Combining Cloud Properties from CALIPSO, CloudSat, and MODIS for Top-of-Atmosphere (TOA) Shortwave Broadband Irradiance Computations: Impact of Cloud Vertical Profiles

Seung-Hee Ham; Seiji Kato; Fred G. Rose; Sunny Sun-Mack; Yan Chen; Walter F. Miller; Ryan C. Scott

doi:10.1175/JAMC-D-21-0260.1

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Journal of Applied Meteorology and Climatology

Abstract
- Significance Statement
1. Introduction
2. Data and method
3. Impact of the CCM-merged cloud profiles on the TOA SW BB irradiance computations
4. Impact of the CER on the irradiance by spectral regions
5. Discussions
6. Summary
Acknowledgments.
Data availability statement.
APPENDIX A
- Constraining the CCM Cloud Extinction Profile with the MODIS COD
APPENDIX B
- Importance of Constraining with the MODIS VSCOD
APPENDIX C
- The Impacts of the Cloud Source of the Radiative Transfer Inputs
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Fig. 1.

Hierarchy of the cloud products to generate profiles of CCM-merged cloud extinction coefficient k_ext and particle effective radius r_e. The cloud phase is determined at each vertical computational model layer, and then different hierarchies are applied to (left) liquid- and (right) ice-phase clouds. If the first choice of the cloud product is not available, the next choice is used until all properties are filled. The default values of ice and liquid r_e are 30 and 13 μm, respectively, which is based on 1-yr MODIS observations.

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Fig. 2.

A schematic diagram of how the profiles of CCM-merged (a) cloud extinction coefficient k_CCM and (b) CER r_CCM profiles are generated. Note that cloud-top and cloud-base boundaries are determined from CloudSat and CALIPSO, but not by MODIS. Even though CALIPSO and/or CloudSat indicate the cloud layer (gray areas), it does not always mean that valid cloud extinctions and effective radius profile are available from the CALIPSO CPro, CloudSat 2B-CWC, or CloudSat 2C-ICE product. In this case, we assume cloud extinction coefficient for these layers using MODIS cloud properties on the basis of the hierarchy of the cloud products shown in Fig. 1.

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Fig. 3.

Input (a),(c) cloud extinction coefficient (km⁻¹) and (b),(d) CER (μm) profiles averaged over the (top) 30°S–30°N region and (bottom) 60°–40°S region using methods 1, 2, 3, and 4 described in the text. The cloud profiles are computed for four seasonal months of data (January, April, July, and October) in 2008. In (a) and (c), cloud extinction coefficient profiles from methods 3 and 4 are very close each other, and thus the profile from method 4 is given as a dashed line to distinguish it from method 3.

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Fig. 4.

Biases in TOA SW BB irradiance (W m⁻²) computed with methods (a) 1, (b) 2, (c) 3, and (d) 4. The biases are computed with a 2°-grid interval. In averaging four monthly means (January, April, July, and October 2008), equal weights are applied, i.e., (January + April + July + October monthly means)/4. The number (#) in the parentheses represents the number of 2°-grid boxes used for computing the global means.

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Fig. 5.

One-to-one scatterplots between CERES-derived and computed TOA SW BB irradiances ( $F_{SW}^{TOA}$ ) (W m⁻²). Each data point is obtained from a CERES footprint, and then the frequency is counted for the $F_{SW}^{TOA}$ bins with a 10-W m⁻² interval and for the $F_{SW}^{TOA}$ -bias bins with a 5-W m⁻² interval. The computations are performed using methods (top left) 1, (top right) 2, (bottom left) 3, and (bottom right) 4 for January, April, July, and October 2008. Red lines in the left plot of each method are mean values of the $F_{SW}^{TOA}$ biases for the given observed $F_{SW}^{TOA}$ bins with a 10 W m⁻² interval. The number (#) in each panel represents the number of CERES footprints used for the computations.

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Fig. 6.

As in Fig. 5, but for CERES footprints with ice-topped cloud cases. The ice-topped cloud cases are defined when the ice cloud fraction is larger than 80% within the CERES footprint. The cloud layers above the 253.15-K temperature are considered to be ice clouds. The CERES footprints can still contain underlying mixed- or liquid-phase clouds.

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Fig. 7.

As in Fig. 5, but for CERES footprints for pure liquid-phase cloud cases. The pure liquid-phase cloud cases are defined when the liquid cloud fraction is larger than 80% and ice clouds do not exist within the CERES footprint. The cloud layers below the 273.15-K temperature level are considered to be liquid-phase clouds.

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Fig. 8.

(a) TOA SW BB reflectance $R_{SW}^{TOA}$ , (b) TOA upward SW BB irradiance ( $F_{SW}^{TOA}$ ; W m⁻²), and (c) input column ice CER (μm), as a function of MODIS visible scaled cloud optical depth. The $R_{SW}^{TOA}$ is defined as (TOA upward SW BB irradiance)/(TOA downward SW BB irradiance). The values of $R_{SW}^{TOA}$ are from CERES observations or computations using methods methods 1, 2, 3, and 4 (colors). To obtain the relations, CERES footprints are sampled over the MODIS VSCOD bins with a 0.4 interval. Then mean values of the $R_{SW}^{TOA}$ , $F_{SW}^{TOA}$ , or input column ice CER are computed for each VSCOD bin. The number of CERES footprints used for each VSCOD bin is given by dashed lines (right y axis). Only CERES footprints with ice-topped cloud cases are used. The numbers given in (b) are the mean difference in $F_{SW}^{TOA}$ and its relative difference, computed from methods 3 and 4 when VSCOD is between 19.6 and 20.0. Note that the ice CER r_e distributions from methods 1–3 are nearly overlapped in (c). The CERES footprints for 60°S–60°N are used.

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Fig. 9.

(a) SSA and (b) 1 − SSA for the 18 SW narrow bands, as a function of r_e from the THM.

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Fig. 10.

Computed TOA SW NB ( $F_{SW, i}^{TOA}$ ) and BB ( $F_{SW}^{TOA}$ ) irradiances with various r_e values. VSCOD is fixed as (top) 2, (middle) 20, and (bottom) 30. (a),(c),(e0 Absolute differences of TOA SW irradiances from those with r_e = 20 are obtained. (b),(d),(f) Relative changes of the TOA SW irradiances to those with r_e = 20 μm are obtained. Since CCM-merged ice CER reaches to 65 μm, whereas MODIS ice CER is around 20 μm (Fig. 8c), the changes from r_e = 20 μm to r_e = 65 μm suggest possible positive biases due to the use of MODIS ice CER. Solar zenith angle is held as 0°, and a single cloud layer is assumed to be at 10–12 km. The midlatitude summer standard profiles are used along with the ocean surface albedo.

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Fig. 11.

As in Fig. 8b, but for spectrally integrated irradiances for (a) 0.18–0.89 μm (B01–B12), (b) 0.89–1.04 μm (B13), (c) 1.04–1.41 μm (B14), (d) 1.41–1.90 μm (B15), (e) 1.90–2.5 μm (B16), and (f) 2.5–4.0 μm (B17–B18). Since the CERES instrument observes SW BB irradiances but not spectral irradiances, observed irradiances are not available in this figure. The numbers given in the panels are the mean SW irradiance difference and its relative difference, computed from methods 3 and 4 when VSCOD is between 19.6 and 20.

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Fig. 12.

As in Fig. 4, but for daytime (SZA < 82°) TOA LW BB irradiance biases.

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Fig. A1.

As in Fig. 4d, but k_CCM(z) is constrained by MODIS cloud optical depth using Eq. (A1), instead of MODIS VSCOD. Specifically, βk_CCM(z) and r_CCM(z) profiles are used for TOA SW BB computations.

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Fig. B1.

(a) Computed minus CERES-derived TOA SS BB irradiance $F_{SW}^{TOA}$ . Also shown are scatterplots (b) between CERES-derived $F_{SW}^{TOA}$ and bias in $F_{SW}^{TOA}$ and (c) between CERES-derived and computed $F_{SW}^{TOA}$ . The computation is performed using k_CCM, r_CCM, and Φ_CCM, defined in section 2a(5). However, k_CCM is not constrained by MODIS VSCOD. Therefore, this method is the same as method 4 but with α = 1. Four seasonal months (January, April, July, and October) in 2008 are used. The number (#) in (a) represents the number of 2°-grid boxes used for the global means. The number (#) in (c) represents the number of CERES footprints used in the scatterplots.

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Fig. C1.

The frequency of CERES footprints when (top left) CALIPSO, (top right) CloudSat 2C-ICE, (bottom left) CloudSat 2B-CWC liquid, and (bottom right) 2B-CWC ice cloud products are used in generating cloud input profiles. For example, for the occurrence of the CALIPSO usage in the top-left panel, it is computed as (the number of CERES footprints with CALIPSO being used)/(total number of CERES footprints) for each 2°-grid box. When multiple cloud products are used for one CERES footprints, the frequency of all of the corresponding products is counted. Therefore, the sum of the four panels can be over 100%. The frequency is computed for four seasonal months (January, April, July, and October) in 2008.

