Importance and estimation of aerosol vertical structure in satellite ...

Importance and estimation of aerosol vertical structure in satellite ocean-color remote sensing Lucile Duforêt, Robert Frouin, and Philippe Dubuisson

The vertical distribution of absorbing aerosols affects the reflectance of the ocean-atmosphere system. The effect, due to the coupling between molecular scattering and aerosol absorption, is important in the visible, especially in the blue, where molecular scattering is effective, and becomes negligible in the near infrared. It increases with increasing Sun and view zenith angles and aerosol optical thickness and with decreasing scattering albedo but is practically independent of wind speed. Relative differences between the top of the atmosphere reflectance simulated with distinct vertical distributions may reach approximately 10% or even 20%, depending on aerosol absorption. In atmospheric correction algorithms, the differences are directly translated into errors on the retrieved water reflectance. These errors may reach values well above the 5 ⫻ 10⫺4 requirement in the blue, even for small aerosol optical thickness, preventing accurate retrieval of chlorophyll-a [Chl-a] concentration. Estimating aerosol scale height or altitude from measurements in the oxygen A band, possible with the polarization and directionality of the Earth’s reflectance instrument and medium resolution imaging spectrometer, is expected to improve significantly the accuracy of the water reflectance retrievals and yield acceptable [Chl-a] concentration estimates in the presence of absorbing aerosols. © 2007 Optical Society of America OCIS codes: 010.0010, 010.1110.

1. Introduction

In ocean-color studies, information about chlorophyll-a [Chl-a] concentration or particles suspended in water is obtained from the water-leaving radiance. When retrieved from space, the water-leaving radiance represents a small fraction (10% or less) of the total top of the atmosphere (TOA) radiance,1,2 thus efficient atmospheric correction algorithms must be applied to remove the influence of the scattering by molecules and aerosols, absorption by aerosols, and reflection by the surface. Current atmospheric correction algorithms3– 6 assume that aerosols are either located below molecules or that their concentration decreases with altitude following an exponential law with a typical aerosol scale height. The treatment is not satisfactory for some aerosol types, especially absorbing aerosols, dustlike or pollution type, as pointed out by Gordon.4 L. Duforêt ([email protected]) and P. Dubuisson ([email protected]) are with the Ecosystèmes Littoraux et Côtiers, Université du Littoral Côte d’Opale, 32 Avenue Foch, 62930 Wimereux, France. R. Frouin ([email protected]) is with the Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0224, USA. Received 11 July 2006; accepted 22 September 2006; posted 20 October 2006 (Doc. ID 72541); published 12 February 2007. 0003-6935/07/071107-13$15.00/0 © 2007 Optical Society of America

For these aerosols, coupling between absorption by aerosols and scattering by molecules tends to decrease the TOA radiance, but strongly depends on the vertical distribution of the aerosols. Consequently, using a fixed distribution may result in large, unacceptable errors on the water-leaving radiance. Gordon4 and Ding and Gordon7 have provided examples of the errors on water-leaving radiance. Even if the aerosol models are determined correctly, depending on vertical structure the retrieved values may be in error by as much as ten times the inaccuracy requirement for biological applications, i.e., ⫾5 ⫻ 10⫺4, at 490 nm, for case I waters.4,6 The situations analyzed were limited and Gordon4 indicated that more study is required for a quantitative assessment of the impact of vertical structure in a strongly absorbing atmosphere. In this study the impact of the aerosol vertical structure on performance of standard atmospheric correction algorithms is analyzed in detail. Varied aerosol amounts and types, as well as geometric conditions, are considered. An accurate radiative transfer model of the coupled ocean-atmosphere system is used in the simulations, in which absorption-scattering interactions are taken into account carefully. The resulting errors on water-leaving radiance, or equivalently reflectance, and [Chl-a] concentration are quantified. A method is proposed to estimate the aerosol scale 1 March 2007 兾 Vol. 46, No. 7 兾 APPLIED OPTICS

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height or altitude from polarization and directionality of the Earth’s reflectance (POLDER) or medium resolution imaging spectrometer (MERIS) measurements in the 763 nm oxygen A band, and its accuracy is evaluated. In view of the method’s accuracy, potential improvements for retrieval of water reflectance and [Chl-a] concentration are investigated. 2. Top of the Atmosphere Reflectance Simulations

Reflectance ␳共␪s, ␪v, ⌬␾, ␭兲 is defined from radiance L共␪s, ␪v, ⌬␾, ␭兲 as ␳共␪s, ␪v, ⌬␾, ␭兲 ⫽

␲L共␪s, ␪v, ⌬␾, ␭兲 , Es cos ␪s

(1)

where ␪s and ␪v are the Sun and view zenith angles, ⌬␾ is the relative azimuth angle equal to ␾s ⫺ ␾v with ␾s and ␾v the Sun and view azimuth angles, respectively, ␭ is the wavelength of the radiation, and Es is the solar constant outside the atmosphere. The TOA reflectance is simulated from visible to near infrared with a radiative transfer model accounting for molecule and aerosol scattering, aerosol and gas absorption, and interactions between scattering and absorption.8 The model is based on the plane-parallel atmosphere approximation, and the radiative transfer equation, describing radiative processes, is numerically solved with the adding-doubling method.9 For each atmospheric layer, the adding-doubling method requires as an input gaseous absorption optical thickness and scattering parameters, namely, phase function, single-scattering albedo, and scattering optical thickness. The phase function of the mixture of aerosols and molecules is defined as the weighted average of molecule and aerosol phase functions, where the weights are the corresponding scattering optical thicknesses. The gaseous absorption optical thickness needed to estimate the transmittance is calculated using a high spectral resolution line-by-line (LBL) code.10 However, the LBL approach is time consuming and is used only when the gas contribution needs to be accounted accurately such as in the oxygen A band. The gaseous absorption optical thickness can also be calculated at a moderate spectral resolution by a simplified code based on the correlated k distribution approximation.11–13 This approach is less time consuming but less accurate and is used when the effect of gaseous absorption on the signal is not predominant. Since the upward reflectance is sensitive to the lower boundary conditions, reflection of the atmospheric radiation field on the surface has to be taken into account accurately. So a wavy sea-surface description based on Fresnel equations and the Cox– Munk wave slope probability density distribution is included in the model.14 For the purpose of this study, the ocean (water body) is considered totally absorbing, so multiple crossings at the air–sea interface are not taken into account. Thus in the simulations, the water reflectance is null, and the TOA reflectance is equal to the atmospheric path reflectance generated 1108

