Volume 119, Issue 2 p. 943-963
Research Article
Free Access

Effects of 3-D clouds on atmospheric transmission of solar radiation: Cloud type dependencies inferred from A-train satellite data

Seung-Hee Ham

Corresponding Author

Seung-Hee Ham

NASA Langley Research Center, Hampton, Virginia, USA

Correspondence to: S.-H. Ham, [email protected]

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Seiji Kato

Seiji Kato

NASA Langley Research Center, Hampton, Virginia, USA

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Howard W. Barker

Howard W. Barker

Environment Canada, Toronto, Ontorio, Canada

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Fred G. Rose

Fred G. Rose

Science Systems and Applications Inc., Hampton, Virginia, USA

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Sunny Sun-Mack

Sunny Sun-Mack

Science Systems and Applications Inc., Hampton, Virginia, USA

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First published: 04 January 2014
Citations: 20


Three-dimensional (3-D) effects on broadband shortwave top of atmosphere (TOA) nadir radiance, atmospheric absorption, and surface irradiance are examined using 3-D cloud fields obtained from one hour's worth of A-train satellite observations and one-dimensional (1-D) independent column approximation (ICA) and full 3-D radiative transfer simulations. The 3-D minus ICA differences in TOA nadir radiance multiplied by π, atmospheric absorption, and surface downwelling irradiance, denoted as πΔI, ΔA, and ΔT, respectively, are analyzed by cloud type. At the 1 km pixel scale, πΔI, ΔA, and ΔT exhibit poor spatial correlation. Once averaged with a moving window, however, better linear relationships among πΔI, ΔA, and ΔT emerge, especially for moving windows larger than 5 km and large θ0. While cloud properties and solar geometry are shown to influence the relationships amongst πΔI, ΔA, and ΔT, once they are separated by cloud type, their linear relationships become much stronger. This suggests that ICA biases in surface irradiance and atmospheric absorption can be approximated based on ICA biases in nadir radiance as a function of cloud type.

Key Points

  • The 3-D minus ICA irradiance is obtained at TOA, atmosphere, and surface level
  • For larger scale, linear relationships emerge among the three difference terms
  • Cloud type determines the relationships among the three difference terms

1 Introduction

An important branch of the Clouds and Earth's Radiant Energy System (CERES) satellite experiment, beyond estimation of Earth's top of atmosphere (TOA) radiation budget [Wielicki et al., 1996; Loeb et al., 2005, 2007], is estimation of corresponding surface and atmospheric radiation budgets [Charlock et al., 1997; Su et al., 2005; Kato et al., 2008, 2011, 2013]. These quantities are obtained by applying one-dimensional (1-D) solutions of the radiative transfer equation to atmospheres whose cloud properties are inferred from coeval Moderate Resolution Imaging Spectroradiometer (MODIS) radiances and temperature and humidity profiles taken from reanalysis. Applying the 1-D models with the independent column approximation (ICA) neglects net horizontal radiation transport and produces demonstrable errors, especially for solar radiation, in estimated instantaneous radiances and irradiances [e.g., Marshak et al., 1995; Davis et al., 1997; Barker et al., 1999; Di Giuseppe and Tompkins, 2003a, 2005; Scheirer and Macke, 2003; O'Hirok and Gautier, 2005]. For the time being, however, full three-dimensional (3-D) solutions appear to be computationally too demanding, so it would be useful to have an intermediate step that attempts to understand errors in 1-D estimates at an instantaneous time scale.

While many case studies have examined the effects of neglecting 3-D transfer of solar radiation for cloudy atmospheres (see above references), it is difficult to generalize their results. This is because the magnitude and sign of 3-D effects are influenced much by solar geometry and cloud microphysical and macrophysical structural characteristics. This is complicated by the fact that models are often used to construct 3-D cloud fields that neither encompass all types of cloud nor portray all types of clouds satisfactorily. While current cloud-radar and lidar can provide more realistic vertical profiles, they only provide two-dimensional (2-D) cross sections. Pincus et al. [2005] reported that the magnitude of ICA biases for 2-D cloud fields are likely to underestimate their 3-D counterparts due to fewer cloud edges.

The purpose of the current study is to explore the hypothesis that errors in atmospheric and surface irradiances caused by the ICA can be approximated, and thus accounted for, through knowledge of TOA radiance errors incurred by the ICA. This is based on the fact that ICA errors in TOA radiance can be relatively easily inferred from satellite observation; difference between satellite-measured radiances and their ICA counterparts attributed solely to radiative transfer. This approach is not possible for estimation of ICA errors in atmosphere or surface level since satellites directly measure TOA radiance only. In this study, we will show that ICA errors for TOA radiances correlate well with corresponding errors for atmosphere and surface budgets, and thus, ICA errors for atmosphere and surface budgets can be also inferred from satellite observation.

The 3-D cloud fields used in this study were obtained by applying Barker et al.'s [2011] EarthCARE cloud construction algorithm to 2-D MODIS imagery [Barnes et al., 1998] and merged cloud profiles [Kato et al., 2010] derived from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) lidar [Winker et al., 2009] and CloudSat radar [Stephens et al., 2008] data. Cloud types derived from CloudSat data [Sassen and Wang, 2008] were also used to categorize results for analysis of 3-D effects. Many studies have examined 3-D, actually 2-D, effects for particular cloud types [e.g., Di Giuseppe and Tompkins, 2003a, 2003b; Hogan and Kew, 2005; Marchand and Ackerman, 2004; Zhong et al., 2008], but only a few have considered multiple cloud types [O'Hirok and Gautier, 2005; Varnai, 2010]. In contrast, the present study, which resembles Barker et al. [2012], considers many samples of 3-D fields for numerous cloud types.

Section 2 describes both satellite data and the models used in this study. Section 3.1 demonstrates the strong linear relations amongst differences between 3-D and ICA values of TOA nadir radiance, atmospheric absorption, and surface irradiance. Section 3.2 discusses factors influencing the linear relations, while section 3.3 shows scale-dependent linear relations as functions of cloud type. Section 3.4 discusses the scales at which 3-D effects become important and corrections needed. A summary is given in section 4.

