The direct radiative forcing of aerosols (DARF) can be defined as the difference between the upward radiation flux at the TOA measured in background (Fcl) and polluted (Fpol) conditions: DARF=Fcl-Fpol. For each scene observed by CERES, Fpol can be directly obtained from the mean flux at the TOA for each 0.5∘ × 0.5∘ grid cell. To calculate the instantaneous DARF, we need to estimate what would be the flux at the TOA for background conditions (Fcl) for the same illumination geometry of the polluted scene. To perform this estimate, scenes that presented aerosol optical depth (AOD) smaller than 0.1 were selected, and considered as background scenes. This threshold was selected by analysing AERONET's AOD during the wet season. For each cell, the flux at the TOA observed for background scenes (Fcl) during the 40 months studied period was plotted against the cosine of the solar zenith angle (cos⁡(θ0)). An example of this plot, for the grid cell centred at latitude 8.75∘ S and longitude 53.75∘ W, is shown in Fig. 1. A correlation coefficient of 0.94 between Fcl and cos⁡(θ0) was observed for the data points within this cell indicating the adequacy of the linear approximation. It is worth emphasizing that this example is not a best-case scenario. In fact, more than 80 % of the cases analysed showed a correlation larger than 0.90 between Fcl and cos⁡(θ0).

The solar zenith angle varied from about 10 to 52∘ at Terra satellite passage time over the Amazonia during the study period. For this solar zenith angle range, Fcl varies linearly with cos⁡(θ0). By adjusting a linear fit to the data points within each cell we can calculate Fcl(θ0) for any illumination geometry, according to Fcl(θ0)=Acos⁡(θ0)+B, where A and B correspond to the slope and the intercept of the linear fit, respectively.

To assess the instantaneous DARF, the mean solar zenith angle within each cell during the satellite passage time was identified for every polluted scene. For each cell, the instantaneous DARF was evaluated as the difference between Fcl(θ0) and the mean flux at the TOA retrieved by CERES in polluted conditions (Fpol(θ0)), as previously stated in Eq. (1). The uncertainty of the DARF in each cell (σDARF), was computed using error propagation, according to σDARF2=σA2cos⁡2(θ0)+σB2+2cov(A,B)cos⁡(θ0)+σFpol2, where σA, σB and cov(A,B) are the uncertainty of the slope, intercept and the covariance between the slope and the intercept, respectively; σFpol is the uncertainty of the flux in each cell for the polluted condition.

As already discussed, to convert CERES radiance measurements to radiative flux at the TOA it is necessary to define the angular distribution models (ADMs) for different scenes (Loeb et al., 2005). In a recent work, Patadia et al. (2011) pointed out that the angular distribution models currently used by CERES team to derive shortwave fluxes at the TOA over land in cloud-free conditions do not take into account aerosol properties in the observed scene. This can result in large errors in the shortwave fluxes derived by this sensor for areas with high concentrations of aerosols, such as the Amazonia during the biomass burning season. To estimate the impact of the anisotropy caused by high aerosol loading on the flux at the TOA, Patadia et al. (2011) developed a methodology to obtain new empirical angular distribution models for the Amazon Basin region during the dry season. The authors used radiance measurements obtained by CERES shortwave channel over the Amazonia for different view and solar illumination geometries between 2000 and 2008. In a later work they assessed the difference between the DARF evaluated using both CERES ADMs and their new empirical ADMs (Patadia and Christopher, 2014). They found that, on average, CERES DARF relates to the corrected DARF calculated with their empirical ADMs, according to the following equation: DARFcorrected=DARF-17.12AOD-0.93. The correction proposed by Patadia and Christopher (2014) was applied to the CERES-MODIS DARF estimates introduced in the previous section.

A discrete-ordinate radiative transfer (DISORT) code (Stamnes et al., 1988) was used to expand the instantaneous radiative forcing, calculated for the satellite passage time, to 24 h averages. MODIS BRDF/Albedo Model (MCD43B1) retrievals (Schaaf et al., 2002) over the studied area were used to develop the surface albedo models used in the radiative transfer calculations. Aerosol optical properties retrieved by the AERONET (Aerosol Robotic Network) ground-based sun photometers (Dubovik and King, 2000) located in the Amazonia during the dry season were also used in this computation. For a detailed description of the methodology used to perform this expansion please refer to Sena et al. (2013).

