Using broadband shortwave radiance measurements from the Clouds and Earth Radiant Energy System (CERES) sensors onboard the Terra and Aqua satellites, empirical angular distribution models (EADM) are constructed for smoke aerosols. These EADMs are constructed for smoke aerosols emitted during the biomass burning season (August-October), in South America. All available years (2000–2008) of both rotating azimuth plane and cross-track radiance data from CERES have been utilized. Aerosol scenes are identified using coincident aerosol optical thickness retrievals from the Moderate Resolution Imaging Spectroradiometer (MODIS). The new EADMs are used to estimate top-of-atmosphere (TOA) shortwave flux for cloud free scenes. The CERES clearly shows the angular dependence of shortwave radiance on smoke aerosol optical thickness. A comparison of TOA shortwave fluxes estimated from the new smoke EADM with the existing CERES TOA shortwave fluxes shows that the CERES fluxes are higher (lower) for aerosol optical thickness less (greater) than 0.3, largely due to the use of aerosol optical thickness in characterizing the new EADMs developed in this study. Empirical ADMs for smoke aerosols over land are developed for the first time in this study, and our results demonstrate that large amounts of aerosols emitted during biomass burning activities contribute to the anisotropy of the radiance distribution at the TOA. Therefore, it is imperative to include aerosol information in the angular distribution models, especially now that more than a 10 year record of Terra data is available.
 The Earth's radiation budget, governed by the absorption of solar radiation and emission of terrestrial radiation, determines the general circulation of the atmosphere that drives the Earth's weather and climate. Until the advent of Clouds and Earth's Radiant Energy System (CERES) mission [Wielicki et al., 1996], radiation budget instruments such as the Earth Radiation Budget Experiment (ERBE) [Barkstrom, 1984] and the Scanner for Radiation Budget (ScaRab) [Kandel et al., 1998] provided broadband radiative flux information. To study the role of clouds and aerosols in the Earth's radiative balance, the CERES-Terra mission provides coincident data sets of broadband radiative flux and clouds and aerosols properties from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument onboard the same satellites (Terra and Aqua). These measurements are used to improve the understanding of cloud-aerosol-radiation interaction and its representation in global climate models. These data sets have also been widely used for studying the role of aerosols in modulating the top-of-atmosphere (TOA) radiative balance. Both global and regional shortwave aerosol radiative forcing (SWARF) has been calculated empirically using these data sets in several studies [Christopher et al., 2000; Loeb and Kato, 2002; Zhang et al., 2005b; Patadia et al., 2008a, 2008b; Kim and Ramanathan, 2008]. The accuracy of the radiation budget calculations rely greatly on the accuracy of the broadband radiative flux data sets. One of the challenges in determining accurate radiative fluxes involves the construction of accurate angular distribution models (ADM) that are used to convert the TOA broadband radiance measurements to fluxes.
 The angular distribution factor or ADM is a measure of deviation of scattered radiation from isotropic distribution and it is defined as the ratio of Lambertian to non-Lambertian flux. The purpose of the ADM is to estimate the radiative flux from a radiance observation made in a single direction. Several approaches have been adopted for developing the angular distribution models. Using Nimbus 7 ERBE observations from April 1979 to June 1980, Suttles et al. [1988, 1989] developed the first generation of empirical ADMs (EADM) for 12 scene types that were a combination of five different surface types and four cloud categories. These ADMs used only the broadband radiance measurements and could not identify smoke and clouds adequately within the ERBE pixels. Loeb et al. [2003a] made major improvements by developing empirical ADMs using shortwave, longwave and window radiance measurements from the CERES instrument onboard the TRMM satellite. Scene types were increased to ∼200 in the shortwave and several hundred in the longwave. High spatial resolution spectral imager measurements from the Visible Infrared Scanner (VIRS) were used for scene identification. Nine months of coincident multiangle broadband CERES measurements were used to construct empirical ADMs for each scene type. Improved scene identification and better ADM sensitivity to parameters that strongly influence anisotropy, result in a more reliable data set for studying radiative processes [Loeb et al., 2003a]. In fact, Loeb et al. [2003b] show that ADM and clear-sky scene identification differences between ERBE and CERES-TRMM can lead to root-mean-square differences of 8 Wm−2 in 1° daily mean shortwave cloud radiative forcing.
