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  • View in gallery

    Schematic diagram showing two ice crystal habits and their mixing ratios of the two-habit model. Habit 1 is a roughened single column with aspect ratio 2a/Dmax =1, and habit 2 is an ensemble of 20 randomly generated aggregates. Individual aggregate shape consists of 20 randomly distorted hexagonal columns. The mixing ratio of habits 1 and 2 add up to one (fsingle + faggregate = 1).

  • View in gallery

    Comparison between the measured (from 11 field campaigns) and THM-based theoretical microphysical properties, for (top) ice water content and (bottom) median mass diameter.

  • View in gallery

    (a),(b) Bulk extinction efficiency Qe, (c),(d) single-scattering albedo w, and (e),(f) asymmetry factor against wavelength for SMOOTH, ROUGH, and THM at effective diameter 65 μm.

  • View in gallery

    Asymmetry factor as a function of ice particle size for SMOOTH, ROUGH, and THM ice particle models at a wavelength of 0.65 μm.

  • View in gallery

    Difference in (a) ice cloud optical depth, (b) ice particle size, and (c) ice cloud effective height between retrievals using THM and SMOOTH at the daytime Aqua overpass time (THM minus SMOOTH).

  • View in gallery

    SW TOA flux (a) difference (W m−2) and (b) relative difference (%) between calculations with retrievals from THM combined with THM forward radiative transfer minus retrievals from SMOOTH combined with SMOOTH forward radiative transfer.

  • View in gallery

    As in Fig. 5, but for SW surface downward flux difference.

  • View in gallery

    SW TOA flux (a) difference (W m−2) and (b) relative difference (%) between calculations with retrievals from THM combined with THM forward RT minus retrievals from SMOOTH combined with THM forward RT.

  • View in gallery

    As in Fig. 7, but for SW surface downward flux difference.

  • View in gallery

    As in Fig. 5, but for LW surface downward flux difference.

  • View in gallery

    (a) Regional average and (b) zonal average computed minus CERES-observed SW TOA flux difference for March 2008. Only regions with 80% or more ice cloud coverage during each day of the month are included in the monthly average.

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Impact of Ice Cloud Microphysics on Satellite Cloud Retrievals and Broadband Flux Radiative Transfer Model Calculations

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  • 1 NASA Langley Research Center, Hampton, Virginia
  • 2 Department of Atmospheric Sciences, Texas A&M University, College Station, Texas
  • 3 Science Systems and Applications, Inc., Hampton, Virginia
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Abstract

Ice cloud particles exhibit a range of shapes and sizes affecting a cloud’s single-scattering properties. Because they cannot be inferred from passive visible/infrared imager measurements, assumptions about the bulk single-scattering properties of ice clouds are fundamental to satellite cloud retrievals and broadband radiative flux calculations. To examine the sensitivity to ice particle model assumptions, three sets of models are used in satellite imager retrievals of ice cloud fraction, thermodynamic phase, optical depth, effective height, and particle size, and in top-of-atmosphere (TOA) and surface broadband radiative flux calculations. The three ice particle models include smooth hexagonal ice columns (SMOOTH), roughened hexagonal ice columns, and a two-habit model (THM) comprising an ensemble of hexagonal columns and 20-element aggregates. While the choice of ice particle model has a negligible impact on daytime cloud fraction and thermodynamic phase, the global mean ice cloud optical depth retrieved from THM is smaller than from SMOOTH by 2.3 (28%), and the regional root-mean-square difference (RMSD) is 2.8 (32%). Effective radii derived from THM are 3.9 μm (16%) smaller than SMOOTH values and the RMSD is 5.2 μm (21%). In contrast, the regional RMSD in TOA and surface flux between THM and SMOOTH is only 1% in the shortwave and 0.3% in the longwave when a consistent ice particle model is assumed in the cloud property retrievals and forward radiative transfer model calculations. Consequently, radiative fluxes derived using a consistent ice particle model assumption throughout provide a more robust reference for climate model evaluation compared to ice cloud property retrievals.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Norman G. Loeb, norman.g.loeb@nasa.gov

Abstract

Ice cloud particles exhibit a range of shapes and sizes affecting a cloud’s single-scattering properties. Because they cannot be inferred from passive visible/infrared imager measurements, assumptions about the bulk single-scattering properties of ice clouds are fundamental to satellite cloud retrievals and broadband radiative flux calculations. To examine the sensitivity to ice particle model assumptions, three sets of models are used in satellite imager retrievals of ice cloud fraction, thermodynamic phase, optical depth, effective height, and particle size, and in top-of-atmosphere (TOA) and surface broadband radiative flux calculations. The three ice particle models include smooth hexagonal ice columns (SMOOTH), roughened hexagonal ice columns, and a two-habit model (THM) comprising an ensemble of hexagonal columns and 20-element aggregates. While the choice of ice particle model has a negligible impact on daytime cloud fraction and thermodynamic phase, the global mean ice cloud optical depth retrieved from THM is smaller than from SMOOTH by 2.3 (28%), and the regional root-mean-square difference (RMSD) is 2.8 (32%). Effective radii derived from THM are 3.9 μm (16%) smaller than SMOOTH values and the RMSD is 5.2 μm (21%). In contrast, the regional RMSD in TOA and surface flux between THM and SMOOTH is only 1% in the shortwave and 0.3% in the longwave when a consistent ice particle model is assumed in the cloud property retrievals and forward radiative transfer model calculations. Consequently, radiative fluxes derived using a consistent ice particle model assumption throughout provide a more robust reference for climate model evaluation compared to ice cloud property retrievals.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Norman G. Loeb, norman.g.loeb@nasa.gov