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Fig. C2.

TOA SW BB irradiance biases (W m⁻²) depending on which cloud product is used, where the frequency of CERES footprints is given in Fig. C1. Method 4 is used for the computations. The number (#) shown in parentheses in each panel represents the number of 2°-grid boxes for obtaining global means.

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Fig. C3.

As in Fig. C2, but without constraining k_CCM(z) with MODIS VSCOD (i.e., α = 1).

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EDITORIAL

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Editorial Type:: Article

Article Type:: Research Article

Combining Cloud Properties from CALIPSO, CloudSat, and MODIS for Top-of-Atmosphere (TOA) Shortwave Broadband Irradiance Computations: Impact of Cloud Vertical Profiles

Seung-Hee Ham

Seung-Hee Ham ^aScience Systems and Applications, Inc., Hampton, Virginia

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Seiji Kato

Seiji Kato ^bNASA Langley Research Center, Hampton, Virginia

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Fred G. Rose

Fred G. Rose ^aScience Systems and Applications, Inc., Hampton, Virginia

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Sunny Sun-Mack

Sunny Sun-Mack ^aScience Systems and Applications, Inc., Hampton, Virginia

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Yan Chen

Yan Chen ^aScience Systems and Applications, Inc., Hampton, Virginia

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Walter F. Miller

Walter F. Miller ^aScience Systems and Applications, Inc., Hampton, Virginia

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Ryan C. Scott

Ryan C. Scott ^bNASA Langley Research Center, Hampton, Virginia

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Online Publication:: 21 Sep 2022

Print Publication:: 01 Oct 2022

DOI:: https://doi.org/10.1175/JAMC-D-21-0260.1

Page(s):: 1449–1471

Received:: 17 Dec 2021

Accepted:: 12 Jul 2022

Published Online:: 21 Sep 2022

Displayed acceptance dates for articles published prior to 2023 are approximate to within a week. If needed, exact acceptance dates can be obtained by emailing amsjol@ametsoc.org.

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Abstract

Cloud vertical profile measurements from the CALIPSO and CloudSat active sensors are used to improve top-of-atmosphere (TOA) shortwave (SW) broadband (BB) irradiance computations. The active sensor measurements, which occasionally miss parts of the cloud columns because of the full attenuation of sensor signals, surface clutter, or insensitivity to a certain range of cloud particle sizes, are adjusted using column-integrated cloud optical depth derived from the passive MODIS sensor. Specifically, we consider two steps in generating cloud profiles from multiple sensors for irradiance computations. First, cloud extinction coefficient and cloud effective radius (CER) profiles are merged using available active and passive measurements. Second, the merged cloud extinction profiles are constrained by the MODIS visible scaled cloud optical depth, defined as a visible cloud optical depth multiplied by (1 − asymmetry parameter), to compensate for missing cloud parts by active sensors. It is shown that the multisensor-combined cloud profiles significantly reduce positive TOA SW BB biases, relative to those with MODIS-derived cloud properties only. The improvement is more pronounced for optically thick clouds, where MODIS ice CER is largely underestimated. Within the SW BB (0.18–4 μm), the 1.04–1.90-μm spectral region is mainly affected by the CER, where both the cloud absorption and solar incoming irradiance are considerable.

Significance Statement

The purpose of this study is to improve shortwave irradiance computations at the top of the atmosphere by using combined cloud properties from active and passive sensor measurements. Relative to the simulation results with passive sensor cloud measurements only, the combined cloud profiles provide more accurate shortwave simulation results. This is achieved by more realistic profiles of cloud extinction coefficient and cloud particle effective radius. The benefit is pronounced for optically thick clouds composed of large ice particles.

Corresponding author: Seung-Hee Ham, seung-hee.ham@nasa.gov

Abstract

Significance Statement

Corresponding author: Seung-Hee Ham, seung-hee.ham@nasa.gov

Keywords: Clouds; Cloud microphysics; Cloud radiative effects; Cloud retrieval; Cloud water/phase; Satellite observations

1. Introduction

Passive imagers such as Moderate Resolution Imaging Spectroradiometer (MODIS) (Salomonson et al. 1989; Barnes et al. 1998) measure narrowband radiances reflected or emitted from cloud layers, from which cloud properties are retrieved (e.g., Nakajima and King 1990; Minnis et al. 2011a,b; Platnick et al. 2017). These passive-sensor retrievals can only provide column-integrated cloud properties. Because cloud vertical structures are not derived, we need to assume cloud vertical profiles for radiative transfer calculations. A simple assumption often used is that the cloud extinction coefficient and cloud effective radius (CER) are uniform within a cloud layer. This assumption works well in reproducing top-of-atmosphere (TOA) visible or shortwave infrared (SWIR) channel radiances that are used for cloud retrievals. However, it can also introduce significant biases at channels where strong gaseous or cloud absorption occurs, especially for multilayered or geometrically thick clouds (Ham et al. 2009; Ham and Sohn 2012; Kato et al. 2011). This would also affect the TOA shortwave (SW) broadband (BB) simulation accuracy. Assuming a constant number concentration with a monotonic increasing of the cloud water content for boundary layer clouds (e.g., Bennartz 2007; Bennartz and Rausch 2017; Grosvenor et al. 2018) or parameterizing the shape of cloud profiles depending on the cloud type (e.g., Ham et al. 2013) would provide more realistic cloud vertical structures than the homogeneous assumption, but these do not resolve instantaneous variations of the cloud profiles.

Active sensors provide range-resolved measurements, which are typically better able to constrain vertical profiles of cloud and aerosol properties than measurements from passive sensors. These include Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) aboard Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) (Winker et al. 2003, 2007, 2009) and Cloud Profiling Radar (CPR) (Mace and Wrenn 2013; Stephens et al. 2002, 2008) aboard CloudSat, which belong to the A-Train constellation. CALIOP lidar is suited for the detection of thin cloud layers with a high vertical resolution, while CloudSat radar can observe through optically thick water clouds, and it is sensitive to larger cloud particles. Therefore, the synergy of CALIPSO and CloudSat can improve cloud detections (Kato et al. 2010; Mace et al. 2007, 2009; Delanoë and Hogan 2010; Mace and Zhang 2014; Ham et al. 2021), and these can be also used for improvements of radiative transfer computations (Kato et al. 2011; Henderson et al. 2013; Matus and L’Ecuyer 2017; L’Ecuyer et al. 2019; Hang et al. 2019).

However, there are also limitations of the active sensors. For example, the CALIPSO footprint size (70 m) is much smaller than the CloudSat footprint size (1.4 × 1.8 km²), meaning that the perfect collocation between the two active sensors is not possible. The spaceborne CALIPSO lidar signal often has a small signal-to-noise ratio at a single lidar beam, often requiring spatial averaging for detecting optically thin clouds (Winker et al. 2009; Vaughan et al. 2009). Also, the CALIPSO lidar signal is fully attenuated for the cloud optical depth > 10 (Young et al. 2018), whereas the CloudSat signal is adversely affected by surface clutter, causing cloud amounts below 1 km in altitude to be underestimated (Marchand and Mace 2018; Ham et al. 2017b). Moreover, rain particles increase the radar signal significantly, and thus CloudSat cloud retrievals are not reliable for precipitating cases (Berry et al. 2020).

To overcome limitations of the active sensor detections and produce profiles of cloud products that are more consistent with Clouds and the Earth’s Radiant Energy System (CERES) TOA outgoing radiation, Kato et al. (2011) merged cloud profiles from active and passive sensors. In this approach, the merged profiles are normalized by MODIS visible scaled cloud optical depth (VSCOD) [=visible cloud optical depth × (1 − asymmetry parameter)]. This ensures that the cloud parts missed by the active sensors as well as random errors in retrievals are adjusted by MODIS column-integrated optical depth values. We revisit the VSCOD constraining method with the improved versions of CloudSat and CALIPSO datasets. We specifically examine the benefits of the multisensor approach in TOA SW simulations by comparing the results with MODIS-only simulations, where CERES observations are used as references for the radiative closure study. The merged cloud profiles shown in this study can be used for understanding cloud vertical structures and their radiative impacts in cloudy atmosphere.

Section 2 explains how the multisensor cloud information is generated. Section 3 discusses the benefits of the multisensor (active–passive sensor combined) approach over the MODIS-only approach. Section 4 examines the impact of CER for separated spectral regions. Section 5 discusses limitations and uncertainties of this study. Section 6 summarizes the findings of this study.