 The Terra spacecraft was launched on 18 December 1999 and it carries two identical CERES instruments. Unlike the TRMM satellite which made measurement only between 35°N and 35°S due to its non-Sun-synchronous orbit characteristics [Loeb et al., 2003a], Terra provides near global coverage with coarser resolution (altitude of 705 km as opposed to 350 km for TRMM) but increased sampling. The current state-of-art ADMs are more comprehensive and were developed from 24 months of CERES Terra broadband CERES radiance observations at different illumination and viewing conditions which can be obtained from the measurements made in the rotating azimuth and cross track scanning modes of the CERES instruments [Loeb et al., 2005]. These ADMs were also a function of parameters (e.g., surface type, cloud fraction, cloud phase, cloud/aerosol optical depth (AOT) etc.) that strongly influence the Earth's radiation field at the TOA. The scene type parameters were inferred from MODIS. For clear-sky land and deserts, the CERES-Terra ADMs are calculated for every month at 1 × 1 degree latitude-longitude resolution and for every 2 degree solar and viewing angles bins. The radiance is first converted to reflectance. Then, an eight parameter nonparametric BRDF (Bidirectional Reflectance Function) fit from Ahmad and Deering  is applied to the shortwave reflectance for angular bins with sufficient samples in a region. The BRDFs are then integrated to calculate the albedo. The ratio of reflectance to albedo at a given location defines the ADM. In the existing CERES ADMs, if sampling in an angular bin was not big enough, fluxes were estimated from the CERES TRMM (Tropical Rainfall Measuring Mission) ADMs. Loeb et al.  found marked improvements in TOA shortwave flux consistency over clear land and deserts using CERES Terra 1° regional monthly ADMs when compared to CERES TRMM ADMs that were developed for 4 broad classes of vegetation types. These clear-sky land ADMs, however, do not account for aerosols characteristics in the observed scene. Over ocean, theoretical correction is used to account for aerosol optical depth variation in both CERES-TRMM and CERES-Terra ADMs [Loeb et al., 2003a, 2005]. Zhang et al. [2005a] used coincident measurement of shortwave radiances from CERES-Terra and aerosol optical depth and fine mode fraction of AOT from MODIS to explicitly account for AOT variation in their shortwave ADMs for global cloud-free oceans. They conclude that over cloud free oceans, there will be an overall uncertainty of 10% in SWARF estimates if aerosol variations are not considered in constructing ADMs.
 Since no aerosol empirical ADMs are available over land, in this paper, as a first step we developed shortwave empirical ADMs over land for biomass burning aerosols over a region that has high aerosol loading during the S. hemisphere dry season. In events such as the biomass burning in South America, more than 100 Tg [Penner et al., 1992] of aerosols are emitted into the atmosphere and such large concentrations of smoke aerosols will contribute to the anisotropy of the radiance distribution. To estimate this contribution of aerosols to the anisotropy in the TOA radiances, we analyze the TOA shortwave radiance measurements from CERES during the biomass burning season over South America and calculate new smoke empirical ADMs (EADM) as a function of aerosol optical depth, surface albedo and solar-viewing geometry. Midvisible Aerosol optical thickness (AOT) and surface albedo information is used from coincident MODIS data. Our analysis is performed only for cloud free conditions. The cloud-free empirical smoke ADM is then used to convert the TOA shortwave radiance to TOA shortwave flux (ESWF). The new TOA shortwave flux estimated in this study is then compared to the existing TOA CERES SWF (CSWF). By developing new ADMs we can reduce one of the uncertainties in CERES-based methods for calculating the shortwave aerosol radiative forcing [e.g., Patadia et al., 2008a]. The following section 2 describes the study region and the data sets used in this study. The methodology of calculating the smoke ADM is discussed in section 3. Results are presented in section 4 and we discuss the sources of errors and biases in our results in section 5. Conclusions are drawn in section 6. In the rest of the paper, shortwave radiance will simply be referred to as radiance.
2. Study Area and Data
 The area of study is within 0°S–20°S and 40°W–70°W in South America. This region encompasses the biomass burning regions in the Amazon basin and the Cerrado area. Biomass burning occurs in these regions every year during the dry season (August-October) [Prins et al., 1998]. CERES and MODIS data products from the burning season and for years 2000–2008 are used in this study. The CERES instrument onboard Terra and Aqua satellite makes broadband radiance measurements [Wielicki et al., 1996] at the TOA, both in the longwave (LW) and shortwave (SW) parts of the electromagnetic spectrum. The CERES instrument has three channels: a SW channel for measuring reflected sunlight (0.3–5 μm), an infrared (IR) channel (8–12 μm) for measuring Earth-emitted thermal radiation “window” region, and a total channel (0.3–200 μm) for total radiation measurement. CERES has a spatial resolution of 20 km at nadir. There are two identical CERES instruments on Terra and Aqua satellites. Flight Model 1 and 2 on Terra and Flight Model 3 and 4 on Aqua. We use all available data from all four instruments. The CERES data product used in this study is the Edition2B_Rev1 Single Scanner Footprint TOA/Surface Fluxes and Clouds (SSF) product (http://asd-www.larc.nasa.gov/DPC/DPC.html) [Geier et al., 2001] which contains one hour of instantaneous CERES data for a single scanner and merged information from higher-resolution MODIS imager. The higher-resolution MODIS data such as AOT, scene identification and cloud and aerosol properties are averaged over the larger CERES footprint using point spread functions (PSF) [Smith, 1994] and are reported in the SSF product. MODIS level 2 aerosol data is produced at 10 × 10 km spatial resolution (at nadir). The construction of cloud free smoke ADM requires coincident measurements of TOA shortwave radiance, cloud cover, AOT and surface reflectance. The TOA SW radiances, MODIS based AOT, the MODIS based cloud cover [Martins et al., 2002; Minnis et al., 1999, 2003] and Sun-satellite geometry information from the SSF product have been used along with other data quality flags. We use the cloud fraction information to identify clear-sky observations and the PSF weighted MODIS AOT in CERES pixel [Barnes et al., 1998] is used to identify regions where aerosols are present. Although the new MODIS L2 collection 5 data product is now available [Levy et al., 2007] the CERES SSF product that is used for this study has not yet been processed at the Langley Distributed Active Archive Center (DAAC) to include this data and only contains MODIS data from collection 4. The land algorithm for aerosol retrieval uses reflectance from 3 channels (0.47, 0.66, 2.13 μm) and the reported uncertainty in AOT is ±0.05 ± 0.15*AOT0.55 [Remer et al., 2005]. A comparison of collection 4 MODIS AOT at 550 nm against AERONET derived AOT at 550 nm, over S. America, showed that 72% of the 762 retrievals used for comparison, fell within the expected uncertainty of ±0.05 ± 0.15*AOT [Remer et al., 2005]. The study region selected in this study has a dark background. For biomass burning period (Aug-Sep) in S. America, Patadia et al. [2008b] and F. Patadia and S. A. Christopher (Development of empirical angular distribution models for smoke aerosols: 2. Assessment of shortwave radiative forcing, submitted to Journal of Geophysical Research, 2011) compared the MODIS AOTs within the CERES footprint against collocated AERONET AOTs and found good agreement between the two retrievals. The correlation coefficient over 7 different stations was higher than 0.95. However, all comparisons are made when both MODIS and AERONET identify the scene as clear sky. Therefore, cloud contamination in the AOT retrievals cannot be addressed with the above comparisons and is a source of uncertainty while using the retrieved AOTs.