1. Introduction

Earth’s climate is determined by the exchange of radiant energy between the sun, Earth, and space. The absorbed solar radiation fuels the climate system, providing the energy required for atmospheric and oceanic motions. The radiative energy reaching the surface also plays a critical role in the climate system, providing energy to drive the hydrological cycle and the exchange of latent and sensible heat between the surface and atmosphere. A central objective of the Clouds and the Earth’s Radiant Energy System (CERES) is to produce a long-term global climate data record of Earth’s radiation budget from the top of the atmosphere (TOA) down to the surface along with the associated atmospheric and surface properties that influence it. CERES relies on a number of data sources, including broadband radiometers measuring incoming and reflected solar radiation and outgoing longwave radiation, high-resolution spectral imagers, meteorological, aerosol, and ozone assimilation data, and snow and sea ice maps based on microwave radiometer data.

While the TOA radiation budget is most accurately determined directly from accurate broadband radiometer measurements, the surface radiation budget is derived indirectly through radiative transfer model calculations initialized using imager-based cloud and aerosol retrievals and meteorological assimilation data. Because ice cloud particles exhibit a wide range of shapes and sizes that cannot be independently retrieved a priori from passive visible/infrared imager measurements, assumptions about the bulk single-scattering properties of ice clouds are necessary in order to retrieve ice cloud optical properties (e.g., optical depth) from imager radiances and to compute broadband radiative fluxes. Here we show that satellite-derived surface radiative fluxes determined using a consistent ice particle model assumption in the cloud property retrievals and forward radiative transfer model calculation are far less sensitive to the assumed ice particle model than the ice cloud property retrievals themselves. Consequently, surface radiative fluxes provide a more robust reference for climate model evaluation in ice cloud conditions than do ice cloud property retrievals.

The paper examines how the choice of an ice cloud particle model impacts computed shortwave (SW) and longwave (LW) radiative fluxes at the TOA and surface. The ice cloud particle models considered correspond to those from prior, current, and future CERES data product versions. During the CERES Edition2 (and Edition3) processing, ice cloud particles were assumed to be smooth hexagonal columns (Minnis et al. 2011). In the Edition4, roughened hexagonal columns are assumed (Minnis et al. 2017, manuscript submitted to IEEE Trans. Geosci. Remote Sens.). The CERES team is now working on implementing in a future version an ice cloud particle model that consists of roughened hexagonal columns and aggregates of randomly distorted columnar elements. In each case, we use the same ice particle model in both the imager-based cloud retrievals (inverse problem) and the computed radiative fluxes (forward calculation).

In the following, we describe the ice cloud habit optical properties, cloud retrieval approach, and forward radiative transfer model calculations used (section 2). This is followed by results showing the impact of the ice particle models on cloud retrievals and TOA and surface radiative flux calculations (section 3). We also compare instantaneous TOA flux calculations with those observed by the CERES instrument (section 4). A general discussion is provided in section 5 and the main findings are summarized in section 6.

2. Methodology

a. Ice cloud habit optical properties

Assumptions about the bulk single-scattering properties (i.e., the scattering phase function, single-scattering albedo, and extinction coefficient) of an ensemble of ice particles in imager-based ice cloud optical property retrievals have evolved during the CERES project with each new version of the data product (Table 1). In Editions 2 and 3, a smooth-solid hexagonal column ice crystal model (called SMOOTH herein; Minnis et al. 1998) was used to compute the reflectance look-up-tables (LUTs) for visible bands and parameterize the emittance for infrared bands for the ice cloud properties retrievals (Minnis et al. 2011). In SMOOTH, all ice crystals are hexagonal columns with various sizes and aspect ratios (width-to-length ratios , where is semiwidth of hexagonal cross section and is the column length): 5/5, 5/10, 10/10, 20/20, 40/50, 60/120, 100/300, and 160/750 (in unit of μm/μm) (Takano and Liou 1989; Minnis et al. 1998). The reflectance LUTs were developed using an adding and doubling radiative transfer code for cloud optical depths (τ) between 0.25 and 128 and ice-crystal effective diameters between 6 and 135 μm. The particle effective diameter (De) is proportional to the total volume (Vt) and total projected area (At) of an ensemble of ice crystals integrated over the particle size distribution (Foot 1988), particularly, in the form
e1
Table 1.