2. Data and method

The radiative transfer simulation method discussed in this study is intended for CERES–CALIPSO–CloudSat–MODIS (CCCM) release D1 (RelD1) product processing (Atmospheric Science Data Center 2021; Kato et al. 2021). In this algorithm, multisensor cloud properties are combined for a better description of cloud profiles, which are used as model inputs for computing SW and longwave (LW) BB irradiance profiles. Even though the computed irradiances are provided at each CERES footprint, actual radiative computations are performed for each cloud group within a CERES footprint as discussed below. The full description of the earlier version [release B1 (RelB1)] of the CCCM product is provided in Kato et al. (2011), and here we provide a brief description of the algorithm and update since RelB1.

a. Satellite cloud product merging approach

1) Cloud masking and grouping in each CERES footprint

Cloud masks from CALIPSO and CloudSat are combined (Kato et al. 2010, 2011). The CALIPSO cloud mask is from CALIPSO, version 4 (V4), Vertical Feature Mask (VFM) product (Vaughan et al. 2009), and the CloudSat cloud mask is from release 5 (R05) of the CloudSat 2B-CLDCLASS product (Sassen and Wang 2008). The CloudSat cloud mask is provided at a 480-m vertical resolution with oversampling of 240 m, horizontally sampled every ∼1.1 km along the satellite track with a footprint size of 1.4 × 1.8 km². The CALIPSO cloud mask is provided at a 30-m vertical resolution below 8.2 km and at a 60-m resolution above 8.2-km altitude, horizontally sampled every ⅓ km along the satellite track. The CALIPSO and CloudSat cloud boundaries are merged at a CALIPSO horizontal resolution, that is, every ⅓ km along the track. Following the strategy of Table 1 of Kato et al. (2010), we primarily use CALIPSO cloud mask and add CloudSat cloud mask when CloudSat detects additional cloud layers. This includes CloudSat clouds below the altitude where the CALIPSO signal is fully attenuated.

Even though the CALIPSO VFM cloud mask is provided at a ⅓-km horizontal resolution, these are detected from either single lidar beam (⅓ km) or 1-/5-/20-/80-km spatial averaging. As the cloud layer is more tenuous, larger spatial averaging is needed because of the small signal-to-noise ratio (Vaughan et al. 2009). One change in RelD1 over the RelB1 algorithm is that we do not include CALIPSO clouds if the layer is detected by 80-km spatial averaging because these are radiatively unimportant for outgoing SW TOA flux. For example, the integrated attenuated 532-nm backscatter for 80-km-averaging clouds is 30% of that with 20-km-averaging clouds, and 3%–0.3% of 5-km-averaging clouds (Fig. 8 of Vaughan et al. 2009). Another change from RelB1 to the RelD1 CCCM algorithm is that we do not include CALIPSO water clouds below a 4-km altitude detected with any spatial averaging (1, 2, 5, or 20 km). In other words, only water clouds detected from a single beam (⅓ km) are included below 4 km. This is because a strong lidar signal from water particles causes overdetection of boundary layer clouds when the spatial averaging is used (D. Winker 2017, personal communication). Earlier studies (Brunke et al. 2010; Mace and Zhang 2014) also supported this idea that the low-level water cloud amounts with 5-/20-/80-km spatial averaging tend to be overestimated.

Once the merged cloud boundaries are generated at every ⅓ km along the satellite track, these are grouped if the cloud-top and cloud-base boundaries are the same within a CERES footprint. This will generate up to 16 cloud groups in a CERES footprint, where each cloud group contains up to 6 overlapping layers [see Fig. 2 of Kato et al. (2010)]. The reduced number groups are intended for more efficient radiative computations, relative to the computations at a ⅓-km CALIPSO resolution.

2) Obtaining MODIS, CALIPSO, and CloudSat properties in each cloud group

Once cloud groups are determined for each CERES footprint, MODIS pixel resolution (∼1 km) of cloud properties such as cloud optical depth, column CER, or cloud phase are accordingly averaged over each cloud group. A logarithmic scale is used for averaging MODIS cloud optical depths. The MODIS cloud parameters are from an improved version of the CERES Ed4B algorithm (Minnis et al. 2021), which used the two-habit model (THM) for ice cloud scattering parameters (Liu et al. 2014). The same ice habit model is used for radiative transfer simulations.

Note that CERES MODIS cloud product is different from MYD06 cloud product (Platnick et al. 2017). The cloud properties in the two products generally agree well except at cloud edges or polar regions (Minnis et al. 2016; Chiriaco et al. 2007). One strategic difference is that CERES MODIS algorithm tries to retrieve cloud parameters for all cloudy pixels, while MYD06 algorithm only retrieves cloud parameters for cloudy pixels with high confidence. The strategic difference comes from that CERES MODIS algorithm is intended for estimating global radiation budget with including all pixels.

While MODIS cloud properties are averaged for each cloud group, we linearly average CALIPSO and CloudSat cloud profiles for a CERES footprint. These are primarily due to 1) a coarser resolution (5 km) of CALIPSO extinction profiles that cannot resolve variations across cloud groups, 2) large noises in individual CALIPSO extinction profiles, and 3) limitation in storing high-vertical-resolution profiles up to 16 cloud groups in each CERES footprint. The footprint-averaged profiles include cloud extinction profiles from the CALIPSO 5-km cloud profile product (CPro), version 4, (Young and Vaughan 2009; Young et al. 2018), and cloud liquid water content (LWC), ice water content (IWC), water particle CER, and ice particle CER profiles from the CloudSat 2B-CWC release 5 (R05) product (Austin et al. 2009; Austin and Wood 2018). Ice cloud extinction coefficient, ice CER, and IWC profiles from the CloudSat 2C-ICE R05 product (Deng et al. 2010, 2013, 2015) are also averaged.

3) Determining cloud phase of each vertical model layer for each cloud group

The computational model layers for the radiative transfer simulations are defined with a 120-m vertical resolution below the 3-km altitude and with a 240-m resolution between the 3-km and 21-km altitudes. Accordingly, clear or cloudy model layers are determined based on the cloud boundaries of the cloud groups generated in section 2a(1). Then GEOS-5.4.1 reanalysis temperature profiles are used to determine the cloud phase of the model layer. Ice phase is determined for T < 253.15 K, and liquid phase is determined for T > 273.15 K. For the temperature between 253.15 and 273.15 K, ice phase is assumed if valid 2C-ICE parameters exist for the layer. For the rest of the cases for 253.15 ≤ T ≤ 273.15 K, the CALIPSO phase is used to determine the phase if the confidence of the CALIPSO phase is medium or high. If the CALIPSO phase is not available, MODIS cloud phase is used for the layers with 253.15 ≤ T ≤ 273.15 K. Note that the CERES MODIS algorithm provides a phase value as 1 for the pure liquid and 2 for the pure ice clouds. We assume liquid phase for the group if 1 ≤ MODIS phase value < 1.5, and ice phase if 1.5 ≤ MODIS phase value < 2.

4) Merging CALIPSO, CloudSat, and MODIS cloud properties for each cloud group

Depending on the cloud phase of the vertical model layer, different methods are used to assign cloud extinction coefficient k_CCM(z) and CER r_CCM(z) profiles (Fig. 1). For liquid-phase cloud layers, if available, CALIPSO k_ext(z) is used. If CALIPSO k_ext(z) is not available, 2B-CWC liquid k_ext(z) and r_e(z) are used. If both CALIPSO and 2B-CWC liquid products are unavailable, MODIS k_ext(z) and r_e(z) are used.

For ice-phase cloud layers, k_ext(z) and r_e(z) from the 2C-ICE product are used as a first choice. This is because 2C-ICE parameters are retrieved by combining radar and lidar information, providing superior results than the single radar or lidar sensor retrievals (Deng et al. 2013, 2015). The rest of the hierarchy is similar to those used for liquid-phase cloud layers—that is, CALIPSO, 2B-CWC ice, and MODIS, in that order.

The MODIS k_ext(z) is derived as τ_M/Δz_c where τ_M is the MODIS cloud optical depth and Δz_c is the sum of geometrical cloud thicknesses of all overlapping clouds according to CC cloud boundaries of the group. The 2B-CWC product provides IWC(z), LWC(z), ice r_e(z), and liquid r_e(z), but not cloud extinction coefficients. Therefore, the liquid k_ext(z) is computed using the equation LWC(z) = ⅔ρ_Lk_ext(z)r_e(z), where ρ_L is density of a water particle (1 g cm⁻³). The 2B-CWC ice k_ext(z) is computed using the equation IWC(z) = ⅔ρ_Ik_ext(z)r_e(z), where ρ_I is density of an ice particle (0.917 g cm⁻³). The 2C-ICE product directly provides k_ext(z) and r_e(z) profiles. A schematic diagram in Fig. 2 shows how the cloud extinction and CER profiles are merged based on the hierarchy shown in Fig. 1.