 The surface anisotropy also contributes to TOA anisotropy in scattered radiation. Over land, ADMs are a strong function of surface characteristics such as the surface albedo as suggested by Suttles et al. [1988, 1989]. To characterize the dependence of ADM on surface albedo, we use the MODIS Climate Modeling Grid (CMG) Albedo product (MCD43C3). MODIS data from both Terra and Aqua are used to generate this product. The MODIS albedo product (MOD43) is a clear-sky product which uses atmospherically corrected reflectance to derive BRDF, which is used to calculate the surface albedo. This product provides a 16 day composite of black-sky and white-sky albedo as a level-3 product for MODIS bands 1–7 and also for 3 broad bands (0.3–0.7, 0.7–5.0, 0.3–5.0 μm) at 0.05 degree spatial resolution in geographic projection [Schaaf et al., 2002]. Both directional hemispherical reflectance (black-sky albedo) and bihemispherical reflectance (white-sky albedo) are reported in this data product. The broadband black-sky (directional hemispherical or direct) surface albedo from MCD43C3 product is used in this study to characterize the TOA SWR. This product was collocated in space and time with the CERES-SSF product.
 The CERES SSF data product reports the solar zenith (SZA), viewing zenith (VZA) and relative azimuth angles (RAA) at the surface for each CERES pixel. In this study the TOA shortwave radiance is analyzed and EADMs are constructed as a function of the surface albedo (discussed below), aerosol optical thickness and Sun-satellite viewing geometry. Information on the aerosol particle size and properties would add value to the EADM estimation. However, the particle size information from the MODIS satellite product is only in its beta version and is not recommended for use in scientific studies [Levy et al., 2009]. AERONET provides this information but the sample size of data would not be enough to calculate the smoke EADMs. Moreover, our calculations are restricted to ADMs for smoke aerosols from biomass burning in South America. Previous studies show that number and mass of biomass burning smoke aerosols are overwhelmingly in the accumulation mode [Reid et al., 2005; Patadia et al., 2008b] and have particle sizes (volume mean diameter) in a narrow range of 0.26–0.3 μm [Reid et al., 2005]. The following section provides details on construction of the EADMs.
3.1. Theoretical Basis for Constructing ADM
 To study the effects of aerosols on Earth's radiation budget, knowledge of how the radiant exitance or flux at the TOA is altered in the presence and absence of aerosols is required. Flux is the radiant energy emitted or scattered by the Earth-atmosphere per unit area. Spaceborne sensors can measure the TOA radiances (I) which can be integrated over the solid angle and converted to Flux (F) as follows:
where θo is the solar zenith angle, θ is the observer viewing zenith angle, and ϕ is the relative azimuth angle defining the azimuth angle position of the observer relative to the solar plane. If the surface that reflects the radiant energy is considered isotropic/Lambertian (radiation is reflected uniformly in all directions), then from equation (1) the flux can be approximated as:
 However, in reality land and ocean surfaces are non-Lambertian/anisotropic in nature and hence the reflected radiation is a strong function of Sun and viewing geometry. Previous studies [Loeb et al., 2005; Zhang et al., 2005a] have also demonstrated that changes in the physical and optical properties of a scene (e.g., surface type, cloud fraction, cloud/aerosol optical thickness etc) have a strong influence on the anisotropy of the radiation at the TOA. Neglecting these effects result in large TOA flux errors [Chang et al., 2000]. To account for this anisotropy in radiance distribution at TOA, ADMs or anisotropic factors that relate radiance to flux for given observing conditions are required. Thus, an ADM is a function (R) that compares the radiance from a surface to that from a Lambertian surface and provides anisotropic factors for determining the TOA flux from an observed radiance as follows:
 The anisotropic factors (R) can be determined both theoretically [Li et al., 2000] and from satellite observations i.e., empirically [Loeb et al., 2005; Zhang et al., 2005a]. Since the CERES measures radiance in cross-track, rotating azimuth plane and along-track directions, it acquires data/radiance (I) over a wide range of angles. Consequently, the CERES measurements can be directly used to calculate F(θo) using equation (1) and to construct empirical ADMs using equation (3). Furthermore, because CERES and MODIS are on the same satellite, the ADMs can be derived as a function of MODIS-based scene-type parameters that have a strong influence on radiance anisotropy. Since CERES is on a polar Sun-synchronous orbiter, obtaining data over the entire solid angle to calculate F(θo), is however a challenge.
