A High-Spectral-Resolution Radiative Transfer Model for Simulating

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A High-Spectral-Resolution Radiative Transfer Model for Simulating Multilayered Clouds and Aerosols in the Infrared Spectral Region CHENXI WANG AND PING YANG Department of Atmospheric Sciences, Texas A&M University, College Station, Texas

XU LIU Science Directorate, NASA Langley Research Center, Hampton, Virginia (Manuscript received 11 March 2014, in final form 26 September 2014) ABSTRACT A fast and flexible model is developed to simulate the transfer of thermal infrared radiation at wavenumbers from 700 to 1300 cm21 with a spectral resolution of 0.1 cm21 for scattering–absorbing atmospheres. In a single run and at multiple user-defined levels, the present model simulates radiances at different viewing angles and fluxes. Furthermore, the model takes into account complicated and realistic scenes in which ice cloud, water cloud, and mineral dust layers may coexist within an atmospheric column. The present model is compared to a rigorous reference model, the 32-stream Discrete Ordinate Radiative Transfer model (DISORT) code. For an atmosphere with three scattering layers (water, ice, and mineral dust), the rootmean-square error of the simulated brightness temperatures at the top of the atmosphere is approximately 0.05 K, and the relative flux errors at the boundary and internal levels are much smaller than 1%. Within the same computing environment, the fast model runs more than 10 000, 6000, and 4000 times faster than DISORT under single-layer, two-layer, and three-layer cloud–aerosol conditions, respectively. With its computational efficiency and accuracy, the present model may optimally facilitate the forward radiative transfer simulations involved in remote sensing implementations based on high-spectral-resolution and narrowband infrared measurements and in the data assimilation applications of the weather forecasting system. The selected 0.1-cm21 spectral resolution is an obstacle to extending the present model to strongly absorptive bands (e.g., 600–700 cm21). However, the present clear-sky module can be substituted by a more accurate model for specific applications involving spectral bands with strong absorption.

1. Introduction The microphysical and radiative properties of cloud and aerosol are the major sources of uncertainties in the atmospheric sciences (Stocker et al. 2013). During the first years of the twenty-first century, various state-ofthe-art airborne and spaceborne instruments were deployed to improve the understanding of cloud and atmospheric aerosol. With observations by active sensors, such as the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) (Winker et al. 2010) and CloudSat (Stephens et al. 2002), researchers were able to construct a global-scale, three-dimensional map of cloud

Corresponding author address: Prof. Ping Yang, Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77843. E-mail: [email protected] DOI: 10.1175/JAS-D-14-0046.1 Ó 2015 American Meteorological Society

and aerosol distributions. In addition, it is found that the averaged occurrence of multiple cloud layers is about 50% and may be as large as 60% in the tropical western Pacific, equatorial South America, and Africa (Kato et al. 2010; Liu et al. 2012; Mace et al. 2009). Devasthale and Thomas (2011) reported that in some regions, such as the northern Pacific Ocean, western Africa, and western South America, the occurrence frequencies of aerosol– water overlap approached 20%. Despite the high frequency of overlap between cloud and aerosol (hereafter referred to as scattering layers) in real atmospheres, some widely used cloud–aerosol retrieval algorithms remain restricted to conditions with only one scattering layer (Hsu et al. 2006; Levy 2009). For a single-scatteringlayer scene, a forward radiative transfer model (RTM) is unnecessary in the operational retrieval algorithm because satellite observations can be efficiently simulated using precomputed single-layer cloud–aerosol lookup

