Next-generation angular distribution models for top-of-atmosphere radiative flux calculation from CERES instruments : validation

Radiative fluxes at the top of the atmosphere (TOA) from the Clouds and the Earth’s Radiant Energy System (CERES) instrument are fundamental variables for understanding the Earth’s energy balance and how it changes with time. TOA radiative fluxes are derived from the CERES radiance measurements using empirical angular distribution models (ADMs). This paper evaluates the accuracy of CERES TOA fluxes using direct integration and flux consistency tests. Direct integration tests show that the overall bias in regional monthly mean TOA shortwave (SW) flux is less than 0.2 Wm and the RMSE is less than 1.1 Wm. The bias and RMSE are very similar between Terra and Aqua. The bias in regional monthly mean TOA LW fluxes is less than 0.5 Wm and the RMSE is less than 0.8 Wm for both Terra and Aqua. The accuracy of the TOA instantaneous flux is assessed by performing tests using fluxes inverted from nadirand oblique-viewing angles using CERES along-track observations and temporally and spatially matched MODIS observations, and using fluxes inverted from multi-angle MISR observations. The averaged TOA instantaneous SW flux uncertainties from these two tests are about 2.3 % (1.9 Wm) over clear ocean, 1.6 % (4.5 Wm) over clear land, and 2.0 % (6.0 Wm) over clear snow/ice; and are about 3.3 % (9.0 Wm), 2.7 % (8.4 Wm), and 3.7 % (9.9 Wm) over ocean, land, and snow/ice under all-sky conditions. The TOA SW flux uncertainties are generally larger for thin broken clouds than for moderate and thick overcast clouds. The TOA instantaneous daytime LW flux uncertainties derived from the CERESMODIS test are 0.5 % (1.5 Wm), 0.8 % (2.4 Wm), and 0.7 % (1.3 Wm) over clear ocean, land, and snow/ice; and are about 1.5 % (3.5 Wm), 1.0 % (2.9 Wm), and 1.1 % (2.1 Wm) over ocean, land, and snow/ice under all-sky conditions. The TOA instantaneous nighttime LW flux uncertainties are about 0.5–1 % (< 2.0 Wm) for all surface types. Flux uncertainties caused by errors in scene identification are also assessed by using the collocated CALIPSO, CloudSat, CERES and MODIS data product. Errors in scene identification tend to underestimate TOA SW flux by about 0.6 Wm and overestimate TOA daytime (nighttime) LW flux by 0.4 (0.2) Wm when all CERES viewing angles are considered.


Introduction
The Clouds and the Earth's Radiant Energy System (CERES) instruments have been providing top-of-atmosphere (TOA) radiative fluxes to the scientific community since the late 1990s, and have resulted in about 900 peer-reviewed journal publications with over 26 000 citations (as of October 2014).These fluxes have been instrumental in advancing our understanding of the effects of clouds and aerosols on radiative energy within the Earth-atmosphere system.
The CERES instrument consists of a three-channel broadband scanning radiometer (Wielicki et al., 1996).The scanning radiometer measures radiances in shortwave (SW, 0.3-5 µm), window (WN,(8)(9)(10)(11)(12) channels at a spatial resolution of ∼20 km at nadir.The longwave (LW) component is derived as the difference between total and SW channels.These measured radiances at a given Sun-Earth-satellite geometry are converted to outgoing reflected solar and emitted thermal TOA radiative fluxes using CERES angular distribution models (ADMs).
Published by Copernicus Publications on behalf of the European Geosciences Union.Su et al. (2015) described the methodology used to develop the next-generation CERES ADMs, which were developed using the latest cloud algorithms (Minnis et al., 2010).These newly developed ADMs are used to produce the Edition 4 Single Satellite Footprint TOA/Surface Fluxes and Clouds (SSF) product for Terra and Aqua and Edition 1 SSF product for Suomi NPP, whereas fluxes in the Edition 2 and 3 SSF products are inverted using the ADMs described in Loeb et al. (2005).These ADMs are constructed using data taken in the rotating azimuth plane (RAP) scan mode.In this mode, the instrument scans in elevation as it rotates in azimuth, thus acquiring radiance measurements from a wide range of viewing combinations.Distinct ADMs are developed for different scene types, which are defined using a combination of variables (e.g., surface type, cloud fraction, cloud optical depth, cloud phase, aerosol optical depth, precipitable water, lapse rate).Scene type classifications are based upon imager (Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua and Visible Infrared Imaging Radiometer Suite (VIIRS) on NPP) measurements within each CERES footprint.The CERES/MODIS and CERES/VIIRS cloud algorithms retrieve cloud fraction, cloud optical depth, cloud top and effective pressure/temperature (among other variables) for every MODIS and VIIRS pixel (Minnis et al., 2010).These pixel-level cloud properties are spatially and temporally matched with the CERES footprint, and are averaged over the CERES footprints by accounting for the CERES point spread function (PSF, Smith, 1994).Spectral radiances from MODIS and VIIRS observations are also averaged over CERES footprints weighted by the CERES PSF, and are used for scene type classifications.Meteorological fields used for scene type classifications are from the Global Modeling and Assimilation Office's Goddard Earth Observing System (GEOS) version 5.4.1 data assimilation system for CERES.This version provides consistent analysis over the entire CERES data record.

