ρca decrease with wavelength. As the molecular and aerosol scattering decreases with wavelength, multiple interactions decrease so the coupling terms are smaller. Note that, the spectral dependency and the order of magnitude of the atmospheric terms displayed in Figs. 2 and 3 are not modified significantly if we change the wind speed, the aerosol properties (type, optical thickness, and scale height), and the relative azimuth angle except for ϕ = 0° because of glitter pattern (but this case is not considered here, remember that Eq. 2 is valid when the glitter influence is neglected). Figure 5 displays the spectral dependency of transmittances tc (Fig. 5a) and tma (Fig. 5b) according to the sun zenith angle. Similar figures would be obtained for the spectral dependency of tc and tma according to the view zenith angle. Note that transmittances are simulated over a black surface as defined in Eq. (2), and (4) according to Tanré et al. (1979).

Figure 2: Spectral dependence of atmospheric reflectance for nine studied cases (DTB9) as a function of the geometry (θs, θv). (a) Reflectance for an atmosphere with molecules, aerosols and clouds. (b) Molecular reflectance. (c) Aerosol reflectance. (d) Cloud reflectance. Red, blue, and green curves correspond to (θs = 5°, θv = 10°), (θs = 60°, θv = 74°), and (θs = 60°, θv = 10°), respectively. The relative azimuth angle is of 45°.

The cloud transmittance tc is slightly dependent of wavelength (Fig. 5a). For example, changes in tc values are less than 2% when the wavelength varies from 407 to 913 nm. The very slight decrease in tc can be explained by a very slight decrease of the single scattering albedo for water droplets, i.e., ω0 = 0.9998 at 913 nm instead of 0.9999 at 407 nm.

Figure 4: Sea surface reflectance, at 440 nm, due to the specular reflection of the diffuse skylight as function of the geometry. The relative azimuth angle is of 45°.

Figure 3: Spectral dependence of coupling terms for nine studied cases (DTB9) as a function of the geometry (θs, θv). Reflectance due to interactions between: (a) molecules and aerosols, (b) molecules and clouds, (c) aerosols and clouds, and (d) molecules, aerosols, and clouds. . Red, blue, and green curves correspond to (θs = 5°, θv = 10°), (θs = 60°, θv = 74°), and (θs = 60°, θv = 10°), respectively. The relative azimuth angle is of 45°.

Notice that cloud water droplets absorb at large wavelengths, for example ω0 = 0.8965 at 4 µm. The cloud transmittance decreases with the sun zenith angle. For θs = 5° (Fig. 5a solid line), the cloud transmittance at 440 nm is 0.91 whereas it is 0.74 for θs = 60° (Fig. 5a dotted line). Indeed, when θs increases, multiple scattering events are more frequent and increase the probability for a photon to be absorbed by the ground. Spectral variations in are quite important (Fig. 5b). For example, for θs = 30° (Fig. 5b dashed line), tma is equal to 0.70 at 407 nm, whereas it is equal to 0.90 at 913 nm. The decrease of tma at short wavelength can also be explained by multiple scattering events, which increase in number. Like tc, tma decreases with the sun zenith angle. For example, tma at 440 nm is 0.74 when θs = 5°, whereas it is 0.57 when

θs = 60°. Decomposition of the TOA reflectance The accuracy of Eq. (5) is quantified by comparing the real and apparent TOA reflectance (ρreal and ρ, respectively) from 407 to 670 nm, from theoretical computations of DTB. The real reflectance is computed for an atmosphere including molecules, aerosols and a cloud layer, reflection of the skylight on the wavy sea-surface, and the diffuse boundary marine reflectance. The apparent reflectance is calculated according to Eq. (5) considering separately the atmospheric and marine reflectance. So, the atmospheric path reflectance ρpath is simulated with the diffuse boundary reflectance equal to zero. The transmittances of the cloud layer and of the atmosphere with aerosols and molecules are simulated considering a black surface according to Tanré et al. (1979). Differences are quantified by the mean absolute percentage difference (ΔD), the root-mean-square error (RMSE), and the bias (δ): ΔD(%) = (100/N) ∑i = 1,…,N [Abs(ρi

real – ρi)/ρi] (6) RMSE = [(1/N) ∑i = 1,…,N (ρi

real – ρi)2]1/2 (7) δ = (1/N) ∑i = 1,…,N (ρi

real – ρi) (8) where N is the number of study cases. The apparent reflectance is then regressed against the real one using a least-square fit. The slope (A), intercept (B) and coefficient of determination (R2) are summarized in Table 1. Because of the large number of numerical simulations (54, 432 000), statistics are not calculated over the whole DTB (too time consuming on this large dataset using the R