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tables (LUTs) for reflectivity, transmissivity, and emissivity in conjunction with some simplifications of the atmosphere and surface correction (Kaufman et al. 1997; Wang and King 1997; Platnick et al. 2003). For scenes with multiple scattering layers, an RTM is indispensable for accurate modeling and retrieval implementation. A significant number of computations cannot be avoided if an accurate RTM is employed to map the properties of atmospheric components to observational space (Kokhanovsky et al. 2010). For this reason, Chang and Li (2005) developed a simplified method to efficiently infer multilayered cloud optical thickness values using a combination of several solar reflection bands and thermal infrared (IR) bands. In their retrieval algorithm, relatively large uncertainties may result from not using a rigorous RTM and ignoring the effects of multiple scattering in thermal IR bands and cloud particle size. RTMs encompass the most important physical processes related to atmospheric constituents [e.g., clouds and gases (Kokhanovsky et al. 2010)] and are, therefore, widely used in cloud and aerosol retrieval algorithms (e.g., Doutriaux-Boucher and Dubuisson 2009; Garnier et al. 2012; Poulsen et al. 2011; Francis et al. 2012; Kahn et al. 2014; Dubuisson et al. 2014; Iwabuchi et al. 2014; Yi et al. 2014) and sensitivity studies (e.g., Kahn et al. 2004; Jin and Nasiri 2014). With increasing effort dedicated to quantifying radiative forcings and climate feedbacks of different atmospheric constituents and detecting climate change signals, a pressing need arises as to how to efficiently facilitate the forward simulations of spectrally resolved outgoing longwave radiation (OLR) at the top of the atmosphere (TOA), of the surface downwelling longwave radiation (DLR), and of fluxes at arbitrary atmospheric levels (Leroy et al. 2008; Huang et al. 2010; Chen et al. 2013; Huang 2013). RTMs used in these studies, for example, the moderate resolution atmospheric transmission (MODTRAN), version 5 (Anderson et al. 2007), are shown to have approximately a 1-K rootmean-square error (RMSE) in the longwave region under overcast-sky conditions (Chen et al. 2013). Some rigorous RTMs, such as the Discrete Ordinate Method Radiative Transfer model (DISORT) code (Stamnes et al. 1988; Dubuisson et al. 1996), the adding–doubling RTM (Twomey et al. 1966; Hansen and Hovenier 1971), and the successive order of scattering method (Heidinger et al. 2006; Lenoble et al. 2007), consider scattering, absorption, and thermal emission in plane-parallel atmospheres. These RTMs are usually referred to as benchmarks for precise simulations; however, tremendous demands on computation restrict the applications of these models if large temporal and spatial scales are involved. To alleviate the computational burden, various fast RTMs have been developed for diverse atmospheres.

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For example, Saunders et al. (1999) developed a fast RTM [Radiative Transfer for the Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) (RTTOV)], which simulates outgoing radiances at the TOA in cloudy atmospheres. To reduce computational time, the improved RTTOV does not consider cloud scattering effects, leading to relatively large errors in the brightness temperature (BT) difference between the 8.7- and 12-mm bands. Liou et al. (1988) developed a radiative transfer formulation based on the delta-four-stream (D4S) approximation. The speed of D4S is approximately 150 times faster than the doubling method (Liou et al. 2005), while the simulation error in terms of radiance is limited to 0.4% (Yue and Liou 2009). Dubuisson et al. (2005) developed three RTMs that are applicable to purely absorbing media, partially absorbing media without scattering effects, and scattering media. The three RTMs are designed to simulate TOA radiances and brightness temperatures measured by the three IR channels (8.7, 10.6, and 12 mm) of the Infrared Imaging Radiometer (IIR). Wei et al. (2004) and Wang et al. (2011, 2013b) developed fast IR RTMs for single-layer cloudy atmospheres using precomputed LUTs for both water and ice clouds. The computational efficiencies of these fast IR RTMs are three orders of magnitude higher than the DISORT, and the TOA BTs simulation errors are smaller than 0.2 K. Niu et al. (2007) developed a fast IR RTM to simulate the TOA radiances under conditions with two cloud layers. However, the previous IR RTM neglects the zenith-angle dependence of the incident radiance and integrates cloud bidirectional reflectivity and transmissivity over all incident angles, formalizing an oversimplified scheme and incurring an increase in simulation errors. Fast RTMs based on the adding– doubling principle were developed by Zhang et al. (2007) for IR regions and by Wang et al. (2013a) for visible (VIS) and shortwave infrared (SWIR) regions. The two RTMs can be applied to multiple scatteringlayer scenes and fully consider the zenith-angle dependence of the incident radiance field, which provides high accuracy but with low computational efficiency compared to other fast RTMs. This study is aimed at filling the gap between the rigorous and oversimplified fast RTMs and providing a flexible and reliable modeling capability for various research purposes. To increase the computational efficiency without significantly reducing accuracy, we use a hybrid algorithm to consider cloud–aerosol reflectivity and transmissivity in the IR region. Instead of solely using either local albedo and transmittance or bidirectional reflectivity and transmissivity, we fully consider the zenithangle dependence of the incident field associated with