5) Constraining CCM-merged cloud profile with MODIS information

As mentioned earlier, CALIPSO and CloudSat provide detailed cloud vertical profiles, but these often miss the cloud bottom parts. To overcome this issue, the CCM-merged cloud extinction profile [k_CCM(z)] is constrained by the MODIS VSCOD, by following the approach of Kato et al. (2011):

τ_{M} [1 - g (r_{M}, Φ_{M})] = α \int_{z_{B}}^{z_{T}} k_{CCM} (z) {1 - g [r_{CCM} (z), Φ_{CCM} (z)]} d z,

(1)

where τ_M is a cloud optical depth, r_M is a CER, and Φ_M is a cloud phase from MODIS. In addition, k_CCM(z), r_CCM(z), and Φ_CCM(z) are cloud extinction coefficient, CER, and phase profiles merged from CCM, respectively. An asymmetry parameter g is a function of the CER and phase. The asymmetry parameter of water particles is computed based on Mie scattering theory, and the asymmetry parameter of ice particles is computed using the THM. The asymmetry parameter, cloud optical depth, and extinction coefficient profile in Eq. (1) are defined at a visible wavelength (0.65 μm), but these are omitted in the notation. Using Eq. (1), the scaling factor α is obtained, and the scaled cloud extinction profile αk_CCM(z) along with r_CCM(z), and Φ_CCM(z) profiles are used for radiative transfer computations.

Note that for a weak cloud-absorbing wavelength, such as a visible wavelength, the TOA irradiance is mainly driven by VSCOD (van de Hulst 1974). This means that the TOA visible irradiance is mainly a function of MODIS VSCOD:

F_{VIS} \approx F_{VIS} {τ_{M} [1 - g (r_{M}, Φ_{M})]} .

(2)

Combining Eqs. (1) and (2) results in

F_{VIS} (τ_{M}, r_{M}, Φ_{M}) \approx F_{VIS} [α k_{CCM} (k), r_{CCM} (k), Φ_{CCM} (z)] .

(3)

Equation (3) implies that either MODIS cloud properties (τ_M, r_M, and Φ_M) or CCM combined properties [αk_CCM (k), r_CCM(k), and Φ_CCM(z)] would reproduce the visible irradiances close to the observed values. However, for strong cloud-absorbing wavelengths, the irradiance is not strictly a function of VSCOD. As a consequence, TOA SW BB irradiances

F_{SW}^{TOA}

computed using MODIS-only and CCM-combined cloud properties can be also significantly different. This will be discussed in section 4.

In constraining CCM-merged profiles with MODIS, the cloud optical depth (COD) can be also considered using the relation

τ_{M} = β \int_{z_{B}}^{z_{T}} k_{CCM} (z) d z

(e.g., Leinonen et al. 2016; Henderson et al. 2013). However, if we use βk_CCM(z) along with r_CCM(z) and Φ_CCM(z), positive biases in

F_{SW}^{TOA}

generally occur because the cloud phase often switches rom liquid to ice by implementing Φ_CCM(z) (appendix A). In addition, without constraining with MODIS VSCOD, significant negative biases in

F_{SW}^{TOA}

are generated that are due to the missing cloud parts by CALIPSO and CloudSat (appendix B). When αk_CCM(z), r_CCM(z) and Φ_CCM are used, the simulation accuracy remains similar for different cloud sources because of the constraining with MODIS VSCOD (appendix C).

b. MODIS cloud standard and enhanced algorithms

In the CCCM algorithm, two kinds of MODIS cloud retrieval algorithms are used. The first is the standard cloud algorithm, which uses MODIS radiances for retrieving cloud optical depth, CER, cloud phase, and height. The second is the enhanced MODIS cloud algorithm, which is forced to have the CALIPSO cloud-top height, when CALIPSO detects a single cloud layer (Sun-Mack et al. 2008). Then the remaining cloud variables such as cloud optical depth and CER are retrieved. By using CALIPSO information, enhanced cloud-top heights of cirrus clouds are slightly higher and cloud fractions are larger, relative to the standard MODIS parameters. When the enhanced MODIS cloud parameters are used, the global mean biases in $F_{SW}^{TOA}$ are smaller than those computed with the standard MODIS cloud parameters by 4 W m⁻², and it is closer to the CERES observations, even though general spatial patterns of the $F_{SW}^{TOA}$ biases are similar (not shown). Therefore, we only show simulation results with the enhanced MODIS cloud parameters in this study.

Note that the spatial coverage of MODIS cross-track scanner is wider than that of CALIPSO and CloudSat (CC) along-track scanners. As a result, MODIS cloud properties are available over the entire CERES footprint, while CC cloud properties are only available over a narrow portion within a CERES footprint. In this study, for a consistent sampling of active and passive sensors, we only use MODIS cloud properties sampled over the CC satellite track, that is, MODIS cloud properties averaged over the cloud groups. Note that the narrow spatial sampling of cloud properties causes random SW biases relative to CERES observations, but it is not in a systematic way (Ham et al. 2015). Specifically, the SW simulations with the entire-footprint-cloud sampling have smaller root-mean-square (RMS) biases than those from the narrow cloud sampling by 40% but the mean values are close to each other (Ham et al. 2015).

For the period we considered for radiative transfer computations, one of or both CALIPSO and CloudSat were not operating for 22.7%, 1.0%, 12.4%, and 5.5% of total CERES observations in January, April, April, and October 2008, respectively. We analyze CERES footprints observed when both CALIPSO and CloudSat were operating in this study.

c. Other radiative transfer inputs

Temperature and humidity profiles are from GEOS, version 5.4.1, Atmospheric Data Assimilation System (ADAS). Version 5.4.1 is between those used for Modern-Era Retrospective Analysis for Research and Applications (MERRA, version 5.2.0; Rienecker et al. 2011) and MERRA-2 (version 5.12.4) (Gelaro et al. 2017) data products. Skin temperatures are described by retrieved values from clear-sky MODIS 11-μm channel observations by CERES–MODIS cloud algorithm (Minnis et al. 2021). If MODIS-retrieved skin temperatures are not available, GEOS-5.4.1 skin temperature is used.

Aerosol properties are described by the Model for Atmospheric Transport and Chemistry (MATCH) Ed4 hourly product (Collins et al. 2001; Fillmore et al. 2022). The MATCH product is produced by data assimilation of MODIS collection-6 aerosol optical depths with considering aerosol transport via convection, boundary layer transport, and scavenging and deposition. The MATCH product provides aerosol optical depths for six compositions, that is, small dust, large dust, sulfate, sea salt, soot, soluble particles, and insoluble particles. If CALIPSO aerosol properties are available, CALIPSO dust fraction is used to modify the dust fractions of MATCH aerosol compositions (i.e., small and large dust) (Kato et al. 2011, 2021). Also, if available, CALIPSO aerosol layer boundary heights are used to assign aerosol extinction profiles between the top and base heights for the given aerosol optical depth. If MODIS aerosol optical depths at multiple wavelengths are available, these are also used for the spectral dependency of aerosol optical depths; otherwise, the prescribed spectral dependency is used in the Fu–Liou model. The scattering parameters such as single scattering albedo and asymmetry parameters are predefined for each aerosol type in the Fu–Liou model.

Ocean surface albedo is from the empirical model (Jin et al. 2004). Land surface albedo is from the collection- 6 MODIS bidirectional reflectance direction function (BRDF) (MCD43C1) product (Strahler et al. 1999), whose accuracy is better than 5% at most validation sites (e.g., Wang et al. 2014; Z. Wang et al. 2019). Snow/ice surface albedo is described by the surface history albedo map, which was derived from clear-sky CERES measurements (Rutan et al. 2006).

CloudSat radar reflectivity increases with cloud particle size with a sixth-power law [Z ∝ N(D)D⁶]. As a result, rain particles significantly increase the radar reflectivity, causing large uncertainties in the retrievals. Specifically, the number concentration N(D) of the particles and particle size D tend to be overestimated and underestimated, respectively, causing the overestimation of cloud extinction coefficient (Fig. S1 in the online supplemental material). Therefore, 2B-CWC liquid cloud parameters are not used if the 2B-CLDCLASS product (Sassen and Wang 2008) indicates the existence of liquid precipitation or possible drizzle.

For about 3% of observations, MODIS cloud properties are not available for some cloud groups. In these cases, the corresponding cloud group is removed, and the areas of other cloud groups within the same CERES footprint are expanded to conserve the total area of cloud groups.

d. Radiative transfer model

Radiative transfer simulations are performed using the four-stream Fu–Liou model (Fu and Liou 1993; Fu et al. 1997) modified by the National Aeronautics and Space Administration (NASA) Langley Research Center, that is, a flux model of CERES with k distribution and correlated k for radiation [Fu–Liou–Charlock–Kato–Kratz–Rose (FLCKKR); Kratz and Rose 1999; Kato et al. 1999, 2005; Rose et al. 2006). In the Fu–Liou model, 18 spectral intervals, referred to as 18 narrow bands (NBs) in this study, are considered for TOA SW BB (

F_{SW}^{TOA}

; 0.18–4 μm) computations (Table S1 in the online supplemental material). These spectral intervals were considered to treat Rayleigh scattering and gas absorption efficiently (Rose et al. 2006). The irradiances at NB (

F_{SW, i}^{TOA}

) and BB (

F_{SW}^{TOA}

) are in watts per meter squared, which are spectrally integrated for the given interval, and they satisfy the relation

F_{SW}^{TOA} = \sum_{i = 1}^{18} F_{SW, i}^{TOA} .