2 Data and Model

2.1 CloudSat-CALIPSO-MODIS Merged Cloud Data

Cloud properties used in this study came from an intermediate product of the merged data set of CALIPSO [Winker et al., 2009], CloudSat [Stephens et al., 2008], CERES [Wielicki et al., 1996], and MODIS [Barnes et al., 1998] referred to here as the CCCM data product [Kato et al., 2010]. It consists, in part, of CALIPSO- and CloudSat-derived cloud properties collocated to 1 km resolution MODIS pixels. Note that horizontal resolution of CALIPSO's vertical feature mask (VFM) [Vaughan et al., 2009] is 333 m and that of CloudSat's 2B-CLDCLASS cloud mask [Sassen and Wang, 2008] is 1.4 km across track and 1.8 km along track. Therefore, 1 km × 1 km grid of CCCM data includes three CALIPSO VFM profiles and the closest CloudSat cloud mask profile from the grid. CCCM also provides MODIS cloud parameters such as cloud optical thickness τ, effective radius, cloud thermodynamic phase, and effective height [Minnis et al., 2011a, 2011b].

In this study, CloudSat-CALIPSO merged cloud boundaries are obtained by following the strategy in Kato et al. [2010, Table 1]. When both Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) aboard CALIPSO and Cloud Profiling Radar (CPR) aboard CloudSat detect the top of a cloud, the larger value is used. When both CALIOP and CPR detect the base of a cloud, CALIOP cloud base is used to assign base height since radar measurements may be influenced by precipitation. When CALIOP misses a cloud layer but CPR detects it, CPR cloud boundaries are used, and vice versa. If both CALIOP and CPR miss a cloud layer, but MODIS τ > 0, MODIS effective height [Minnis et al., 2011a, 2011b] is used along with the assumption that cloud thickness is 0.5 km.

After obtaining cloud boundaries from CloudSat, CALIPSO, and MODIS data, extinction coefficient is calculated using MODIS τ and the assumption of vertical homogeneity; i.e., extinction coefficient = MODIS τ/cloud layer thickness. The homogeneous assumption is also applied to multilayered cloud. Therefore, columnar τ is partitioned according to the thickness of each cloud layer. Cloud particle effective radius and thermodynamic phase are fixed at constant MODIS-derived values throughout each column. Since MODIS τ are available during Sun-up conditions only, this study used just 1 h of CCCM data taken on 1 November 2010, 02 UTC. This solar-illuminated hour provided cloud properties for a 17,500 km length of satellite ground track.

2.2 Assignment of Cloud Type for Merged Cloud Data

Cloud type of a CALIPSO-CloudSat-MODIS merged cloud layer is determined using cloud scenario in CloudSat's 2B-CLDCLASS data. These data classify clouds into either cirrus (Ci), altostratus (As), altocumulus (Ac), stratus (St), stratocumulus (Sc), cumulus (cu), nimbostratus (Ns), or deep convective (Dc) clouds. Table 1 shows how the 2B-CLDCLASS algorithm defines cloud types; more details are available at (http://www.cloudsat.cira.colostate.edu/ICD/2B-CLDCLASS/2B-CLDCLASS_PDICD_5.0.pdf). The current CloudSat algorithm reports all low-level clouds as Sc. This is because of radar signal contamination in the lowest three or four bins (~ 1 km) [Sassen and Wang, 2008]. Note also that the horizontal extent shown in Table 1 does not necessarily mean the length of a continuous cloud layer. Cloud elements for some cloud types, such as Sc and Cu, have small horizontal extents. Therefore, clusters of such kinds of broken clouds are defined if similar vertical structure is observed within 30 km of minimum searching area.

Table 1. Characteristics of Eight Cloud Types Defined in CloudSat 2B-CLDCLASS Algorithm [Sassen and Wang, 2008]
Cloud Type Horizontal Dimension Vertical Dimension Base Height Precipitation
Cirrus (Ci) 103 km Moderate > 7 km None
Altostratus (As) 103 km Homogeneous Moderate 2–7 km None
Altocumulus (Ac) 103 km Inhomogeneous Shallow or moderate 2–7 km Virga possible
Stratus (St) 102 km Homogenous Shallow 0–2 km None or slight
Stratocumulus (Sc) 103 km Inhomogeneous Shallow 0–2 km Drizzle or Snow possible
Cumulus (Cu) 1 km Isolated Shallow or moderate 0–3 km Drizzle or Snow possible
Nimbostratus (Ns) 103 km Thick 0–4 km Prolonged rain or snow
Deep convective clouds (Dc) 10 km Thick 0–3 km Intense shower of rain or hail possible

If CloudSat misses a cloud layer, yet it is detected by either CALIPSO, MODIS, or both, the cloud type of the layer is determined by appealing to the closest CloudSat cloud pixel as follows (see Figure 1a). The target pixel is assigned the cloud type of the CloudSat pixel if (1) the CloudSat footprint is located in the 21 km × 21 km area surrounding the target pixel and (2) differences of cloud top and base altitudes over the CloudSat footprint and the target pixel are < 0.5 km. If there are multiple CloudSat footprints satisfying these two conditions, the closest CloudSat footprint is used to assign cloud type. If multiple CloudSat footprints satisfy these conditions and are equidistant from the target pixel, yet their cloud types differ, the cloud type of the target pixel is assigned as mixed. If there is no close CloudSat footprint satisfying the above two conditions, the threshold of the cloud height difference between the cloud in the target pixel and surrounding CloudSat footprints is increased from 0.5 km to 1.0 km and the process is repeated. If there is still no suitable CloudSat footprint found after this process, cloud type is assigned according to cloud base height. For base heights < 2 km, between 2 km and 7 km, or ≥ 7 km, cloud type is assigned as St, As, or Ci, respectively. Because the current version of CloudSat algorithm reports all low-level clouds as Sc, St can be only reported by the method described here. Therefore, St defined in this study are mostly optically thin, detectable by CALIPSO only, and are shown to be mostly located between broken Sc with a small horizontal extent. Hence, characteristics of St defined in Table 1 may differ from those in this study.

Details are in the caption following the image
(a) Flow diagram of the algorithm to obtain CloudSat-like cloud type from CALIPSO-CloudSat-MODIS merged cloud layers. (b) CloudSat cloud type (top) provided by 2B-CLDCLASS and CloudSat-like cloud type obtained from the algorithm in this study (bottom).

Figure 1b compares the original CloudSat cloud types and cloud types determined by this process for the merged cloud layers. It suggests that this cloud type determination algorithm is feasible because vertically contiguous clouds display constant types with no obvious discontinuity from the original CloudSat cloud type.