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cloud bidirectional transmissivity and, for simplicity, assume a fully isotropic incident field when calculating scattering-layer reflection. Although the assumption causes errors in the simulation of reflected radiation and the errors could be amplified once the scattering layer has a large albedo, the present RTM is quite accurate for a wide variety of atmospheric remote sensing applications. Moreover, the model simulations, including spectrally resolved radiances and fluxes at arbitrary atmospheric levels, facilitate theoretical studies of radiative forcing and climate change. The paper is organized into six sections. The methodology details are described in section 2. Section 3 introduces the single-scattering and microphysical properties of water and ice cloud particles and of dust aerosols. In section 4, we compare simulations of the present RTM with the 32-stream DISORT. A case study is given in section 5 to demonstrate the potential applications of the RTM to cloud property retrieval implementations and in cloud radiative forcing studies. Section 6 presents a summary with the conclusions.

2. Methodology We wish to emphasize that the present model is a onedimensional IR RTM that deals with multilayered clouds and aerosols in plane-parallel atmospheres. Furthermore, in the thermal IR spectral region, because of strong absorption, albedos of scattering layers and the surface are generally much smaller than 1. For example, Fig. 1 shows the global albedo a variations with respect to optical thickness and wavenumber for ice and water clouds and mineral dust aerosol. The global albedo (also called spherical albedo) is defined as a(n) 5 2

ð1

A(m, n)m dm ,

(1)

0

where A(m, n) is the local albedo (also called planetary albedo) and is defined as A(m, n) 5

1 p

ð 2p ð 1 0

R(m, f; m0 , f0 ; n)m0 dm0 df0 .

(2)

0

In Eqs. (1) and (2), m and m0 are absolute values of the cosine of the incident and outgoing zenith angles, respectively; f and f0 are the incident and outgoing azimuthal angles; n is the wavenumber; and R is the bidirectional reflectance distribution function (BRDF). The local albedo strongly depends on the viewing zenith angle and can exceed 0.5 for a scattering layer with an optical thickness value of 1 and a viewing zenith angle near 908 (i.e., m is close to 0). The global albedo, which is

FIG. 1. Global albedos for (top) water cloud, (middle) ice cloud, and (bottom) mineral dust aerosol. The cloud particles satisfy the gamma distribution with an effective variance of 0.1. The effective particle size values for water and ice clouds are 24 and 50 mm, respectively. A bilognormal size distribution is used to specify dust aerosol. The fine and coarse modes (specified in terms of diameter) are 0.4 and 3 mm, respectively. The standard deviations for the two modes are 1 mm.

an integral of the local albedo over all incident angles, indicates the fraction of incident flux reflected by a layer. Although the global albedo varies with particle size, here we visualize it as a function of n and optical thickness with a given effective particle size. The global albedo values are shown to be smaller than 5% in the IR window region between 700 and 1300 cm21, except for the water cloud albedo at wavenumbers larger than 1100 cm21 (Fig. 1, top). For this reason, two additional approximations are made to reduce the computational burden of the RTM: 1) the higher-order reflections from the surface and/or scattering layers are not considered