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by the solar radiation scattered by the atmosphere and its interaction with the surface plus the surface reflectance due to sunglint. Reflection by individual whitecaps is neglected, which is adequate for the purpose of our study, and, in general, for low surface wind speeds because the surface area covered by whitecaps is small, and so, on average (at the scale of a pixel), reflection is weak. The model8 has been successfully compared with a successive-orders-of-scattering reference model.15 Discrepancies are smaller than the instrumental noise of MERIS, one of the most accurate sensors. The model has been also used to simulate POLDER measurements.16 Observations and numerical simulations agree with respect to the uncertainties on aerosol properties.8 Thus the model accuracy is sufficient to process satellite data from remote sensing and can be used for this study. 3. Impact of Aerosol Vertical Distribution on the Top of the Atmosphere Reflectance A.

Study Cases

Gordon,4 Gordon et al.,17 and Ding and Gordon7 showed that the TOA signal depends significantly on the aerosol vertical distribution when the aerosols are absorbing. In his conclusions, Gordon4 recommended that a quantitative analysis should be carried out to assess more precisely the impact of aerosol profile. Following this recommendation, through a sensitivity study, the impact on the TOA reflectance is quantified as a function of aerosol properties and observation geometry. The impact of aerosol vertical distribution on the TOA reflectance is investigated for two absorbing aerosol models, namely, the World Meteorological Organization (WMO) continental (CONT) and urban (URB) models.18 The aerosol optical properties are computed from Mie theory using the refractive indices, and particle size distributions provided by the WMO database.18 Continental aerosols are moderately absorbing with a single-scattering albedo ␻0共550兲 of 0.89 at 550 nm, and urban aerosols are strongly absorbing with a ␻0共550兲 of 0.64. Simulations show that the impact of vertical structure is negligible for weakly absorbing aerosols [␻0共550兲 of 0.99] represented by the WMO maritime model. Consequently, the results for maritime aerosols are not shown in the paper. The study compares the TOA reflectance obtained with three distinct aerosol vertical distributions. In the first one, aerosols are located between 0 and 0.7 km in the boundary layer below molecules.19 In the second one, aerosol concentration decreases with altitude according to an exponential law with a typical scale height H0 of 2 km.4 In the third one, aerosols are located in a layer between 4 and 5 km because certain aerosol types, such as dustlike or pollution type, often occur in altitude. Note that the first two distributions are currently used in atmospheric correction schemes. The TOA reflectance has been computed for small, moderate, and large aerosol amounts, i.e., the optical thickness

Table 1. Upper and Lower Limits in TOA Reflectancea

⌬共H0 ⫽ 2 km兾4–5 km兲 ␭ (nm) 412.5 490 560

Principal Plane ␶A(550) 0.1 1.0–3.0 0.5–2.5 0.0–2.0

⌬共4–5 km兾0–0.7 km兲

Perpendicular Plane ␶A(550)

0.6 5.5–8.5 2.5–7.0 1.0–5.5

0.1 2.0–3.0 1.5–2.0 1.1–1.5

Principal Plane ␶A(550)

0.6 7.0–8.0 5.0–6.0 3.5–4.5

0.1 2.0–6.0 0.5–4.5 0.0–3.5

0.6 14.0–23.0 5.5–17.5 2.5–12.5

Perpendicular Plane ␶A(550) 0.1 4.5–6.0 3.0–4.0 2.0–3.0

0.6 18.0–22.0 11.5–14.5 7.5–9.5

a

Upper and lower limits of the relative difference (%) in TOA reflectance due to the vertical distribution of strongly absorbing aerosols (URB) for a ␪s of 30° and a surface wind speed w of 2 m s⫺1.

at 550 nm, ␶A共550兲, is equal to 0.1, 0.3, and 0.6. Comparisons are made for two Sun zenith angles ␪s of 30° and 60°, view zenith angles ␪v from 0° to 70°, and relative azimuth angles ⌬␾ of 0° and 180° (principal plane) and 90° and 270° (perpendicular plane). Two values of the surface wind speed, w of 2 and 10 m s⫺1, are used. Gaseous absorption is included in the simulations assuming a standard midlatitude summer atmosphere. The impact of aerosol vertical distribution on the TOA reflectance is simulated in the visible and the near infrared. It is practically null in the near infrared whatever the aerosol amount and model.4 Consequently, results are presented for only three visible spectral bands, ⬃10 nm wide, commonly used in ocean-color remote sensing, i.e., 412.5, 490, and 560 nm. B.

Results

To compare the TOA reflectance computed with the different vertical distributions, relative differences in absolute value are calculated as follows: ⌬共H0 ⫽ 2 km兾4–5 km兲 ⱍ␳共H0 ⫽ 2 km兲 ⫺ ␳共4–5 km兲ⱍ ⫻ 100 共%兲, ⫽ ␳共H0 ⫽ 2 km兲 ⌬共4–5 km兾0–0.7 km兲 ⱍ␳共4–5 km兲 ⫺ ␳共0–0.7 km兲ⱍ ⫻ 100 共%兲, ⫽ ␳共4–5 km兲

(2)

(3)

where ␳共H0 ⫽ 2 km兲, ␳共4–5 km兲, and ␳共0–0.7 km兲 are the TOA reflectances computed using an aerosol concentration following an exponential law with H0 of 2 km and using aerosols located between 4 –5 and 0–0.7 km. ⌬共H0 ⫽ 2 km兾0–0.7 km兲 is calculated in the same way as ⌬共H0 ⫽ 2 km兾4–5 km兲, but it is not