2.3 Three-Dimensional Cloud Construction From CALIPSO, CloudSat, and MODIS

The merged cloud information is only available along the A-train track where CALIPSO and CloudSat cloud profiles are provided. Therefore, a 3-D cloud construction algorithm [Barker et al., 2011] is used to extend 2-D nadir profiles into the cross-track direction. It is assumed that cloud properties between two close pixels are similar if the 2 pixels have similar TOA radiances for MODIS multiple channels, provided that atmospheric and surface conditions are also similar [Barker et al., 2011]. Thus, for a pixel located outside the A-train nadir track, an A-train nadir track pixel is chosen by minimizing
where rk(i,j) is recipient pixel radiance, rk(m,0) is donor pixel radiance (i.e., along the A-train track), and k is MODIS band index. MODIS channels used are 0.65, 2.1, 8.5, and 12 µm, and search lengths along the nadir track extend for 200 km in total. Barker et al. [2011] showed that these four channels provide sufficient information to reconstruct cloud visible optical thickness and altitude. Once the donor pixel is identified its profile of cloud properties gets mapped into the recipient pixel. This algorithm is applied to 40 pixels in both cross-track directions, thus resulting in constructed cloud field that measures ~81 km wide and ~17,500 km long.

2.4 Radiative Transfer Simulation

Shortwave radiation from 0.1754 µm to 4.0 µm is subdivided into 18 bands for narrowband simulation [Rose et al., 2006]. For each band, gaseous absorption and molecular scattering coefficients are estimated for the midlatitude summer profile [McClatchey et al., 1972]. Gaseous absorption optical depths are computed by the correlated k-distribution method [Kato et al., 1999], while a simple relation with pressure and temperature profiles [Fu and Liou, 1993] is applied to compute molecular scattering optical depths. Aerosol is ignored in the simulations.

Scattering properties for nonspherical cloud particles [Yang et al., 2003, 2005] and water particles from Mie theory are tabulated for 58 effective radius bins between 5 and 90 µm and for 18 spectral bands. Extinction efficiency, single-scattering albedo, and phase function are interpolated for the 18 bands to give values that correspond to MODIS radius.

Ocean surface spectral albedo is a function of solar zenith angle θ0, near surface wind speed, atmospheric transmittance, and ocean chlorophyll concentration [Jin et al., 2004]. For this study, wind speed and chlorophyll concentration are fixed at 5 m s−1 and 5 mg m−3, respectively.

Narrowband simulations for 18 bands are performed using the Intercomparison of 3-D Radiation Code (I3RC) [Cahalan et al., 2005] community Monte Carlo model [Pincus and Evans, 2009]. For the 3-D simulations it is assumed that 1 km × 1 km cells are either filled uniformly with cloud properties or entirely devoid of cloud. Because this model requires a large amount of memory, the 3-D field constructed in section 2.3 is divided into 500 km long sections with 100 km overlapping margins at each end, thus producing subdomains that measure 81 km and 700 km in the cross-track and along-track directions. Vertical grids consist of 63 levels from 0 km to 100 km. Therefore, each subdomain has a volume of 700 km long (= 500 km + 100 km margin × 2 sides) × 81 km wide × 100 km high. To avoid unwanted effects setup by cyclic horizontal boundary conditions, 5 km and 100 km on both outer edges are discarded for cross- and along-track directions, respectively. Simulation results for 500 km long × 71 km wide × 100 km high are used for the analysis.

Two θ0 values of 0° and 60° are considered. For θ0 = 60°, it is assumed that sunlight comes from the north. Note that although solar azimuth angle is fixed, the relative azimuth angle between satellite track and Sun directions varies with latitude. The total number of photons is set as 10,000 × the number of columns in the subdomain (= 700 × 81 × 10,000 = 5.67 × 108). Incident photons are distributed randomly across the top boundary. Cloud particle scattering phase functions have 398 scattering angles.

ICA simulations with the Monte Carlo model are performed by forcing photons to move vertically only. Therefore, photons do not across columns during the simulation. In contrast, three directional photon movements are allowed in full 3-D simulation. Broadband quantities are computed by weighting narrowband irradiances from the I3RC model by their solar incoming irradiances.

2.5 Quantification of 3-D Effects (= 3-D Minus ICA Irradiances)

Letting I, A, and T represent broadband TOA nadir radiance, atmospheric absorption, and surface irradiance, respectively, 3-D radiative effects are defined as
where subscripts indicate results from 3-D and ICA simulations. TOA nadir radiances are at the top of the domain (i.e., 100 km). Only nadir direction radiances are considered since 3-D and ICA simulated scenes are not matched for oblique views, and thus, direct comparison is not possible. Apparent cloud fraction differs from 1-D and the location of clouds is horizontally shifted in 3-D simulations when viewing zenith angle deviates from 0°. Examination of nadir view radiance is acceptable given that most of sensors (particularly active ones) observe Earth close to nadir. The factor π approximately converts nadir radiances to upwelling TOA irradiances. Hence, πΔI, ΔA, and ΔT are in units of W m−2.

Note that MODIS cloud properties are retrieved based on one-dimensional (1-D) transport theory and thus are affected by 3-D effects. Nevertheless, for this study 3-D cloud fields provided by MODIS, CALIPSO, and CloudSat are treated as “the truth” and 3-D biases as the difference between 3-D and ICA simulations. Therefore, the 1-D assumption affecting cloud retrievals is not addressed directly in this study.

3 Results

3.1 Positive Correlation Between πΔI, ΔA, and ΔT

Figures 2a and 2b show vertical cross section of extinction coefficient (km−1) and effective radius along the satellite track computed with the assumption of vertically homogeneous extinction coefficient profile for CALIPSO-CloudSat-MODIS merged cloud boundary (section 2.1). Figures 2c and 2d show overhead views of constructed τ and effective radius from the 3-D construction method (section 2.3), while Figures 2e and 2f show corresponding original MODIS τ and effective radius. Slight differences between the constructed and MODIS cloud parameters exist near 67.40°S−66.57°S. This is because the MODIS algorithm assigned cloud phase as ice, while the construction method filled cloud phase as liquid (not shown). Liquid droplets have larger asymmetry factors, and thus, the pixels assigned as liquid show larger τ for the same visible reflectance. For most other regions, constructed and original cloud parameters agree quite well. This suggests that cloud morphologies produced by the 3-D construction method (section 2.3) are likely to be good renditions.

Details are in the caption following the image
Vertical cross sections of (a) extinction coefficient (km−1) and (b) effective radius (µm) along the CALIPSO and CloudSat satellite ground track. Downward looking images of (c) cloud optical thickness τ and (d) effective radius (µm) obtained from the 3-D construction method. Downward looking images of MODIS (e) τ and (f) effective radius. The cloud field was observed on 1 November 2010 02 UTC.