Ice cloud particle models used in CERES processing.

Table 1.

Recognizing the importance of surface texture (i.e., the degree of surface roughness) on the single scattering properties of ice clouds, the SMOOTH models were replaced in Edition 4 with hexagonal ice columns with roughened surfaces (called ROUGH herein) having the normalized roughness parameter set equal to 1 (Yang et al. 2008a; Minnis et al. 2010; Minnis et al. 2017, manuscript submitted to IEEE Trans. Geosci. Remote Sens.). Particle surface roughness smooths out the scattering maxima and peaks in the angular distribution of scattered energy, leading to a featureless phase function (Yang et al. 2008a). The effect on ice cloud property retrievals is to produce smaller retrieved τ and larger ice particle size (De) (Rolland et al. 2000; Yang et al. 2008b).

More recently, Liu et al. (2014b) introduced a two-habit model (THM) that provides a better representation of ice clouds. In the THM, the ice cloud consists of an ensemble of hexagonal columns and 20-element aggregates with specific habit fractions at each particle size bin. In this study, we further improve the THM. Specifically, the elements of an aggregate in the THM are assumed to be randomly distorted hexagonal columns with a distortion parameter of [note that the physical meaning of the parameter is explained in Yang and Liou (1998)]. The effect of random distortion of an ensemble of regular particle shapes on light scattering computation is equivalent to the counterpart of the surface roughness, as illustrated by Liu et al. (2014a). Thus, we use an ensemble of aggregates composed of randomly distorted columns as a surrogate of an aggregate with surface roughness. Figure 1 schematically illustrates the particle morphologies of the THM. While Edition 2, 3, and 4 ice particle models use discrete particle size distributions, the THM uses continuous particle size distributions to compute bulk scattering properties. In this study, gamma-like particle size distributions with the effective variance of 0.1 are used. Extensive yet efficient light scattering simulations at virtually continuous 189 size bins made this model improvement possible. For the single-scattering simulations, we use the invariant imbedding T-matrix method (Bi and Yang 2014) for small and moderate size parameters (kD < 40, where k is the incident wavenumber, and D is the particle maximum dimension defined as the height for the single hexagonal column habit whereas the maximum distance between any two points for the aggregate habit), whereas an improved geometric optics method (Yang and Liou 1996) is used for large size parameters (kD ≥ 40). The electromagnetic edge effect or the tunneling effect is appropriately included in the scattering, absorption, and extinction efficiencies based on the methodology reported in Yang et al. (2013). The development of THM is largely guided by comparing the microphysical parameters from in situ measurements and THM-based calculations. In particular, following Baum et al. (2005), we use the THM to compute the ice water content (IWC) and median mass diameter and compare the theoretical results with the counterparts measured during 11 field campaigns (Miloshevich and Heymsfield 1997; Heymsfield and Miloshevich 2003; Heymsfield et al. 2003, 2004; and references cited therein). As shown in Fig. 2a, the theoretical IWC values are quite consistent with the measurements. However, the theoretical median mass diameter values are slightly lower than the TRMM measurements with very large particles (median mass diameter larger than 400 μm). The TRMM particle size distribution is quite unique and contains a significant portion of very large particles (see Fig. 1 in Baum et al. 2005). Thus, THM does not well approximate the shapes of extremely large particles such as those observed in the TRMM measurement. We call special attention to the fact that the THM improves the spectral consistency in the remote sensing of ice clouds from different wavelengths: optical thicknesses retrieved from two MODIS solar bands are in close agreement with those inferred from the MODIS infrared window measurements (Liu et al. 2014b).

Fig. 1.
Fig. 1.

Schematic diagram showing two ice crystal habits and their mixing ratios of the two-habit model. Habit 1 is a roughened single column with aspect ratio 2a/Dmax =1, and habit 2 is an ensemble of 20 randomly generated aggregates. Individual aggregate shape consists of 20 randomly distorted hexagonal columns. The mixing ratio of habits 1 and 2 add up to one (fsingle + faggregate = 1).

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Fig. 2.
Fig. 2.