detailed in the study because it is always of the same order of magnitude as ⌬共H0 ⫽ 2 km兾4–5 km兲. The ⌬s were calculated as a function of view zenith angle ␪v up to 70°, an upper limit in ocean color remote sensing. The upper and lower limits of the ⌬ ranges are presented in Tables 1 and 2 for strongly or moderately absorbing aerosols. First, the effect of aerosol vertical structure decreases as wavelength decreases. As an example, for strongly absorbing aerosols, the ⌬ values in the perpendicular plane are approximately two times smaller at 560 nm than at 412.5 nm. Second, the ⌬ values increase with the aerosol amount. For strongly absorbing aerosols, the upper limits of the ⌬ ranges are approximately three or four times larger for ␶A of 0.6 than for ␶A of 0.1. Third, the effect increases with aerosol absorption. The ⌬共4–5 km兾 0–0.7 km兲 value reaches 23% for urban aerosols and approximately 10% for continental ones. Fourth, in the perpendicular plane, relative differences are of approximately the same order of magnitude as in the principal plane, except that the lower limit of the ⌬ range is a bit larger. In the principal plane, the intensity of reflected light in the glitter pattern is strong and dominates the TOA signal and tends to mask the effect of the aerosol vertical distribution. In the perpendicular plane, glitter effects are small or null, so minimum differences in TOA reflectance are a bit larger. Further computations with ␪s of 60° show that the effect of vertical structure is stronger for a higher Sun zenith angle. This is related to the higher concentration of absorbing and scattering particles on the light path, related to the air mass, equal to 1兾cos ␪s ⫹ 1兾cos ␪v. However the TOA reflectance is larger at ␪s of 60° than at ␪s of 30°, and the ⌬ values at a ␪s of 60° are quite similar to those at a ␪s of 30°.

Table 2. Same as Table 1 But for Moderately Absorbing Aerosols

⌬共H0 ⫽ 2 km兾4–5 km兲 ␭ (nm) 412.5 490 560

Principal Plane ␶A(550) 0.1 0.0–1.5 0.0–1.0 0.0–1.0

0.6 1.0–5.0 0.0–4.0 0.0–2.5

⌬共4–5 km兾0–0.7 km兲

Perpendicular Plane ␶A(550) 0.1 0.5–1.0 0.5–0.6 0.3–0.5

0.6 2.5–3.5 1.5–2.0 0.9–1.0

Principal Plane ␶A(550) 0.1 0.5–2.0 0.0–1.5 0.0–1.0

0.6 2.5–9.5 0.0–6.5 0.0–4.0

Perpendicular Plane ␶A(550) 0.1 1.0–1.5 0.5–1.0 0.3–0.5

0.6 5.0–6.5 2.5–3.5 1.0–1.5

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Note that, in spite of being composed mainly of dustlike particles, the CONT model is intended to be representative of an aerosol background from continental origin and cannot characterize desert dust. Biomass burning aerosols are not well represented by the WMO models. Therefore the impact of vertical distribution is also investigated for dust and biomass burning models whose optical properties were retrieved from Aerosol Robotic Network (AERONET) groundbased measurements.20 For biomass burning aerosols, when compared with continental aerosols, the ⌬s have the same order of magnitude because the essential parameter ␻0 related to the absorption is rather similar. For dust aerosols, the effect of vertical structure is less important than for continental aerosols but remains significant. Since the results for biomass burning aerosols or dust are similar to those for moderately absorbing aerosols, they will not be discussed further in this study. The influence of surface roughness on the above results has been tested. Relative differences are computed as previously but for a rough sea-surface driven by a wind speed w of 10 m s⫺1. Conclusions are similar to the ones obtained for w of 2 m s⫺1. Minimum and maximum relative differences are almost identical. 4. Impact of Aerosol Vertical Distribution on the Retrieval of Water Reflectance and Chlorophyll Concentration A.

Signal Decomposition

The purpose of the atmospheric correction is to retrieve the water reflectance from the total signal backscattered to space by the water body, surface, and atmospheric system. The total reflectance at the TOA, at a wavelength ␭ in the absence of whitecaps, can be written as ␳t共␭兲 ⫽ ␳path共␭兲 ⫹ T共␭兲␳g共␭兲 ⫹ t共␭兲␳w共␭兲,

(4)

where ␳path共␭兲 is the atmospheric path reflectance, ␳g共␭兲 is the sunglint reflectance, T共␭兲 is the direct atmospheric transmittance, t共␭兲 is the total diffuse atmospheric transmittance, and ␳w共␭兲 is the water reflectance. The ocean is assumed totally absorbing in the computations allowing separation of the perturbing signal from the signal containing information on the water body. In other words, our radiative transfer model allows computations of ␳path共␭兲 or ␳path共␭兲 ⫹ T共␭兲␳g共␭兲, in the presence of sunglint. In ocean-color remote sensing, however, sunglint conditions are avoided to enhance the contribution of photons that have interacted with the water body, i.e., the term t共␭兲␳w in Eq. (4). The atmospheric path reflectance can be written as19 ␳path共␭兲 ⫽ ␳R共␭兲 ⫹ ␳A共␭兲 ⫹ ␳RA共␭兲,

(5)

where ␳R共␭兲 is the reflectance from multiple scattering by air molecules in the absence of aerosols, ␳A共␭兲 1110

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is the reflectance resulting from multiple scattering in the absence of air molecules, and ␳RA共␭兲 is the “coupling term” between Rayleigh and aerosol scattering. The terms ␳R共␭兲, ␳A共␭兲, and ␳RA共␭兲 account for the specular reflection of the atmospherically scattered radiation by the sea surface. In atmospheric correction algorithms, ␳R共␭兲 can be easily computed and subtracted from ␳path共␭兲 because the Rayleigh phase function is well known, and the Rayleigh optical thickness can be calculated according to surface pressure. Thus, atmospheric correction algorithms attempt to determine ␳A共␭兲 ⫹ ␳RA共␭兲. Consequently, it is more relevant to compare differences in ␳A共␭兲 ⫹ ␳RA共␭兲 than in ␳path共␭兲. When ␳R共␭兲 is removed from ␳path共␭兲, the differences due to the vertical structure of strongly or moderately absorbing aerosols can be larger than the signal itself, i.e., they can represent more than 100% of ␳A共␭兲 ⫹ ␳RA共␭兲. B.