Figure 3 shows spatial distributions of πΔI, ΔA, and ΔT for the same domain as in Figure 2. Solar zenith angle θ0 is fixed as 60° for the simulation. The scale dependence of πΔI, ΔA, and ΔT is investigated by spatially averaging with different moving window sizes of (1 km)2, (5 km)2, (11 km)2, and (21 km)2. As window size increases, small perturbations in πΔI, ΔA, and ΔT are progressively removed. However, even for a (21 km)2 moving window, deviations in πΔI and ΔA often reach 10 W m−2, while for ΔT they reach 25 W m−2. Large deviations occur at the transition zones from optically thick to thin clouds and in regions where multilayer clouds are present (Figure 2). Note that the Sun is on the right front side of the domain with the θ0 of 60°, and the incoming solar irradiance at TOA is 693.5 W m−2. Therefore, 10 and 25 W m−2 variations correspond to 1.4 and 3.6% of incoming solar irradiance. Except for the transition zone and multilayer cloud area, most deviations of πΔI, ΔA, and ΔT are smaller than 5 W m−2 (< 1%).

Details are in the caption following the image
Spatial distribution of (a) πΔI, (b) ΔA, and (c) ΔT averaged by moving windows of size: 1, 5, 11, and 21 km. πΔI, ΔA, and ΔT are defined as 3-D minus ICA TOA nadir radiance multiplied by π, atmospheric absorption, and surface downward irradiance, respectively. All variables are in W m−2. Solar zenith angle θ0 is fixed as 60° in the simulation. Solar azimuth angle is set as right front direction, 52.7° tilted from the ground track.

Figure 3 shows that the spatial pattern of πΔI, ΔA, and ΔT and their signs are similar, even though their magnitudes differ. Similarities are clearly apparent when small-scale noise is removed; for the 21 km moving window, πΔI, ΔA, and ΔT show positive values near 68.23°S and negative values near 67.40°S. This implies that 3-D enhancement (or reduction) of nadir radiance, atmospheric absorption, and surface irradiance occurs at a similar distance from the source. This can be understood intuitively. At the sunny side of cloud layer, horizontal radiation transport enhances cloud illumination, which leads to increases in cloud reflection, absorption, and transmission relative to the ICA. At the backside of cloud is the corresponding cloud shadow, which has reduced values of reflection, absorption, and transmittance relative to the ICA. However, since the amplitudes and locations where reflection, absorption, and transmittance are enhanced or reduced do not match exactly, πΔI, ΔA, and ΔT might be correlated better at a larger scale than at 1 km. Another reason for increasing the correlation with the size of moving window is that Monte Carlo noise can be significant at the 1 km scale as only 10,000 photons are used per column.

To further investigate the relationship among πΔI, ΔA, and ΔT, Figure 4 shows scatterplots of πΔI versus ΔA (first column) and πΔI versus ΔT (second column) for the 17,500 km domain. Solar zenith angle θ0 is fixed as 60° for this simulation. The scatterplots are generated using different moving windows. As window size increases, the positive correlation appears more clearly among πΔI, ΔA, and ΔT. Moreover, for the 21 km window, a linear relationship between two parameters of πΔI, ΔA, and ΔT emerges, although a mixture of several cloud types having different slopes might exist, especially for πΔI versus ΔT. Factors influencing the slope are discussed in the next section.

Details are in the caption following the image
Scatterplots of (first column) πΔI versus ΔA, and (second column) πΔI versus ΔT for a 17,500 km long by 71 km wide domain observed on 1 November 2010 02 UTC using moving windows of size: 1, 5, 11, and 21 km (first to fourth row, respectively). Black solid lines are linear regression fits, and its parameters are listed on each panel. Solar zenith angle θ0 is fixed as 60°.

3.2 Relationship Among πΔI, ΔA, and ΔT Depending on Cloud Properties and Solar Geometry

In this section, relationships among πΔI, ΔA, and ΔT as a function of cloud properties and solar zenith angle (θ0) are examined using a 5 km moving window. The reason for using a 5 km window size is that it is large enough to observe correlations among πΔI, ΔA, and ΔT (see Figure 4), yet small enough to have uniform cloud properties within a window. The relations due to different window sizes are examined in section 3.3.

In Figure 5, the scatterplots with a 5 km moving window shown in Figure 4 are separated further into ranges of averaged τ in the moving window. For clear pixels, τ is set for 0. Stronger linear relationships among πΔI, ΔA, and ΔT appear once scenes are separated by τ range compared to Figure 4 (second row).

Details are in the caption following the image
Same as 5 km scatterplots in Figure 4 but partitioned according to mean cloud optical thickness in 5 km moving windows. Solar zenith angle θ0 is fixed as 60°.

Slopes of the regression lines between πΔI and ΔA, and between πΔI and ΔT, hereafter S(πΔI, ΔA) and S(πΔI, ΔT), respectively, decrease as τ increases. Except for very thin τ, nadir radiance and absorption increase with τ, and surface irradiance decreases with τ. Therefore, the range of πΔI and ΔA increases, and ΔT decreases with τ, which is apparent comparing variation ranges of πΔI, ΔA, and ΔT between 0 ≤ τ <5 and 15 ≤ τ <20. This causes a decrease of S(πΔI, ΔT) with τ. In addition, the magnitude of πΔI increases faster than that of ΔA with respect to τ, leading to decreasing S(πΔI, ΔA) with τ.

Similar to Figure 5, Figure 6 shows relationships among πΔI, ΔA, and ΔT but for θ0 of 0°. Compared to Figure 5, Figure 6 shows smaller S(πΔI, ΔA) and S(πΔI, ΔT). This is because πΔI has a similar magnitude for both θ0, while the range of ΔA and ΔT are smaller for θ0 = 0° than for θ0 = 60°. In addition, correlations among πΔI, ΔA, and ΔT for θ0 = 0° (Figure 6) are less than those for θ0 = 60° (Figure 5). For an oblique Sun, shadowing and illumination depend on the Sun's position and cause enhancements and reductions of reflected, absorbed, and transmitted irradiances relative to ICA values [e.g., Marshak et al., 1995]. Therefore, ΔA, πΔI, and ΔT tend to have similar signs and patterns of deviations. For overhead Sun, radiation escapes from a cloudy region to a clear region, and it mostly propagates downward [Barker and Li, 1997; Fu et al., 2000; Pincus et al., 2005]. This causes a decrease in nadir radiance and surface irradiance for cloudy regions (negative πΔI and ΔT). However, atmospheric absorption does not always decrease because horizontal radiation transport can increase photon path lengths and thus column absorption [e.g., Marshak et al., 1998; Varnai, 2010; Song and Min, 2011]. Moreover, photon leakage increases surface irradiance in nearby clear region, but it does not noticeably increase TOA radiance. As a consequence, πΔI, ΔA, and ΔT are weakly related for overhead Sun, showing a weaker correlation between πΔI and ΔA and between πΔI and ΔT.

Details are in the caption following the image
Same as Figure 5 but θ0 = 0°.