In Brazil, most fires occur on the southern and eastern borders of the Amazon Basin, in a region known as the “arc of deforestation” (Malhi et al., 2008; Morton et al., 2008). During the dry season low-level Easterly winds dominate the atmospheric circulation over central South America (Nobre et al., 1998). Due to this dynamical feature, smoke particles are transported towards the forest and the Andes mountain range, where eventually wind direction changes (Freitas et al., 2009). Biomass burning aerosols can be transported over long distances away from their sources (Andreae et al., 2001; Freitas et al., 2005; Longo et al., 2009; Mishra et al., 2015) and cover large areas of up to millions of km2 (Prins et al., 1998). Aerosol transport during the biomass burning season can significantly modify the spatial distribution of the DARF from one day to another. Two examples of the spatial distribution of the 24h-DARF, for 13 and 15 August 2005, are shown in Fig. 2, with their respective uncertainties. Composite images from MODIS's red, blue and green spectral channels are also shown in this figure.

Figure 2 shows that, on 13 August 2005, the smoke plume covers a large area of the Brazilian Amazonia, between 4 and 12∘ S and 55 and 70∘ W. The 24h-DARF over the area was particularly high for that day, varying from about -30 to -15 W m-2. On 15 August 2005, we note that the smoke plume has moved southeast, following the Andes mountain range line, strongly impacting the southern Amazonia, western Bolivia and northern Paraguay. The area located between 8 and 20∘ S and 57 and 65∘ W showed the highest 24h-DARF values for that day, also ranging from -30 to -15 W m-2. The 24h-DARF showed in Fig. 2b was, on average, -14.3 ± 0.3 W m-2 on 13 August and -15.6 ± 0.3 W m-2 on 15 August. These results clearly show the importance of wind circulation in the transport of aerosol plumes and how atmospheric dynamics may influence the shortwave radiative balance of the region.

Due to the short lifetime of aerosols in the atmosphere, the DARF may vary largely during the 2 months of the biomass burning season. To analyse this temporal variability, the average of the 24h-DARF over the study area was calculated for each day of the year. Time series of the mean daily DARF during the biomass burning season from 2000 to 2009 are illustrated in Fig. 3. Due to a problem in CERES-SSF data processing, the year 2004 presents a high amount of missing values for aerosol and cloud properties in its database. Therefore this year was not included in Fig. 3, nor in the forthcoming analysis.

Figure 3 shows that, besides its large interannual variability, the DARF also varies widely along the biomass burning season. Different temporal patterns along the biomass burning season are observed depending on the year. For example, for most of 2005's dry season, the DARF showed little variation, averaging around -9 ± 2 W m-2. On the other hand, in 2007, the DARF became gradually more negative, starting around 0 W m-2 in the beginning of August and reaching values of the order of -25 W m-2 at the end of September. However, 2005 and 2007 both present similar mean 24h-DARF during the burning season, as will be shown in the next section (Fig. 4). The DARF was also near-constant during the dry season of 2009. For most of the years, however, the temporal variation pattern during the biomass burning season was neither constant nor linear. In 2002 the DARF decreases in the beginning of the dry season and then saturates at about -5 W m-2. In 2006 the DARF follows a similar pattern to that of 2002, saturating at about -10 W m-2 and increasing once again in the end of September. For the remaining years (2000, 2001, 2003 and 2008) the seasonal variability of the DARF was more complex, with the DARF increasing/decreasing more than once during this 2-month period.

The interannual variability of the DARF can also be observed. The impact of smoke aerosols in the radiative balance of 2005 and 2007 was very pronounced, while the DARF was very close to zero during the whole biomass burning season of 2009. The high DARFs in 2005 and 2007 are associated with severe droughts that contributed to forest and savanna fires and high aerosol loadings in these years (Marengo et al., 2008; Ten Hoeve et al., 2012). On the other hand, the rainfall over the Amazonia in 2009 was extremely high (Satyamurty et al., 2013), which contributed to the decrease in the number of fire sources and the efficient removal of smoke aerosols from the atmosphere. These results indicate that rainfall patterns and the interannual variability of the DARF are likely related. Socio-economical changes, related to land-use and deforestation, can also affect aerosol loading (Davidson et al., 2012), and therefore contribute to the DARF variability.

The daily DARF variations from one day to another, shown in this figure, are mainly due to changes at the MODIS imaged area, which varies according to the satellite track. Due to its polar orbiting track, every day the scanned area slightly changes, finally repeating itself after about 16 days. Depending on Terra track, for some cases MODIS does not cover areas heavily impacted by smoke aerosols, and the mean 24h-DARF could be underestimated. Cloud cover can also change significantly in short periods of time (2–3 days), and this can strongly impact daily DARF retrievals. Furthermore, the daily DARF variation is also influenced by changes in fire source location and transport along the biomass burning season.