Error on the Water Reflectance Retrieval

According to Eq. (4), outside the glitter pattern, the atmospheric correction errors due to aerosol vertical distribution occur on ␳path共␭兲 and can be directly related to ␳w共␭兲. To a first approximation, the water reflectance is assumed to be isotropic. As shown by Yang and Gordon,21 the total diffuse transmittance is independent of the aerosol vertical distribution even if the aerosol is strongly absorbing. Therefore the ⌬␳w共␭兲 error on the water reflectance can be written as ⌬␳path共␭兲兾t共␭兲. The transmittance t共␭兲 is dependent on ␪s and ␪v and is exactly calculated by means of our radiative transfer model considering molecule and aerosol scattering and aerosol and gas absorption. It is relatively small at large view zenith angles when aerosols strongly absorb compared with moderately absorbing aerosols. The ⌬␳w共␭兲 errors are equal to ⌬共␭, H0 ⫽ 2 km兾4–5 km兲兾t共␭兲 when atmospheric correction algorithms consider that the concentration of aerosols follows an exponential law with H0 of 2 km, whereas the aerosols are actually confined between 4 and 5 km. Figures 1 and 2 display ⌬␳w共␭兲 equal to ⌬共␭, H0 ⫽ 2 km兾4–5 km兲兾t共␭兲 at 490 and 560 nm as a function of ␪v. The Sun zenith angle is 30°, and the aerosols are urban or continental with an optical thickness of 0.1 and 0.6. Only results in the backward principal plane (⌬␾ of 180°) and in the perpendicular plane (⌬␾ of 90°) are presented, since forward principal plane conditions are generally avoided in ocean-color remote sensing. ⌬␳w共␭兲 is larger at 490 nm than at 560 nm. This is directly related to ⌬共H0 ⫽ 2 km兾4–5 km兲, which is larger at shorter wavelengths. ⌬␳w increases with the view and Sun zenith angles, and the aerosol absorption and optical thickness, because ⌬共H0 ⫽ 2 km兾 4–5 km兲 increases whereas the diffuse transmittance decreases. The errors on water reflectance are a bit larger in the backward principal plane. This is related to the values of the scattering angle ⌰. For a Sun zenith angle of 30°, the angle ⌰ varies from 150° to 180° in the backward principal plane and from 115° to 150° in the perpendicular plane. Besides, the Rayleigh scattering function slightly increases when

Fig. 1. Error ⌬␳w on the water reflectance at 490 nm when atmospheric correction algorithms suppose that the aerosol concentration follows an exponential law with H0 of 2 km whereas aerosols are actually between 4 and 5 km. ⌬␳w is given for a ␶A共550兲 of 0.1 or 0.6 and for (a) strongly (URB) or (b) moderately (CONT) absorbing aerosols with a ␪s of 30°. Relative azimuth angles are 90° and 180°.

⌰ increases from 90° to 180°. The Rayleigh scattering is, therefore, a bit more effective in the backward principal plane because ⌰ reaches larger values. Consequently, ⌬共H0 ⫽ 2 km兾4–5 km兲 is larger because the impact of the aerosol vertical distribution depends on the interaction between molecule scattering and aerosol absorption. In atmospheric correction algorithms, the accuracy threshold required on ␳w共␭兲 is 5 ⫻ 10⫺4 at 490 nm and 2 ⫻ 10⫺4 at 560 nm.4,6 For moderately absorbing aerosols, the simulations show that ⌬␳w共␭兲 is smaller than the accuracy threshold for a small optical thickness (i) in the backward principal plane as long as ␪v is less than 10° at 490 nm and 5° at 560 nm, (ii) in the perpendicular plane as long as ␪v is less than 40° whatever ␭ [Figs. 1(b) and 2(b)]. For strongly absorb-

ing aerosols, the ⌬␳w共␭兲 values are always unacceptable whatever the wavelength, the aerosol amount and the view zenith angle. For example, ⌬␳w共490兲 is 2 ⫻ 10⫺3 and ⌬␳w共560兲 is 8 ⫻ 10⫺4 for a small aerosol optical thickness in the perpendicular plane and for a ␪v of 40° [Figs. 1(a) and 2(a)]. Note that the ⌬␳w values at 490 and 560 have also been calculated for a high Sun zenith angle of 60° but results are not presented, since ⌬␳w values are always unacceptable whatever the wavelength, the view zenith angle, the aerosol type and amount. Even more unacceptable errors are made on the water reflectance when ⌬␳w共␭兲 is ⌬共␭, 4–5 km兾 0–0.7 km兲兾t共␭兲, i.e., when aerosols are between 4 and 5 km but are assumed between 0 and 0.7 km, because ⌬共␭, 4–5 km兾0–0.7 km兲 is larger than ⌬共␭, H0 ⫽

Fig. 2. Same as Fig. 1 but ⌬␳w is given at 560 nm. 1 March 2007 兾 Vol. 46, No. 7 兾 APPLIED OPTICS

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Fig. 3. Relative error (%) of the [Chl-a] due to aerosol vertical structure. The actual (prescribed) [Chl-a] is 0.03 mg m⫺3, and ␪s is 30°.

2 km兾4–5 km兲 (see Subsection 3.B). The simulations thus indicate that the aerosol vertical distribution has to be known to retrieve, with the desired accuracy, the water reflectance from the total TOA reflectance. They confirm, for a wider range of situations, the findings of Ding and Gordon7 and Gordon.4 C. Error on the Chlorophyll Concentration Retrieval

For case 1 waters, the near-surface [Chl-a] concentration can be predicted from the irradiance reflectance spectrum Rw共␭兲 by means of a bio-optical semiempirical model.22 The irradiance reflectance, also called the irradiance ratio, is defined as the ratio of the upward flux Eu共0⫺, ␭兲 and downward flux Ed共0⫺, ␭兲 just below the sea surface. Using the reflectance ratio at 490 and 560 nm, [Chl-a] can be estimated by the following polynomial22: log关Chl-a兴 ⫽ a0 ⫹ a1Y ⫹ a2Y 2 ⫹ a3Y 3,

(6)

where Y ⫽ log关Rw共490兲兾Rw共560兲兴. If an error ⌬Rw共␭兲 is made on Rw共␭兲 at 490 and 560 nm due to the aerosol vertical distribution. Y is modified as follows:

冋

Y⬘ ⫽ log

册

Rw共490兲 ⫹ ⌬ Rw共490兲 , Rw共560兲 ⫹ ⌬ Rw共560兲

(7)

and an estimated [Chl-a] concentration can be obtained by using Y= in Eq. (6). Note that errors calculated in Subsection 4.B are not on irradiance ratios below the surface but water reflectance above the surface. However ␳w共␭兲, assumed to be isotropic, can be approximately related to Rw共␭兲 using a proportionality factor23,24: ␳w共␭兲 ⫽ 1112