Cloud layer geometrical thickness is also shown to influence S(πΔI, ΔA) and S(πΔI, ΔT). For a given τ, S(πΔI, ΔA) and S(πΔI, ΔT) increase with cloud layer thickness (not shown). This suggests that clouds with larger-side areas experience larger 3-D effects on atmospheric absorption and surface irradiance (larger ΔA and ΔT). However, τ usually increases with cloud layer thickness but S(πΔI, ΔT) and S(πΔI, ΔT) both decrease with τ. Therefore, for geometrically thick clouds, effects of cloud layer thickness and τ partly cancel. As a result, if cloud layer thickness varies within a τ range, a mixture of several linear relationships can exist.

Earlier studies, and above results, indicate that the relationships among πΔI, ΔA, and ΔT depend strongly on cloud macroscopic properties such as τ or cloud layer thickness. Therefore, if scenes are separated by cloud type, a linear relationship among πΔI, ΔA, and ΔT might appear more clearly. In the remaining of this section, therefore, relationships among πΔI, ΔA, and ΔT are as a function of CloudSat-derived cloud type and extended by the algorithm explained in section 2.2.

Table 2 shows mean and standard deviation of τ, cloud top height, and cloud layer geometrical thickness for eight cloud types. Dc clouds show the largest τ, followed by Ns, Ac, and Cu, with Ci clouds having the smallest. In addition, Dc and Ci have tops over 12 km, while St and Sc clouds have tops below 2 km. Layer thicknesses for Dc and Ns are comparable to their top heights, meaning that their bases are close to the surface. Layer thicknesses for Ac, St, Sc, and Cu clouds are < 2 km.

Table 2. Mean and Standard Deviation of Cloud Optical Thickness τ (Second Column), Cloud Top Height (km) (Third Column), and Cloud Layer Thickness (km) (Fourth Column) for the Selected Eight Cloud Types in This Studya
Cloud Type Cloud Optical Thickness Cloud Top Height (km) Cloud Layer Thickness (km)
Cirrus (Ci) 2.20 ± 2.61 12.77 ± 2.27 2.36 ± 1.35
Altostratus (As) 5.02 ± 4.47 8.49 ± 3.12 4.48 ± 2.96
Altocumulus (Ac) 13.59 ± 8.46 4.74 ± 0.98 1.60 ± 0.95
Stratus (St) 2.96 ± 3.10 1.06 ± 0.65 0.35 ± 0.28
Stratocumulus (Sc) 6.03 ± 9.07 1.66 ± 0.71 0.78 ± 0.59
Cumulus (Cu) 12.64 ± 16.49 2.28 ± 1.16 1.47 ± 1.14
Nimbostratus (Ns) 20.84 ± 20.06 8.93 ± 2.73 8.46 ± 2.71
Deep convective cloud (Dc) 60.02 ± 50.03 12.12 ± 1.17 11.56 ± 1.19
  • a Mean and standard deviation are given as (mean) ± (one standard deviation).

Figure 7 shows πΔI, ΔA, and ΔT generated with a 5 km moving window using data shown in Figure 4 (θ0 = 60°) for eight cloud types. The dominant cloud type for each 5 km × 5 km moving window is determined as follows. A cloud type is assigned to the window only if more than 90% of the window is occupied by a single-layer and single cloud type. If multilayer clouds, multiple cloud types, or clear pixels occupy more than 10% of the window, it is flagged as mixed and not considered here. Black lines in Figure 7 represent linear regression fits. Grey lines represent running mean of ΔA (left column of each cloud type) and ΔT (right column) for ±10 W m−2 ranges of the given πΔI. Running means are obtained only if there are more than 50 samples in a given πΔI range. Standard deviations of the averaged samples and their uncertainties are given in Figure 8.

Details are in the caption following the image
Same 5 km scale scatterplots shown in Figure 4 (second row) but partitioned into eight cloud types. When a 5 km moving window contains more than 10% of either multilayered, multiple cloud types, or clear-sky, the window is designated as mixed and not used in the analyses. Black lines represent linear regression fits. Grey lines represent running means of ΔA (left column of each cloud type) or ΔT (right column) for successive 10 W m−2 wide windows of πΔI. Running means are obtained only if there are more than 50 samples for a given 10 W m−2 wide πΔI bin. Standard deviations of the averaged samples and their uncertainties are shown in Figure 10. Solar zenith angle θ0 is fixed as 60°.
Details are in the caption following the image
Standard deviation of ΔA (left column of each cloud type) and ΔT (right column) for 10 W m−2 bins of πΔI shown in Figure 7. Dotted lines indicate 95% confidence interval of the standard deviation as obtained by the bootstrap technique. Dashed line in the right column of each cloud type represents the number of samples for the 10 W m−2 bins of πΔI. Solar zenith angle θ0 is 60°.

As expected, separating by cloud type effectively cluster groups having similar S(πΔI, ΔA) and S(πΔI, ΔT). With the exception of Ns, each cloud type has a distinct single linear relationship between πΔI and ΔA (left column of each cloud type in Figure 7) and πΔI and ΔT (right column of each cloud type in Figure 7). Ci and As have small τ values (Table 2) and thus show the largest S(πΔI, ΔA) and S(πΔI, ΔT). St and Sc also have comparable τ ranges to those of Ci and As, but their thicknesses are smaller (< 1 km). As a result, St and Sc show smaller S(πΔI, ΔA) and S(πΔI, ΔT). Amongst the eight cloud types, St shows the smallest range of πΔI, ΔA, and ΔT because of small τ.

On the other hand, Ac, Ns, and Dc have large τ values (> 10), and so S(πΔI, ΔT) and S(πΔI, ΔT) are smaller than those for optically thinner clouds of moderate geometric thicknesses such as Ci and As. For the cases examined in this study, Ac clouds tend to be located between multilayered cloud systems. Because neighboring higher clouds can alter direct solar irradiance incident on Ac clouds in the 3-D simulations, πΔI and ΔA can be extremely large. As a result, Ac shows a higher frequency of large deviations of πΔI and ΔA, compared to other optically thick clouds such as Cu, Ns, and Dc. Note that ΔT for Ac has small variation because Ac cloud has a moderate τ, and surrounding multilayered clouds can reduce the direct irradiance incident on Ac. Even though Cu has a similar magnitude of τ and layer thickness to Ac type, Cu is often present as an isolated cloud system. As a result, they show larger variations of ΔT due to photon leakage from neighboring clear regions, and thus, S(πΔI, ΔT) is larger in comparison to Ac. However, only small numbers of samples are observed for Cu and Ac, and thus, more cases need to be included to generalize these interpretations.