W. Su et al.: Validation of the next-generation angular distribution models
The main objective of this paper is to validate the TOA SW and LW fluxes inverted using the ADMs developed by Su et al. (2015).As there are no direct radiative flux measurements at the TOA, we have to rely on indirect approaches to assess the errors in the TOA SW and LW fluxes due to uncertainties in ADMs.We use the direct integration (DI) method (Suttles et al., 1992;Loeb et al., 2003Loeb et al., , 2007a) ) to assess the flux errors on a regional and global scale (Sect.2).To assess the errors in instantaneous TOA fluxes, we rely on flux consistency tests between CERES and MODIS (Sect.3) and among different MISR (Multi-angle Imaging Spectro-Radiometer) cameras (Sect.4).As ADMs depend on scene type, misclassification of scene type will lead to incorrect selections of anisotropic factors and thus errors in the TOA fluxes.We take advantage of the merged CALIPSO, Cloud-Sat, CERES, MODIS (C3M) data product (Kato et al., 2010) to assess the flux errors due to scene identification uncertainties (Sect.5).

Shortwave
The direct integration (DI) method calculates the regional seasonal all-sky fluxes by directly integrating the CERES measured radiances (I o ) from both cross-track and rotating azimuth plane measurements: (1) Radiance measurements are composited over a region of 10 • latitude × 10 • longitude and over a 3-month period to ensure the full range of viewing zenith (θ ) and relative azimuth angle (φ) coverage needed for flux computation in a region.However, the standard DI approach also requires uniform angular sampling in each region.This requires that all portions of a 10 • latitude × 10 • longitude region contribute equally to the mean radiances in all angular bins.This requirement is problematic for CERES on Terra and Aqua, as their sunsynchronous orbits introduce a strong correlation between latitude and solar zenith angle (θ 0 ) and φ.
To overcome the limitation of the sun-synchronous orbit, the standard DI method was modified by constructing two sets of DI ADMs (Loeb et al., 2007a).One set is based upon the CERES measured radiance (I o ) and the other set is based upon the ADM-predicted radiance ( Î , see Eq. ( 1) in Su et al., 2015).Both I o and Î are sorted by viewing geometry (θ 0 , θ, φ) and the regional angular bin mean radiances (I o (θ 0 , θ, φ, reg) and Î (θ 0 , θ, φ, reg)) are used to construct the all-sky DI ADMs: and (3) Doing so ensures that both sets of the DI ADMs have the same sampling coverage, as for each I o , the CERES ADMs provide an Î .The two sets of seasonal ADMs are applied to the crosstrack data of the middle month of each season (i.e., January, April, July, and October) to calculate the instantaneous TOA fluxes for each 1  × 10 • .These gridded instantaneous fluxes are then converted to equivalent 24 h fluxes by applying a scaling factor determined from the ratio of the total daily insolation to the mean insolation at the satellites' overpass times.We then calculate the differences between these two sets of gridded 24 h fluxes and these differences are assumed to be representative of the monthly mean TOA flux error from uncertainties in the CERES ADMs. Figure 1 shows the monthly regional TOA SW flux error due to ADM uncertainties for 2002 CERES cross-track measurements on Terra.Here the flux error is defined as flux inverted from R minus flux inverted from R o .The gray color indicates that the TOA SW flux error is less than 1 Wm −2 , and about 86 % of the 1 • × 1 • grid boxes of the 4 months are shown in this color.There are about 5 % of the grid boxes that have a flux error greater than 2 Wm −2 , and they are mostly over high-latitude regions.The large uncertainties seen over the north of Greenland are due to snow identification errors.Some footprints over the glacial and rocky areas there are determined to be completely covered by a mixture of fresh and permanent snow.But it appears that these footprints are actually only partly covered by snow (especially in summer when the snow has melted).This means the ADM-predicted radiance is much higher than the actual radiance, leading to the high uncertainties for the spring and summer seasons.
Table 1 summarizes the global monthly mean TOA SW flux biases and RMSEs for the 4 months we discussed in Fig. 1 along with those for CERES Aqua 2004.SW flux biases and RMSEs derived using the Edition 3 SSF data and ADMs developed by Loeb et al. (2005) are included (in parentheses) for comparison.The magnitude of the largest SW flux bias in the Edition 4 SSF is 0.2 Wm −2 for July 2002, which is about half of the bias in the Edition 3 SSF.The RMSEs of Edition 4 SSF data are all smaller than those in Edition 3 SSF data.Comparison between the TOA SW flux errors derived using the Edition 4 SSF data and ADMs from Su et al. (2015) and using the Edition 3 SSF data and ADMs from Loeb et al. (2005) shows reduced biases for nearly all grid boxes with notable improvements over high-latitude regions.The improved flux accuracy is a result of improvements made in scene type identification (Minnis et al., 2010) and in anisotropy characterization (Su et al., 2015).