In previous studies (Patadia et al., 2008; Sena et al., 2013), the average of the direct radiative forcing of aerosols during the biomass burning season over the Amazonia was also calculated by using CERES and MODIS sensors. In those approaches, the average flux for clean conditions during the biomass burning season (BBSFcl) for each cell grid was estimated from the intercept of the regression between TOA fluxes and AOD retrievals from August to September. The mean DARF during the biomass burning season (BBSDARF) was then calculated by subtracting the mean flux at the TOA (BBSFpol) from the mean flux for clean conditions (BBSFcl) observed as averages during this 2-month study period. The DARF calculated using this methodology considers the total effect of aerosols. Since the flux for clean conditions (Fcl) is defined for AOD = 0, the effect of smoke aerosols cannot be isolated from the effect of background aerosols. Thus the total effect of aerosols from both background and polluted conditions are included in the BBSDARF.

The new methodology introduced here (Sect. 2.1), provides the 24h-DARF for each individual day, with a much higher temporal resolution than the one used in previous studies. Furthermore this new methodology considers a more realistic clean condition, by defining Fcl in the presence of background aerosols. Since background aerosols are always present in the atmosphere, the contribution of background aerosols to the radiative balance should not be considered as forcing in the strict sense. In fact, some authors define the contribution of background + polluted aerosols as the direct radiative effect instead of direct radiative forcing (e.g. Yu et al., 2006).

In this section we have compared the DARF obtained using the new methodology introduced in Sect. 2.2 with the seasonal DARF values calculated previously by Sena et al. (2013). For this comparison, the daily DARF, obtained in this work, was averaged between the months of August and September of each year (〈24h-DARF〉BBS). To ensure that we make a fair comparison, the corrections proposed by Patadia and Christopher (2014), and used for the evaluation of the 24h-DARF in this paper (Sect. 2.2), were also applied a posteriori to the Sena et al. (2013) seasonal forcing (BBSDARF). Figure 4 shows the mean AOD at 550 nm during the biomass burning, and the comparison between 〈24h-DARF〉BBS and BBSDARF, calculated over the studied area, from 2000 to 2009. Once again, 2004 was excluded from the analysis, due to CERES-SSF database problems discussed in the previous section.

Figure 4 shows that the 〈24h-DARF〉BBS is always lower than the BBSDARF. The average of the BBSDARF for this 10-year period (2000 to 2009) is -8.2 ± 2.1 W m-2, while the 10-year average of the 〈24h-DARF〉BBS is -5.2 ± 2.6 W m-2. Two factors contribute to this difference: (i) different references were used at the assessment of the clean flux, Fcl, in each methodology (AOD = 0 vs. background conditions), and (ii) CERES-SSF product provides an older MOD04 collection before 2005, and this strongly affects BBSDARF retrievals. In the following paragraphs, these DARF differences and their sources will be further explored.

SBDART (Santa Barbara DISORT Radiative Transfer model) (Richiazzi et al., 1998) calculations suggest that the contribution of background aerosols at AOD = 0.1 to the 24h-DARF over the Amazonia is about -2 W m-2. Hence, the contribution of background aerosols may explain the magnitude of the differences in the radiative forcings obtained from 2005 on, but not before that year. Part of the DARF differences observed from 2000 to 2003 are very likely associated with the aerosol optical properties contained in CERES-SSF product, Edition 3A, used both in this work and by Sena et al. (2013). This product provides aerosol optical properties calculated using MODIS aerosol algorithm MOD04 collection 4 until mid-2005, and MOD04 collection 5 after that date. A major difference between aerosol optical depths obtained by these two collections is due to the fact that collection 4 does not allow negative values of AOD, while for collection 5, the lowest limit for the AOD is -0.05, to account for the uncertainty of the retrieved AOD. Therefore, for low aerosol loading, when AOD from MOD04 collection 4 is projected to CERES lower resolution, it may be overestimated, since negative AOD values were removed from the average. Thus, when applying the methodology used by Patadia et al. (2008) and Sena et al. (2013), to CERES-SSF data that contained MOD04 collection 4 AOD, the BBSFcl is underestimated and, therefore, the BBSDARF is overestimated (Fig. 5). This explains the differences between both DARF evaluations observed in Fig. 4.