Figure 5: Spectral dependence of the transmittance for an atmosphere (a) with clouds only, and (b) with aerosols and molecules. Solid, dashed and dotted lines correspond to θs = 5°, 10°, and 60°, respectively.

software). Comparisons are presented for the different chlorophyll concentrations cited above (0.3, 3.0 and 30.0 mg m-3) and for two sun zenith angles of 5° and 60°. Firstly, statistics were calculated considering reflectance from 400 to 670 nm (Table 1). Differences between the real and apparent TOA reflectance are very small as the RMSE is less than 1.10-

5, the bias in absolute value is less than 3.10-4, the intercept is rather null, and the coefficient of determination is close to 1.0. Note that, the mean relative difference is less than 0.35%. Statistics were also calculated only for reflectance at 410

nm and 670 nm (Tables 2 and 3). Similar results as those displayed in Table 1 are obtained. This analysis shows that [ρw + Ss](Sm + Sa + Sc) <<1 and can be neglected, whatever the wavelength. Consequently, we can consider that the decomposition of the TOA reflectance according to Eq. (5) is correct; therefore it will be used in the proposed algorithm.

Atmospheric functions The atmospheric path reflectance, ρpath, varies smoothly as a function of wavelength (Fig. 3c). It can therefore be well approximated by a polynomial with a few terms, i.e.: ρpath ≈ a0 λ-l + a1 λ-m + a2 λ-n (9) where l, m, and n are non-negative integers. Twenty combinations of (l, m, n) exponents were tested, with the (l, m, n) exponents varying between 0 and 5. They correspond to the number of 3-combinations for a set with 6 elements. Among the 20 (l, m, n) combinations, the (0, 1, 4) combination gives the smaller differences between real and modeled atmospheric path reflectance (results for the various combinations are not shown here), i.e., the polynomial a0 + a1 λ−1 + a2 λ-4 provides the most accurate representation of ρpath. The mean absolute percentage difference ΔD, the RMSE, and the

bias δ are calculated according to Eqs. (6), (7), and (8), with ρi the atmospheric path reflectance as modeled by the polynomial (Eq. 9) and ρi

real the real atmospheric path

Table 1: Comparison between the ‘real’ and the apparent (as modeled by Eq. 5) TOA reflectance from 400 to 670 nm. The number of theoretical simulations is 6 ×7 × 85,050 = 3,572,100.

Table 4: Comparison between the atmospheric reflectance modeled by the a0 + a1 λ-1 + a2 λ-4 polynomial and the ‘real’ one from 407 to 913 nm. The sun zenith angle is of 5°, 30° and 60°. The number of theoretical simulations is 3 x 850, 500 = 2,551,500.

Table 2: comparison between the ‘real’ and the apparent (as modeled by Eq. 5) TOA reflectance at 410 nm. The number of theoretical simulations is 6 ×85,050 = 510,300.

Table 3: Comparison between the ‘real’ and the apparent (as modeled by Eq. 5) TOA reflectance at 670 nm. The number of theoretical simulations is 510,300..

reflectance as computed with GAMEAD. Agreement is good between real and modeled atmospheric reflectance as ΔD, the RMSE, and the bias are small (Table 4). The slope of the regression between real and modeled values and the coefficient of determination are very close to 1. Figure 6 displays the statistical distribution of the relative error (ρpath

real - ρpath)/ρpath

real. Maximum errors reach 3%. However, for a sun zenith angle of 60°, 95% of the errors are between -1% and 1%. For sun zenith angles of 5° and 30°, they become 96% and 98%, respectively. Note that the same polynomial has already been used in the POLYMER algorithm designed to retrieve ocean color parameters in the sun glint pattern (Steinmetz et al., 2011). Moreover, it is in agreement with the spectral shape of the different atmospheric terms presented in Figs. 3 and 4, i.e., the various terms can be interpreted physically. The a0 term accounts for a spectrally flat component, for example the cloud reflectance; the a1λ-1 term accounts for a signal with a weak spectral dependence, for example the aerosol reflectance; and the a2λ-4 term accounts for a signal with a strong spectral dependence, for example the molecular reflectance or the coupling between scattering my molecules and droplets. The actual spectral dependencies of the various atmospheric components may vary, as illustrated in Fig. 1c. These variations of spectral dependency will by automatically taken into account in the polynomial fitting process, leading to a balance between the three terms a0, a1, and a2.