Longwave
The TOA longwave (LW) flux is a weak function of solar zenith angle, thus the correlations between latitude and θ 0 and φ introduced by a sun-synchronous orbit have a negligible effect on the sampling issue associated with the standard Figure 2 shows the regional distributions of TOA LW flux errors for the 4 months of 2002 using CERES Terra cross-track measurements.Here the flux error is defined as ADM-derived LW fluxes minus the DI LW fluxes.The TOA LW flux errors are less than 1 Wm −2 for about 87 % of the 1 • × 1 • regions (shown in gray color).Only 1.2 % of the 1 • × 1 • regions have flux errors greater than 2 Wm −2 , and they are mostly located over the sea ice and the Antarctic permanent snow regions.Table 2 summarizes the global monthly mean TOA LW flux biases and RMSEs for CERES Terra 2002 and for CERES Aqua 2004.LW flux biases and RMSEs derived using the Edition 3 SSF data and the ADMs from Loeb et al. (2005) are also included for comparison.The TOA LW biases for the Edition 4 SSF are less than 0.5 Wm −2 and the RMSEs are less than 0.8 Wm −2 for all months.In comparison, the TOA LW biases in the Edition 3 SSF are slightly smaller than those in the Edition 4 SSF, but their RMSEs are similar.This indicates that the small biases seen in the Edition 3 SSF product are often a result of compensating errors.This is confirmed by examining the regional and zonal distributions of the mean absolute biases (not shown).The most noticeable differences are over 50-70 • S, where the mean absolute biases in the Edition 4 SSF are higher for April and July.As described in Su et al. (2015), the new method used to construct LW ADMs over cloudy snow/ice scenes takes the cloud emissivity into account (via cloud optical depth).This could mean that cloud optical depth retrieval over sea ice under large solar zenith angles (> 60 • ) is less reliable, but further study is needed to quantify the cloud optical depth retrieval error.

Instantaneous TOA flux consistency test between CERES and MODIS
As flux should be independent of the satellite viewing geometry, we use a consistency check, in which fluxes for the same footprint inverted from different viewing geometries are compared, to assess the accuracy of instantaneous flux due to uncertainties in anisotropy characterization.However, the consistency test is not a guarantee of absolute accuracy as it does not account for potential bias errors that are independent of viewing geometry (Loeb et al., 2003), such as scene identification errors.
CERES views the same footprint from different viewing angles when operating in along-track mode.We choose not to directly compare fluxes inverted from different CERES angles, as the shape and size of the CERES footprints change with viewing zenith angle.Instead, we take advantage of the collocated MODIS pixels within a CERES footprint.The MODIS imager observes the same area as CERES within approximately 2 min, but from viewing zenith angles close to nadir.The MODIS pixel-level data are spatially and temporally matched with the CERES footprints, and are averaged over the CERES footprints by accounting for the CERES PSF.These CERES footprints are classified into 55 categories of cloud types, which are functions of cloud layer, cloud fraction, cloud optical depth, and cloud effective pressure (Table 4).Among them type 0 is for clear sky, types 1 to 27 are for single-layer cloud types, and types 28 to 54 are for multi-layer cloud types.
Narrowband radiances from MODIS channels of 0.65, 0.86, and 1.63 µm are converted to broadband shortwave radiance as follows: Narrowband radiance from the 11 µm MODIS channel is converted to broadband longwave radiance as follows: Regression coefficients (a i , i = 0, 3 and b i , i = 0, 1) are determined using collocated CERES cross-track near-nadir observations (θ < 10 • ) and MODIS observations.Regressions are derived on a daily basis for each equal-area 1 • latitude × 1 • longitude region, and separate daytime and nighttime LW regressions are obtained.Only CERES footprints belonging to the dominant cloud type over the 1 • × 1 • region are included in the regression to minimize the narrowbandto-broadband regression errors caused by spectral changes for different cloud types (including clear, see Table 4).Only those regions that have a RMSE less than 3 % in SW narrowband-to-broadband conversion are included in the SW analysis, and the narrowband-to-broadband conversion errors are generally about 1 % for different cloud types.Over the clear ocean, footprints with a glint angle less than 40 • are not included in the SW analysis.For LW, only those regions that have a RMSE less than 0.5 % in narrowband-tobroadband conversion are included in the analysis.Although these narrowband-to-broadband conversions are useful for some applications, they cannot replace the broadband observation to accurately account for the long-term changes in both regional and global TOA radiation (Loeb et al., 2007b).
The "broadband" imager radiances (I md sw and I md lw ) are then converted to fluxes using the CERES shortwave and longwave ADMs and the MODIS viewing geometries.The nearnadir-viewing imager flux is then compared with the obliqueviewing (50 • < θ < 60 • ) CERES flux for the same footprint.
Here we used 137 days of CERES along-track observations.For a population of N CERES footprints, the relative RMSE between fluxes F (θ n i ) inverted from near-nadir-viewing geometries and fluxes F (θ o i ) inverted from oblique-viewing geometries is used to quantify the TOA flux consistency: × 100 %. ( 6)