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and 2) the incident radiance field is assumed to be isotropic in order to use a local albedo in calculating the scattering-layer reflection. To efficiently consider scattering, absorption, and emission of both the atmospheric nonscattering layer [i.e., no cloud or aerosol particles exist (herein referred to as clear layer)] and the scattering layer, we use the rigorous 32-stream DISORT to generate an effective temperature (teff,g) LUT for the clear layers and four LUTs—azimuthally averaged BRDF R, averaged bidirectional transmission distribution function (BTDF) G, effective emissivity E, and effective temperature teff,s—for the scattering layers. Azimuthally averaged LUTs are used because the source of thermal infrared radiation is independent of the azimuthal angle. The quantity teff,g is defined to consider the nonisothermal feature of a clear layer. For example, the outgoing thermal emission I of an isothermal clear layer with temperature t at two boundaries can be expressed as follows: 0 0 t dt B(t) exp 2 m m 0 tg , 5 B(t) 1 2 exp 2 m

I [ (m) 5 I Y (m) 5

ðt

g

[Y teff ,g 5 t1 1 (t2 2 t1 ) 3

(3)

21 tg [Y I (m) 3 1 2 exp 2 , m (4)

where B21 is the inverse Planck function, and t1 and t2 are the temperatures at the clear-layer upper and [Y lower boundaries. To derive teff ,g associated with a clear layer with an arbitrary boundary temperature, [Y (m) of we can first calculate the outgoing radiances Iref a clear layer with reference boundary temperatures tref,1 (upper: 245 K) and tref,2 (lower: 250 K) using the 32-stream DISORT and then derive the effective tem[Y perature teff ,g,ref of the reference layer using Eq. (4).

[Y teff ,g,ref 2 tref,1

tref,2 2 tref,1

.

(5)

The clear-layer effective temperature is a function of upper- and lower-layer boundary temperatures, optical [Y thickness, viewing zenith angle, and wavelength. The teff ,g LUT is calculated at 40 optical thickness values from 0.001 to 50 and 16 viewing angles coinciding with the double Gaussian quadrature points. It should be emphasized that [ Y teff ,g and teff,g are different if the layer is not isothermal. [Y Four additional LUTs for R, G, E, and teff ,s are defined to take into account the scattering, absorption, and emission effects of a scattering layer. The definitions of R and G can be expressed as follows: ð 1 2p R(m, m0 ) 5 R(m, m0 , f, f0 )d(f 2 f0 ) , (6) 2p 0 G(m, m0 ) 5

where B indicates the Planck function, t g is the optical thickness of the clear layer, and the superscripts [ and Y are used to distinguish between the upward and downward directions. For simplification, we have omitted the wavenumber subscript n in Eq. (3). The Planck function is calculated at monochromatic wavelengths and assumed to be a constant within a 0.1-cm21 spectral interval. However, if a clear layer is vertically nonisothermal, the outgoing thermal emissions are determined by the internal temperature profile; to simplify, we assume the internal temperature within the layer to vary linearly with height. The effective temperature of the clear layer is defined as follows: [Y 21 teff ,g (t g , m, t1 , t2 ) 5 B

[Y Furthermore, teff ,g (t g , m, t1 , t2 ) can be derived with a linear interpolation:

1 2p

ð 2p

G(m, m0 , f, f0 )d(f 2 f0 ) ,

(7)

0

where G is the layer BTDF. Again, we use the DISORT to simulate R and G of a scattering layer by assuming an incident beam illuminating the top of a nonemitting medium. The local albedo involved in Eq. (2) can be expressed by integrating R(m, m0 ) over the incident zenith angles: ð1 (8) A(m) 5 2 R(m, m0 )m0 dm0 . 0

The effective emissivity of an isothermal nonclear layer with temperature t is defined as the outgoing emission divided by the blackbody emission at the same temperature: E(m) 5