(4)

As mentioned earlier, simulations of TOA SW BB irradiances are performed for each cloud group. Then the irradiances computed for the cloud groups are averaged by their areas to generate the irradiance of each CERES footprint. For evaluation of computed irradiances, CERES-derived TOA SW and LW BB irradiances (Loeb et al. 2003; Su et al. 2015a,b) are used as references.

3. Impact of the CCM-merged cloud profiles on the TOA SW BB irradiance computations

In this section, we examine the impact of the CALIPSO–CloudSat–MODIS (CCM)-merged k_CCM and r_CCM profiles on the TOA SW BB irradiance ( $F_{SW}^{TOA}$ ) simulations. To quantify the impact, we compare the simulation results using k_CCM(z) and r_CCM(z) profiles (method 4, described in section 2) with three control runs (methods 1–3). These methods are considered to highlight the effect of overlapping clouds (methods 1 vs 2), inhomogeneous cloud extinction profile (methods 2 vs 3), and inhomogeneous CER profile (methods 3 vs 4).

Method 1 consists of MODIS optical cloud properties + MODIS cloud boundary. MODIS column cloud properties including cloud optical depth τ_M, CER r_M, phase Φ_M, and cloud-top and cloud-base heights are used to compute k_ext(z), r_e(z), and Φ(z) profiles for each cloud group, using a vertically homogeneous assumption. The k_ext(z) profile is computed as τ_M/Δz_c, where Δz_c is a MODIS geometrical thickness of the cloud layer (=MODIS cloud-top height minus cloud-base height). Note that the MODIS Ed4B algorithm assumes a single-layer cloud to get an effective cloud height. Then cloud layer thickness, cloud-top height, and base height are computed from the empirical formulas depending on the cloud phase and optical depth [Eqs. (27)–(30) of Minnis et al. 2011a]. When the MODIS enhanced algorithm is used, the cloud-top heights are described from CALIPSO while other optical parameters are retrieved (section 2b). Constant r_M and Φ_M values are applied throughout the cloud column.

Method 2 consists of MODIS optical cloud properties + CC cloud boundary. MODIS column cloud properties (τ_M, r_M, and Φ_M) are expanded between CC-detected cloud boundaries of the cloud group. Note that one cloud group can have up to six overlapping clouds (section 2). The k_ext(z) is computed as τ_M divided by the sum of cloud geometrical thicknesses of all overlapping cloud layers. As a result, cloud optical depths of the overlapping cloud layers are distributed from τ_M, proportional to the geometrical thickness of the respective cloud layer.

Method 3 consists of CCM k_ext + CCM phase + MODIS r_e + CC cloud boundary. CCM-merged cloud extinction [k_CCM(z)] and phase [Φ_CCM(z)] profiles (section 2) are used but with a constant MODIS CER (r_M) between CC-detected cloud-top and cloud-base heights. If MODIS phase (Φ_M) is not matched with CCM-merged cloud phase [Φ_CCM(z)] and thus r_M cannot be used at a certain level (z), the default values of water (=13 μm) and ice (=30 μm) CER values are used. The α′ parameter is applied to k_CCM(z) for a consistent VSCOD with the MODIS value for each cloud group. Note that α′ in method 3 is different from α in method 4 because of the different CER profiles.

Method 4 consists of CCM k_ext + CCM phase + CCM r_e + CC cloud boundary. The method described in section 2 is used. Specifically, the CCM-merged cloud extinction coefficient [k_CCM(z)], CER [r_CCM(z)], and phase [Φ_CCM(z)] profiles are generated, as described in Fig. 2. The α parameter is applied to k_CCM(z) for a consistent VSCOD with MODIS [Eq. (1)].

Note that all four methods give the same VSCOD for each cloud group. This is because methods 1 and 2 use MODIS cloud optical depth and CER and thus have a VSCOD as τ_M(1 − g_M), whereas method 3 and method 4 apply the scaling factor (α′ or α) to k_CCM(z) to have a consistent value to the MODIS VSCOD [Eq. (1)]. The input cloud extinction and CER profiles from the four methods are compared in Fig. 3. In comparison with method 1, method 2 gives slightly larger cloud extinction coefficient values near the cloud tops, for example, 12–15 km in Figs. 3a or 7–12 km in Fig. 3c. This is because the cloud extinction coefficient is homogeneously distributed by including optically thin cirrus cloud layers detected from CALIPSO. In contrast, CCM-merged cloud extinction profiles (methods 3 and 4) show smaller weights at the cloud upper part and larger weights at the cloud bottom (e.g., 0–2 km in Figs. 3a,c), relative to method 2.

While methods 1, 2, and 3 only take MODIS CER information, method 4 uses CCM-combined CER, showing much larger variations than other methods. Specifically, CER from method 4 varies from 20 to 60 μm, whereas CER from methods 1–3 is around 20 μm (Figs. 3b,d). The large differences are shown for high-latitude or high-altitude regions, where ice clouds are abundant. This is more clearly shown when the profiles are separated by cloud phase (Figs. S2 and S3 in the online supplemental material). This indicates an underestimation of MODIS ice CER, as also noted in earlier studies (Stein et al. 2011; Stubenrauch et al. 2013; Marchant et al. 2020; Yost et al. 2021). Note that the CCCM algorithm uses MODIS CER retrieved from the 3.7-μm channel (Minnis et al. 2011a), which tends to be smaller than that MODIS CER retrieved from the 2.1- or 1.6-μm channels for ice clouds. This is because the cloud absorption at the 3.7-μm channel is larger than at the 2.1- or 1.6-μm channel, and thus the 3.7-μm channel is more sensitive to the shallow cloud-top layers, where small ice cloud particles appear. In contrast, the 2.1- or 1.6-μm channel contains information of deeper cloud layers because of the smaller cloud absorption, which is not used in this study.

Water CERs from the four methods generally agree well below 3-km altitude over the tropical region (Fig. 3b and supplemental Fig. S3). Earlier studies show that MODIS water CER is often positively biased (e.g., Painemal and Zuidema 2011; Min et al. 2012; Noble and Hudson 2015) by up to 5 μm, but the magnitude of the water CER biases is much smaller than that of MODIS ice CER biases (up to 40 μm).

Although all of methods 1, 2, and 3 use MODIS CER information, the input CER profiles in Fig. 3 are slightly different because of the different cloud boundaries (methods 1 vs method 2) or different cloud extinction coefficients (method 2 vs method 3) that are used as weights in averaging CER profiles.

Using cloud input profiles derived by the four methods, four sets of $F_{SW}^{TOA}$ are computed. These are then compared with CERES-derived values in Fig. 4. $F_{SW}^{TOA}$ is significantly positively biased over cloudy regions when method 1 or 2 is used. The magnitude of $F_{SW}^{TOA}$ biases by method 2 is larger than that by method 1. This suggests that simply using active-sensor-derived cloud-top and cloud-base heights and expanding MODIS cloud properties between them would not improve $F_{SW}^{TOA}$ computations. This is because the actual cloud extinction profile is more complicated than the homogeneous condition, as shown in Fig. 3. For example, the ice cloud extinction coefficient and CER of deep convective clouds tends to decrease with height (Ham et al. 2013; C. Wang et al. 2019), and the liquid cloud extinction coefficient of the boundary layer clouds tends to increase with height by following adiabatic conditions. By taking the CCM-combined cloud extinction profile (α′k_CCM) by method 3 (Fig. 4c), the positive biases are reduced relative to method 2. Method 4 shows a further improvement of $F_{SW}^{TOA}$ computations over method 3 in the mean. However, regional biases also exist with method 4, and the lower global mean is being achieved through a cancellation of errors over land and ocean (Table 1). Nonetheless the overall improvement indicates that CER profiles also play an important role in $F_{SW}^{TOA}$ computations. Differences between method 3 and method 4 are larger over deep convective (western Pacific Ocean), ice cloud regions (storm-track regions), or multilayered cloud regions (L’Ecuyer et al. 2019; Hang et al. 2019), whereas the differences are smaller over liquid-phase cloud regions (eastern Pacific Ocean). This is because the water CER is less variable than ice CER, and MODIS and CCM-combined CERs agree better (Fig. 3; also Fig. S3 in the online supplemental material). Separating by each month (Fig. S4 in the online supplemental material) shows similar patterns of the biases. The positive SW biases shown in methods 1–3 are also similar to those found in SW biases in C. Wang et al. (2019), where the SW biases due to the underestimated MODIS CER were examined.