␲Lw共␭, 0⫹兲 Ed共␭, 0⫹兲

⯝ 0.54 Rw共␭兲,

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(8)

where Lw共␭, 0⫹兲 is the water-leaving radiance and Ed共␭, 0⫹兲 is the downward solar flux just above the surface. Equation (7) then becomes

冋

Y⬘ ⯝ log

册

Rw共490兲 ⫹ ⌬␳w共490兲兾0.54 . Rw共560兲 ⫹ ⌬␳w共560兲兾0.54

(9)

The error on [Chl-a], due to ⌬␳w, is expressed in terms of relative error (%) ⌬关Chl-a兴 ⫽

关Chl-a兴actual ⫺ 关Chl-a兴estimated , 关Chl-a兴actual

(10)

where the actual (prescribed) [Chl-a] is 0.03, 0.3, or 3.1 mg m⫺3. Figures 3–5 display the relative error ⌬关Chl-a兴. ⌬关Chl-a兴, like ⌬␳w共␭兲, depends on the Sun and view angles, and on aerosol optical thickness and type. In the following, ⌬关Chl-a兴 errors are discussed with respect to the accuracy goal of ⫾35% for biological applications as recommended by Hooker et al.25 First, differences between the actual and the estimated [Chl-a] are more important when aerosols strongly absorb as shown in Figs. 3, 4, and 5. This is due to larger errors on the water reflectance (see Subsection 4.B). Second, [Chl-a] of 0.03 or 0.3 mg m⫺3 is overestimated, whereas the larger [Chl-a] of 3.1 mg m⫺3 is underestimated. For a [Chl-a] of 0.03 mg m⫺3, 关Rw共490兲 ⫹ ⌬Rw共490兲兴兾关Rw共560兲 ⫹ ⌬Rw共560兲兴 is smaller than Rw共490兲兾Rw共560兲, and the estimated [Chl-a] is higher than the actual one. When [Chl-a] increases, Rw共490兲 decreases exponentially whereas Rw共560兲 remains fairly constant or slightly increases. For a [Chl-a] of 3.1 mg m⫺3, Rw共490兲 is small, and 关Rw共490兲 ⫹ ⌬Rw共490兲兴兾关Rw共560兲 ⫹ ⌬Rw共560兲兴 can be larger than Rw共490兲兾Rw共560兲, yielding too low [Chl-a] estimates. Third, the same type of reasoning also explains why, with moderately absorbing aerosols, the [Chl-a] of 0.3 mg m⫺3 is a bit underestimated

Fig. 4. Same as Fig. 3, but for an actual [Chl-a] concentration of 0.3 mg m⫺3.

in the perpendicular plane for a ␶A共550兲 of 0.6 and overestimated in the backward principal plane irrespective of ␶A共550兲 [Fig. 4(b)]. Interestingly, ⌬[Chl-a] decreases for ␪v above 60° in the perpendicular plane even though ⌬Rw共490兲 and ⌬Rw共560兲 increase with ␪v. In this case, the relative differences ⌬Rw共490兲兾 Rw共490兲 and ⌬Rw共560兲兾Rw共560兲 become similar, reducing the error in the reflectance ratio. The conditions, i.e., observation geometry and aerosol optical thickness, for which [Chl-a] is estimated with an accuracy goal to within ⫾35%, are given in Table 3 for a ␪s of 30°. The [Chl-a] of 0.3 mg m⫺3 is well estimated whatever the aerosol type and amount. Unacceptable estimates are generally obtained at low and high [Chl-a], except when aerosols are moderately absorbing or when the aerosol amount is low. Note that ⌬关Chl-a兴 has also been calculated for ␪s of 60° but is

not presented since ⌬关Chl-a兴 is larger. In fact, when ␪s is 60°, [Chl-a] is correctly estimated only for very small ␪v. 5. Improvements Knowing the Aerosol Vertical Distribution

The current atmospheric correction algorithms of the Sea-viewing Wide Field-of-View Sensor (SeaWIFS) and MERIS have been adapted by Gordon4 and Antoine and Morel,6 respectively, to retrieve the water reflectance in the presence of both nonabsorbing and absorbing aerosols. However, absorbing aerosols are not accounted for in the SeaWIFS data analysis system (SeaDAS) code used to generate the standard SeaWIFS products and publicly available. The vertical structure of absorbing aerosols is included by combining a given distribution with an aerosol type to define

Fig. 5. Same as Fig. 3, but for an actual [Chl-a] concentration of 3.1 mg m⫺3. 1 March 2007 兾 Vol. 46, No. 7 兾 APPLIED OPTICS

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Table 3. Conditions of View Zenith Angle ␪va

Strongly Absorbing Aerosols [Chl-a] (nm) 0.03 0.3 3.1

⌬␾ ⫽ 180° ␶A(550)

⌬␾ ⫽ 90° ␶A(550)

Moderately Absorbing Aerosols ⌬␾ ⫽ 180° ␶A(550)

⌬␾ ⫽ 90° ␶A(550)

0.1 0.6 0.1 0.6 0.1 0.6 0.1 0.6 — — — ⱕ40° — ⱕ65° — —b ⬍70° ⱕ65° ⱕ70° ⱕ70° ⱕ70° ⱕ45° ⱕ70° ⱕ70° ⱕ45° — ⱕ55° — ⱕ65° — ⱕ70° —

Error of the estimated [Chl-a] is less than 35% (␪s ⫽ 30°). —indicates that errors of the estimated [Chl-a] are larger than 35% for all view zenith angles. a b

a new candidate model. This method does not consider the vertical structure as an independent parameter, and the accuracy of the atmospheric correction is related to the number of assemblages considered. Another algorithm has been developed by Thieuleux26 and applied to POLDER measurements. Knowledge of aerosol vertical structure is not required, but multidirectional data are needed, and currently only a few sensors allow such measurements. Here we propose to use measurements in the oxygen A band, possible with the POLDER instrument or MERIS, to obtain independent information of the aerosol vertical distribution. A.