I(m) . B(t)

(9)

We use the DISORT to simulate I by assuming a scattering and emitting medium but removing the incoming radiance [Y at the layer boundaries. The derivative of teff ,s is similar to [Y [Y that of teff,g . Additional information about the teff ,s can be found in Wang et al. (2011, 2013b). The LUTs for scattering layers are computed for 16 incident angles and/or viewing angles, 40 optical thickness values (at 0.64 mm), and 18 particle size distributions (see Table 1 for details). Figure 2 is a schematic illustration of an atmosphere with M discretized clear and scattering layers. Three scattering layers are located at layers i, j, and k. The terms Ii21 and Fi21 indicate the radiance and flux at the top of the ith layer. The upward and downward arrows indicate the radiance or flux directions. For example, I0Y (m) indicates the downward radiance at the TOA with

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TABLE 1. Optical thickness and particle size for water cloud, ice cloud, and mineral dust aerosol selected in the LUTs.

Layer type Water cloud

Ice cloud

Mineral dust aerosol

16 viewing/incident angles (cosine)

40 optical thicknesses (0.64 mm)

18 particle size distributions (mm)

0.994 70 0.972 29 0.932 82 0.877 70 0.808 94 0.729 01 0.640 80 0.547 51 0.452 49 0.359 20 0.270 99 0.191 06 0.122 30 0.067 18 0.027 71 0.005 30

0.01, 0.03, 0.05, 0.10, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10, 12, 15, 20, 25, 30, 50

Gamma distribution Effective variance: 0.1 Effective diameter: 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 48, 56, 64, 72, 80, 90, 100 Gamma distribution Effective variance: 0.1 Effective diameter: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180 Bi-lognormal size distribution Fine mode: 0.4 Fine standard deviation: 1.0 Coarse mode: 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4 Coarse standard deviation: 1.0

[ the cosine of the zenith angle m, and FM is the upward flux at the surface. In the thermal IR region, gas molecules absorb and emit energy with negligible scattering; thus, the clearlayer optical properties are determined by the optical [Y thickness t and the effective temperature teff ,g . Therefore, for an arbitrary clear layer x, the downward radiance at the bottom of the layer can be expressed as t g,x t g,x Y Y Y 1Ix21 (m)exp 2 . Ix (m)5B(teff,g,x ) 12exp 2 m m

(10) The first term on the right-hand side of Eq. (10) is the emission contribution; whereas, the second term is the directly transmitted radiance from the top of layer x. For a scattering layer, the scattering contribution needs to be considered in addition to the thermal emission and direct transmission. The radiative transfer processes within a scattering layer can be described in terms of the four LUTs. For example, the downward radiance at the bottom of scattering layer i can be expressed as ti Y Y Y Ii (m) 5 B(teff,s,i )E(ti , Deff,i , m) 1 Ii21 (m) exp 2 m ð1 F [ A (m) Y 1 2 Ii21 (m0 )Gi (m, m0 )m0 dm0 1 i i , p 0 (11) where Deff is the particle effective size (see definition in section 3). The third term on the right-hand side of

Eq. (11) is the diffusely transmitted radiance, and the final term represents the reflection of upward radiation from the lower atmosphere. Consequently, the downward flux at the bottom of an arbitrary layer x can be written as FxY 5

ð 2p ð 1 0

0

IxY (m)m dm df .