Comparison between the measured (from 11 field campaigns) and THM-based theoretical microphysical properties, for (top) ice water content and (bottom) median mass diameter.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

For each of the three ice cloud particle models, an optical property database covering the whole spectral domain was computed, and parameterized optical properties were produced. The wavelength dependence values of bulk extinction efficiency (Qe), single-scattering albedo (ω), and asymmetry factor (g) for SMOOTH, ROUGH, and THM are shown in Figs. 3a–f for an effective diameter of 65 μm. Note that Qe and g for THM are distinctly different from SMOOTH and ROUGH whereas ω values are more consistent. In particular, the THM extinction efficiency is much larger than the SMOOTH and ROUGH counterparts at long infrared wavelengths (λ > 60 μm), as evident from Fig. 3b. The difference of the extinction efficiency (Qe) in the long IR regime is mainly because of the difference of particle size distributions (PSDs) (not shown here) between the THM and the ROUGH model. For an effective diameter of De = 65 μm, the peak of THM’s PSD coincides with the largest peak of the Qe oscillation (van de Hulst 1957) when wavelength is about 100 μm. This coincidence produces large bulk Qe at about λ = 100 μm. A similar coincidence happens for the ROUGH model but at De = 80 μm. In the shortwave regime, the size parameters are large and the extinction oscillates around 2. The extinction minimum near λ = 2.85 μm is due to the well-known Christiansen effect (Liou and Yang 2016; and references cited therein). The THM g values are smaller throughout the visible and near-infrared regions up to 2.7 μm (Fig. 3e). In the visible, THM g values are smaller than in SMOOTH and ROUGH by ~0.05 and ~0.04, respectively. In the midinfrared, a reversal occurs in which THM g exceeds both of its hexagonal column counterparts. To explain the mechanism of the reversal, we notice that the single column habit dominates the THM mixing in the case of De = 65 μm. The aspect ratio for the single column habit is 1. The asymmetry factor of a single column in the visible wavelengths varies with the aspect ratio in a “U” form and reaches the minimum when the aspect ratio is 1 (Fu 2007; Yang and Fu 2009). ROUGH and SMOOTH both have larger aspect ratios and, consequently, have a larger g factor than THM at short wavelengths (<3 μm). On the other hand, at near-thermal wavelengths larger than 3 μm in the absorbing regime, a single column with an aspect ratio of 1 is more absorptive than the ROUGH and SMOOTH counterparts because the former have larger volume for the same particle dimension. From first principles of light scattering theory, the diffraction contributes a larger fraction to the scattered light in the case of the single column habit than for ROUGH and SMOOTH when strong absorption is involved. Because the scattering due to diffraction has a larger g factor than that due to the geometric reflected and refracted rays, THM has a larger g factor than ROUGH and SMOOTH in the absorbing spectral regime.

Fig. 3.
Fig. 3.

(a),(b) Bulk extinction efficiency Qe, (c),(d) single-scattering albedo w, and (e),(f) asymmetry factor against wavelength for SMOOTH, ROUGH, and THM at effective diameter 65 μm.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Figure 4 compares g values against effective diameter at a wavelength of 0.65 μm. The SMOOTH and ROUGH g both increase with effective diameter whereas g for THM shows a slight decrease. Fu (2007) articulates the bulk asymmetry factor of an ensemble of ice crystals with a specific size distribution is largely determined by the effective aspect ratio at a visible wavelength. Both SMOOTH and ROUGH have much larger effective aspect ratios than their THM counterpart, leading to much larger asymmetry factor values in the case of SMOOTH and ROUGH. Furthermore, it should be pointed out that the weighting of the aggregates in THM increases and thus the THM asymmetry factor slightly decreases with effective particle size, particularly when De > 80 μm.

Fig. 4.
Fig. 4.

Asymmetry factor as a function of ice particle size for SMOOTH, ROUGH, and THM ice particle models at a wavelength of 0.65 μm.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

b. Cloud retrieval

The CERES cloud retrieval algorithm determines cloud phase, temperature (Tc), De, and τ using the Visible Infrared Shortwave–Infrared Split-Window Technique (VISST) for daytime, which matches model estimates of radiances from clouds with the observations (Minnis et al. 2011; Minnis et al. 2017, manuscript submitted to IEEE Trans. Geosci. Remote Sens.). Six primary MODIS Aqua imager radiances are used: 0.65 μm [visible (VIS)], 1.24 μm [near-infrared (NIR)], 2.13 μm (NIR), 3.79 μm [shortwave infrared (SIR)], 11.0 μm [infrared (IR)], and 12.0 μm [split-window channel (SWC)]. In addition to those wavelengths, the CERES cloud detection algorithm relies on MODIS bands at 0.469, 0.858, 1.38, 6.72, 8.55, 11.03, 12.02, and 13.34 μm (Minnis et al. 2008; Q. Z. Trepte et al. 2017, unpublished manuscript). The VIS channel is primarily used to estimate τ, the IR channel is for Tc, the SIR channel is used to retrieve particle size, and the SIR and SWC are used in phase selection. In CERES Edition 4, particle sizes are also estimated using the two NIR bands. For the pixel location and time, cloud height (zc) and pressure are found by matching Tc to an altitude in the Global Modeling and Assimilation Office (GMAO) Goddard Earth Observing System (GEOS) model version 5 0.4.1 (GMAO-G541) vertical profile of temperature that is modified in the boundary layer using empirical regional lapse rates (Sun-Mack et al. 2014). If the underlying surface is identified as snow or ice, the SIR-IR-NIR technique (SINT) is applied (Minnis et al. 2011). SINT uses the 1.24-μm channel to compute the VIS optical depth. All ice crystal reflectance lookup tables (LUTs) are computed for the 0.65-, 3.79-, 2.13-, and 1.24-μm channels based on radiative transfer computations based upon the radiative transfer model described in Minnis et al. (1993). Corrections for atmospheric absorption employ the correlated k distribution method (Kratz 1995) with the absorption coefficients computed for the spectral response functions of the various channels (Minnis et al. 2011).

