2.1. Scene Identification
 Fields of view were identified as cloud-free if they exhibited locally uniform reflected sunlight and thermal emission on scales of ∼8 km (2 × 2 pixel arrays) for the 4-km AVHRR Global Area Coverage (GAC) observations. For cloud-free ocean scenes, the standard deviation of the 0.64-μm (AVHRR Channel 1) reflectance for localized arrays of pixels had to be less than 0.004. The standard deviation of the 11-μm (AVHRR Channel 4) emission had to be less than 0.5 mW m−2 sr−1 cm, equivalent to ∼0.3 K for the brightness temperatures associated with the cloud-free oceans. Away from regions of sun glint, cloud-free ocean scenes were required to have a ratio of the near infrared (0.84 μm, AVHRR Channel 2) reflectance to visible (0.64 μm, AVHRR Channel 1) reflectance that was less than 0.85. Overcast pixels produce values of near unity for this ratio while pixels with vegetated land produce values >1. Here, sunlight was taken to be outside of the sun glint region if the light was reflected at angles greater than 40° from the direction of specular reflection for a flat surface.
 Within each ∼250-km scale region, the distribution of radiances for pixels that exhibited locally uniform reflection and emission and which also had low near infrared to visible reflectance ratios were used to establish thresholds for visible reflectances and 11-μm emission suitable for the cloud-free ocean pixels. Of the radiances for these pixels, the 95th percentile of the visible reflectance was taken as an upper limit and the 5th percentile of the 11-μm emission was taken as a lower limit for cloud-free pixels. These thresholds were applied to all fields of view that exhibited locally uniform emission and reflection and which had low near infrared to visible reflectance ratios and lay within a 150-km scale subregion centered within the larger ∼250-km scale region.
 Likewise, fields of view were identified as overcast by a single-layered cloud system if they exhibited locally uniform emission at 11 μm. For overcast pixels, the standard deviation of the 11-μm radiance for the pixel arrays had to be less than 0.5 mW m−2 sr−1 cm, which for low-level clouds is equivalent to a standard deviation of 0.4 K in brightness temperatures. Pixels that exhibited neither locally uniform reflectances nor locally uniform emitted radiances were presumed to be partly cloud covered. The 50th percentile of the reflectances for the partly cloudy pixels was used as a minimum reflectance for pixels to be identified as overcast by optically thick clouds. This visible threshold was applied to the fields of view exhibiting locally uniform emission that were not cloud-free in order to identify fields of view that were overcast by optically thick, layered cloud systems.
 This pixel identification process was repeated region by region and subregion by subregion until all fields of view within the overpass were identified. The regions and subregions were overlapped to ensure that all pixels were identified.
 The identification scheme was designed to identify ensembles of pixels that were representative of cloud-free pixels and pixels overcast by optically thick, layered clouds within the ∼150 km region being studied. The scheme does not identify all cloud-free fields of view, nor does it identify all overcast fields of view within the region. In particular, cloudy fields of view overcast by a system of clouds residing in multiple cloud layers along with fields of view overcast by thin cirrus are identified as being partly cloud covered. For cloud-free fields of view, the identification scheme specifically avoids individual fields of view that may be surrounded by cloud and are thus likely to be cloud contaminated in favor of fields of views that are contiguous with all pixels exhibiting properties that are typical of cloud-free scenes. As discussed by Tahnk and Coakley , about 15% of the 4-km AVHRR GAC fields of view were typically identified as being cloud-free for the Indian Ocean in the Northern Hemisphere. Thus, fields of view suitable for aerosol retrievals were plentiful. The majority of the 4-km fields of view were found to be partly cloudy. Relatively few (<5%) were identified as being overcast by single-layered optically thick clouds and of these, a sizable fraction were associated with upper-level systems. By varying the criteria used to identify cloud-free fields of view, so that the identified fields of view were subjected to greater and lesser levels of cloud contamination, cloud contamination was found to contribute less than 0.05 to the retrieved 0.55-μm aerosol optical depth. Here, 0.55-μm is used as the reference wavelength for reporting aerosol optical depths. This level of cloud contamination is less than half of the average optical depths found for pristine ocean regions of the Southern Hemisphere.
2.2. Aerosol and Radiative Transfer Models
 Table 1 lists characteristics of the aerosol models used in the retrievals. The properties are given for a relative humidity of 70%. As mentioned in the introduction, the average continental and tropical marine aerosol models were taken from Hess et al. . These models, along with the FFP model, are multicomponent models. For comparison, retrievals were also performed with the models used in the NOAA Phase 1 and Phase 2 retrieval algorithms [Stowe et al., 1997]; these are single-component models.