 In this study only cloud free shortwave ADMs are built for biomass burning season (August-October) over South America using CERES Terra and Aqua TOA shortwave radiances. Due to their submicron particle sizes, smoke aerosols have no impact on the longwave [Kaufman et al., 2002]. There are no shortwave empirical ADMs for smoke aerosols to our knowledge and the only theoretical work for smoke aerosols over land is from Li et al. . In this study, all snow-free and cloud-free (identified from MODIS-SSF) CERES SW radiances are sorted by season (August-October) and binned into angular bins of surface albedo, AOT, θo, θ, and ϕ. For a given albedo bin, AOT bin (j), θo bin (i), θ bin (k), and ϕ bin (l), the ADM (Rj(θoi, θk, ϕl)) is then determined from the CERES radiances using the following relation:
where Ij is the average CERES radiance in angular bin (θoi, θj, ϕk) and in a given albedo and AOT bin (j), and Fj is the upwelling flux in solar zenith angle bin, θoi for scene type (defined by AOT) j and can be determined by integrating Ij over all solid angles [Loeb et al., 2003a] using equation (1). For building empirical ADMs, as in this study, data are available in only finite angular bins. For integrating this data to find Fj, equation (1) can be written as the following summations:
Rj can now be estimated by using (5) in (4). Rj value of 1 is indicative of reflected radiation being isotropic.
 However, to ensure conservation of radiation energy, it is important to normalize Rj over the solid angles. The normalization condition for Rj can be obtained by substituting equation (3) in (1) to get:
To construct the empirical smoke ADMs, equation (4) and (5) are used. The normalization condition in equation (7) is used as a constraint in building the ADMs. Once the ADMs are developed, they are used to convert the TOA shortwave radiances to fluxes. To compare these fluxes (ESWF) against the existing TOA CERES SWF (CSWF), the ESWF at 20 km is calculated using equation (8):
where re is the mean radius of Earth (6371 km) and hsfc and h20 are the surface and 20 km reference levels respectively. The 20 km reference level corresponds to the effective top-of-atmosphere in Earth radiation budget studies [Loeb and Kato, 2002].
3.2. The Terra Empirical Smoke ADM Development
3.2.1. Quality Control of the Data
 Determination of anisotropy in TOA shortwave radiances requires observation of a given scene from different illumination and viewing geometry. Of the two CERES instruments (FM1 and FM2), the one in rotating azimuth plane (RAP) scanning mode of operation makes such observations. The second instrument takes observations in cross-track scanning mode. For obtaining a large sample size of data, both RAP and cross track data from the two CERES instruments onboard both Terra and Aqua satellites are combined for this study. This yields 22 months of dry season (August-October of 2000–2008) data. This data is then subset to correspond to the study area bounded within 0°–20°S and 40°W–70°W. The smoke ADM is constructed for cloud free conditions only. We call this the cloud-free empirical ADM (EADM) for smoke aerosols. A stringent cloud clearing of the data is performed by using 3 different cloud fraction parameters from the CERES-SSF data file. All data points that are 99.5% cloud free qualify as the clear-sky data.
3.2.2. Collocating Clear-Sky Flux With Surface Albedo
 The EADM in this study is characterized as a function of SZA, VZA, RAA, AOT and surface albedo (SALB). The solar-viewing geometry and AOT are acquired from the CERES-SSF data. The shortwave surface albedo is prescribed from the MODIS Albedo product (MCD43C3). For spatiotemporal correspondence of the two data sets, the MCD43C3 data product is collocated in space and time with the CERES-SSF clear-sky data. The MCD43C3 data is available at 0.05 degree spatial resolution while the resolution of CERES observation at nadir is of 20 km. For collocating the 2 data sets, a day, month and year matching is first obtained. Then, all the MCD43C3 data points that fall within a CERES footprint are accumulated. For each CERES pixel, the arithmetic mean SALB, standard deviation in surface albedo and the number of pixels used to calculate the mean and the standard deviation are stored for further analysis.