The clear sky atmospheric transmittance tma in Eq. (5) can be modeled accurately according to Tanré et al. (1979): tma ≈ exp[-(τm + τa)]exp[(0.52τm + γaτa)/cos(θ)] (10) where tm and ta are the molecule and aerosol optical thickness, respectively, θ denotes solar or viewing zenith angle, and γa = (1 + <cosΘ>a)/2 where <cosΘ>a is the anisotropic factor of the aerosol scattering phase function. The parameter γa is fairly constant for most aerosol models and equal to 0.66 (Tanré et al., 1979), which gives for tma: tma ≈ exp[-(0.48τm + 0.17τa)/cos(θ)] (11)

3. ATMOSPHERIC CORRECTION ALGORITHM 3.1 General Description The algorithm does not retrieve marine reflectance directly, but parameters that govern marine reflectance, from which marine reflectance can be computed. It is based on Eq. (5), which becomes, using Eq. (9) and Eq. (11): ρ(λ) ≈ a0 + a1 λ-1 + a2 λ-4 + exp{-[0.48τm(λ) + 0.17τa(λ)]m} Tc ρw(λ, C, bbs) (12) where Tc is the total cloud transmittance along the path Sun to surface and surface to sensor (depends on θs and θv), C is

Figure 6: Relative difference between the “real” path reflectance computed by GAMEAD and the path reflectance modeled by the a0 + a1 λ-1 + a2 λ-4 polynomial. The sun zenith angle is of 5°, 30° and 60°.

the chlorophyll concentration, bbs is a coefficient introduced to account for deviations from the backscattering coefficient of “average” phytoplankton and/or backscattering by non-algal particles, and m is the air mass [m = 1/cos(θs) + 1/cos(θv)]. In Eq. (12), the symbols denoting geometry have been dropped for clarity. The cloud transmittance Tc is assumed constant with wavelength, a good approximation (see Section 2.3 and Fig. 6a). It is estimated separately from measurements in the near infrared (see Section 3.2 below). The marine reflectance ρw is related to C via the reflectance model of Morel and Maritorena (2001). A more complicated reflectance model could be used to account for phytoplankton variability and the eventual presence of other constituents whose concentrations do not co-vary with C, but this would make the inversion problem more difficult. The aerosol optical thickness τa is specified from satellite climatology, which is justified since its impact on the second term of Eq. (12) is generally small, especially over the open ocean (low aerosol content). For an aerosol optical thickness of 0.1 and an air mass of 3, the impact of aerosols on the marine signal, i.e., the last term on the right-hand side of Eq. (12), is only 5%. Once Tc is determined, the inversion problem is reduced to retrieving the parameters a0, a1, a2, C, and bbs from ρ measurements in a number of spectral bands in the visible and near infrared. This can be accomplished using a spectral matching scheme, see for example Steinmetz et al. (2011) for the POLYMER algorithm. Since ρpath generally dominates ρ, molecular reflectance ρm, which can be calculated accurately as a function of surface pressure and wind speed, is beforehand subtracted from ρ. Note that including Tc as part of the set of unknown parameters to retrieve by the spectral matching scheme would make the inversion less robust and unstable. 3.2 Estimation of cloud transmittance TOA reflectance observations in the near infrared (e.g., 869 nm for MODIS), where clouds do not absorb, molecular scattering is reduced (scattering by aerosols, molecules, and droplets are less coupled), and the water body is generally black, are used to estimate the cloud transmittance Tc. The modeling is based on plane-parallel theory, and the effects of clouds and other constituents are decoupled. The planetary atmosphere is therefore modeled as a clear-sky atmosphere positioned above a cloud/surface layer. This approach was shown to be valid by Frouin and Chertock (1992) to estimate surface solar irradiance from satellite data. The various steps to estimate Tc are described below. First, the cloud albedo Ac(θs), assumed independent of wavelength (see Section 2), is obtained from the TOA reflectance in the selected spectral band centered on λk in the near infrared, ρ(θs,θv,ϕ,λk), following Tanré et al. (1979). Taking into account the bidirectional character of the cloud/surface layer reflectance, we have: ρ(θs,θv,ϕ,λk) ≈ ρma(θs,θv,ϕ,λk)] + [ρc’(θs,θv,ϕ,λk) -Ac’ (θs) ]B(θs,θv) + Ac’(θs)C(θs,θv) (13) B(θs,θv) = exp[-(τm + τa)m] C(θs,θv) = exp[-(0.48τm + 0.17τa)m] where ρma is the intrinsic atmospheric reflectance due to molecules and aerosols (represents photons that have not interacted with the cloud/surface layer), and ρc’ and Ac’ are the bidirectional reflectance and albedo of the cloud/surface layer, respectively. Eq. (13) can be written as: ρ(θs,θv,ϕ,λk) ≈ ρma(θs,θv,ϕ,λk)] + [Ac(θs)/F(θs,θv,ϕ) - Ac (θs)]B(θs,θv) + [Ac(θs) - As(θs)]C(θs,θv) (14) where F is a bidirectional reflectance factor to convert cloud bidirectional reflectance into albedo (F = Ac/ρc), and As is the surface albedo (essentially due to Fresnel reflection). In this expression, ρc’ and Ac’ are approximated by ρc + As and Ac + As, respectively. This allows one to compute the cloud albedo as:

Αc(θs ) ≈ [ρ(θs,θv,ϕ,λk) - ρma(θs,θv,ϕ,λk- As(θs)C(θs,θv)]/[B(θs,θv)/F(θs,θv,ϕ) - B(θs,θv) + C (θs,θv)] (15) In Eq. (15), the bidirectional reflectance factor F is computed according to Zege (1991), for a typical thin and extended liquid water cloud with a Henyey-Greenstein scattering phase function (anisotropy factor of 0.844) from Hansen (1969).

The surface albedo As is parameterized as a function of angular geometry and wind speed according to Jin et al. (2004). The reflectance ρma is modeled using the quasi single-scattering approximation: ρma = (τmPm + ωaτaPa)/[4cos(θs)cos(θv)] (16) where Pm and Pa are the respective phase functions of molecules and aerosols, and ωa is the single scattering albedo of aerosols. The aerosol optical parameters are specified from satellite climatology, since they are not determined in the presence of clouds. Since F and As depend on cloud optical thickness, τc, and total optical thickness, respectively, the initial τc is replaced by the estimated τc (step described below) in a second iteration. Second, the cloud optical thickness τc, defined for an extinction efficiency factor of 2, is obtained from Ac(θs) according to Coakley and Chylek (1975), and then used to compute Tc(θs,θv): τc = cos(θs)Ac(θs) /{βc(θs)[(1 – Ac(θs)]} (17) Tc(θs,θv) = [1 - Ac(θs)]{ 1 - [βc(θv)τc/cos(θv)]/[1 + βc(θv)τc/cos(θv)]} (18) where the backscattering coefficient βc is taken from Stephens (1978). Other models relating Ac to τc may be used alternatively, e.g., Fitzpatrick et al. (2004).

4. APPLICATION TO MODIS IMAGERY Figure 7 displays MODIS imagery of the Bay of Biscay acquired on 29 April 2005, showing semi-transparent clouds in the center of the bay. In the RGB image (Fig. 7, left), the broad ocean features can be distinguished through the thin clouds. Bright mesoscale eddies are observed, suggesting the presence of reflective phytoplankton species, perhaps

coccolithophores. In the 869 nm TOA reflectance image (Fig. 7, right), the significant impact of the clouds is revealed, preventing the retrieval of ocean color products by the standard SeaDAS algorithm when the reflectance is above typically 0.03, i.e., in a major part of the image. The modified POLYMER algorithm was applied to the MODIS imagery of Fig. 7, to retrieve C, bbs, and therefore ρw in all the area of the image for which the TOA signal was not saturated in the 748 nm spectral band. The saturated areas are depicted in white. Figure 8 displays the estimated cloud optical thickness τc and cloud transmittance Tc, obtained using

Figure 7: MODIS imagery of the bay of Biscay, 29 April 2005, showing thin clouds. (Left): True color image. (Right): TOA reflectance at 869 nm.

