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Appendix S1
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Comparison between Angular Correction Factors from ICA simulation and CERES ADM
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As explained in Section 2.3, the angular correction factor is defined as the ratio between ICA-
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simulated radiances at nadir (In) and CERES viewing angles [I(θv, ϕ)]. For the case used in this
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study, solar zenith angle (θ0) was between 30° and 80°; viewing zenith angle (θv) was between 5°
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to 20°; and relative azimuth angle (ϕ) was between 90° and 270° (Figs. S1a and S1b). Therefore,
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the exact nadir-view FOV collocated with CALIPSO’s and CloudSat’s ground-tracks did not
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occur in the CERES observation. Despite a broad range of solar and viewing geometries,
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according to ICA simulation (Fig. S1c) and those extracted from CERES ADM (Fig. S1d), In and
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I(θv, ϕ) have a strong correlation > 0.99. The number of data points in Fig. S1d is smaller than in
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Fig. S1c because of limited coverage of CERES SSF data along the satellite’s track (see Section
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2.3). In Figs. S1c and S1d, regression slope > 1 and offset > 0, indicate that I(θv, ϕ) is slightly
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larger than In, and thus angular correction factor M(θv, ϕ) is slightly greater than 1. This is
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because radiance increases with θv with a local maximum peak at θv > 0° when the sun is not
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overhead (Loeb et al., 2005; Loeb et al., 2007).
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Figure S2 shows the angular correction factor from ICA simulations [MICA(θv, ϕ)] as a
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function of solar and viewing geometries, cloud fraction, and cloud optical thickness τ. As also
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shown in Fig. S1c, the angular correction factor MICA(θv, ϕ) is mostly > 1 (Figs. S2a-h) because
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θ0 > 0°. Once τ exceeds1, the variation range of MICA(θv, ϕ) decreases with τ (Figs. S2g and S2h)
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because radiance from optically thicker clouds tends to be more isotropic than from optically
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thinner clouds (Loeb et al., 2005; Loeb et al., 2007). The influence of τ should be more
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prominent for overcast scenes, and therefore, larger variations of angular correction factor appear
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for larger cloud fraction (Figs. S2e and S2f).
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In Fig. S3, the angular correction factor from CERES ADM [MCERES(θv, ϕ)] is represented in
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the same way as Fig. S2. The dependence of MCERES(θv, ϕ) on viewing geometry and θ0 is quite
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similar to MICA(θv, ϕ) (Figs. S2a−S2d versus Figs. S3a−S3d). However, when cloud fraction is
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smaller than 20% or τ < 1, there is a noticeable difference between MICA(θv, ϕ) and MCERES(θv, ϕ);
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i.e. MICA(θv, ϕ) is larger than 1 but MCERES(θv, ϕ) is close to 1. Possible reasons for this difference
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are: 1) aerosol effects are ignored in ICA simulation; 2) FOVs with small cloud fraction and τ <
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1 tend to be surrounded by thicker clouds so that there is an inward net flux affecting CERES
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ADM; and 3) MODIS-derived cloud fraction and optical thickness for such FOVs could be
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underestimated and this affects classification of scene-type and compositing CERES ADM.
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Except for these differences for clear or broken cloud conditions, angular correction factors from
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ICA simulations and CERES ADMs generally agree well.
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Even though the angular correction factor ranges from 0.8 to 1.4, most of the large deviations
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for both ICA simulation and CERES ADM (Figs. S2g and S2g) occur for small τ (< 10). This
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means that absolute changes in radiance by angular correction are insignificant. This is consistent
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with the relationship shown in Figs. S1c and S1d: In and I(θv, ϕ) have a strong correlation, and
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that some of FOVs with small radiance values (< 100 W m-2) show more than ±10% differences
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(red lines). Therefore, In is a good proxy for I(θv, ϕ) in the context of the analyses done here.
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List of Figures
Figure S1. Distributions of (a) solar zenith angle (θ0) and CERES viewing zenith angle (θv), and
(b) viewing azimuth angle relative to North (ϕv) and its relative azimuth angle to the Sun
(ϕ) for CERES footprints that contained the CALIPSO and CloudSat ground-track. (c)
Comparison between ICA-modeled radiances at nadir (In) and CERES-viewing angle
[I(θv, ϕ)]. (d) Same as (c) but from CERES angular distribution model (ADM). Red solid
lines in (c) and (d) represent ±10% differences.
Figure S2. Angular correction factor [MICA(θv, ϕ)] as a function of (a) solar zenith angle (θ0), (b)
CERES viewing zenith angle (θv), (c) and (d) CERES relative azimuth angle (ϕ), (e) and
(f) cloud fraction (%), and (g) and (h) cloud optical thickness (τ). Dot color represents
different ranges of CERES viewing zenith angles (left columns) and solar zenith angles
(right columns). The angular correction factor was obtained from ICA simulation.
Figure S3. Same as Fig. S2 but the angular correction factor was computed from CERES angular
distribution model [MCERES(θv, ϕ)].
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Figure S1. Distributions of (a) solar zenith angle (θ0) and CERES viewing zenith angle (θv), and
(b) viewing azimuth angle relative to North (ϕv) and its relative azimuth angle to the Sun (ϕ) for
CERES footprints that contained the CALIPSO and CloudSat ground-track. (c) Comparison
between ICA-modeled radiances at nadir (In) and CERES-viewing angle [I(θv, ϕ)]. (d) Same as
(c) but from CERES angular distribution model (ADM). Red solid lines in (c) and (d) represent
±10% differences.
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Figure S2. Angular correction factor [MICA(θv, ϕ)] as a function of (a) solar zenith angle (θ0), (b)
CERES viewing zenith angle (θv), (c) and (d) CERES relative azimuth angle (ϕ), (e) and (f)
cloud fraction (%), and (g) and (h) cloud optical thickness (τ). Dot color represents different
ranges of CERES viewing zenith angles (left columns) and solar zenith angles (right columns).
The angular correction factor was obtained from ICA simulation.
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Figure S3. Same as Fig. S2 but the angular correction factor was computed from CERES angular
distribution model [MCERES(θv, ϕ)].
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