c. Forward radiative transfer

The broadband forward radiative transfer computations use a modified version of the NASA Langley Fu–Liou radiative transfer code (Fu and Liou 1993; Fu et al. 1998; Kratz and Rose 1999; Kato et al. 1999, 2005). The model includes sources of optical properties for water clouds (Hu and Stamnes 1993), whereas ice cloud properties have been modified from the original Fu (1996) data to ensure consistency with those corresponding with the ice cloud habit assumed in the cloud retrievals. Aerosol optical properties are taken from the software package OPAC (Optical Properties of Aerosols and Clouds; Hess et al. 1998; Tegin and Lacis 1996; D’Almeida et al. 1991). Rayleigh scattering coefficients are based upon the Moderate Resolution Atmospheric Transmission (MODTRAN) model (Shettle et al. 1980). Gas absorption is based upon HITRAN 2000 restructured into sets of correlated-k coefficients dependent upon gas mixing ratio, pressure, and temperature according to the method described by Kato et al. (1999). An 18-band shortwave gamma-weighted two-stream algorithm (GWTSA) solver is used for shortwave, and horizontal inhomogeneity in the cloud τ domain is quantified as a gamma distribution, using inputs of a linear and a log averaged τ (Kato et al. 2005). The longwave portion uses a more traditional two/four-stream solver for its 14 bands (Fu et al. 1997). Temperature, humidity, and ozone profiles are obtained from the GEOS 5.4.1 assimilation provided by GMAO at NASA Goddard. Vertical profiles and total aerosol τ are from the Model for Atmospheric Transport and Chemistry (MATCH; Collins et al. 2001).

As described earlier, cloud properties of fractional coverage, phase, τ, zc, and De are retrieved from MODIS multichannel radiances and averaged into a region consistent with the CERES instrument field of view (FOV) with a size of approximately 20 km at nadir. It is on this FOV scale that the forward radiative transfer computations are performed.

The basic version of the code can be obtained from https://www-cave.larc.nasa.gov/cgi-bin/lflcode/accesslfl.cgi (note that this version does not include the THM ice cloud optical properties).

3. Results

For each of the three ice particle models listed in Table 1, the CERES Ed4.0 cloud detection and optical property retrieval code was run to produce cloud optical property retrievals from MODIS Aqua data for 1–10 March 2008. As differences were most pronounced between the THM and SMOOTH models, for clarity, we only show comparisons for those two cases. The influence of ice particle model on the CERES daytime cloud mask is shown in Table 2. In 99.98% of the MODIS pixels processed, the cloud mask produced identical results for THM and SMOOTH. Similarly, the agreement for daytime cloud phase (water versus ice) was 98.6% (Table 3). Thus, because the THM and SMOOTH populations are nearly identical, sampling differences play a minor role in explaining THM and SMOOTH cloud property retrieval differences.

Table 2.

Daytime cloud mask comparison using SMOOTH and THM models for Aqua-MODIS in March 2008.

Table 2.
Table 3.

Daytime cloud phase comparison using SMOOTH and THM models for Aqua-MODIS in March 2008.

Table 3.

THM and SMOOTH ice cloud τ, zc, and De retrieval differences at the Aqua overpass time are shown in Figs. 5a–c for 1–10 March 2008. While ice cloud τ differences are generally within ±1.0 equatorward of 30° latitude, THM values are smaller than SMOOTH by 5.0 or more at middle and high latitudes across all longitudes, both in the Northern and Southern Hemispheres. The smaller THM τ values are a direct result of the THM’s smaller visible g compared to SMOOTH (Fig. 4). According to similarity theory (van de Hulst 1974), the reflected radiance at nonabsorbing wavelengths is proportional to τ(1 − g). A smaller g for THM implies a smaller τ is necessary to match the MODIS-observed 0.65-μm radiance. Differences are more pronounced at higher latitudes because scattering angles are closer to the principal plane, where sensitivity to g is greater. Overall, the τ difference is −2.3 (−28% of global mean) and the root-mean-square difference (RMSD) is 2.8 (32% of the global mean).

Fig. 5.
Fig. 5.

Difference in (a) ice cloud optical depth, (b) ice particle size, and (c) ice cloud effective height between retrievals using THM and SMOOTH at the daytime Aqua overpass time (THM minus SMOOTH).