Table 1. Properties of Aerosols at 70% Relative Humiditya
|Component||Number Fraction||Effective Radius, μm||0.55-μm Extinction Efficiency||Ångström Coefficient||0.65-μm Extinction Efficiency||Single-Scattering Albedo||Asymmetry Parameter||0.80-μm Extinction Efficiency||Single-Scattering Albedo||Asymmetry Parameter|
|Sea salt (acc. mode)||0.017||1.324||2.56||−0.08||2.62||1.000||0.781||2.64||1.000||0.785|
|Sea salt (coarse mode)||2.17×10−6||10.860||2.11||−0.03||2.12||1.000||0.848||2.13||1.000||0.844|
|Sea salt (acc. mode)||1.20×10−4||1.324||2.56||−0.08||2.62||1.000||0.781||2.64||1.000||0.785|
|Sea salt (coarse mode)||1.11×10−6||10.860||2.11||−0.03||2.12||1.000||0.848||2.13||1.000||0.844|
|NOAA Phase 2|
|NOAA Phase 1|
 Aerosol properties were retrieved by matching observed reflectances for the cloud-free fields of view to those computed for a particular aerosol. The reflectances were calculated using DISORT [Stamnes et al., 1988]. Absorption by O3, O2, and H2O within the AVHRR Channel 1 and 2 passbands was treated using the correlated k-distributions described by Kratz . The McClatchey et al.  tropical climatological profiles of temperature and humidity were used to calculate the reflectances. As discussed in section 4, using midlatitude summer climatological profiles in place of the tropical profiles had little effect on the retrieved optical depths. Following Rajeev et al. , the aerosols were uniformly mixed below 1 km and distributed with a scale height of 0.8 km between 1 and 8 km. No aerosol was placed above 8 km. The vertical distribution is consistent with that derived from lidar returns in the INDOEX region as reported by Satheesh et al. . In addition, optical properties of the aerosols were calculated using a relative humidity of 78% for 0−1 km, 62% for 1−2 km, and 35% above 2 km as proposed by Satheesh et al.  based on radiosonde data collected at KCO for the February–March, 1998 INDOEX FFP. Rajeev et al.  adopted the same profile of relative humidity for retrievals of optical depths using the FFP aerosol model.
 Reflectances were calculated for aerosol optical depths at a standard wavelength of 0.55 μm. The optical depths ranged from 0–0.9 in steps of 0.1; the solar zenith angle ranged from 0°–85° in steps of 5°; the cosine of the view zenith angle ranged from 0.3–1.0 in steps of 0.1, and the solar relative azimuth angle ranged from 0°–180° in steps of 10°. The ocean surface was taken to be Lambertian with an albedo of 0.005 at both wavelengths. This value is somewhat elevated from that expected for water surfaces for radiation reflected in the direction of backward scattered sunlight. The slight elevation is meant to account for the small contribution to the reflected light from sun glint-specifically, radiation that is reflected by the ocean surface and then scattered by the atmosphere into the radiometer's field of view. The value chosen for the albedo minimized the average differences between optical depths retrieved at both visible and near infrared wavelengths and those measured at the surface. When comparing with observed reflectances, the calculated reflectances were linearly interpolated to the desired Sun-Earth-satellite geometry.
2.3. Aerosol Retrieval Schemes
 Three types of retrievals were used. In the simplest scheme, reflectances were calculated for a single aerosol model and then optical depths were retrieved by seeking agreement between calculated and observed reflectances at one wavelength, for example, the 0.64-μm Channel 1 of AVHRR [Stowe et al., 1997; Rajeev et al., 2000].
 In the second, the new scheme developed for this study, two aerosol models were used and reflectances were calculated for the visible and near infrared wavelength channels of the AVHRR. The retrieved optical depth and the fraction of each aerosol type contributing to the retrieved optical depth were selected so that the observed visible and near infrared reflectances agreed with the calculated values as illustrated in Figure 1. The reflectances in the figure are the isotropic reflectances given by
where I is the radiance as measured by the radiometer; F is the value of the solar constant appropriate for the spectral channel of the radiometer and the time of year, and μ0 is the cosine of the solar zenith angle. The reflectances at the two wavelengths were calculated for the viewing geometry associated with the observation as given by the solar zenith angle, θ0, the satellite zenith angle, θ, and the solar relative azimuth angle, ϕ. Aerosol properties at 0.65 μm were used in calculations of the reflectances for AVHRR Channel 1 at 0.64 μm, and properties at 0.80 μm were used in calculations of the reflectances for AVHRR Channel 2 at 0.84 μm.