TOA observations in the 869 nm spectral band. The τc values are in the range 0-0.8, and Tc varies from 0.85 to 1. Note that Tc is not exactly equal to 1 in some clear areas, which may be partly due to uncertainties in the aerosol properties (taken from climatology).

Figure 9 displays the resulting C (Fig. 9, right) in comparison with the SeaDAS C (Fig. 9, left). Values are similar with both algorithms. The modified POLYMER algorithm retrieves values in almost all the area excluded by the SeaDAS algorithm (depicted in gray). Spatial coverage is increased by 31.4% (from 67.5% to 98.9%). The spatial field of C

exhibits continuity between cloudy areas and adjacent clear areas. A band of relatively higher C near the shelf break off Brittany, a known feature resulting from lifting of the thermocline by internal waves, is completely characterized when using the modified POLYMER algorithm. The bbs values (Fig. 10) are relatively high, reaching 0.04 m-1 in the region of mesoscale eddies, which confirms the presence of more reflective species than the “average” phytoplankton of the Morel and Maritorena (2002) model.

Figure 8: Cloud Optical thickness (left) and cloud transmittance (right) estimated by the modified POLYMER algorithm for MODIS imagery of the Bay of Biscay, 29 April 2005.

Figure 9: Chlorophyll concentration estimated from SeaDAS (left) and modified POLYMER algorithm (right) for MODIS imagery of the Bay of Biscay, 29 April 2005. Spatial coverage is increased by 31.4% using the modified POLYMER algorithm.

Figures 11 and 12 display the retrieved ρw in selected spectral bands, i.e., centered on 412 and 547 nm, respectively, by the modified POLYMER and SeaDAS algorithms (right and left panels, respectively). The spatial field of ρw is less noisy when obtained with the modified POLYMER algorithm, especially in the blue, and the values are slightly larger. This is evidenced in the ρw histograms of Fig. 13, which also shows unrealistic negative values in the 667 nm spectral band and some very small values in the 412 nm band with the SeaDAS algorithm. The C histograms (Fig. 12) indicate, however, a small shift toward higher values with the modified POLYMER algorithm, despite the generally lower ρw

SeaDAS values in the blue.

Figure 10: (Left): bbs (m-1) obtained from the modified POLYMER algorithm for MODIS imagery of the Bay of Biscay, 29 April 2005. (Right): Histogram of bbs values. The high values indicate the presence of reflective phytoplankton species, possibly coccolithophores.

Figure 11: Marine reflectance at 412 nm estimated from SeaDAS (left) and modified POLYMER algorithm (right) for MODIS imagery of the Bay of Biscay, 29 April 2005.

5. CONCLUSIONS Atmospheric correction of ocean-color imagery can be performed through semi-transparent clouds. This was demonstrated by applying a modified POLYMER algorithm to MODIS imagery of the Bay of Biscay. The algorithm separately determines cloud transmittance from observations in the near infrared, where clouds are not absorbing, the

Figure 12: Marine reflectance at 547 nm estimated from SeaDAS (left) and modified POLYMER algorithm (right) for MODIS imagery of the Bay of Biscay, 29 April 2005.

Figure 13: Histograms of marine reflectance at 421, 547, and 667 nm and chlorophyll concentration obtained by SeaDAS and the modified POLYMER algorithm.

ocean is generally black, and coupling between the various scattering processes is reduced. The estimates of chlorophyll concentration and marine reflectance exhibited spatial continuity from cloud-free areas to cloudy areas. In clear sky conditions, the values were comparable to those retrieved with the standard SeaDAS algorithm. The algorithm can be applied operationally. The MODIS cloud optical thickness product could be used directly to estimate cloud transmittance. Even though the findings are promising, application to other cloud situations and evaluation against in situ measurements is still necessary to definitely conclude about algorithm accuracy. By processing some cloud situations, the daily ocean coverage 15-20% with standard algorithms, is expected to increase substantially. For the MODIS imagery of the Bay of Biscay, spatial coverage increased from 67.5% to 98.9%. This will allow a better description of biological phenomena, such as phytoplankton blooms. The increase coverage will improve the operational utility of ocean color data from space, and may lead to important new information about the temporal variability of biological processes.

ACKNOWLEDGMENTS The National Aeronautics and Space Administration and the National Atmospheric and Oceanic Administration provided funding for this work. The technical support of Mr. John McPherson, Scripps Institution of Oceanography, University of California at San Diego, is gratefully acknowledged.

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