3.2.3. Selection of Angular Bins
 The EADMs are now constructed using the sorting into angular bin method [Suttles et al., 1988]. In this study, the data is sorted into SALB, SZA, VZA, and RAA bins for building the empirical smoke ADM. A frequency distribution (Figure 1) of each of these parameters is used to determine a viable size of each of these bins. The geographic bound of the study area and the requirement of observations from dry season for building the EADM, restrict the availability of illumination conditions. The polar orbiting Sun-synchronous orbit of Terra and Aqua satellites also exacerbates this problem. In this study, majority of the data pertains to SZA between 20 and 50 degrees (see Figure 1). The SALB over the study region during August-October ranges from >5% to <40%. However, ∼90% of the data belongs to SALB between 10% and 18% (see Figure 1). The AOT in the study area ranges between 0.02 and 3.0 during the burning season. Frequency distribution (see Figure 1) of AOT also indicates that most (∼90%) of the data pertains to AOT in the range of 0.02–0.6. Therefore, the EADMs are constructed only for the above range of SALB, AOT and SZA, i.e., for bins containing ∼90% of the data. The angular bins defined in this study are as follows: SALB = [0.0, 0.1, 0.12, 0.13, 0.14, 0.16]; AOT = [0.0, 0.05, 0.1, 0.15, 0.3, 0.6]; SZA = [20, 30, 40, 50]; 10 degree VZA bins and 30 degree RZA bins. Now, for a given SALB, AOT and SZA bin, the EADM value is estimated using equation (4) above. This requires two pieces of information: (1) the mean shortwave radiance in a given bin (calculation discussed in preceding paragraph) and (2) the shortwave flux for a given SALB, AOT and SZA bin.
3.2.4. Estimating the Bin-Averaged Radiance
 For EADM calculation, in a given surface albedo, AOT, SZA, VZA and RZA bin, the mean and standard deviation of the radiance is first calculated. However, the data may not be distributed evenly within a given bin. To avoid obtaining a radiance value that is biased toward an extreme end of a bin, all the above bins (in section 3.2.3) are subdivided into half. A mean of the radiances is first obtained for the subbins and then the average of the mean radiances over the original bin is obtained (Ij). If the number of data points in a certain bin was less than 8, the mean value was deemed unrepresentative and treated as missing. We arrived at this criterion requiring at least 8 data points by analyzing the standard deviation of radiance in a given bin. This bin-averaged radiance value (Ij) is used to calculate the anisotropy factor or EADM. The underlying assumption in this method is that the radiance is constant in the bins defined above. To validate this assumption, the standard deviation in each bin is analyzed and it is found to vary from 0.004 to 32.8 Wm−2 sr−1 with a mean value of 2.9 ± 1.54 Wm−2 sr−1. From the histogram of the standard deviation in radiances in each bin (Figure 2), we find that 60% of the data showed a standard deviation in radiance of <2.5 Wm−2 sr−1, for 85% it was <3.5 Wm−2 sr−1, for 90% of the data, it was <4 Wm−2 sr−1 and for 99% it was <6.2 Wm−2 sr−1. Only 0.3% data had standard deviation ≥6.2 Wm−2 sr−1. Only data with standard deviation <4 Wm−2 sr−1 (i.e., 90% of the data) was retained for further analysis. Considering the requirement of appropriate data sample size in each bin, we regard this variation in radiance adequate for calculating the empirical ADM values.
3.2.5. Angular Bins With Missing Data
 After the mean of shortwave radiance (Ij) is calculated (as discussed above), it is used to calculate the shortwave flux for a given SALB, AOT and SZA bin using equation (5). This integration (equation (5)) also requires radiance values in all viewing (0–90) and relative azimuth angle bins (0–180). Unfortunately, for certain combinations of SALB, AOT and SZA bins, the mean values are not available from CERES measurements. Values in some bins were either missing or were questionable because of small sample size. On the other hand, for a given SALB and AOT bin, two other problems were encountered: (1) data from an entire solar zenith angle were missing and (2) data in some viewing zenith angle bins, generally the largest bins (70–90 degree), were missing. As discussed before, data from SZA bins are expected to be missing because Terra and Aqua are in morning and afternoon Sun-synchronous orbits respectively. Also, the study is limited to a dry season (August-October) and a particular region in South America (0°–20°S; 40°E–70°E) and therefore, the correlation between latitude and SZA will result in all Sun angles not being sampled. Therefore, the smoke ADMs are built only for the solar zenith angles available in the data.
 As for the second problem involving data missing from VZA bins, two methods were adopted to fill in the missing data values. First, for a given VZA, we know that the radiance distribution is symmetric about RAA = 180 (backscattering direction) i.e., for azimuth angle there is symmetry about the principle plane (plane containing the ray from the Sun to the target area and the zenith ray that is normal to the target area). Considering this symmetry, the radiance value in a missing RAA bin1 is filled in from its mirror RAA bin2 (RAA bin2 = 360-RAA bin1). For example, RAA bin [0–30] is the mirror bin for RAA bin [330–360] and vice versa. Second, if most of the bins for the range of VZA (0–90) and RAA (0–360) are populated by first method, then the remaining missing values are filled in by simple cubic spline interpolation technique. Interpolation is done along the azimuth direction. It must be noted that the EADM in this study are calculated only for those cases where most of the VZA and RAA bins were populated. In the existing CERES ADMs, if sampling in an angular bin was not big enough, fluxes were estimated from the CERES TRMM ADMs.
 After obtaining radiance values in all the angular bins, the EADM value is estimated using equations (4) and (5). The EADM values are then subjected to the normalization criteria in equation (7) so that the EADM values satisfy the normalization within ±0.001. After normalization condition is satisfied, the TOA shortwave fluxes are calculated using equation (3). The estimated SWF is converted to SWF at 20 km using equation (8).