Table 1

Shortwave biases (W m⁻²) to CERES observations when the computations are performed using methods 1–4. For the given domain, the mean bias is provided. Also, the RMSD is given in parentheses.

The positive SW biases shown on land regions such as North Africa, the Arabian Peninsula, India, the Himalayas, and the Taklamakan Desert are likely related to the aerosol or surface albedo assumptions. This is confirmed by the fact that a similar distribution of SW biases appears for clear-sky (cloud free) composites (Fig. S5 in the online supplemental material). In contrast, while SW biases over the Arctic are positive in all skies (Fig. 4), these are negative or small positive in clear-sky composites (Fig. S5). This indicates large uncertainties in MODIS cloud detections over a highly reflective surface, and the MODIS cloud optical depth might be overestimated.

When one-to-one scatterplots are made between observed and computed $F_{SW}^{TOA}$ (Fig. 5), methods 1, 2, and 3 have positive biases in $F_{SW}^{TOA}$ for bright targets (see the red lines for $F_{SW}^{TOA}$ > 600 W m⁻²). Method 3 produces slightly reduced positive biases in $F_{SW}^{TOA}$ for bright targets, relative to methods 1 and 2. This implies that the positive biases are partly caused by the vertically homogeneous assumption of the cloud extinction coefficient. When the CCM-merged CER profiles are used by method 4, the positive biases are mostly removed for the bright targets. Therefore, the positive biases at the bright targets in methods 1–3 are primarily caused by using the underestimated MODIS ice CER, used for the entire cloud columns.

To examine the impact of ice and liquid CER on SW computations, clouds are separated by phase. Specifically, we determine whether the column contains ice or liquid clouds using temperature profile and CC cloud boundaries. The cloud layers located above the 253.15-K temperature level are considered as ice clouds. The cloud layers below the 273.15-K temperature level are considered as liquid clouds. It is rare that ice clouds only exist in a column without liquid clouds, particularly for deep convective systems. Considering that the reflected solar radiation is significantly affected by ice CER at the cloud-top layers, we select ice-topped clouds to examine the impact of ice CER (Fig. 6). The ice-topped cloud cases are defined if the ice clouds fraction is larger than 80% within the CERES footprint, regardless of the existence of the mixed/liquid clouds below. For examining liquid CER, we consider pure liquid-phase cloud cases, which are defined when the liquid cloud fraction is larger than 80% and ice clouds do not exist within the CERES footprint (Fig. 7). For more sophisticated determination of the cloud phase beyond this study, CloudSat–CALIPSO combined 2B-CLDCLASS-lidar product (Sassen et al. 2008) can be considered in the future.

It is found that the positive $F_{SW}^{TOA}$ biases for the bright targets only occur in the ice-topped clouds, but not in pure liquid-phase clouds. This also confirms that the positive $F_{SW}^{TOA}$ biases are mainly related to the underestimated MODIS ice CER. Even though larger positive $F_{SW}^{TOA}$ biases are noted for ice-topped clouds in methods 1–3, root-mean-square-difference (RMSD) is smaller than that for liquid-phase clouds. This may well be because ice-topped clouds usually have a horizontally homogeneous structure, while pure liquid-phase clouds are often formed in small-scale broken clouds, causing larger random errors in the computed $F_{SW}^{TOA}$ .

The relationship between TOA BB SW reflectance ( $R_{SW}^{TOA}$ ) (TOA upward SW irradiances divided by solar incoming irradiance), and MODIS VSCOD is investigated in Fig. 8. This is done by sorting CERES footprints by MODIS VSCOD into 0.4-interval bins and computing the mean values of $R_{SW}^{TOA}$ for the VSCOD bins. In Fig. 8, only CERES footprints with the ice-topped cloud cases are used to focus on the ice CER.

In Fig. 8a, $R_{SW}^{TOA}$ computed by methods 1, 2, and 3 are larger than CERES observations, whereas $R_{SW}^{TOA}$ computed by method 4 better agrees with the CERES observations. A similar result is also shown in Fig. 8b when TOA SW BB irradiances ( $F_{SW}^{TOA}$ ) are compared. The differences in $R_{SW}^{TOA}$ or $F_{SW}^{TOA}$ computed by the four methods depend on the VSCOD. For example, the differences in $F_{SW}^{TOA}$ between methods 3 and 4 are around 28.0 W m⁻² when MODIS VSCOD is 19.6–20.0, corresponding to 3.8% of the mean value. In contrast, when MODIS VSCOD < 3 (optically thinner clouds), the $F_{SW}^{TOA}$ values computed from the four methods converge. The larger differences in $F_{SW}^{TOA}$ for the larger VSCOD are related to the larger differences in the input ice CER. In Fig. 8c, the column CER {=[3/(2ρ_ice)](IWP/τ)} values from the four methods are compared. The column CER from method 1, 2, or 3 (from MODIS) is smaller than that from method 4 (from CCM), and the differences become more significant for VSCOD > 3. In other words, the underestimation of the MODIS ice CER is more serious for optically thicker clouds, causing larger positive biases in $F_{SW}^{TOA}$ .

Note that the number of CERES footprints rapidly decreases with MODIS VSCOD (dashed lines in Fig. 8). As a result, even though instantaneous positive biases for bright targets are significant in methods 1–3 (up to 28.0 W m⁻²), the positive $F_{SW}^{TOA}$ biases are smoothed and reduced in global or monthly means (see global means in Fig. 4).

When a similar plot is generated for pure liquid-phase clouds, differences among the four methods are negligible (Fig. S6 in the online supplemental material). In addition, MODIS VSCOD for pure-liquid-phase clouds rarely exceeds 10, which corresponds to $F_{SW}^{TOA}$ of 600 W m⁻². Therefore, the positive biases in $F_{SW}^{TOA}$ for bright targets ( $F_{SW}^{TOA} > 600 W m^{- 2}$ ) shown in Fig. 5 are related to the MODIS ice CER issues in ice-topped or mixed-phase clouds.

4. Impact of the CER on the irradiance by spectral regions

The different results between methods 3 and 4 suggest that ice CER can impact SW BB irradiances ( $F_{SW}^{TOA}$ ) considerably for optically thick clouds. In this section, we quantify the impact of ice CER by spectral regions.

The cloud absorption is spectrally dependent since the imaginary part of the refractive index, or m_i, varies by wavelength (Hale and Querry 1973; Warren and Brandt 2008). In general, m_i increases with a wavelength in the SW BB spectral region (0.18–4.0 μm), meaning larger cloud absorption at the SWIR spectral region, relative to the ultraviolet (UV) or visible spectral region. As a result, when the single scattering albedo (SSA) is computed for the 18 NBs (Fig. 9), SSAs are smaller in the SWIR spectral region (B15–B18; 1.4–4 μm), relative to the UV to the visible spectral region (B01–B12; 0.18–0.89 μm) (Twomey 1976). In addition, the SSA for cloud-absorbing bands (B15–B18) decreases with an increasing CER (Twomey and Bohren 1980). In contrast, the SSA at the non-cloud-absorbing bands (B01–B12) is not sensitive to the CER since it is nearly 1 regardless of the CER.

The result of sensitivity tests in Fig. 10 is to quantify the impact of the ice CER on the TOA SW NB irradiances ( $F_{SW, i}^{TOA}$ ). For the simulation, a single layer at 10–12 km is assumed. While VSCOD is held fixed as 2, 10, or 20, the ice CER is changed from 20 to 70 μm. For cloud-absorbing NBs such as B15–B18, as the ice CER increases, the SSA decreases (Fig. 9), cloud absorption increases, and TOA NB irradiance decreases (Fig. 10). In contrast, non-cloud-absorbing NBs such as B01–B12 show negligible changes with CER.

In Fig. 8c, for optically thick clouds (VSCOD > 10), CCM-merged column CER reaches 65 μm, whereas MODIS CER stays around 20 μm. Therefore, the differences in NB ( $F_{SW, i}^{TOA}$ ) or BB ( $F_{SW}^{TOA}$ ) with changing ice CER from 20 to 65 μm in Fig. 10 roughly estimate the positive radiative biases due to the underestimated MODIS ice CER. The changes of B15–B18 due to the CER (from 20 to 65 μm) are significant, up to 50% (Figs. 10b,d,f). As a result, SW BB irradiance also changes up to 5% (black lines of Figs. 10b,d,f). The relative changes of NB ( $F_{SW, i}^{TOA}$ ) and BB ( $F_{SW}^{TOA}$ ) with the ice CER remain similar regardless of VSCOD (=2, 10, or 20) (Figs. 10b,d,f).