Both Ns and Dc have a large τ (> 20) (Table 2), but Ns has broader distributions of τ and layer thicknesses with multiple peaks (not shown). This is why scatterplots of Ns in Figure 7 show multiple linear relations between the two radiative parameters in interest. The relation between πΔI and ΔT for Dc seems better described by a quadratic function (grey line in Figure 7). But, as Figure 8 shows, this might be related to an insufficient number of samples for πΔI > 50 W m−2.

Figure 8 shows standard deviations of ΔA (left) and ΔT (right) for ranges of πΔI, for θ0 = 60°. This indicates the uncertainty range of estimated ΔT and ΔA using the running mean method. For all cloud types, standard deviation of ΔA is smaller than that of ΔT because, in general, A < T. Also, relative magnitude of standard deviation of ΔA (divided by mean of A) is also shown to be smaller than the corresponding value for ΔT (not shown). For πΔI from −50 W m−2 to +50 W m−2, where numbers of samples are larger (dashed line in Figure 8), the standard deviation is usually smaller. Therefore, the running mean method is most reliable for estimation of ΔA and ΔT for small values of πΔI. For the case of Dc, the number of samples is small for πΔI > 50 W m−2, and so the accuracy of running mean is reduced in this range.

In Figure 9, scatterplots between πΔI and ΔA, and πΔI and ΔT are given for the eight cloud types as in Figure 7 but for θ0 of 0°. Compared to Figure 7 (θ0 = 60°), correlations are weaker and S(πΔI, ΔA) and S(πΔI, ΔT) are smaller in Figure 9 (θ0 = 0°). This is consistent with the comparison between Figures 5 and 6. Optically thicker clouds, such as Ac, Cu, Ns, and Dc, show smaller slopes than other cloud types. Ac shows negative S(πΔI, ΔT), and Dc shows negative S(πΔI, ΔA).

Details are in the caption following the image
Same as Figure 7 but for θ0 = 0°.

Figure 10 gives standard deviations of ΔA and ΔT as a function of πΔI for θ0 = 0°. Compared to those for θ0 = 60° (Figure 8), standard deviations in Figure 10 are smaller, even though the correlation is weaker. This is because slopes between πΔI and ΔA [S(πΔI, ΔA)], and πΔI and ΔT [S(πΔI, ΔT)] are smaller, reducing the standard deviation for a given πΔI range.

Details are in the caption following the image
Same as Figure 8 but for standard deviation of ΔA (left column of each cloud type) and ΔT (right column) in Figure 9 (θ0 = 0°).

Overall large correlations in Figures 710 suggest that errors in surface irradiance (−ΔT = T1-D − T3-D) and atmospheric absorption (−ΔA = A1-D − A3-D) due to the ICA assumption can be estimated from errors in nadir radiance (−ΔI = I1-D − I3-D) for selected cloud scene types. One way to infer ICA bias in nadir radiance (−ΔI) is to compare CERES-measured radiances to 1-D-modeled radiances. This can be estimated simply using the linear regression results (black lines in Figures 7 and 9). However, if a nonlinear relationship exists among πΔI, ΔA, and ΔT, the running mean curve (grey lines in Figures 7 and 9) can be used for estimating ΔA and ΔT from πΔI. The 1-D modeling error compared with CERES observations includes errors due to inputs. The instantaneous error due to inputs can be evaluated by comparing 3-D simulations with CERES observations when the difference between 1-D-modeled and CERES-observed radiances is large.

Strong linear relations were also found among πΔI, ΔA, and ΔT for narrowband results (not shown). Since each narrowband has unique cloud and gaseous absorptances, S(πΔI, ΔA) and S(πΔI, ΔT) depend on spectral band. For example, between 0.60 and 0.69 µm, where cloud reflection is much larger than cloud absorption, S(πΔI, ΔA) is much smaller than its broadband counterpart. Between 3.5 and 4.0 µm, where cloud extinction is due mostly to absorption, S(πΔI, ΔA) is larger than the broadband value. When these S(πΔI, ΔA) and S(πΔI, ΔT) are applied to infer ΔA and ΔT from the satellite-measured πΔI (i.e., 3-D measured minus 1-D-modeled radiances), it should be noted that visible narrowband πΔI can be underestimated. This is because cloud properties are retrieved from measured visible band, and thus, 1-D-modeled narrowband radiance is correlated with measured radiance.

3.3 Scale Dependence of Linear Relations Among πΔI, ΔA, and ΔT

In the previous section, a 5 km moving window was used to examine the influence of cloud properties and solar geometry on the linear relationships among πΔI, ΔA, and ΔT. This section documents how linear relationships change as a function of size of moving window. Figures 11 (θ0 = 60°) and 12 (θ0 = 0°) show the correlation coefficient between πΔI and ΔA [C(πΔI, ΔA)], between πΔI and ΔT [C(πΔI, ΔT)], and between ΔT and ΔA [CT, ΔA)] as a function of the size of (square) moving window going from 1 km to 51 km. Black lines indicate correlation coefficients for all scenes including clear areas, and the different colored lines indicate correlation coefficients for eight cloud types. Similar to the process used for Figure 7, the dominant cloud type is assigned for each moving window if >90% of the window is covered by a single-layered and single cloud type. Therefore, the number of samples for each cloud type generally decreases with moving window size, because most of large moving windows contain mixed cloud types. The correlation coefficient is computed only if the number of samples in a group is > 1000.

Details are in the caption following the image
Correlation coefficients between (a) πΔI and ΔA [C(πΔI, ΔA)], (b) πΔI and ΔT [C(πΔI, ΔT)], and (c) ΔT and ΔA [C(ΔT, ΔA)]. The correlation coefficient is computed for smoothed irradiance fields using different moving window sizes from 1 km to 51 km. Different colored lines represent eight cloud types, while black lines represent correlation coefficients for all-skies (i.e., including all cloud types and clear-sky). Cloud type is assigned for each moving window when 90% of the area is covered by a single-layer cloud and single cloud type. Correlation coefficient is obtained only if the number of samples is > 1000. Solar zenith angle θ0 is fixed as 60°.
Details are in the caption following the image
Same as Figure 11 but for θ0 = 0°.

When θ0 is 60°, all C(πΔI, ΔA), C(πΔI, ΔT), and CT, ΔA) are positive, indicating that 3-D radiation affects πΔI, ΔT, and ΔA in the same way (Figure 11). For all scenes (black line) and eight cloud types (colored line), C(πΔI, ΔA), C(πΔI, ΔT), and CT, ΔA) rapidly increase as size of moving window increases from 1 km to 10 km. The rate of increase becomes smaller around 10 km. This indicates that there is a slight mismatch in the spatial distribution of πΔI, ΔA, and ΔT that is smoothed out in a scale > 10 km. Increase of correlations with scale is also associated with the number of photons used for Monte Carlo simulations (10,000 × columns). The insufficient photon numbers cause noticeable noise at scales < 5 km thereby reducing linear correlations among πΔI, ΔA, and ΔT.