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Differences in effective radius are also quite large (Fig. 5b). The THM values at middle and high latitudes can be smaller by 5 μm or more compared to SMOOTH retrievals, while differences are smaller at low latitudes. Overall, the global mean effective radius difference is −3.9 μm (16% of the global mean) and RMSD is 5.2 μm (21% of the global mean). It is interesting that both cloud τ and De retrievals are smaller for THM compared to SMOOTH. As already noted, THM ice cloud τ retrievals are smaller than SMOOTH because the g for THM at visible wavelengths is smaller. However, it is not so obvious why the De retrievals should also be smaller. According to similarity theory (van de Hulst 1974), at wavelengths where cloud absorption is significant (NIR and SIR), the radiance is proportional to S = (1 − ω)/(1 − ωg), where ω is single scattering albedo. Since the CERES cloud algorithm uses SIR (3.79 μm) to infer De, and since ω is smaller and g is larger for THM than SMOOTH at this wavelength (see Figs. 3c and 3e), S(THM) > S(SMOOTH) for a given De. To match the observed radiance, De must therefore be smaller for THM than SMOOTH. If one were using NIR bands (1.24 or 2.13 μm) to retrieve particle size instead of the SIR channel, THM De retrievals would be larger than SMOOTH since the NIR THM g is smaller than that for the SMOOTH model (Fig. 3e). Since the NIR bands penetrate deeper into a cloud than the SIR band, this implies that THM would yield smaller particle sizes near the top of the cloud and larger particle sizes deeper into the cloud compared to SMOOTH.

Differences in zc are generally positive everywhere (Fig. 5c), exceeding 1 km in portions of the Southern Ocean, the Pacific Ocean, and over Asia. The THM zc values exceed those for SMOOTH by 290 m on average globally and the regional RMSD is 375 m. Because THM τ values are smaller than those from SMOOTH (Fig. 5a), the contribution by surface emission transmitted through thin cirrus is greater for THM. To match the observed 11-μm radiance, emission from the cirrus cloud itself must therefore be smaller for THM, resulting in larger zc retrievals.

Results in Figs. 5a–c clearly demonstrate the importance of ice particle model assumptions in ice cloud optical property retrieval from satellite. However, for radiative flux calculations, if consistent ice particle model assumptions are made in both the cloud property retrieval and forward TOA and surface broadband radiative flux calculations, how sensitive are the results to the ice particle model assumption? Previous studies (Yang et al. 2007; Yi et al. 2017) comparing TOA radiation calculations for ice clouds inferred using cloud retrievals from different versions of MODIS “Collections” (King et al. 2008; Platnick et al. 2017) have found differences in global mean SW TOA cloud radiative effect (CRE) as high as 23 W m−2 [e.g., Collection 6 minus Collection 5.1 in Yi et al. (2017)]. However, because the MODIS Collections compared used different instrument calibration, cloud masks, and cloud retrieval methodologies in addition to ice particle models, it is unclear how much of the difference was actually due to the ice particle model assumption alone. To address this in the context of the ice particle models in Table 1, we compare SW TOA flux calculations in which the THM and SMOOTH are consistently used in cloud property retrievals and forward flux calculations. Importantly, we use identical cloud mask, cloud retrieval, and forward radiative transfer model methodologies in both cases. At the TOA, Fig. 6a shows that differences are generally positive in the tropics and negative at high latitudes but remain less than 5 W m−2, corresponding to relative differences of within 3% (Fig. 6b). Overall, the regional RMSD is ~1%. Regional differences in SW surface flux calculations are positive everywhere (Figs. 7a,b), reaching 15% in Greenland, but the overall regional RMSD is only 1%. The reason for the positive differences is likely because of the smaller optical thicknesses and smaller De for THM, resulting in increased transmission in water vapor and near-infrared cloud absorption bands.

Fig. 6.
Fig. 6.

SW TOA flux (a) difference (W m−2) and (b) relative difference (%) between calculations with retrievals from THM combined with THM forward radiative transfer minus retrievals from SMOOTH combined with SMOOTH forward radiative transfer.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Fig. 7.
Fig. 7.

As in Fig. 5, but for SW surface downward flux difference.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Next, we investigate the impact of using one ice particle model in the cloud property retrievals and a different model in the forward radiative transfer (forward RT) model calculations. Figures 8 and 9 show differences for calculations with retrievals from THM combined with THM forward RT minus retrievals from SMOOTH combined with THM forward RT. At the TOA (Figs. 8a,b), the overall regional RMSD is 2%, about twice that obtained when a consistent ice particle model is used in both cloud retrievals and forward RT calculations. Over regions such as the Maritime Continent, the southern Pacific convergence zone (SPCZ), and the northeastern Pacific Ocean, the differences can reach 5% (Fig. 8b). Here, the differences are negative everywhere, likely because of the larger retrieved cloud τ obtained by assuming the SMOOTH ice particle model. At the surface (Figs. 9a,b), local regional differences double in many places compared to the case in which consistent models are used in the retrievals and forward RT calculations. The overall regional RMSD is 1.5%.