4. Results and Discussions
 Under cloud free conditions, the TOA radiance distribution over land depends on several factors including surface heterogeneity, surface type, aerosols in the atmosphere and the solar and viewing geometry. Figure 3 illustrates the dependence of TOA radiance on surface albedo, solar, viewing and the relative azimuth angle respectively, as a function of MODIS AOT. The increase in radiance with increasing AOT is evident from Figure 3. For example, in Figure 3a, for SZA bin 20–30, VZA bin 20–30, RAA bin 30–60 and SALB bin 0.1–0.2, the radiance increases from ∼40 to ∼55 Wm−2 sr−1 for increase in AOT from 0.02 to 0.6. The magnitude, slope and variance in the radiance with respect to AOT, however, depend on the combination of other parameters as shown in Figure 3. More reliable data set for studying radiative processes can be obtained by characterizing the ADMs by parameters that strongly influence anisotropy in TOA radiance [Loeb et al., 2003a]. The dependence of TOA radiance on aerosol optical depth (Figure 3) suggests the need to include the aerosol dependence while developing ADMs.
 As discussed earlier, for a given surface albedo, AOT and SZA bin, from equation (4) it is evident that there are 2 pieces of information that are required for constructing empirical ADM: (1) Mean radiance in a VZA and RZA bin (2) the outgoing shortwave flux (Fj). As discussed earlier, the major problem that is encountered is that of data missing from the viewing and relative azimuth angular bins. In the absence of data in all solid angle bins, calculation of Fj cannot be performed. In this study, the missing data is filled (criterion a) by using the assumption of symmetry around 180 degree RAA and (criterion b) fitting a cubic spline curve to the data. Details of the filling methods are discussed in the methods section. Figure 4 shows an example of the success of using the above 2 bin-filling criteria. The data in Figure 4 pertains to a SALB between 12% and 13%, AOT between 0.1 and 0.15 and solar zenith angle between 40 and 50 degree. The small brown dots are the original pixel level CERES radiance. The black dots are the bin-averaged radiance values. Figures 4a–4h each belong to the VZA bin indicated in the plot. First, for all VZA bins, the symmetry around the principle plane is clearly evident in Figure 4, i.e., the shape of the curve for RAA of 0–180 is the same as that for RAA of 180–360. This facilitates implementation of bin-filling criterion a above. For VZA between 0 and 40, there is data in every RAA bin. However, for VZA of 40–90, several RAA bins do not have data. For 40 < VZA < 90, criterion a is first applied to the data and the filled in radiance values are shown as blue dots. In the 70–90 VZA bin, all RAA bins could not be populated using criterion a alone. A cubic polynomial was fitted to the existing data and the anomalous radiance values in bins 0 and 360 were filled in (see red dots in Figure 4). This procedure was applied to all the data. The complete filled-in data for all combinations of the 5 parameter bins were visualized as in Figure 4. This was done to make sure that the data sample in each bin was sufficient to obtain the bin-averaged radiance value, there are no anomalous values and that the filling criteria were being adequately programmed. Those combinations of bins that had insufficient data and the radiance variations were unrealistic have not been used in this study.
 The CERES radiance in higher VZA bins is unreliable [Loeb et al., 2005]. Most methods rely on using radiative transfer (RT) calculations of SWR for VZA > 80 [Loeb et al., 2003a; Loeb et al., 2005]. We could not resort to the RT method because when we used the Santa Barbara Discrete Ordinate Atmospheric Radiative Transfer (SBDART) model, it was not able to reproduce the radiance observations in the bins where data is available. Therefore, radiance simulations from SBDART, for those bins where data is not available, are deemed unusable in this study. However, for calculating Fj, we require data in all the VZA and RAA bins. Therefore, we resort to CERES observations for all VZA bins while bearing in mind that the data in the higher VZA bins may not be representative. The use of CERES observations at higher VZA bins poses an uncertainty in our flux (Fj) and ADM calculation. We assess this uncertainty by varying the shortwave radiance in VZA = 70–90 bin by ±10%. This results in a ±2 Wm−2 (1.35%) difference in Fj and the ADM values differ by ±0.013 (1.32%).
 Examples of the dependence of EADM on RAA and VZA are shown in Figure 5. Each plot in this example belongs to a given SALB, AOT and SZA bin, as indicated. Variation of EADM is shown for RAA bins (0–180). In each plot of the Figure 5, we find that the anisotropic factor increases with increase in RAA except for VZA = 0–10 where the EADM is nearly constant, as expected. The peak in the EADM occurs at RAA = 180 which is the backscattering direction (Sun side). The peak is expected at RAA = 180 and is caused by the opposition effect or the hot spot which is a directional signature of surface reflectance over rough surfaces such as the broadleaf forest area in our study region. It is observed when the target is illuminated from directly behind observer (i.e., RAA = 180 which is defined as the Sun side in this study) at which phase angle there are no shadows from the target. The peak is pronounced for clear atmospheric conditions and we see the magnitude of EADM (at RAA = 180) decreases with increase in AOT value (Figures 5d–5i). The dependence of EADM on SALB, AOT, SZA and VZA is discussed in detail below.