The correlation coefficient can decrease, however, if the size of moving window is too large. For example, when instantaneous variations of πΔI, ΔA, and ΔT for Sc are averaged by a large moving window, the variability due to relationships among them are also smoothed out so that they are less correlated each other.

Correlation coefficients for scenes separated by cloud type (colored lines in Figure 11) are mostly larger than for all-sky (black line in Figure 11). This indicates that cloud types have their own linear relationships, which are determined by properties such as τ and layer thickness. When scale is greater than 10 km, each cloud type shows C(πΔI, ΔA) > 0.8 (Figure 11a). C(πΔI, ΔT) is also greater than 0.7, except for Ns, when scale > 10 km (Figure 11b). Figure 11c shows that ΔA and ΔT are also correlated well and are similar to πΔI and ΔA. Ac and St clouds have small horizontal extents and are surrounded by other cloud types or clear regions. As a result, most of the moving windows that are > 10 km that contain Ac or St are classified as mixed, and there are too few samples to obtain reliable correlation coefficients.

Figure 12 shows that C(πΔI, ΔA), C(πΔI, ΔT), and CT, ΔA) for θ0 = 0° are much smaller than those for oblique Sun as seen in Figure 11 (cf. Figures 7 and 9). Moreover, the correlation does not continuously increase with scale, when θ0 = 0°, showing more irregular and unstable patterns with scale. While the standard deviation for θ0 = 0° is smaller than that for θ0 = 60° when πΔI is small for most cloud types, the weaker correlation for θ0 = 0° suggests that 3-D effects on atmospheric absorption and surface irradiance can be more reliably estimated for large θ0. Considering that θ0 for A-train observations are mostly between 30° and 80°, it is expected that πΔI, ΔA, and ΔT will have strong correlations between each other at CERES footprint scale (~ 20 km) and that πΔI can provide estimates of ΔA or ΔT.

For this study, clouds were resolved down to 1 km resolution. It is likely, however, that variability at scales smaller than 1 km influences the scale-dependent correlations among πΔI, ΔA, and ΔT. To examine influence of subgrid variability on these relations, radiative transfer simulations are performed on two high-resolution (35 m) 3-D cloud fields based on Atlantic Stratocumulus Transition Experiment (http://www.euclipse.nl/wp3/ LES_Data/ASTEX/Dales). For θ0 = 0° and 60°, C(πΔI, ΔA) increases relative to values inferred from satellite data at scales between 0.035 and 1.785 km (not shown), but corresponding values of C(πΔI, ΔT) and CT, ΔA) are largely unchanged. These preliminary results imply that C(πΔI, ΔA) obtained at the 1 km scale, as shown in Figures 11 and 12, might be slight underestimates. Clearly, more high-resolution studies of this kind are needed before generalizations can be drawn.

3.4 Necessity and Feasibility of Application of the Linear Relationships Among πΔI, ΔA, and ΔT

This section investigates the cloud type-dependent scales at which instantaneous πΔI, ΔA, and ΔT become significant and 3-D effects need to be taken into account.

Table 3 lists averages and standard deviations of πΔI, ΔA, and ΔT for all-sky, clear-sky, and clouds separated by type for a 71 × 17,500 km domain. Cloud type is determined for every 1 km × 1 km pixel. Domain averages of πΔI, ΔA, and ΔT for all-sky are negligible (< 5 W m−2) for both θ0 but can be significant for some cloud types.

Table 3. Mean and Standard Deviation of πΔI, ΔA, and ΔT for a 17,500 km Long by 71 km Wide Domain Observed on 1 November 2010 02 UTCa
θ0 = 0° θ0 = 60
Scene Type πΔI ΔA ΔT πΔI ΔA ΔT
All −4.9 ± 50.8 0.4 ± 21.3 1.7 ± 94.2 −0.3 ± 30.4 1.1 ± 26.9 −1.8 ± 92.9
Clear 1.7 ± 3.6 3.7 ± 9.5 29.5 ± 60.6 −0.2 ± 5.4 −0.1 ± 15.3 −14.0 ± 76.1
Ci 2.0 ± 34.7 −5.1 ± 24.9 −18.5 ± 121.5 3.9 ± 21.6 3.7 ± 28.6 −4.7 ± 111.9
As −4.4 ± 46.6 −1.9 ± 19.2 −15.8 ± 94.5 0.8 ± 25.3 2.5 ± 25.6 10.3 ± 101.6
Ac 20.2 ± 76.5 12.5 ± 22.5 24.0 ± 93.0 −17.2 ± 79.6 −12.2 ± 38.5 8.3 ± 95.1
St 3.3 ± 33.2 4.8 ± 16.4 −3.3 ± 101.0 −4.5 ± 23.8 −4.6 ± 21.1 3.2 ± 107.2
Sc −7.1 ± 51.7 1.9 ± 17.4 −21.0 ± 110.3 −4.7 ± 33.8 −2.8 ± 23.9 13.3 ± 116.0
Cu −31.8 ± 87.1 −4.7 ± 22.2 −33.8 ± 108.5 −3.2 ± 44.2 2.2 ± 30.9 23.2 ± 124.2
Ns 11.6 ± 86.8 4.5 ± 27.2 2.2 ± 60.8 −7.7 ± 58.0 −5.8 ± 37.0 −1.4 ± 41.2
Dc −33.9 ± 102.1 3.7 ± 39.7 −7.1 ± 44.3 10.2 ± 66.1 13.9 ± 49.5 22.5 ± 63.1
  • a Mean and standard deviation are given as (mean) ± (one standard deviation). Here πΔI, ΔA, and ΔT are in units of W m−2.

For θ0 = 0°, values of πΔI are As (−4.4 W m−2), Sc (−7.1 W m−2), Cu (−31.8 W m−2), and Dc (−33.9 W m−2). As mentioned earlier, for these conditions, radiation escapes from cloudy regions into neighboring clear regions primarily in the downward direction and so enhances clear-sky T. Correspondingly, πΔI for θ0 = 60° are Ci (3.9 W m−2), As (0.8 W m−2), and Dc (10.2 W m−2) because of enhanced reflection due to cloud side illumination [Welch and Wielicki 1984; Barker and Li, 1997]. However, these interpretations are not always true for all cloud types because the eventual 3-D effects are also influenced by horizontal scale of cloud and surrounding structure.