Estimation of the Aerosol Vertical Distribution

Interaction between oxygen absorption and multiple scattering due to aerosols can provide information about the vertical distribution of aerosols. Previous studies have shown the role of aerosol scattering on the signal measured in the oxygen A band.11,27,28 Indeed, in the spectral range of the oxygen A band (759 to 770 nm), the reflected solar radiation measured at the top of the atmosphere depends on the oxygen absorption, surface reflectance, and vertical distribution of scatterers (aerosols and molecules). Over the ocean, the effect of atmospheric components is predominant, since the surface reflectance is small. Oxygen absorption as well as Rayleigh scattering depends on the surface pressure, which can be obtained accurately from meteorological models. Consequently, measurements of oxygen absorption over the ocean should provide information about the aerosol vertical distribution, at least in theory. Note that this determination will be not possible for bright surfaces (over land or in sunglint conditions), because most of the signal at the TOA comes from the surface in this case. Oxygen absorption can be estimated from space, using data from the POLDER instrument or MERIS. Indeed, these two radiometers have two adequate spectral bands in the oxygen A band. These bands are centered at 763 nm (10 nm wide) and 765 nm (40 nm wide) for the POLDER instrument and 761.75 nm (3.75 nm wide) and 753.75 nm (7.5 wide) for MERIS. The signal in bands at 763 and 761.75 nm is strongly attenuated by oxygen absorption, whereas the signal in the other bands is only partially attenuated. As an 1114

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Fig. 6. Aerosol layer altitude ZA 共km兲 as a function of the reflectance ratio using the oxygen A band channels of POLDER. Simulations are presented for ␪s of 0°, 30°, and 60°, and for ␪v of 30° and ⌬␾ of 0°, assuming an urban aerosol model with an optical thickness ␶A共550兲 of 0.3.

example, the mean altitude of a 1 km thick urban aerosol layer is reported in Fig. 6 as a function of the POLDER reflectance ratio R, i.e., ratio of the reflectance at 763 nm, ␳共763兲, to the reflectance at 765 nm, ␳共765兲, simulated with the radiative transfer model described in Section 2. The curves in Fig. 6 show that it is possible to estimate the altitude of an aerosol layer over dark surfaces from absorption in the oxygen A band if the aerosol model and optical thickness and the observation geometry are known. Simulations have been carried out to assess theoretically the sensitivity of the reflectance measured by POLDER in the oxygen A band to the surface reflectance 共␳s兲, the aerosol model, and the altitude of a 1 km thick aerosol layer 共ZA兲. The reflectance at 765 nm, ␳共765兲, and the reflectance ratio, R ⫽ ␳共763兲兾␳共765兲, were simulated for different observation angles and for three aerosol amounts. Table 4 presents the changes in ␳共765兲 and in ␳共763兲兾␳共765兲 due to ⌬ZA of 1 km, a ⌬␳s of 0.01 and a change of the aerosol model, i.e., from moderately to strongly absorbing aerosols. Table 4 shows that the reflectance ratio ␳共763兲兾 ␳共765兲 is sensitive to the altitude of the aerosol layer, whereas ␳共765兲 is insensitive. ␳共763兲兾␳共765兲 and especially ␳共765兲 depend strongly on the surface reflectance and on the aerosol model and optical thickness. First, the surface reflectance ␳s is due mostly to Table 4. Sensitivity of the Reflectance in the Oxygen A Band Measured by POLDER

Reflectance Ratio R ⫽ ␳(763)兾␳(765)

Reflectance at 765 nm ␳(765) ␶A(550) 0.1 0.3 0.6

⌬␳s

⌬Model

⌬ZA

0.0072 0.0031 0.0001 0.0063 0.0070 0.0003 0.0052 0.0105 0.0005

␶A(550) 0.1 0.3 0.6

⌬␳s

⌬Model

⌬ZA

0.0161 0.0019 0.0077 0.0099 0.0027 0.0138 0.0058 0.0039 0.0176

Table 5. Theoretical Accuracya (km) on the Aerosol Layer Altitude ZA

Model Dust

Continental

Urban

␶A(550)

0.1

0.3

0.6

0.1

0.3

0.6

0.1

0.3

0.6

POLDER

2

0.7

0.4

1.2

0.5

0.4

0.7

0.4

0.3

a

The accuracy (i.e., rms error) has been estimated from simulations assuming an uncertainty of ⫾1% on the reflectance ratio, three aerosol models, and three ␶A values at 550 nm and various Sun and view zenith angles (␪s ⫽ 0°, 30°, and 60°; ␪v ⫽ 0° to 60°, ⌬␾ ⫽ 0° to 180°).

Fresnel reflection and can be estimated as a function of the Sun and view zenith angles in the POLDER observation geometry. Second, the effect of aerosol model and optical thickness is reduced in the reflectance ratio of close channels ␳共763兲兾␳共765兲. To a first approximation, ␳共765兲 and ␳共763兲 are governed by single scattering and are rather proportional to ␻0共␭兲pA共␭兲␶A共␭兲 with pA共␭兲 the aerosol phase function. The effect of the aerosol model and optical thickness related to ␻0共␭兲pA共␭兲␶A共␭兲 is compensated in the reflectance ratio. The proposed method consists in simulating ␳共765兲 and ␳共763兲兾␳共765兲 as a function of the aerosol model, ZA, ␶A, ␳s, ␪s, ␪v, and ⌬␾ to obtain parameterizations as in Fig. 6. The simulations were carried out using the radiative transfer model presented in Section 2 and stored in look-up tables (LUTs). Then, from the POLDER geometry (␪s, ␪v, and ⌬␾), the appropriate parameterization of ZA ⫽ f 关␳共763兲兾␳共765兲兴 is chosen using ␳共765兲 to estimate the effect of the aerosol model and optical thickness. Finally, ZA is estimated from the measurement of ␳共763兲兾␳共765兲. Note that the proposed method does not consist in determining accurately the aerosol