TOA SW flux consistency under clear conditions
We first examine the SW flux consistency for CERES clear footprints (cloud fraction< 0.1 %).Over ocean there are 22 137 clear CERES along-track footprints, and the relative RMSE is 4.1 % (3.4 Wm −2 ).Among these clear oceanic footprints, 20 298 have valid MODIS aerosol retrievals (Remer et al., 2008).To investigate whether ψ depends on aerosol optical depth (AOD), these footprints are sorted by AOD and then divided into 10 bins, each with an equal number of samples.Fig. 3 shows the mean oblique-view CERES fluxes and the relative RMSEs between the near-nadir-view and oblique-view fluxes for the 10 bins.As expected, the fluxes increase as AOD increases, but the relative RMSEs remain around 2.8 % for the first nine bins and increase to about 6.6 % for the last bin.For this bin, AOD has a large range of values (from 0.19 to 1.74).This covers a large range of anisotropy that was not fully captured by the CERES clearocean ADMs, which were constructed for low-, mid-, and high-AOD bins (Su et al., 2015).Additionally, these large AOD retrievals are more likely to be affected by cloud contamination (Zhang and Reid, 2006), which can also increase the RMSE as the anisotropy under clear sky is different from that under cloudy sky.
To test if ψ depends on aerosol fine-mode fraction, we stratify the clear-ocean samples by AOD, θ 0 , and MODIS fine-mode fraction.Fig. 4 shows the relative RMSE ψ as a function of MODIS fine-mode fraction for four populations, and the occurrence frequency for each fine-mode fraction bin of each population.For the population with AOD < 0.1 and θ 0 < 50 • , which consists about 37.4 % of the total sam-  ple, the relative RMSEs are about 3-4 %.For the population with AOD < 0.1 and θ 0 >50 • , which consists about 21.1 % of the total sample, the relative RMSEs are about 3 % except for one fine-mode fraction bin.For the population with AOD >0.1 and θ 0 < 50 • , which consists about 28.8 % of the total sample, the relative RMSEs are about 3∼5 %.For the population with AOD >0.1 and θ 0 >50 • , the relative RMSEs are about 6∼8 % for fine-mode fraction greater than 0.4, but these bins are only 7 % of the total population.These relative RMSEs are smaller than those presented in Loeb et al. (2007a) and show less dependence on MODIS fine-mode fraction.
Over land there are 210 808 clear CERES along-track footprints, and the relative RMSE is 3.4 % (9 Wm −2 ).Among these footprints, 208 297 have valid MODIS Dark Target (Levy et al., 2010) or Deep Blue (Hsu et al., 2004) retrievals.For a given footprint, we use the AOD from the Dark Tar-get retrieval if it is available, otherwise AOD from the Deep Blue retrieval is used.Similar to clear ocean, these clear footprints are sorted by AOD and then divided into 10 equal sample number bins. Figure 5a shows the mean oblique-view CERES fluxes and the relative RMSEs for the 10 AOD bins.The relative RMSEs range from 2.8 to 4.4 % and do not show any dependence on AOD.We also examine the clear footprints over the Amazon region (0-30 • S, 40-80 • W).As the Amazon is very cloudy, we only have 3132 clear CERES along-track footprints with valid aerosol retrievals.Figure 5b shows the mean oblique-view CERES fluxes and the relative RMSEs for the 10 equal-sample-number bins.As the mean AOD increases from near zero (first bin) to about 0.55 (last bin), the relative RMSEs remain fairly constant (range between 3.3 to 5.1 %) and exhibit no dependence on AOD.This means that the CERES ADMs over clear land do not introduce an AOD-dependent flux uncertainty, as the relative RMSE is an indication of ADM uncertainty.This is in stark contrast to Patadia et al. (2011), in which their empirical ADMs produced a sharp jump of about 4 Wm −2 in SW flux at an AOD of 0.3.This unphysical jump in SW fluxes could be caused by the coarse angular resolution used by Patadia et al. (2011) and the fact that most of the angular bins for large AOD cases are based upon theoretical calculations.

TOA SW flux consistency under cloudy conditions
Figures 6, 7, and 8 show the instantaneous footprint-level relative RMSE of TOA SW flux (ψ, Eq. 6) for different cloud types (defined in Table 4) over ocean, land, and snow/ice.For each surface type, the top row is for high clouds, the middle row is for mid-clouds, and the bottom row is for low clouds; the left column is for partly cloudy conditions, the middle column is for mostly cloudy conditions, and the right column is for overcast conditions.The bars on the left are for single-layer cloud types and the hatched bars on the right are  for multi-layer cloud types.The color of the bar indicates the occurrence frequency of a cloud type.Due to data availability and RMSE restriction in narrowband-to-broadband conversion, we are not able to provide ψ for every cloud type.
Over ocean, the relative RMSE is larger under thin broken clouds than under moderate and thick overcast clouds.Overcast low clouds with moderate optical depth have the highest occurrence frequency (23 %) over ocean and the relative RMSE for these clouds is around 3.5 % (11 Wm −2 ).The overall instantaneous SW flux are consistent to within 5.3 % (15 Wm −2 ) over ocean.Over land, only about 40 % of the CERES along-track footprints are cloudy.The relative RMSE is again larger under thin broken clouds than under moderate and thick overcast clouds, and the all-sky relative RMSE is 5.2 % (16 Wm −2 ).Over snow and ice, the relative RMSE is 3.0 % (8.8 Wm −2 ) under clear-sky conditions.Under cloudy conditions, the relative RMSE shows less dependence on cloud height and the all-sky relative RMSE is 6.7 % (18 Wm −2 ).The relative RMSEs for the multi-layer clouds are larger than those for the single-layer clouds over all three surface types, with the largest difference over ocean and the smallest difference over snow/ice.This could be caused by the parallax effect, as we used surface as the reference level, or due to the fact that the ADMs were developed without separating single-layer clouds from multi-layer clouds.The relative RMSEs for clear ocean and clear land are smaller than those provided in Loeb et al. (2007a), but the relative RM-SEs for all-sky conditions are comparable.Large reductions in relative RMSEs are noted for both clear-and all-sky conditions over snow and ice, because of improved cloud algorithms and ADMs over polar regions (Su et al., 2015;Corbett and Su, 2015).