The solar zenith angle strongly influences the upward flux at the TOA (FTOA). CERES fluxes retrievals obtained over the same surface, for the same aerosol loading and same atmospheric conditions, and at different illumination geometry will present different FTOA. In the previous methodology used in Sena et al. (2013), 2 months of data were used to estimate the BBSDARF through the linear fit of FTOA by AOD. Thus, flux measurements performed on different days and at different times (and therefore different solar zenith angles) contributed to increase the dispersion of the points on the y-axis, increasing the uncertainty of BBSDARF. In the new methodology, the DARF is obtained as a function of the solar zenith angle, which eliminates the noise caused by solar zenith angle variations, observed in previous studies. This was another important improvement of the methodology proposed in this work over the previously used methodology.

It is also important to emphasize that both methodologies are applied only in cloud-free conditions. MODIS Level 3 cloud fraction retrievals indicate that during the study period (August to September) the cloud fraction over Amazonia is on average about 47 %, during Terra morning passage (about 10:30 a.m. LT), increasing to about 56 %, during the afternoon (Aqua passage time is about 1:30 p.m.). Therefore, the mean 〈24h-DARF〉BBS over the whole study area weighted by cloud cover is about -2.6 W m-2.

The mean correlation between the AOD 550 nm and the 〈24h-DARF〉BBS from 2000 to 2009 is -0.86 ± 0.03, which is better than the mean correlation between the AOD and BBSDARF previously obtained, of -0.75 ± 0.05. This is another indication that the new daily methodology proposed here is more robust to evaluate the DARF than the seasonal averaged methodology used in previous studies.

AERONET is one of the most successful ground-based global networks of sun/sky radiometers for studying and monitoring aerosol physical properties around the world (Holben et al., 1998). Direct and almucantar measurements from AERONET radiometers are used to retrieve AOD and several column-averaged aerosol optical and physical properties in different spectral bands. Extinction measurements on the spectral channel centred at 940 nm are used to assess column water vapour (Halthore et al., 1997). In its inversion product version 2.0, AERONET provides cloud-free sky DARF estimates evaluated using the radiative transfer code GAME (Global Atmospheric Model) (Dubuisson et al., 1996). The aerosol and surface models used in GAME are based on mean column averaged aerosol optical properties retrieved by AERONET's inversion algorithm (Dubovik and King, 2000) and surface properties retrieved by MODIS bidirectional reflectance product (Lucht et al., 2000; Schaaf et al., 2002), respectively.

The CERES-MODIS DARF, calculated according to the methodology described in Sect. 2.1, was compared with the DARF reported by AERONET's inversion product. For this, we selected forcing results, located within ± 25 km of the AERONET sites that operated in the Amazonia during the study period (Abracos Hill, Alta Floresta, Balbina, Belterra, Cuiabá, Ji-Paraná and Rio Branco). AERONET's almucantar measurements, needed to calculate the radiative forcing, are made only when the solar zenith angle is larger than 50∘. However, during the dry season, at the time Terra overpasses the study region (around 10:30 LT), the solar zenith angle is on average around 33∘. For this reason, there were no coincident instantaneous DARF retrievals from CERES-MODIS radiometers and AERONET sun photometers. To compare the results, the instantaneous DARF, obtained by both CERES-MODIS and AERONET, were expanded to 24 h average DARF using the methodology described in Sena et al. (2013). A comparison between the 24h-DARF at the TOA obtained using AERONET and CERES-MODIS is shown in Fig. 6.

By applying a linear fit to the data points of Fig. 6, we see that the 24h-DARF derived from CERES-MODIS relates with the 24h-DARF reported by AERONET through the following equation: DARFCERES-MODIS24h=(1.07±0.04)DARFAERONET24h-(0.0±0.6). According to this equation, the agreement between CERES-MODIS and AERONET 24h-DARF is acceptable within the standard deviations of the fitted parameters. This is a remarkable result, since the 24h-DARF retrievals, shown in Fig. 6, were obtained by applying completely different methodologies, and using different instruments. AERONET sun photometers are at the surface and CERES-MODIS instruments are at 705 km aboard Terra satellite both looking at the atmospheric column. Besides that, as explained above, the instantaneous observations that were used to calculate the 24h-DARF, compared in our analysis, were performed at different hours of the day. All those differences contribute to the dispersion of about 5 W m-2 around the adjusted line. The uncertainties involved in the surface and aerosol optical models used in GAME's radiative transfer code to calculate AERONET's DARF can also contribute to this dispersion. These results indicate a high agreement between the 24h-DARF obtained by these two independent procedures.