model and optical thickness and ␳s but in estimating them approximatively to choose the more appropriate parameterization of ZA. The expected inaccuracy of the aerosol altitude ZA retrieved from the POLDER measurements has been evaluated with simulations. Typical uncertainties ⌬R ⫽ ⫾1% on the reflectance ratio R, essentially due to interband calibration errors,29 have been introduced to estimate a theoretical inaccuracy on ZA. The results are summarized in Table 5. The inaccuracy is defined as the rms error using all the viewing conditions. For a heavily loaded atmosphere [␶A共550兲 of 0.6], the expected inaccuracy on ZA is small, ⬃0.4 km. The efficiency of the technique is higher when multiple scattering is less important and the accuracy of the method is then better for absorbing aerosols. For low optical thickness, the inaccuracy can reach 2 km for moderately absorbing aerosols. In this case, the uncertainties on ␳s and ␻0 are of the same order of magnitude as the variations on ZA. Consequently, the proposed method is accurate only for an aerosol optical thickness higher than 0.2 with POLDER. To sum up, the method is less accurate at low optical thickness and for moderately absorbing aerosols, but in this case, the impact of the vertical distribution is less important, as shown previously. The method is illustrated over a set of POLDER images of a dust plume off the coast of Africa. Figure 7(a) displays the scene acquired on 1 May 2003 and Fig. 7(b) the corresponding aerosol altitude estimated over the Atlantic Ocean from measurements in the oxygen A bands. The POLDER instrument observes the same terrestrial target (pixel), from 12 different viewing directions during the same orbit. Consequently, the values of ZA, presented in Fig. 7(b), are average values over the 12 POLDER view directions.

Fig. 7. (a) POLDER image for a dust plume off Africa on 1 May 2003 and (b) estimation of the altitude of the aerosol layer from measurements in the two oxygen A bands of the POLDER instrument. 1 March 2007 兾 Vol. 46, No. 7 兾 APPLIED OPTICS

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Table 6. Theoretical Accuracy (km) of the Layer Altitude ZA Estimated for a Dust Plume Off the Coast of Africa

␶A(550)

具ZA (km)典

⌬ZA (km)

0–0.1 0.1–0.2 0.2–0.5 ⬎0.6

3.6 3.7 3.6 2.8

1.3 1.1 0.8 0.6

The altitude of the aerosol layer is detected at ⬃2 km. It is a typical altitude for Saharan dustlike particles.30 Note that high altitudes at approximately 4 and 5 km correspond to an aerosol optical thickness less than 0.2. Consequently, they are not typical since for small aerosol amounts, the method is inaccurate. The sensitivity of the estimated ZA to the POLDER view direction is tested. The values of ZA obtained for all the view directions are averaged for every pixel of every scene, and the corresponding standard deviation is calculated. Table 6 displays the average value of ZA and the standard deviation for all the pixels of all the scenes as a function of the aerosol optical thickness. The estimation is shown to be more reliable for a large aerosol amount since the standard deviation decreases as ␶A decreases. This is consistent with the results of the sensitivity study presented in Table 5. B. Improvements on Water Reflectance and Chlorophyll-a Concentration Retrievals

To demonstrate the potential of the differential method to estimate the aerosol altitude in ocean-color remote sensing, the case of aerosols located between 4 and 5 km is considered. Based on Table 5, the aerosol altitude is assumed to be determined with an inaccuracy of ⫾0.5 km. The differences in TOA reflectance and the resulting errors on the retrieval of water reflectance and [Chl-a] concentration are computed for strongly absorbing aerosols and a Sun zenith of 30°, as in Subsections 4.B and 4.C. Qualitatively, the differences in TOA reflectance, and consequently, water reflectance and chlorophyll concentration, are expected to be larger when the altitude of the aerosol layer is overestimated. When the aerosols are located higher in the atmosphere, i.e., between 4.5 and 5.5 km (i.e., altitude error of ⫹0.5 km), the quantity of light that enters in the atmosphere at 5 km is smaller than when the aerosols are located between 4 and 5 km (i.e., the reference situation). When aerosols are lower in the atmosphere, i.e., between 3.5 and 4.5 km (altitude error of ⫺0.5 km), the quantity of light that enters at 5 km is basically the same as for the reference situation. The difference in reflected signal at the TOA is therefore larger when ZA is overestimated than underestimated, yielding larger errors in the former situation. The resulting errors of ␳w at 490 and 560 nm, ⌬␳w共490兲 and ⌬␳w共560兲, are estimated as in Subsection 4.B, but are not shown. They are now smaller than 5 ⫻ 10⫺4 and 2 ⫻ 10⫺4, respectively, in the 1116

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Fig. 8. Relative error (%) on [Chl-a] when the altitude of the URB aerosol layer is underestimated or overestimated by 0.5 km. The actual [Chl-a] is 0.03 mg m⫺3 and ␪s is 30°.

presence of strongly absorbing aerosols, when the optical thickness is small (0.1) and the view zenith angle is not too large 共⬍15°兲. For a large aerosol optical thickness, ⌬␳w共490兲 and ⌬␳w共560兲 are always larger than the accuracy threshold, but they are much smaller than the values obtained by assuming a scale height of 2 km (three or four times smaller). In other words, the gain in ␳w retrieval accuracy is substantial, but it is yet insufficient for some situations, particularly at large optical thickness and view zenith angle. The resulting errors of [Chl-a] concentration are given in Figs. 8 –10. Improvements can be observed on the estimate of [Chl-a] concentration. For a small aerosol optical thickness, [Chl-a] is now correctly estimated in most cases. For a large optical thickness, [Chl-a] of 0.3 mg m⫺3 is always less than 35% (Fig. 9). The [Chl-a] of 3.1 mg m⫺3 can be correctly retrieved for view zenith angles not too large but maximum errors on [Chl-a] reach ⬃80% (Fig. 10). Minimum errors on [Chl-a] of 0.03 mg m⫺3 are ⬃50%, and max-

Fig. 9. Same as Fig. 8 but for an actual [Chl-a] of 0.3 mg m⫺3.