TOA LW flux consistency
Figures 9, 10, and 11 show the instantaneous footprint-level relative RMSEs for daytime TOA LW flux (ψ, Eq. 6) for different cloud types over three surface types, the nighttime counterparts are shown in Figs. 12, 13, and 14.The daytime relative RMSEs are generally larger than the nighttime ones, possibly because the LW ADMs did not consider the effect of solar zenith angle and relative azimuth angle on anisotropy.Over ocean, the relative RMSEs are 0.9 % (2.5 Wm −2 ) and 0.8 % (2.3 Wm −2 ) for clear-sky daytime and  though the amount that the error increases is smaller than that reported by Loeb et al. (2007a).This reduction in error for high clouds is probably because the ADMs used here apply the mean observed radiance instead of the radiance derived from a third-order polynomial fit (Su et al., 2015), which improves the anisotropy characterization for high clouds.

TOA flux uncertainty
The relative RMSEs between fluxes derived from nadirand oblique-viewing angles can be used to test how well the CERES ADMs characterize the anisotropy of the Earth scenes, but it is more important to provide the TOA flux uncertainty to the scientific community.Loeb et al. (2003Loeb et al. ( , 2007a) )  is the derived SW radiance for the j th MISR camera.Regression coefficients c 0 , c 1 , c 2 , and c 3 are determined from coincident CERES SW and MISR narrow-band radiances using 107 days of merged SSFM product.Separate regressions are derived for predefined intervals of solar zenith angle, viewing zenith angle, relative azimuth angle, cloud fraction, effective cloud top pressure, precipitable water, and surface type.The sample numbers (N) required to minimize the narrow-to-broadband regression error are listed in Table 6 for different surface types.
We then infer the TOA SW flux from I ms_j sw for each of the MISR angles: where R(θ 0 , θ j , φ j ) is the CERES SW anisotropic factor corresponding to the scene types determined from MODIS measurements, and θ 0 , θ j , φ j corresponds to the solar zenith angle, viewing zenith angle, and the relative azimuth angle of the MISR j th camera.Thus for each CERES footprint, we can have up to nine SW fluxes inferred from MISR measurements.The standard deviation (σ ) of these fluxes is used to measure the uncertainty of CERES ADMs.Only footprints with at least five valid MISR SW fluxes are included in this analysis.Over clear ocean and sea ice, MISR viewing angles that are within 15 • of the specular direction are not included in this analysis.For a population of M CERES footprints, we examine the relative flux consistency by using the coefficient of variation, which is defined as: where F ms i is the averaged TOA SW flux from all available MISR angles for the ith CERES footprint.
We assume two sources of uncertainties contribute to the relative consistency of the TOA SW fluxes (a third source will be addressed in Sect.4.2).The first source is how well the CERES SW ADMs characterize the anisotropy for a given scene type, and the second source is how accurate the narrowband-to-broadband regressions are.The second uncertainty source is estimated by comparing the co-aligned CERES and MISR camera measurements (when their viewing zenith angles and relative azimuth angles are within 2 • ).We then determine the ADM error ( ADM ) by subtracting the narrowband-to-broadband regression error ( NB ) from the total error ( T ), as in Loeb et al. (2006): ADM is used to assess the TOA SW flux consistency due to uncertainties in CERES ADMs.4).The height of the bar indicates the flux consistency due to ADMs ( ADM ), and the error bar indicates the contribution to the total consistency from narrowband-to-broadband regressions.The color of the bar indicates the occurrence frequency of a cloud type.

TOA SW flux consistency by cloud type
Over ocean, single-layer low clouds account for 43 % of the cloudy scenes and ADM is less than 4 % except for thin clouds under overcast conditions.Multi-layer low clouds account for 13 % of the cloudy scenes and ADM is less than 7 %.For mid-and high clouds, ADM are generally larger than those for low clouds.Additionally, thin cloud types have larger ADM compared to moderate and thick cloud types under most circumstances.Table 6 summarizes the TOA SW flux consistency due to ADM uncertainties for clear-sky, single-layer clouds, multi-layer clouds, and all-sky conditions.The SW fluxes are consistent to within 3.5 % (3.0 Wm −2 ) and 6.2 % (15.9 Wm −2 ) for clear-sky and all-sky conditions.For single-layer clouds the SW fluxes are consistent to within 4.6 % (12.7 Wm −2 ) and for multi-layer clouds Table 6.Flux consistency due to ADM uncertainty using MISR measurements for clear-sky, single-layer cloud (S), multi-layer cloud (N), and all-sky conditions over three surface types.N is the minimum sample number required to derive the regression coefficients; ADM is the relative consistency due to ADM uncertainty before removing the parallax effect; PX is the contribution of parallax effect to the total consistency; ADM is the relative consistency due to ADM uncertainty after removing the parallax effect.For the MISR Level 1 data, we now expand the total error into three error sources (ADM, narrowband-to-broadband regression, and parallax): while for the MISR Level 2 data, we assume the parallax effect is negligible, thus the total error is composed of only errors from ADM and narrowband-to-broadband regression: The difference between these two equations allow us to quantify the parallax effect as: As the matching criteria used for MISR Level 1 and Level 2 data bias the footprints to homogenous scenes, the parallax effect reported here should be considered as the lower bound of the parallax effect.The ADM errors derived with the subset MISR Level 1 data are indeed smaller than those derived with the full Level 1 data, supporting the hypothesis that scenes included in the subset are more homogenous.Note the matched MISR data are only used to derive PX , whereas ADM is derived using the full Level 1 data.Over oceans, the parallax effect PX is 1.7 % and 3.3 % for single-layer low and high clouds, and is 2.4 % and 3.7 % for multi-layer low and high clouds.The parallax effect is indeed larger for high clouds than for low clouds.Considering all single-layer (multi-layer) clouds, the parallax effect is estimated to be 2.2 % (2.8 %); this results in a parallax effect of about 2.3 % under all-sky conditions.Taking these parallax effects into account, the flux consistency due to ADM uncertainty (using full MISR Level 1 data, ADM ) is reduced to about 5.8 % for all-sky, 4.1 % and 7.9 % for single-and multi-layer clouds (Table 6).The CERES SW anisotropic factors have a strong dependence on viewing zenith angle.For example, the anisotropic factors for clouds with ln(f τ ) = 6 are smaller than the anisotropic factors for clouds with ln(f τ ) = 7 for small viewing zenith angles, but the reverse is true for large viewing zenith angles (see Figs. 5a and 9a in Su et al., 2015).Thus misclassification of scenes can result in either overestimation or underestimation of anisotropic factors depending on the viewing zenith angle, which leads to underestimation or overestimation of the TOA fluxes depending on the viewing zenith angle.It is therefore desirable to assess the flux uncer-tainty using a realistic CERES viewing zenith angle distribution (blue line in Fig. 19).To accomplish this, we assume the near-nadir viewing cloud property differences between the standard algorithm and the enhanced algorithm are representative for the whole CERES swath (covers about 24 • longitude).We then repeat the flux calculation using all CERES viewing geometries sampled for each 0.2 • latitude by 24 • longitude bin for each day.We choose this bin size as it produces the most realistic daily grid-average viewing zenith angle distribution (red line in Fig. 19). Figure 18b shows the TOA SW flux differences accounting for the "realistic" CERES viewing geometries.The global monthly mean difference is reduced to −0.6 Wm −2 , because thin clouds have larger anisotropic factors than thick clouds for oblique viewing zenith angles, thus partly compensating the flux differences when only near-nadir viewing zenith angles are considered.There are 59.3 % of the 1 • × 1 • regions that have a flux difference less than 1 Wm −2 and 81.8 % of the regions that have a flux difference less than 2 Wm −2 .