It is also important to intercompare satellite remote sensing retrievals with ground-based measurements. In order to properly do that, we compare CERES-MODIS data at the TOA with SolRad-NET (Solar Radiation Network) pyranometers at the bottom of the atmosphere (BOA), using SBDART calculations to link BOA to TOA. To formulate the surface models used in SBDART, we selected 50 km × 50 km areas centred at the AERONET stations listed in Sect. 4.1. For each selected area, the spectral surface albedo was obtained from the linear interpolation of MODIS MCD43B1 surface albedo retrievals in seven wavelengths (Lucht et al., 2000; Schaaf et al., 2002). The aerosol models used in these simulations were built using daily averages of intrinsic aerosol optical properties retrieved by AERONET. The aerosol optical depth and column water vapour measured by AERONET sun photometers within ± 1/2 h of Terra's timepass over each site were also used as inputs in the radiative transfer code. The shortwave downward flux at the surface and the DARF at the TOA were computed by SBDART and compared with ground-based sensors solar flux measurements and with CERES-MODIS DARF, respectively.

Figure 7 shows the comparison between the downward flux at the surface (F↓BOA) calculated by SBDART between 0.3 and 2.8 µm and coincident solar flux measurements at the surface in the same spectral range from SolRad-NET pyranometers, that are collocated with AERONET sun photometers. A linear fit of the downward flux measured by the pyranometer at the surface (FBOAPYRANOMETER) and calculated by SBDART (FBOASBDART) indicate that these variables are related through the following equation: FBOAPYRANOMETER=(1.00±0.04)FBOASBDART-(20±27). Equation (6) shows that the agreement between calculated and measured BOA fluxes is acceptable within the standard deviations. The apparent mismatch of about 20 W m-2 between the calculated and measured values represents approximately 2.2 % of the downward flux at the surface, and this is close to the instrumental uncertainty of the pyranometer, reported as 2 %. These results show a good agreement between the downward irradiance at the surface, calculated using SBDART and SolRad-NET pyranometer measurements.

The intercomparison between the instantaneous TOA DARF obtained using CERES-MODIS and calculated using SBDART is shown in Fig. 8. The data points in this graph have a dispersion of about 10 W m-2 around the 1 : 1 line. A linear fit of the data plotted in Fig. 8 shows that the instantaneous TOA DARF obtained from CERES-MODIS and from SBDART relate through the following equation: DARFCERES-MODIS=(0.86±0.06)DARFSBDART-(6±2). Several issues in this comparison must be taken into account. First the upward flux is strongly influenced by the surface reflection. MODIS sensor presents low spectral resolution in the shortwave spectrum and this limits the surface albedo model used as input in SBDART. Secondly, the atmosphere has to be taken into account twice: on the downward and upward path. This amplifies any inaccuracy in the optical properties assumed in the SBDART calculations.

Small deviations in the estimates of aerosol single-scattering albedo can generate large differences in the forcing calculated by radiative transfer codes (Loeb and Su, 2010; Boucher et al., 2013). To assess the impact of the uncertainties associated with different single-scattering albedo values, the 24h-DARF was computed in SBDART as a function of AOD at 550 nm for different values of single-scattering albedo at 440 nm (ω0=0.89, 0.92 and 0.95) (Fig. 9). The differences of ± 0.03 in ω0, used in these simulations, correspond to the uncertainty of the single-scattering albedo inverted by AERONET.

According to Fig. 9, a variability of 0.03 in the estimate of the single-scattering albedo for the mean AOD observed over the Amazonia (0.2 to 0.4) would affect the 24h-DARF in about 1 to 2 W m-2. To evaluate if these values are consistent with the 24h-DARF variation observed by AERONET, the database was divided in AOD bins of 0.05 and the standard deviation of AERONET's 24h-DARF on each bin was analysed. This analysis showed that for AOD varying from 0.2 to 0.4, the standard deviation of AERONET's 24h-DARF on each bin varied between 1.5 and 2.7 W m-2. This variation is higher than the one obtained using SBDART, because in those simulations, only single-scattering albedo was changed and other aerosol and atmospheric properties were fixed. However, there are other variables that influence the 24h-DARF observed by AERONET besides single-scattering albedo, such as scattering phase function, size distribution and atmospheric water vapour content. These values are very significant and they show that aerosol single-scattering albedo is a critical parameter to accurately assess DARF.

Considering all potential sources of uncertainties on aerosol and surface albedo models used in SBDART to compute the DARF, it is possible to consider the comparison shown in Fig. 8 as satisfactory. It is important to note that this validation consists of an indirect comparison, since, as previously discussed, it is not possible to obtain the flux at the TOA by direct methods.