Figure 1. Calculated and observed 0.64 and 0.84-μm reflectances for ∼100 km region of the Arabian Sea. Average values are given for the solar zenith, θ0, satellite zenith, θ, and relative solar azimuth angles, ϕ, of the observations. Observations (×) are from the NOAA-14 AVHRR for a pass during the INDOEX Intensive Field Phase, February 1999. Reflectances are given for the average continental (dashed line) and tropical marine aerosol models of Hess et al. . Dotted lines are lines of constant 0.55-μm optical depth (indicated by the adjacent numbers) for mixtures of the average continental and tropical marine aerosol.
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 Figure 1 shows the cloud-free reflectances for the individual models, the tropical marine aerosol (solid line) and the average continental aerosol (dashed line). For the range of optical depths considered in this study, the reflectances are almost linearly proportional to the optical depths even for sizable aerosol burdens. As a result, the reflectances at any two wavelengths are almost linearly related. The figure shows that even for 0.55-μm optical depths as large as 0.9, departures of the reflectances from a linear relationship are small. Consequently, a natural rendition of the reflectances would be as a mixture of the reflectances contributed by each component. To the extent that the reflectances are linear in optical depth, this treatment is equivalent to taking the aerosol to be a mixture of the optical depths of the two aerosol components, which in turn, is equivalent to taking the aerosol to be a mixture of number concentrations. The dotted lines joining the lines associated with the individual models are thus lines of constant optical depths for various aerosol mixtures. The combined reflectance is then given by
where ri(τ) is the cloud-free ocean reflectance in AVHRR channel i = 1, 2 when the optical depth of the mixed aerosol is τ at the standard wavelength; riC(τ) is the channel i reflectance for the cloud-free ocean over which an average continental aerosol has optical depth τ at the standard wavelength; riM(τ) is the corresponding reflectance for the tropical marine aerosol; f is the fraction of the mixture that is taken to be the average continental aerosol, and 1–f is the fraction of the mixture that is taken to be the tropical marine aerosol. As defined, f plays the role of a mixing fraction as commonly used to describe the thermodynamic properties of air parcels that undergo mixing. In this case, for f = 1, the aerosol is the average continental aerosol; for f = 0, the aerosol is the tropical marine aerosol. Because the slopes of the Channel 2 to Channel 1 reflectances are numerically rather similar for the average continental and the tropical marine aerosols, which, of course, is unfortunate for the design of a retrieval scheme, the slope of the Channel 2 to Channel 1 reflectances is approximately given by
where ri0 is the ocean reflectance under cloud-free and aerosol-free conditions for channel i. In addition, since the reflectances are almost linearly related for the range of optical depths being considered, (2) is approximately equivalent to
with τ0 a reference optical depth at the standard wavelength. Here τ0 = 0.9. For each cloud-free pixel, f is derived from (3). In other words, the aerosol mixing fraction, f, is derived from the slope of the Channel 1 to Channel 2 reflectance departures from the values expected for cloud-free and aerosol-free conditions. Once f is determined, the optical depth at the standard wavelength is derived from the reflectances themselves, as given by (1).
 Discrepancies between values of the slopes calculated using (1) separately for Channels 1 and 2 and those obtained using (3) arise because the reflectances are, in fact, nonlinear functions of the optical depths. For the range of 0.55-μm optical depths considered here (0.1 ≤ τ ≤ 0.9), the nonlinearity is relatively weak as long as the solar zenith and satellite zenith angles are less than 65° and the 0.55-μm optical depth is less than 0.9. Of the data analyzed, few retrievals were encountered with such large satellite and solar zenith angles and such large optical depths. Simulations were performed in which reflectances were calculated using (1) and f was derived using (3). In the simulations, the range of viewing geometries used in the retrievals was explored, with the exception that the solar zenith and satellite zenith angles were limited to being less than 65°. The results of the simulations indicated that the nonlinearity of the reflectances biased f slightly toward 1. The retrievals favored the average continental aerosol. The retrieved values of f had a bias of 0.06 and an RMS difference about the bias of 0.1. The retrieved values of τ had a negligible bias with an RMS difference of 0.01. Of course, the nonlinearity of the reflectances could be accounted for in the retrievals by, for example, iterating the solutions for f and τ until suitable convergence criteria were met. The scheme described here, however, was adopted because it was simple and produced results that were reasonably accurate.