Longwave
Cloud fraction, cloud top temperature, visible cloud optical depth, ice/liquid water effective sizes, surface skin temperature, precipitable water, and lower-tropospheric lapse rate (measured over the lowest 300 hPa) are used to select the LW anisotropic factors.Figure 20a and c show the four-seasonalmonth mean daytime and nighttime TOA LW flux differences using scene identifications from the standard and enhanced cloud algorithms.The global mean flux difference is 0.8 and 0.3 Wm −2 for daytime and nighttime, respectively.The largest regional differences are up to 5 Wm −2 , and are observed over land during daytime.The flux differences are caused by the cloud property differences between the standard and the enhanced cloud algorithms, as the standard cloud algorithm misses thin clouds, which have larger LW anisotropic factors than thick clouds at the near-nadir viewing geometries that are included in the C3M data product (see Fig. 16b in Su et al., 2015).As a result, fluxes inverted using scene identifications from the enhanced cloud algorithm are smaller than those using scene identifications from the standard cloud algorithm over most regions.Here we have only addressed the flux uncertainty from scene identification errors that affect the selection of anisotropic factors used in radiance-to-flux conversion.Scene identification errors could also cause misclassifications of scenes used in building the CERES ADMs.However, we do not have enough data to assess the ADM uncertainties from scene identification errors.