Figure 6 shows sample EADMs as a function of surface albedo (SALB) and VZA. The SZA bin for above plots is 30–40.The positive values of VZA correspond to RAA bin 0–30 (forward scattering direction) and negative values of VZA correspond to RAA bin 150–180 (backscattering direction/Sun side). The 3 plots belong to 3 different AOT bins while the different line colors depict different SALB bins. Two effects are observed when SALB increases. First, in forward (backward) scattering direction, the EADM value decreases (increases) with increase in SALB. Second, increasing AOT increases variance in EADM as well as its magnitude in the backscattering direction. This shows that the anisotropy in radiance field changes with changing AOTs. As expected, a peak in the EADM is observed in the backward scattering direction, when the SZA bin value (30–40 here) is nearly equal to the VZA bin value.
Figure 7 is similar to Figure 5 except it shows the sample EADMs as a function of AOT (colored lines) and VZA in forward and backscattering directions. The five plots belong to 5 different SALB bins while the different line colors depict different AOT bins. Figure 7 shows that for each SALB bin, EADM value increases with increase in AOT in the forward scattering direction for VZA > 30. For VZA between 0 and 30 degrees, the variation of EADM with AOT is very small. However, in the backward scattering direction, EADM value decreases with increase in AOT in all SALB bins. When the scattering in forward direction increases, the backward scattering decreasing and therefore at RAA = 180 we see the decrease in EADM values with increase in AOT.
 The solar zenith angle dependence of EADM values is shown in Figure 8. We find that the EADM values decrease with increase in the given SZA range (20–50) in forward (backscattering) direction for 0 < VZA < 50 (0 < VZA < 40). See Figures 8a and 8d for an example. Figures 8a and 8d also show that the EADM values decrease with increase in AOT for angular bins mentioned above. In the forward (RAA = 0–30) and backscattering (RAA = 150–180) directions, EADM increases with SZA for VZA > 50 and 40 respectively (see Figures 8b, 8c, 8e, and 8f). In the forward scattering direction (Figures 8b and 8e), EADM increases with increase in AOT for higher viewing zenith angles (VZA > 50). In the backscattering direction (RAA = 150–180), however, EADM decreases (Figures 8c and 8f) with increase in AOT for VZA > 40.
 Finally, the new EADM are used to calculate the instantaneous TOA shortwave fluxes as follows. A look-up table consisting of the SALB, AOT, SZA, VZA, RAA, the TOA bin-average SWR, Fj, and the EADM value is generated. This look-up table is used to identify the EADM value for a given CERES radiance observation and to convert this radiance to TOA instantaneous flux using equation (3). As suggested by Loeb and Kato , the TOA instantaneous flux is defined at 20 km using equation (8). Figure 9 shows the intercomparison of shortwave flux (ESWF) at 20 km calculated from new EADM (dashed line) and CERES SWF (CSWF) from the SSF product (solid line) against AOT. Figure 9 shows that for AOT < 0.3, ESWF is less than the CSWF and for AOT > 0.3 the ESWF is higher than the CSWF. The differences can be attributed to aerosol information used in estimating the empirical anisotropic factors. A spatial distribution of AOT shows that AOT > 0.3 comes from the Amazon region with broadleaf forest area while AOT < 0.3 mostly belongs to the Cerrado or Savanna-like region. Since the two areas have differing ecosystem types, the microphysical properties of aerosols from burning of these fuels are different and so are the optical properties such as the AOT [Reid et al., 2004, 2005]. Since EADMs are sorted by these AOT values, the spatial distribution of AOT manifests into the differences in ESWF and CSWF around AOT = 0.3, as shown in Figure 9. Figure 9 also shows that ESWF has a higher slope than the CSWF. We further investigate the nature of the differences in CSWF and ESWF by comparing them for (1) average aerosol skies during biomass burning period (2) heavy aerosol skies, and (3) totally clear sky (AOT = 0.03). The average, heavy and clear aerosol skies are defined by AOT values. Results for the above scenarios are tabulated in Table 1 and shown in Figure 10. Table 1 shows mean AOT and SWF values over the AOT bin and SWF Difference = CERES_SWF – EADM_SWF. We find that for average AOT conditions (0.17) and average surface albedo values (0.135, see bin 0.12–0.14 values in Figure 10), the difference between CSWF and ESWF is <−0.4 Wm−2 (i.e., EADM flux is biased higher). For lower and higher AOT values, the difference varies from −4.6 to 3.3 Wm−2. This analysis shows that the CERES SWF is biased higher (lower) in regions with AOT less (greater) than the seasonal average AOT over the study region. This is because the CSWF correspond to some average AOT conditions as all cloud free observations that contain aerosols are used in the CERES clear-sky ADM construction over land. Therefore, when AOT is lower than the average, the CSWFs are higher and vice versa. Figure 10 depicts the above and clearly shows that that for average AOT and average SALB (0.12–0.14) conditions, ESWF is indeed close to CERES derived shortwave fluxes. These differences between CSWF and ESWF have important implications for shortwave aerosol radiative forcing (SWARF) estimates. SWARF is the difference between TOA SWF in the absence and presence of aerosols. The lower slope value of CSWF indicates that SWARF will be underestimated when CSWF is used for SWARF calculation. In a companion paper, the SWARF for the study region and period is estimated using existing CSWF and ESWF from this study and differences are discussed in detail therein.