(12)

With the boundary condition that I0Y (m) 5 0 in the thermal IR region, the downward radiance and flux can be derived from Eqs. (9)–(12) at each atmospheric level. The upward radiance at the bottom of an arbitrary layer is contributed by the transmission, emission, and reflection of the lower layers. For a clear layer x where the scattering effect can be neglected, the upward radiance at the bottom of the x 2 1 layer is in a form similar to Eq. (10): t g,x t g,x [ [ [ (m) 5 B(teff ) 12 exp 2 (m) exp 2 1 I . Ix21 x ,g,x m m (13) If a scattering layer (e.g., the ith layer in Fig. 2) is considered, the upward radiance at the top of the ith layer [ ) is expressed as (e.g., Ii21 ti [ [ [ Ii21 (m) 5 B(teff )E(t , D , m) 1 I (m) exp 2 i ,s,i i eff ,i m ð1 Y F A (m) 1 2 [Ii[ (m0 )Gi (m, m0 )] dm0 1 i21 i . p 0 (14)

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FIG. 2. Illustrative diagram for a discretized atmosphere, including three scattering layers.

Similarly, the upward flux at the bottom of an arbitrary layer x can be written as ð 2p ð 1 Fx[ 5 Ix[ (m)m dm df . (15) 0

0

The lower boundary condition can be expressed as [ IM 5 B(ts )(1 2 As ) 1

Y FM As , p

(16)

where ts and As are the surface temperature and albedo. Using Eqs. (10)–(16) with the precomputed LUTs, the RTM efficiently simulates radiances at 32 zenith angles (16 upward and 16 downward) and flux at any given altitude within a plane-parallel atmosphere. Furthermore, radiances can be calculated at user-defined viewing angles using an exponential interpolation.

3. Absorption properties of atmosphere and scattering properties of cloud and aerosol particles A precomputed database is used to simulate clear-sky optical thickness (Wang et al. 2013a). The database

stores gas transmittances at a 0.1-cm21 spectral resolution, which are integrations of monochromatic transmittances calculated with the rigorous line-by-line radiative transfer model (LBLRTM) (Clough et al. 2005) for major absorptive gases such as H2O, CO2, and O3. Specifically, transmittances of H2O and O3 are functions of gas concentration, air temperature, and pressure, whereas O2 and CO2 are considered wellmixed gases with fixed concentrations of 0.209 3 106 and 385 ppmv, respectively. We wish to emphasize that calculations of transmission, scattering, and emission of multiple layers are quite accurate at monochromatic wavelengths. However, equations and formulations shown in section 2 are based on a 0.1-cm21 spectral resolution. Within a narrow spectral interval, an implicit assumption is that the gas absorption, the optical properties of atmospheric particles, and the Planck function have little variations. The assumption is true for the Planck function and the atmospheric particle optical properties, which smoothly vary in the thermal infrared region. For absorptive gases, however, the assumption

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becomes problematic. Wang et al. (2013b) compared narrowband clear-sky transmittance values that are integrals of transmittance with three different spectral intervals: quasi monochromatic (0.001 cm21), 0.1 cm21, and 1.0 cm21. The 0.1-cm21 spectral interval was found to have only a 0.1% relative error, while the 1.0-cm21 interval had a 4% relative error. Therefore, the 0.1-cm21 spectral interval, which maintains reasonable accuracy in the simulations, can be applied to current highspectral-resolution sensors, such as the Atmospheric Infrared Sounder (AIRS) (Aumann et al. 2003) with an averaged 1.5-cm21 full width at half maximum (FWHM) near 1000 cm21 and the Infrared Atmospheric Sounding Interferometer (IASI) (Blumstein et al. 2004) with a fixed 0.5-cm21 FWHM between 645 and 1210 cm21. In addition, the model can be applied to various narrowband imagers by considering instrument spectral response functions (SRF). However, limitations in the current clear-sky database model are obvious. For example, calculations at thousands of 0.1-cm21 spectral grids are required in order to simulate observations in a single narrow band, because IR narrow bands always span several hundred wavenumbers. Furthermore, the 0.1-cm21 spectral interval may lead to larger errors in strongly absorptive bands, such as the CO2 vibrational band (600–700 cm21) and the water vapor vibrational– rotational band (1300–2000 cm21). The single-scattering properties of cloud and aerosol particles are fundamental to the RTM for scattering atmospheres. Numerous methods have been developed to simulate the single-scattering properties (e.g., the extinction efficiency, single-scattering albedo, and phase function) of spherical and nonspherical particles (e.g., Mishchenko et al. 2000; Bi et al. 2009a,b; Liu et al. 2013; Bi and Yang 2014). For water cloud, the classic Lorenz– Mie theory (Bohren and Huffman 2008) is used to calculate the single-scattering properties of liquid water droplets in a wide size range. The assumed water cloud particle size distribution is the gamma size distribution (Mishchenko et al. 2002) with an effective variance of 0.1. The effective water cloud particle size varies from 2 to 100 mm (see Table 1). The effective particle size is defined as follows (Hansen and Travis 1974; Foot 1988): ðD