In Fig. 11, similar figures to Fig. 8b are generated but separated by spectral regions, that is, 0.18–0.89 μm (B01–B12), 0.89–1.04 μm (B13), 1.04–1.41 μm (B14), 1.41–1.90 μm (B15), 1.9–2.5 (B16), and 2.5–4.0 μm (B17–B18). The six spectral regions are considered by grouping several NBs that show similar sensitivity of the TOA SW NB irradiance to the ice CER in Fig. 10. Methods 1–4 produce similar results for 0.18–0.89-μm irradiances (Fig. 11a), where cloud absorption is negligible. In contrast, more noticeable differences are shown for the other five spectral regions (Figs. 11b–f). In these spectral regions, methods 1–3 produce larger irradiances than method 4 due to the underestimated MODIS ice CER. The positive biases of methods 1–3 are significant for 1.04–1.41 μm (Fig. 11c) and 1.41–1.90 μm (Fig. 11d), that is, 10.4 W m⁻² (11.5%) and 8.4 W m⁻² (44.5%), respectively, when VSCOD = 19.6–20.0. The 1.90–2.5 μm (55.9%) or 2.5–4.0 μm (27.7%) spectral regions also show significant positive biases in a relative sense, but their absolute magnitude is small due to the small incoming solar radiation. Table 2 lists the differences in irradiances for 15 spectral regions between methods 3 and 4 for the VSCOD bin with 19.6–20.0.

Table 2

Spectrally integrated TOA upward irradiances for the given wavelength range, computed using method 3 (M3) and method 4 (M4). The values of M3 and M4 are averages of irradiances of CERES footprints with VSCOD between 19.6 and 20.0. In the computations, CERES footprints with ice-topped cloud cases are considered. These are when ice clouds with the temperature <253.15 K exist for at least 80% of the area of the CERES footprint. The absolute and relative (%) differences between M3 and M4 are also provided in the fourth and fifth columns, showing mostly positive biases in M3 because of the underestimated MODIS ice CER. The VSCOD range of 19.6–20.0 is arbitrarily chosen, but a similar magnitude of the biases is expected for VSCOD > 5 according to Fig. 8 and Fig. 11.

In conclusion, the underestimated MODIS ice CER for optically thick clouds (Fig. 8c) causes underestimation of cloud absorption and overestimation of TOA reflection mainly at SWIR (1.04–1.90 μm) spectral regions (Fig. 11 and Table 2). This also causes positive biases in SW BB irradiances (Fig. 8), particularly for bright targets (Fig. 5).

In Fig. 11, the comparison of the simulation results with observations was not possible since CERES does not provide spectral observations. However, considering method 4 produces the closest SW BB irradiances to CERES observations (Fig. 8) among the four methods, it is expected that method 4 would produce more accurate spectral irradiances than other methods. If the spectrally resolved irradiance measurements are available from future sensors (e.g., Stephens et al. 2021), these can be used for more rigorous validation of the CER from the radiative closure experiment.

5. Discussions

While the multisensor approach shows overall improvements in SW computations relative to the MODIS-only simulations, the current input cloud datasets and merging strategy also need further improvements. For example, CALIPSO V4 cloud extinction coefficient profile have large fluctuations near the lidar attenuation level (not shown), and further refinement is required to exclude these noisy cases. The level 2B radar-only cloud water content (2B-CWC-RO) product retrieves three unknown parameters (i.e., total number concentration, geometrical mean radius, and distribution width parameter) with the measured radar reflectivity (Austin et al. 2009), and as a result, the solution is overly dependent on a priori condition. This can be also a problem in precipitating cloud cases where the rain drop size is much bigger than a priori value. The passive MODIS cloud retrievals inherently are affected by three-dimensional (3D) radiative effects, and the impact would depend on the solar zenith angle, as also discussed in appendix B. MODIS cloud retrievals also have larger uncertainties over a highly reflective surface such as snow and sea ice. In addition, the different ice habit assumptions are used for ice satellite products, which is also responsible for differences in ice CER or cloud extinction coefficients across the products. In Ham et al. (2017a), it was shown that the spherical ice particle assumption used in 2B-CWC product causes the overestimation of ice CER by up to 30%. Further study is required to examine a consistency across the satellite products for a better multisensor merging strategy.

Our focus to this point has been on the TOA SW BB irradiance ( $F_{SW}^{TOA}$ ) simulations, the comparison of the computed TOA LW BB irradiances ( $F_{LW}^{TOA}$ ) with observations also gives an idea of how accurate the cloud input profiles are used for simulations (Fig. 12). Among the four methods, method 2 shows the largest negative biases in $F_{LW}^{TOA}$ over cloudy regions. This is related to the overestimation of the cloud extinction coefficient near cloud tops, as also shown in Fig. 3, which also caused positive biases in $F_{SW}^{TOA}$ (Fig. 4). While smaller magnitudes are noted in method 4 by implementing αk_CCM and r_CCM profiles relative to method 2, negative biases in $F_{LW}^{TOA}$ still remain.

This the negative LW biases in method 4 imply that the shape of αk_CCM(z) might be biased, and the radiative center of the cloud extinction coefficient profile is too high. In other words, it indicates that cloud extinction coefficients near cloud upper parts might be overestimated, and those at lower parts might be underestimated, particularly over the regions where multilayer clouds are frequently appeared (L’Ecuyer et al. 2019; Hang et al. 2019).

This can happen when CALIPSO signal is fully attenuated by upper clouds and CloudSat misses clouds below 1 km altitude due to surface clutter. The missed cloud parts are compensated by the increased cloud extinction coefficients at other altitudes with an increasing α factor. Another possible reason for the biased radiative center might be related to systematic biases in some of satellite products considered in this study, causing the biased radiative center height.

Note that the impact of the biased radiative center of [k_CCM(z) or r_CCM(z)] on TOA SW ( $F_{SW}^{TOA}$ ) simulations is relatively small, once the merged profile is constrained by MODIS VSCOD [=αk_CCM(z)]. However, it does not necessarily mean that the surface radiation or heating rate profile computed from αk_CCM(z) are accurate. Therefore, to gain further insight into the merged cloud profiles, validation using surface ground SW and LW measurements are desired.

The phase determination in this study also needs further improvement in the future. In this study, the phase is determined based on CALIPSO VFM phase and the availability of 2C-ICE for the temperature transition zone (253.15 < T < 273.15 K). However, the liquid phase can be still present for 233.15 < T < 253.15 K. In addition, for the given vertical model layer, we only consider either the ice or liquid phase, but not the coexistence of both phases. The quantification of each phase amount in each model layer and implementation of mixed-phase cloud scattering properties can be considered in future studies. Also, when the SW biases are computed by latitude (Fig. S7 in the online supplemental material), method 4 gives slightly larger negative SW biases over the high-latitude ocean than the tropical ocean. Over the high-latitude regions, low clouds near the surface are often missed by CALIPSO and CloudSat, meaning that liquid-phase clouds amounts are underestimated. With the same VSCOD, the liquid-phase cloud assumption gives larger TOA SW irradiances than the ice-phase cloud assumption. Therefore, the larger negative SW biases in the high-latitude region can be improved if the missed low-level liquid-phase clouds are included.

Note that the SW and LW biases shown in this study are significantly improved from the earlier version of CCCM product (RelB1) (Kato et al. 2011; Atmospheric Science Data Center 2021). The changes are the result of the combination of many factors, for example, modification of Fu-Liou transfer model, implementation of 2C-ICE product and CALIPSO phase parameter, updates of the ice habit model both for cloud retrievals and forward computations, version upgrades of MODIS, CALIPSO, and CloudSat products, and fixed coding errors.

6. Summary

In this study, we merge CALIPSO and CloudSat active sensors and MODIS passive measurements to build cloud vertical profiles and use them for SW BB ( $F_{SW}^{TOA}$ ) irradiance computations (Figs. 1, 2). The CCM-merged cloud extinction profile (k_CCM) is constrained by MODIS VSCOD, using the α factor, for compensating missing cloud parts by CALIPSO and CloudSat [Eq. (1)].

The CCM-merged cloud extinction profile (αk_CCM) generally shows a maximum near the cloud base, especially for ice or deep convective clouds (Fig. 3). This indicates that a constant extinction coefficient derived by an assumption of a vertically homogeneous cloud between CC-derived cloud-top and cloud-base boundaries (method 2) would cause an overestimate of cloud extinction coefficients in the cloud upper part and an underestimate in the lower part. As a result, method 2 does not improve $F_{SW}^{TOA}$ computations when compared with MODIS-only simulations (method 1) (Fig. 4). In contrast, the use of CCM-merged cloud extinction coefficient profile (αk_CCM) (method 3) slightly improves $F_{SW}^{TOA}$ simulations but the positive $F_{SW}^{TOA}$ biases remain for bright targets ( $F_{SW}^{TOA} > 600 W m^{- 2}$ ) (Fig. 5c).