Table 1. Mean Difference Between CERES SWF and EADM SWF Over Different AOT Binsa
Cross-track scan-mode CERES SWF and EADM SWF data for biomass burning season (August-October) from all available years of data (2000–2007) were used in the tabulated calculation. The SWF difference = CERES SWF – EADM SWF.
5. Sources of Uncertainty and Biases in Empirical ADMs
 As discussed in the manuscript, the availability of data in all the angular bins is crucial in calculating the angular distribution models empirically. Several issues related to the data availability can contribute to the uncertainty or biases in the empirical ADMs. The first step toward calculating EADMs is the cloud clearing of the radiance data used to calculate EADMs. Although a very stringent cloud-clearing approach (CERES FOV should be 99.5% cloud free) is adopted in our study, there could still be some cloud contamination. We try to minimize this by using 3 different cloud masks available in the SSF data. Biases or errors due to cloud contamination will be addressed in detail in our future research work. Another source of uncertainty is from the uncertainty in radiance calibration (∼1% [Priestley et al., 2000]). The empirical ADMs in this study are calculated by sorting the radiance data into discrete angular bins. The size of the bins can affect the EADM values. However, as discussed in section 3.2.4, we choose bin sizes such that, over a given bin, the standard deviation in radiances is <4 Wm−2 sr−1. This choice results in the availability of 90% of the clear-sky data and guarantees that the data sample size in a bin is reasonable (at least 8 data points). We use CERES radiances for VZA ranging from 0 to 90 degrees. The CERES radiance in higher VZA bins is, however, not very reliable [Loeb et al., 2005]. This poses an uncertainty in our flux (Fj) and ADM calculation. We assess this uncertainty by varying the shortwave radiance in VZA = 70–90 bin by ±10%. This results in a ±2 Wm−2 difference in Fj and the ADM values differ by ±0.013. We use the MODIS broadband albedo product to characterize the dependence of ADMs on surface properties. Any uncertainty in the albedo product will propagate into the EADM calculations. However, the albedo product is derived from multiple clear-sky observations and “must therefore contend with issues of cloud clearing, snow detection, and aerosol correction as well as sensor-specific matters of view angle, spatial footprint, gridding, repeat cycles, and narrowband-to-broadband conversion. These challenges have been successfully overcome in albedo-retrieving algorithms such as those of MODIS (Lucht et al., 2000; Schaaf et al., 2002, 2008; Wanner et al., 1997)” [Román et al., 2010]. Therefore, we expect any bias introduced to our EADM from the use of MODIS albedo data to be small and this will be estimated in our future work. Another source of bias could be the use of both Terra and Aqua observations. The CERES instruments are not intercalibrated and the same goes for the MODIS instruments on the two satellites. So, there could be two sources of biases due to calibration differences: (1) difference in TOA CERES shortwave radiances (2) differences in MODIS AOT from Terra and Aqua. Loeb et al.  suggest that ADMs from Terra and Aqua differ primarily in polar regions due to differences in cloud mask. On the other hand, studies suggest that the differences in AOD retrievals for both AQUA and Terra MODIS are rather minimum [<1%], and both products perform reasonably well over dark surface such as our study regions. We expect the differences to be within the uncertainty of the aerosol products [Remer et al., 2005; Levy et al., 2009]. We investigate the issues outlined above and validate the shortwave fluxes derived from our EADMS in our companion paper.
6. Summary and Conclusions
 Using 22 months of all available (2000–2008) TOA shortwave radiance measurements from CERES instrument onboard Terra and Aqua satellites, new empirical angular distribution models for smoke aerosols are constructed in this study. The cloud free EADMs are constructed for the biomass burning season (August-October) in South America. The angular models cannot be applied to other geographic regions. Separate ADM will have to be developed even for other biomass burning regions in the world, such as for Africa where the aerosol properties differ from that in South America. The new EADMs are characterized by surface albedo, aerosol optical thickness, solar zenith angle, viewing zenith angle and relative azimuth angle. The existing CERES angular models do not account for aerosols over land. The AOT used to characterize the new EADMs accounts for the variation in aerosol concentration as well as the optical properties of aerosols. The EADM values or the anisotropy increases with increase in AOT except in the backscattering direction (RAA > 150) and for SZA > 30 where the anisotropic factor decreases with increase in AOT. The sensitivity of EADM to AOT is highest in the forward scattering direction (RAA bin = 0–30 in this study). The variation in EADM with AOT is larger when surface is darker (albedo < 14%). Also, the EADM is found to be more sensitive to AOT at higher viewing zenith angles (>40). This study clearly demonstrates the contribution of aerosols to the anisotropy in the scattered radiance field. This study suggests that depending on AOT, the clear-sky TOA CERES shortwave fluxes may be either underestimated or overestimated if aerosol contribution in the ADM in not accounted for. We find that the slope of the empirically derived radiative fluxes and aerosol optical thickness relation is higher than that of the CERES shortwave fluxes and aerosol optical thickness. This suggests that the TOA radiative forcing due to aerosols, under cloud free conditions, could be underestimated when derived from CERES shortwave fluxes. In a companion paper we estimate the shortwave aerosol radiative forcing.