Fig. 10. Same as Fig. 8 but for an actual [Chl-a] of 3.1 mg m⫺3.

imum errors still remain larger than 100% (Fig. 8). However, for such high aerosol loadings, and strongly absorbing aerosols, the uncertainty of ⫾0.5 km on aerosol altitude, which corresponds to an average for low and high ␶A共550兲 values, is lower, ⬃0.3 km. Thus, better results are expected by using the proper uncertainty on aerosol altitude, which depends on aerosol type and amount. Scale height H0 can be estimated instead of ZA, in the same way, from measurements in the oxygen A band. If the differential method allows an estimation of H0 or ZA, it cannot distinguish aerosols distributed according to an exponential law with a scale height H0 or located in a layer at altitude ZA. Consequently, the method is limited by the assumption concerning the parameter to be estimated, i.e., ZA or H0. The retrieval of H0 instead of ZA has been investigated. First, H0 has been computed as a function of the reflectance ratio R for the same geometric conditions and aerosol properties as in Fig. 6. Then, H0 and ZA are retrieved for the same given value of R using H0 ⫽ f⬘关␳共763兲兾␳共765兲兴 and ZA ⫽ f 关␳共763兲兾␳共765兲兴. Finally, the water reflectance is estimated using the retrieved H0 or ZA and the difference between the water reflectance ␳w共H0兲 and ␳w共ZA兲 is calculated. Results show that the difference is always less than 5 ⫻ 10⫺4 at 490 nm and less than 2 ⫻ 10⫺4 at 490 nm. Determining H0 instead of ZA is not really an issue in the retrieval of marine reflectance at 490 and 560 and [Chl-a] concentration. In many cases, absorbing aerosols generally of continental origin, e.g., dust, are encountered in altitude over the oceans, and it is more efficient to estimate ZA instead of H0. 6. Summary and Conclusions

First, the importance of aerosol vertical structure in satellite ocean-color remote sensing has been quantitatively investigated. A wide range of aerosol types and concentrations, and view-Sun geometries, have been considered in the simulations covering expected situations observed from space and therefore allowing a comprehensive study. Vertical structure is shown to

exert a substantial, significant effect for absorbing aerosols in the visible, especially in the blue. It confirms and completes the previous results reported by Ding and Gordon7 and Gordon4 for limited situations. Second, the errors due to simplifying assumptions on aerosol vertical distribution on retrievals of water reflectance and chlorophyll concentration have been quantified. Unacceptable water reflectance errors, i.e., above the uncertainty limit of ⫾5 ⫻ 10⫺4 at 490 nm for clear waters are revealed in many conditions. The errors on water reflectance translate into unacceptable [Chl-a] errors, i.e., above 35%, except when [Chl-a] is moderate 共0.3 mg m⫺3兲. Note that the water reflectance errors due to aerosol structure compensate differently in the reflectance ratio than those that arise from imperfect extrapolation of the atmosphere signal determined at near-infrared wavelengths in standard atmospheric correction algorithms. These errors yield more inaccurate [Chl-a] retrievals at high [Chl-a] values than at low [Chl-a] values, whereas the errors due to aerosol structure may yield reasonable estimates at high [Chl-a] values. In this study, a new and simple method has been proposed to obtain information about aerosol vertical structure. It uses additional information obtained from measurements in two spectral channels located in the oxygen A band, available on the POLDER instrument. The method does not determine the aerosol structure completely, but the average altitude ZA, in the case of a layer, or the scale height H0, in the case of an exponential distribution. Of course, one does not know a priori the type of distribution encountered. The simulations show, however, that the estimated H0 or ZA lead to great improvement in water reflectance and chlorophyll concentration retrievals. Note that more accurate estimates of ZA and H0 are expected using MERIS measurements since the MERIS reflectance ratio is more sensitive to the aerosol vertical profile. Lidars such as the Geoscience Laser Altimeter System (GLAS) and the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) were launched on 12 January 2003 and on 28 April 2006 aboard the Ice Cloud and Elevation Satellite (ICESat) and Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) spacecrafts, respectively. They show promise in retrieving the vertical profile of aerosols by measuring the return signal as a function of time. Spatial coverage is limited, however, since viewing is only effected at nadir. On the other hand, MERIS and the new version of POLDER instrument aboard the Polarisation et Anisotropie des Réflectances au sommet de l’Atmosphère couplées avec avec un Satellite d’Observation emportant un Lidar (PARASOL) microsatellite can provide only one piece of information about aerosol altitude with only two spectral bands and a single viewing angle. The technique provides, however, a better spatial coverage than laser-based systems since it is applicable over the large swath of the instruments. Note that CALIPSO and PARASOL can observe the same target because they fly in tan1 March 2007 兾 Vol. 46, No. 7 兾 APPLIED OPTICS

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dem. Consequently, CALIOP measurements could be used in the future to validate the proposed method. In addition, using more than two spectral bands and兾or multiangular observations in the oxygen A band may give more clues on the vertical profile of aerosol concentration. When the viewing zenith angle increases, for example, so does the air mass, and the associated vertical profile of the atmospheric weighting function for aerosol scattering changes and will have a maximum at higher altitude. Combining spectral differential absorption and multiangular observations in the 763 nm oxygen A band is an interesting perspective, which would lead to more complete information on aerosol structure and, therefore, more accurate retrievals of water reflectance and chlorophyll concentration in the presence of absorbing aerosols. This would improve, in particular, our ability to study western-boundary upwelling systems, which occur in the lee of many continental aerosol sources, from pollution to biomass burning to dust storms. In a final note, for the information on aerosol vertical structure to be used efficiently in standard, two-step atmospheric correction algorithms, the aerosol models need to be determined. Indeed, the simulations indicate different effects for urban and continental aerosols. Using observations at 510 nm (MERIS standard algorithm) only allows detection of absorbing aerosols, for sufficiently large optical thickness since the effect of aerosol absorption is quite small at this wavelength, but does not differentiate between types of aerosols. In the spectral matching algorithm, on the other hand, LUTs can be expanded to include a wide range of aerosol profiles, and the profile can be selected based on the available information on the aerosol vertical structure. Including information in the ultraviolet, where the effect of aerosol absorption is more effective, in the spectral matching algorithm, not possible with current ocean-color sensors, would improve retrievals in the presence of absorbing aerosols. But in this case, information on aerosol structure is more critical, because of its stronger influence on the atmospheric signal. The authors gratefully acknowledge the support from the Centre National des Etudes Spatiales (CNES), the Région Nord-Pas-De-Calais, and the National Aeronautics and Space Administration (NASA). The authors thank David Dessailly for his technical help. References 1. H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978). 2. M. Viollier, D. Tanré, and P. Y. Deschamps, “An algorithm for remote sensing of water color from space,” Boundary-Layer Meteorol. 18, 247–267 (1980). 3. H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33, 443– 452 (1994). 4. H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res. 102, 17081–17106 (1997). 1118

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