Conclusions
We evaluated the TOA flux errors caused by the uncertainties in CERES ADMs that were recently developed using all available CERES RAPs measurements (Su et al., 2015).This set of ADMs are used to produce the CERES Edition 4 SSF data product for Terra and Aqua and Edition 1 SSF data product for Suomi NPP.The TOA fluxes from CERES measurements are fundamental for studying the Earth's radiation budget and quantifying the uncertainties associated with these fluxes is critical in many applications of the CERES fluxes.
We have used the modified direct integration method, in which fluxes inverted from regional (10 • × 10 • ) seasonal allsky ADMs constructed using observed radiances and CERES ADM-predicted radiances are compared to assess the regional monthly mean TOA SW flux uncertainty.The biases in regional monthly mean TOA SW fluxes are less than 0.2 Wm −2 and the RMSE are less than 1.1 Wm −2 .The biases and RMSEs are very similar between Terra and Aqua.The regional monthly mean TOA LW flux uncertainty is assessed using the standard direct integration method, in which ADM-derived TOA LW fluxes are compared with the fluxes derived from regional seasonal all-sky ADMs constructed by directly integrating the CERES measured radiances.The biases in regional monthly mean TOA LW fluxes are less than 0.5 Wm −2 and the RMSEs are less than 0.8 Wm −2 for both Terra and Aqua.
A series of consistency tests were performed to evaluate the instantaneous TOA flux uncertainties.The TOA flux consistencies described in the following two paragraphs are converted to TOA flux uncertainties by multiplying a factor of www.atmos-meas-tech.net/8/3297/2015/Atmos.Meas.Tech., 8, 3297-3313, 2015 about 0.6, which is derived based upon radiative transfer simulations (Loeb et al., 2007a).
We have performed consistency tests using fluxes inverted from nadir-and oblique-viewing angles using CERES alongtrack observations and temporally and spatially matched MODIS observations.Over clear ocean, the SW fluxes are consistent to within 4.1 % (3 Wm −2 ) and show very little dependence on aerosol optical depth when it is less than 0.2.Furthermore, the flux consistency shows a much smaller dependence on aerosol fine mode fraction than previously reported (Loeb et al., 2007a).Over clear land, the SW fluxes are consistent to within 3.4 % (9 Wm −2 ) and again shows nearly no dependence on aerosol optical depth.Under allsky conditions, the SW fluxes are consistent to within 5.3 % (15 Wm −2 ), 5.2 % (16 Wm −2 ), and 6.7 % (18 Wm −2 ) over ocean, land, and snow/ice surfaces.The LW fluxes are consistent to within 1.3 % (1.3 to 4.1 Wm −2 ) under clear conditions.Under all-sky conditions, the LW fluxes are consistent to within between 1.2 % and 2.5 % (2.4-5.9Wm −2 ) over different surfaces.
Another consistency test was performed by collocating CERES Terra measurements with MISR observations.Fluxes inverted from the nine MISR camera angles are used to assess the TOA SW flux uncertainty.MISR Level 1 and Level 2 data are compared to estimate the parallax effect, which is larger for high clouds than for low clouds.The parallax effect estimated here should be regarded as the lower bound, as the matching criteria we used tend to favor the more homogenous scenes.The parallax effect is about 2.3, 0.9, and 0.1 % over ocean, land, and snow/ice.Over ocean, the SW fluxes are consistent to within 3.5 % (3.0 Wm −2 ) and 5.8 % (14.9 Wm −2 ) under clear-and all-sky conditions due to ADM uncertainties.Over land, the SW fluxes are consistent to within 2.0 % (5.4 Wm −2 ) and 3.9 % (11.5 Wm −2 ) under clear-and all-sky conditions due to ADM uncertainties.Over snow/ice, the SW fluxes are consistent to within 3.8 % (11.2 Wm −2 ) and 5.6 % (15.2 Wm −2 ) under clear-and allsky conditions.
As described above, the TOA flux consistency is converted to TOA flux uncertainty by a factor of about 0.6.The TOA instantaneous SW flux uncertainties based upon the averages of the two consistency tests are about 1.9 Wm −2 over clear ocean, 4.5 Wm −2 over clear land, and 6.0 Wm −2 over clear snow/ice; and are about 9.0, 8.4, and 9.9 Wm −2 over ocean, land, and snow/ice under all-sky conditions.The TOA instantaneous LW flux uncertainties are based upon the CERES-MODIS consistency test.The TOA instantaneous daytime LW flux uncertainties are 1.5, 2.4, and 1.3 Wm −2 over clear ocean, land, and snow/ice; and are about 3.5, 2.9, and 2.1 Wm −2 over ocean, land, and snow/ice under all-sky conditions.The TOA instantaneous nighttime LW flux uncertainties are smaller than 2.0 Wm −2 for all surface types.
As the CERES ADMs are scene type dependent, we also assessed the flux uncertainties caused by errors in scene identification using collocated CALIPSO, CloudSat, CERES and MODIS data product.Errors in scene identification tend to underestimate TOA SW flux by about 1.8 Wm −2 when only near-nadir-viewing CERES footprints are used, but the underestimation is reduced to 0.6 Wm −2 when all CERES viewing angles are considered.Errors in scene identification tend to overestimate TOA daytime (nighttime) LW flux by about 0.8 (0.3) Wm −2 when only near-nadir-viewing CERES footprints are used, and the overestimation is reduced to 0.4 (0.2) Wm −2 when all CERES viewing angles are considered.
The consistency tests show that the flux uncertainties for multi-layer clouds and high clouds are larger than for singlelayer clouds and low clouds.This points to the need to further evaluate the ADMs for those cases and will be addressed in the future development of CERES ADMs.Furthermore, CERES Aqua ADMs are used to derive fluxes from radiances measured by the CERES instrument on Suomi NPP.As the altitude of Suomi NPP orbit is higher than that of Aqua, the footprint size of CERES instrument on Suomi NPP is larger than that on Aqua.Will the difference in footprint size cause any uncertainties in Suomi NPP fluxes?Additionally, the channels on VIIRS are different from the channels on MODIS, which can result in differences in retrieved cloud properties and affect the selections of ADMs used for flux inversion.Evaluations of these issues are currently underway and will be addressed in a future publication.

Figure 1 .
Figure 1.Monthly regional mean TOA shortwave flux error from ADM uncertainties for (a) January, (b) April, (c) July, and (d) October 2002 using Terra measurements.

Figure 2 .
Figure 2. Monthly regional mean longwave flux error from ADM uncertainties for (a) January, (b) April, (c) July, and (d) October 2002 using Terra measurements.

Figure 3 .
Figure 3. Mean oblique-view CERES fluxes and the relative RMSE (Eq.6, in %) between oblique-view and near-nadir-view fluxes as a function of MODIS aerosol optical depth over clear ocean.The RMSEs are shown as error bars.

Figure 4 .
Figure 4.The relative RMSEs between oblique-view and near-nadir-view fluxes as a function of MODIS fine-mode fraction separated by aerosol optical depth (τ ) of 0.1 and solar zenith angles (θ 0 ) of 50 • (a), and the occurrence frequency for each population (b).

Figure 5 .
Figure 5. Mean oblique-view CERES fluxes and the relative RMSE (Eq.6, in %) between oblique-view and near-nadir-view fluxes as a function of MODIS aerosol optical depth (a) over clear land and (b) clear Amazon (0-30 • S, 40-80 • W).The RMSEs are shown as error bars.