For example, Ac clouds show somewhat unexpected signs of πΔI; positive πΔI for θ0 = 0° (20.3 W m−2) and for θ0 = 60° (−17.2 W m−2). Possible reasons for this are (1) the number of samples of Ac is relatively small and (2) Ac clouds, in this study, are often located between multilayer cloud systems. Radiation leakage from neighboring upper clouds enhances downward irradiance at the tops of Ac cloud for overhead Sun. For oblique Sun, neighboring upper clouds can cast shadows on Ac clouds.

The mean and standard deviation of ΔA are relatively small for all scene types compared to those of πΔI or ΔT because absolute magnitude of atmospheric absorption is much smaller than TOA or surface irradiance.

When θ0 = 0°, ΔT are Ci (−18.5 W m−2), As (−15.8 W m−2), St (−3.3 W m−2), Sc (−21.0 W m−2), Cu (−33.8 W m−2), Dc (−7.1 W m−2), and clear-sky (+29.5 W m−2). Conversely, for θ0 = 60°, ΔT is positive for most cloud scenes (e.g., Cu (23.2 W m−2) and Dc (22.5 W m−2)). The reasons for these were explained above and have to do with side leakage and illumination.

Because standard deviations of πΔI, ΔA, and ΔT are much larger than their averages (Table 3), it is expected that instantaneous variations are more significant [see Zuidema and Evans, 1998; O'Hirok and Gautier, 2005; Wyser et al., 2005; Song and Min, 2011]. To investigate how instantaneous variability of πΔI, ΔA, and ΔT changes as a function of the size of moving window, root-mean-square (RMS) differences between 3-D and ICA results are defined as
where N is number of moving windows, x(i) is either πI(i), A(i), or T(i) computed from ith moving window, and subscripts 3-D and ICA indicate values from 3-D and ICA simulations.

Figures 13 and 14 show RMS(πI), RMS(A), and RMS(T) for the window size from 1 km to 51 km by cloud type for θ0 of 60° and 0°, respectively. Cloud type is assigned as in section 3.3. Compared to RMS differences with θ0 = 0°, RMS differences for θ0 = 60° slowly decrease with scale. Especially, RMS(T) for θ0 = 60° which is larger than that for θ0 = 0° for high-level cloud cases such as As or Ci. This is because horizontally shifted cloud shadows are generated over the surface in 3-D simulation, and the degree of the shift is proportional to cloud altitude. Overall, RMS(πI), RMS(A), and RMS(T) rapidly decrease when the window size increases from 1 km to 20 km. This is consistent with other previous studies [O'Hirok and Gautier, 2005; Wyser et al., 2005].

Details are in the caption following the image
Root-mean-square (RMS) difference of (a) π times nadir radiance (πI), (b) atmospheric absorption (A), and (c) surface irradiance (T) for θ0 = 60°.
Details are in the caption following the image
Same as Figure 13 but for θ0 = 0°.

4 Summary

In this study, one-dimensional (1-D) independent column approximation (ICA) and full three-dimensional (3-D) simulations were performed to examine 3-D effects on shortwave radiative transfer using cloud fields obtained from A-train satellite observations. Three-dimensional minus ICA differences are analyzed for TOA nadir radiance, atmospheric absorption, and surface downward irradiance, denoted here as πΔI, ΔA, and ΔT, respectively. In 1 km scale pixel-to-pixel comparisons, any pair of πΔI, ΔA, and ΔT fails to show a noticeable correlation. When moving windows larger than 5 km are used to smooth out πΔI, ΔA, and ΔT, however, positive linear correlations emerges among πΔI, ΔA, and ΔT. The slightly different mismatch of spatial patterns of πΔI, ΔA, and ΔT is smoothed out by the moving window leading to stronger linear relationships. This indicates that 3-D enhancements and reductions of nadir radiance, surface irradiance, and atmospheric absorption occur at a similar distance from illuminated or shadowed areas, but not at exactly the same locations. Monte Carlo noise at a small scale is another factor that can slightly reduce correlations among πΔI, ΔA, and ΔT at 1 km pixel resolution.

Cloud properties and solar geometry were shown to affect the linear relations among πΔI, ΔA, and ΔT. As cloud optical thickness τ increases, slopes of regression line between πΔI and ΔA, and πΔI and ΔT, referred to as S(πΔI, ΔA) and S(πΔI, ΔT), decrease. In addition, our results show that S(πΔI, ΔA) and S(πΔI, ΔT) are larger at solar zenith angle θ0 = 60° than at 0°. Furthermore, correlation among πΔI, ΔA, and ΔT is stronger for θ0 = 60° than at 0°. When cloud scenes are partitioned into eight cloud types, each cloud type has, for the most part, a single linear relationship between a pair of πΔI, ΔA, and ΔT.

Correlation coefficients between πΔI and ΔA, and πΔI and ΔT, referred to as C(πΔI, ΔA) and C(πΔI, ΔT), generally increase with the size of moving window between 1 km and 10 km when θ0 is 60°. When the window size is > 10 km, C(πΔI, ΔA) is > 0.8 for all cloud types and C(πΔI, ΔT) > 0.7 except for Ns type. These results suggest that ICA biases of surface irradiance (−ΔT) and atmospheric absorption (−ΔA) can be inferred from ICA biases of nadir radiance (−πΔI) once cloud type is known.

As in earlier studies [e.g., Barker et al., 1999; Marshak et al., 1998], this one found that ICA biases at the global scale are shown to be small. At the scales of most satellite pixels (e.g., 1 to 20 km), however, 3-D effects on instantaneous radiance or irradiance can be significant. Therefore, findings from the current study can be used to infer instantaneous ICA biases. It should be noted, however, that the method can be more reliably applied for scales > 10 km because the correlations found in this study largely increase between 1 km and 10 km.

In this study, we only performed 1-D and 3-D simulations for a cloud domain obtained from 1 h of A-train data. To generalize the linear relationships between πΔI and ΔT, and πΔI and ΔA, more samples are needed. Furthermore, CloudSat-derived Ns has multiple peaks in the τ distribution, which lead to multiple linear relationships between πΔI and ΔT. If Ns is subdivided into two groups, such as core and boundary region of the convective system, single relations with higher correlations might be obtained for each subgroup.


We thank Alexander Marshak for useful discussions and Robert Pincus and Frank Evans for making the I3RC Monte Carlo code publicly available. The work is, in part, supported by the CERES and NASA Energy Water Cycle Study (NEWS) project. S.-H. Ham was also supported by the NASA Postdoctoral Program at the NASA Langley Research Center, administered by Oak Ridge Associated Universities (ORAU).