Fig. 8.
Fig. 8.

SW TOA flux (a) difference (W m−2) and (b) relative difference (%) between calculations with retrievals from THM combined with THM forward RT minus retrievals from SMOOTH combined with THM forward RT.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Fig. 9.
Fig. 9.

As in Fig. 7, but for SW surface downward flux difference.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

Finally, we examine the influence of cloud ice particle model on LW surface flux in Figs. 10a and 10b. In this case, the overall regional RMSD is 0.3%. However, in some locations LW surface fluxes from THM are smaller than SMOOTH by up to 3%. The smaller THM values occur because the retrieved τ and effective radius from THM are smaller than for SMOOTH and the effective cloud height (and therefore cloud base) is higher (see Figs. 5a–c).

Fig. 10.
Fig. 10.

As in Fig. 5, but for LW surface downward flux difference.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

4. Comparison with CERES TOA observations

To place the TOA flux differences associated with the various ice particle model assumptions in the context of comparisons between computed and observed TOA fluxes, we compare in Figs. 11a and 11b computed SW TOA fluxes in CERES SYN1deg_Ed4, which assumes rough hexagonal columns, with diurnally averaged CERES observed values from the same data product for March 2008. Only regions with 80% or more ice cloud coverage during each day of the month are included in the monthly average. Differences reach 15 W m−2 in the deep tropics, such as the west tropical Pacific Ocean. The global mean difference is −4.7 W m−2 (3%) and global RMSD is 11.2 W m−2 (8%). In contrast, the regional 1° × 1° latitude–longitude CERES-observed SW TOA flux uncertainty is estimated to be 2.5 W m−2 (2.5%) under all-sky conditions (Loeb et al. 2018). The results imply that uncertainties in computed SW TOA fluxes associated with the ice particle model assumption cannot explain much of the discrepancy between computed and observed SW TOA fluxes. Other factors, such as cloud mask, phase determination, subpixel inhomogeneity, and, to a lesser extent, surface albedo, likely explain more of the difference.

Fig. 11.
Fig. 11.

(a) Regional average and (b) zonal average computed minus CERES-observed SW TOA flux difference for March 2008. Only regions with 80% or more ice cloud coverage during each day of the month are included in the monthly average.

Citation: Journal of Climate 31, 5; 10.1175/JCLI-D-17-0426.1

5. Discussion

Results in this study have important implications for climate model evaluation. To determine radiative fluxes under ice cloud conditions, general circulation models (GCMs) must predict the ice water content (IWC) and determine the bulk optical properties of the clouds using an assumed ice crystal model. Current GCMs often use empirical data to generate parameterizations of ice crystal optical properties that are functions of effective diameter, IWC, and/or environmental temperature (Fu 1996; Hong et al. 2009; Gu et al. 2011; Yi et al. 2017). However, the different assumptions used in the ice cloud microphysics can have a profound influence on the computed TOA and surface radiative fluxes (Fu 2007; Baran 2012). Baran et al. (2014) note that much of the problem is due to inconsistencies in the shape of the particle size distribution and the area and mass–dimensional relationships between the cloud physics and radiation schemes resulting from assumed relationships between effective diameter and environmental temperature. Because satellite ice cloud property retrievals are also highly dependent upon what assumptions are made regarding the ice cloud particle model, the satellite retrievals arguably provide only a weak constraint on GCM-derived optical properties (e.g., τ and De). The situation could perhaps be ameliorated if the same assumptions about the ice cloud particle model were used in both the GCM and satellite retrievals. In addition, it may be necessary to employ satellite simulators (e.g., Pincus et al. 2012) in order to compare the GCMs and satellite retrievals. This is particularly true since effective diameter retrievals depend strongly upon what spectral band is used in the retrieval (Platnick 2000). It should be pointed out that using the same ice cloud particle model in satellite retrievals and GCM simulations is not a sufficient observational constraint unless the ice cloud particle model is representative of actual cirrus microphysics and the satellite retrievals produce accurate results. Thus, in situ ice cloud microphysical properties are quite valuable in improving ice cloud models used in GCMs and satellite retrievals.

In contrast, the lack of sensitivity to the assumed ice particle model in radiative flux calculations implies that satellite-based TOA and surface fluxes provide a more robust reference for climate model evaluation in ice cloud conditions than cloud property retrievals. When all-sky downward surface radiative flux calculations from the CERES Energy Balanced and Filled (EBAF) product are compared with surface observations (Kato et al. 2013), the bias is <5 W m−2 (2%) for SW downward surface flux and <2.5 W m−2 (0.6%) for downward LW flux. The root-mean-square error (RMSE) is 13 W m−2 (5%) for SW downward flux over ocean and 8 W m−2 (4%) over land. For LW downward flux, the RMSE is 7 W m−2 (2%) for ocean and 8 W m−2 (2.5%) for land.