Figure 8 .
Figure 8. Same as Fig. 6, but over snow and ice.
derived the relationship between TOA flux relative RMSE and flux uncertainty using 1-dimensional (1-D) radiative transfer calculations.These calculations generated SW radiances and fluxes for liquid and ice clouds with optical depths between 0.1 and 200 using angular sampling from CERES Terra along-track SSF data.They used five idealized theoretical ADMs to estimate TOA fluxes from the radiances generated from the radiative transfer calculations.The idealized ADMs are: (1) 1-D water cloud ADMs with variable cloud optical depth, (2) 1-D water cloud ADMs with a fixed cloud optical depth of 10, (3) 1-D ice cloud ADMs with variable cloud optical depth, (4) 1-D ice cloud ADMs with a fixed cloud optical depth of 10, and (5) Lambertian ADMs.The relative RMSEs between nadir-and obliqueviewing zenith angles were compared with the corresponding TOA flux uncertainty determined from the difference between the actual fluxes from the radiative transfer calculations and the fluxes inverted from the idealized ADMs for all the scenes simulated.The ratios of TOA flux uncertainty to TOA flux relative RMSE simulated by Loeb et al. (2007a) ranged from 0.54 to 0.65, and the average is 0.60.the MISR radiances in the blue (0.45 µm), red (0.67 µm), and near-infrared (0.87 µm) bands with a SW broadband radiance: I ms_j sw = c 0 + c 1 I 0.45 + c 2 I 0.67 + c 3 I 0.87 , (7) where I 0.45 , I 0.67 , and I 0.87 denote the MISR blue, red, and near-infrared radiances, and I ms_j sw

Figure 12 .
Figure 12.TOA nighttime LW flux consistency (%) between nadirand oblique-viewing angles for different cloud types over ocean.The left bars are for single-layer clouds, and the right bars (hatched) are for multiple-layer clouds.The color of the bar indicates the occurrence frequency for each cloud type.

Figures 15 ,
Figures 15, 16, and 17  show the TOA SW flux consistency among the MISR camera angles over ocean, land, and snow/ice surface types.The bars on the left are for singlelayer cloud types and the hatched bars on the right are for multi-layer cloud types (see Table4).The height of the bar indicates the flux consistency due to ADMs ( ADM ), and the error bar indicates the contribution to the total consistency from narrowband-to-broadband regressions.The color of the bar indicates the occurrence frequency of a cloud type.Over ocean, single-layer low clouds account for 43 % of the cloudy scenes and ADM is less than 4 % except for thin clouds under overcast conditions.Multi-layer low clouds account for 13 % of the cloudy scenes and ADM is less than 7 %.For mid-and high clouds, ADM are generally larger than those for low clouds.Additionally, thin cloud types have larger ADM compared to moderate and thick cloud types under most circumstances.Table6summarizes the TOA SW flux consistency due to ADM uncertainties for clear-sky, single-layer clouds, multi-layer clouds, and all-sky conditions.The SW fluxes are consistent to within 3.5 % (3.0 Wm −2 ) and 6.2 % (15.9 Wm −2 ) for clear-sky and all-sky conditions.For single-layer clouds the SW fluxes are consistent to within 4.6 % (12.7 Wm −2 ) and for multi-layer clouds

Figure 18 .
Figure 18.TOA SW flux error (Wm −2 ) caused by scene identification uncertainty (standard -enhanced) (a) only using near-nadir viewing geometries, (b) using extended viewing geometries that are similar to the CERES observations.

Figure 19 .
Figure 19.Distributions of grid-averaged viewing zenith angle for CERES data (blue), C3M data (green), and the C3M extended data (red), using data from April 2010.

Figure 20 .
Figure 20.TOA LW flux error (Wm −2 ) caused by scene identification uncertainty (standard -enhanced) (a) daytime LW flux error only using near-nadir viewing geometries, (b) daytime LW flux error using extended viewing geometries that are similar to the CERES observations, (c) same as (a) but for nighttime LW flux error, (d) same as (b) but for nighttime LW flux error.

Table 1 .
Loeb et al. (2005) flux bias and RMSE by season derived from direct integration, using ADMs developed bySu et al. (2015)for the Edition 4 SSF data, and ADMs developed byLoeb et al. (2005)for the Edition 3 SSF data (shown in parentheses) forTerra 2002 and Aqua 2004.

Table 2 .
Loeb et al. (2005)LW flux bias and RMSE by season derived from direct integration, using ADMs developed bySu et al. (2015)for the Edition 4 SSF data, and ADMs developed byLoeb et al. (2005)for the Edition 3 SSF data (shown in parentheses) forTerra 2002 and Aqua 2004.

Table 3 .
Loeb et al. (2005)WN flux bias and RMSE by season derived from direct integration, using ADMs developed bySu et al. (2015)for the Edition 4 SSF data, and ADMs developed byLoeb et al. (2005)for the Edition 3 SSF data (shown in parentheses) forTerra 2002 and Aqua 2004.

Table 4 .
Cloud type classification used in TOA flux consistency tests.Each CERES footprint is assigned a scene identification index from 0 to 54 based upon cloud fraction (f , in %), mean effective cloud top pressure (EP), and cloud optical depth (τ ), and whether one or two cloud layers are observed within the footprint.PCL: partly cloudy; MCL: mostly cloudy; and OVC: overcast.