The positive $F_{SW}^{TOA}$ biases for bright targets are mostly removed when the CCM-merged CER profiles are used for radiative simulations, in addition to CCM-merged extinction coefficient profiles (method 4) (Fig. 5d). Because MODIS ice CER is significantly smaller than CCM-merged CER (Fig. 3), it is concluded that the underestimated MODIS ice CER leads to the positive $F_{SW}^{TOA}$ bases by methods 1–3. The bias in MODIS ice CER is greater for optically thicker clouds (VSCOD > 3) (Fig. 8c), resulting in larger positive biases in $F_{SW}^{TOA}$ for the bright targets (Fig. 8b). The sensitivity test shows that the impact of the CER is negligible for UV to visible spectral regions (<0.8 μm) where cloud absorption is negligible. The impact is significant for the 1.09–1.90 μm spectral region, showing significant changes by the CER (Fig. 10). As a result, depending on the CER source (MODIS or CCM), the differences in irradiances for this spectral region can be up to 10 W m⁻² (Fig. 11), also causing SW BB irradiances by up to 30 W m⁻² (Fig. 8b).

It is also shown that CCM-merged cloud extinction and CER profiles improve LW BB irradiance simulations (method 4), relative to the vertically homogeneous cloud profiles (method 2). However, the negative biases generally appear in the computed LW BB by all four methods, requiring further improvement of the vertical shapes of cloud extinction profiles. We plan to investigate the cause in the future.

Acknowledgments.

This research has been supported by the NASA CERES project and NASA ROSES CloudSat/CALIPSO science team funding to the Langley Research Center.

Data availability statement.

CloudSat, release 5, datasets are available in CloudSat data processing center (http://www.cloudsat.cira.colostate.edu). CALIPSO V4 datasets are available in Atmospheric Science Data Center (ASDC) (https://asdc.larc.nasa.gov). CALIPSO CloudSat CERES and MODIS (CCCM), release D, data are available in the CERES ordering tool (https://ceres.larc.nasa.gov/data/). GEOS products are available through a request to GES DISC (https://disc.gsfc.nasa.gov), and the GOES-5.4.1 is described online (https://gmao.gsfc.nasa.gov/GMAO_products/NRT_products.php).

APPENDIX A

Constraining the CCM Cloud Extinction Profile with the MODIS COD

In this study, we constrain the merged cloud extinction coefficient profile k_CCM with MODIS VSCOD. In earlier studies (Leinonen et al. 2016; Henderson et al. 2013), the COD value has been also used to constrain a cloud extinction profile. That is, the scaling factor β can be considered to satisfy the following equation:

τ_{M} = β \int_{z_{B}}^{z_{T}} k_{CCM} (z) d z .

(A1)

In Fig. A1, TOA SW BB irradiances $F_{SW}^{TOA}$ are computed using βk_CCM and r_CCM, and these are compared with CERES observations. The result shows that $F_{SW}^{TOA}$ is more positively biased, relative to the results from method 4 (Fig. 4d). Note the CCM-merged cloud phase profile often includes both ice and liquid cloud layers, while one cloud phase (either liquid or ice) is used for the entire column in MODIS product. For example, over the storm-track region (60°–40°S), MODIS often detects liquid-phase single-layer clouds, but CCM often indicates multilayered clouds containing liquid and ice phases. Since the asymmetry parameter of water cloud particle is larger (∼0.86) than ice cloud particle (∼0.75), the phase change from liquid to ice will cause an increase of SW irradiance due to the larger reflection if the COD remains the same. Therefore, the large biases in $F_{SW}^{TOA}$ shown in Fig. A1 are mostly related to the cloud phase changes. One way of efficiently taking care of this issue is to use VSCOD. In conclusion, when we constrain the CCM-merged cloud extinction profile with MODIS-column-integrated value with VSCOD, better $F_{SW}^{TOA}$ simulation results (i.e., a better agreement with CERES-derived TOA irradiances) are obtained, relative to the results with COD constraining (the global mean difference is 4.79 W m⁻² as compared with −0.16 W m⁻² by method 4).

APPENDIX B

Importance of Constraining with the MODIS VSCOD

In this study, we constrain the CCM-merged cloud extinction profile with MODIS VSCOD. To examine the impact of the constraining, we compute TOA SW BB irradiances $F_{SW}^{TOA}$ without constraining and compare the results with CERES observations in Fig. B1. Significant negative biases in $F_{SW}^{TOA}$ appear over high-latitude regions. This indicates that MODIS VSCOD is larger than the CCM-merged VSCOD in high-latitude regions.

The differences in VSCOD can happen when 1) the cloud extinction coefficients from CALIPSO and CloudSat are biased, or 2) both CALIPSO and CloudSat miss detections of low clouds (likely below the 1-km altitude). As another explanation, the larger MODIS VSCOD in high-latitude regions may indicate three-dimensional (3D) radiative effects. For large solar zenith angles, the side illumination generally increases cloud reflection (Ham et al. 2014; Singer et al. 2021). The large solar zenith angle often occurs in the high-latitude region. The MODIS cloud optical depth retrievals are performed using a one-dimensional (1D) radiative transfer model and as a result, the 3D radiative effects such as side illumination can increase the MODIS cloud optical depths. In contrast, active sensor measurements are less affected by the 3D radiative effects and do not show such features. Since we use 1D RTM for computing $F_{SW}^{TOA}$ , the increased MODIS CODs would reproduce $F_{SW}^{TOA}$ better than the active-sensor-derived cloud extinction coefficient profile. Further examination is needed to examine 3D radiative effects in MODIS cloud retrievals over high-latitude regions.

APPENDIX C

The Impacts of the Cloud Source of the Radiative Transfer Inputs

In method 4, cloud products from multiple sensors are combined to generate cloud extinction coefficient (αk_CCM) and CER (r_CCM) profiles. As implied in Fig. 2, at the altitude where the source of the product is switched, a discontinuity is expected in k_CCM or r_CCM profiles. Likewise, when the main source of the cloud profile changes depending on the region, a discontinuity is expected. The accuracy of αk_CCM and r_CCM profiles might be affected by the cloud source, which in turn affects the TOA SW BB ( $F_{SW}^{TOA}$ ) simulation accuracy.

Figure C1 shows the relative frequency of CERES footprints where CALIPSO, CloudSat 2C-ICE, CloudSat 2B-CWC liquid, or CloudSat 2B-CWC ice product is used. If multiple products are used within one CERES footprint, all the corresponding products are counted in producing Fig. C1. The frequency of the use of the 2C-ICE cloud product is the largest among the datasets, with a global mean of 53.8%. This is because the 2C-ICE cloud product is used as the first choice for ice clouds, followed by CALIPSO, 2B-CWC ice, and MODIS products (section 2). The usage of the 2B-CWC ice product is low (4.8%) since the availability of the 2B-CWC ice and 2C-ICE products are mostly overlapped, in terms of location and altitude, and 2C-ICE is preferred to the 2B-CWC ice product.

For liquid cloud regions such as the eastern Pacific, CALIPSO cloud k_ext is preferred to 2B-CWC liquid k_ext, showing a higher frequency of CALIPSO usage. Moreover, the clouds below 1-km altitude are often missed by CloudSat, while CALIPSO gives information about these clouds when the lidar is not substantially attenuated by upper-level clouds. The frequency distributions separated for ice-phase and liquid-phase cloud containing cases are also provided as a supplement (Figs. S8 and S9 in the online supplemental material).

The $F_{SW}^{TOA}$ biases are generally similar regardless of the cloud source in Fig. C2. This is mainly because the merged cloud profile is constrained by MODIS VSCOD (αk_CCM). Without the constraining, larger differences are noted depending on the cloud source (Fig. C3).

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Kato, S., S. Sun-Mack, W. F. Miller, F. G. Rose, Y. Chen, P. Minnis, and B. A. Wielicki,

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Combining Cloud Properties from CALIPSO, CloudSat, and MODIS for Top-of-Atmosphere (TOA) Shortwave Broadband Irradiance Computations: Impact of Cloud Vertical Profiles

Abstract

Significance Statement

Abstract

Significance Statement

1. Introduction

2. Data and method

a. Satellite cloud product merging approach

1) Cloud masking and grouping in each CERES footprint

2) Obtaining MODIS, CALIPSO, and CloudSat properties in each cloud group

3) Determining cloud phase of each vertical model layer for each cloud group

4) Merging CALIPSO, CloudSat, and MODIS cloud properties for each cloud group

5) Constraining CCM-merged cloud profile with MODIS information

b. MODIS cloud standard and enhanced algorithms

c. Other radiative transfer inputs

d. Radiative transfer model

3. Impact of the CCM-merged cloud profiles on the TOA SW BB irradiance computations

4. Impact of the CER on the irradiance by spectral regions

5. Discussions

6. Summary

Acknowledgments.

Data availability statement.

APPENDIX A

Constraining the CCM Cloud Extinction Profile with the MODIS COD

APPENDIX B

Importance of Constraining with the MODIS VSCOD

APPENDIX C

The Impacts of the Cloud Source of the Radiative Transfer Inputs

REFERENCES