 To illustrate the relationship between f, τ, and the reflectances, the symbols (×) in Figure 1 represent the reflectances from the NOAA-14 AVHRR for the cloud-free pixels found within a 100-km scale portion of the Arabian Sea during INDOEX. Each point is now interpreted as being due to a specific mixture of the two aerosols and the mixture produces a specific optical depth at the standard wavelength, as indicated in the figure. The discrete values of the observed reflectances are due to changes at the single count level for the AVHRR.
 The average continental and tropical marine aerosol models, described by Hess et al. , were chosen for this retrieval scheme with the following considerations. First, the aerosol over the Indian Ocean was expected to be a mixture of a continental haze with absorbing aerosols, as is the case for the average continental model. Second, the aerosol was also expected to have a prominent marine component, particularly when levels of pollution from the continent were low. Third, the average continental and tropical marine aerosol models serve as standard models and using these models in the retrieval scheme allows an assessment of their utility in estimating aerosol burdens and the direct aerosol radiative forcing. Fourth, of the aerosol models described by Hess et al. , the average continental and tropical marine aerosols, for most viewing geometries, spanned the largest portion of the two-channel reflectance domain like that shown in Figure 1. In other words, the curves in Figure 1 produced individually by these two aerosol models have the largest possible separation. The slopes of these curves are governed primarily by the size of the particles responsible for scattering. In the case of the tropical marine aerosol, the particle sizes are relatively large, effective radius ∼1.0 μm (Table 1), and for the average continental aerosol the particle sizes are relatively small, effective radius ∼0.2 μm. Increasing the amount of sunlight absorbed by these aerosols, by adding soot as an additional component to each, has little effect on the slopes of the reflectance curves. The additional absorption simply diminishes the reflectances produced by a given optical depth thereby leading to higher retrieved optical depths for a given set of reflectances. The NOAA Phase 1 model has smaller particle sizes, and would produce a larger 2-channel reflectance domain when combined with the tropical marine aerosol. This model was not adopted here, however, because the effective radius ∼0.08 μm is well below those found in the INDOEX region [Satheesh et al., 1999; Clarke et al., 2002; Quinn et al., 2002]. For the viewing geometries encountered in INDOEX, the NOAA Phase 2 model produces a slope for the two-channel reflectances that is nearly identical to that of the average continental aerosol, and for most viewing geometries, the FFP model produces a slope similar to that of the tropical marine aerosol, but for some viewing geometries the slope of the reflectances for the FFP model slightly exceeds that of the tropical marine aerosol.
 For simplicity, the retrieval scheme just described will be referred to as the 2-channel, 2-model scheme. To complete this retrieval scheme, rules were prescribed for dealing with reflectances that lay outside the domain bracketed by the reflectances associated with mixtures of the two aerosol models. For reflectances outside the bracketed domain, the retrieved aerosol type was set to the model which had reflectances nearest those observed, either the average continental or the tropical marine aerosol model, and the optical depth was taken to be that which produced the smallest RMS differences between the observed and calculated reflectances for both channels. Because it uses reflectances at two wavelengths in a least squares solution, this procedure differs from that typically employed in single-channel, single-aerosol model retrieval schemes. This 2-channel, single-model scheme is the third retrieval scheme considered here. Sections 4 and 5 explore differences between the results obtained with the different retrieval schemes.
 Interestingly, even though the tropical marine and average continental aerosols bracket the domain of possible reflectances for the two AVHRR channels, a substantial number of observations fell outside of the bracketed domain. In the Southern Hemisphere, for the 8-day sample of data described in section 5, 40% of the reflectances fell within the domain of the two models, 40% fell to the side of the continental aerosol, and 20% fell to the side of the tropical marine aerosol. For the Northern Hemisphere, the percentages were 55% within the domain, 29% on the side of the continental aerosol, and 16% on the side of the marine aerosol. The large fraction of reflectances falling outside the domain is viewed as unsatisfactory. Reflectances that fall to the side of the average continental model may be caused by the nonlinear relationship between the reflectances not being accounted for in the retrievals, but it may also suggest that the particles reflecting the sunlight are smaller than those in the average continental model. The reflectances that fall to the side of the tropical marine aerosol may suggest cloud contamination, either by small amounts of low-level clouds or by thin cirrus. The slope of the reflectances for the tropical marine aerosol is close to that for clouds. Of course, reflectances may fall outside the expected domain because of errors in the calibration of the AVHRR, errors in the model used to calculate the reflected light contributed by the underlying ocean, and errors in accounting for absorption by atmospheric gases. Reducing the number of cloud-free ocean scenes with reflectances that fall outside those expected remains a challenge.