6. Summary and conclusions

The most common method to determine surface radiative fluxes globally is to perform radiative transfer model calculations initialized with satellite imager-based cloud and aerosol retrievals and meteorological assimilation data. When ice clouds are present, assumptions about the scattering properties of the clouds are needed in order to retrieve ice cloud optical properties and to compute broadband radiative fluxes. Ice cloud particles exhibit a wide range of shapes, sizes, and habits that cannot be independently retrieved a priori from passive visible/infrared imager measurements. Over the years, ice cloud particle models have become increasingly sophisticated as more in situ measurements from field campaigns in different regions have become available. The ice particle model is meant to be representative of a range of ice cloud conditions and the bulk single-scattering properties (i.e., the scattering phase function, single-scattering albedo, and extinction coefficient) derived from it are used as input to radiative transfer model calculations, which in turn are used in satellite cloud property retrievals and broadband radiation calculations (Baran 2012; Baran et al. 2014; Liou and Yang 2016).

At the start of the CERES project, ice clouds were assumed to comprise smooth hexagonal ice columns (Editions 2 and 3). Roughened hexagonal ice columns in Edition 4 superseded the smooth properties of prior editions. We further improved the two-habit model (THM) originally proposed by Liu et al. (2014b) to consist of an ensemble of hexagonal columns and 20 elements aggregates with specific habit fractions at virtually continuous particle size bins. The THM closely reproduces ice water contents and median mass diameters found in the in situ measurements of 11 field campaigns and improves the spectral consistency of ice cloud retrievals at different wavelengths (Liu et al. 2014b). The main difference between the optical properties of THM and smooth or roughened hexagonal columns is in the asymmetry parameter (g). The THM g values are much smaller than the other two at visible and near-infrared wavelengths and are more constant across the range of ice particle effective diameter. In the midinfrared, THM g exceeds its counterparts for both hexagonal column models.

When the various ice particle models are used in the CERES production code for a 10-day period in March 2008, we find that the choice of ice particle model has a negligible impact on the daytime cloud mask applied to MODIS pixel data. Similarly, daytime cloud phase (water versus ice) determination is relatively insensitive to ice particle model. In contrast, cloud optical depth and effective particle radius retrievals derived from MODIS Aqua exhibit a strong dependence on what ice particle model is assumed. The differences in optical depth reach 5.0 at middle and high latitudes, but generally remain < 1.0 equatorward of 30° latitude. On a global average, the THM ice cloud optical depth is 2.3 (28%) smaller than SMOOTH, and the RMSD between THM and SMOOTH is 2.8 (32%). The sensitivity to ice particle model is also quite significant in ice cloud effective radius retrievals. THM-derived effective radii can be smaller by 5 μm or more compared to SMOOTH at middle and high latitudes, whereas differences are less pronounced in the tropics. The global mean THM effective radius is 3.9 μm (16%) smaller than SMOOTH and the RMSD is 5.2 μm (21%). Global average effective height retrievals from THM exceed those from SMOOTH by 290 m and the regional RMSD is 375 m.

The sensitivity to ice particle model is much smaller for radiative flux calculations. When the same ice particle model assumption is made in both the cloud property retrieval and forward broadband radiative flux calculations, the regional RMSD in TOA and surface flux between the THM and SMOOTH is only 1% in the SW. When the ice particle model in the cloud property retrievals differs from that in the forward radiative transfer model calculations, the regional RMS error is 2%. The errors caused by using inconsistent ice particle models in the retrievals and forward calculations tend to be systematic both at the TOA and surface, either positive or negative everywhere. In the LW, the sensitivity to what ice particle model is used is 0.3%.

When computed SW TOA fluxes are compared with CERES observed values in regions dominated by ice clouds, the computed values are biased low by 5 W m−2 (3%) and the global RMSD is 11 W m−2 (8%). These differences significantly exceed the SW TOA flux sensitivity to the assumed ice particle model and are likely associated with other factors in the cloud retrieval and forward calculation process. After constraining the computed TOA fluxes to observed values by adjusting the input parameters within their range of uncertainty, computed surface radiative fluxes in the EBAF-SFC product (Kato et al. 2013) are remarkably consistent with surface-based measurements, both over land and ocean. Consequently, owing to the relative insensitivity to ice particle model and good agreement with surface measurements, we conclude that satellite-derived surface radiative fluxes that use a consistent ice particle model assumption in the retrieval and forward model calculation provide a more robust reference for climate model evaluation in ice cloud conditions than do ice cloud property retrievals, which are highly dependent upon ice particle model assumptions.

Acknowledgments

This research has been supported by NASA CERES project. The CERES EBAF Ed4.0 dataset was downloaded from https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAF4Selection.jsp. The NASA Langley Atmospheric Sciences Data Center processed the instantaneous Single Scanner Footprint (SSF) data used as input to EBAF Ed4.0. Portions of light scattering and radiative transfer calculations were conducted with the advanced computing resources provided by Texas A&M High Performance Research Computing.

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