max

3

(D/2) n(D) dD

D

Deff 5 ð Dmin

max

Dmin

2

(D/2) n(D) dD

ðD

max

3 D 5 ð Dmin 2 max

V(D)n(D) dD , A(D)n(D) dD

Dmin

(17) where D is the maximum dimension of a cloud particle (water droplet diameter), V indicates the droplet volume,

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A is the projected area, and n(D) is the size distribution. More challenges exist in the modeling of ice crystals and aerosols because of their nonspherical morphologies (Heymsfield 1975; Heymsfield et al. 2002). The latest single-scattering databases for nonspherical ice crystals and dust particles respectively developed by Yang et al. (2013) and Meng et al. (2010) are used in this study to model ice cloud and mineral dust aerosol layers. The single-scattering properties of ice crystals are generated by using a combination of two numerical approaches: the Amsterdam discrete dipole approximation (ADDA) (Yurkin and Hoekstra 2011) and the improved geometric optics method (IGOM) (Yang and Liou 1996; Bi et al. 2009a). Specifically, the ADDA is employed if the particle size parameter x is smaller than 20, while the IGOM is utilized if x is larger than 20. Here x is defined as x5

2pr , l

(18)

where r is the radius of a particle and l is the wavelength. The ice cloud bulk-scattering properties can be generated by integrating the single-scattering properties over the full range of sizes and habits based on ice particle size and habit distributions (Baum et al. 2005, 2011). Previous studies have shown the advantage of assuming severely roughened aggregates of ice solid columns to be an optimal ice particle morphology for ice cloud models (Holz et al. 2011). Based on the assumption, ice cloud microphysical properties generally match in situ observations, and most importantly, RTM simulations and corresponding cloud optical property retrievals are consistent in different spectral regions and between the intensity and polarization simulations (Holz et al. 2011; Cole et al. 2013). In this study, severely roughened aggregates of ice solid columns, whose sizes are specified in terms of a gamma distribution associated with an effective variance of 0.1, are used to generate ice cloud bulk-scattering properties with Deff varying from 10 to 180 mm. Meng et al. (2010) generated a single-scattering property database for triaxial ellipsoidal mineral dust aerosols. Four numerical methods—the Lorenz–Mie theory (Bohren and Huffman 2008), the T-matrix method (Mishchenko et al. 1997), the ADDA (Yurkin and Hoekstra 2011), and the improved IGOM (Yang et al. 2007; Bi et al. 2009a)—are utilized to cover a wide size parameter range from 0.025 to 1000 and a wide aspect ratio range. In the database, the real part of the mineral dust aerosol refractive index varies from 1.1 to 2.1, and the imaginary part varies from 0.0005 to 0.5. To calculate the bulk-scattering properties of mineral dust particles, we assume a bilognormal size distribution and

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FIG. 3. Comparisons between the fast RTM and the 32-stream DISORT for a typical midlatitude summer atmosphere with two ice cloud layers. The upper ice cloud (CTH 5 12.5 km, t 5 1.0) consists of small ice crystals with Deff 5 30 mm. The lower cloud (CTH 5 7.5 km, t 5 2.0) has more large particles with Deff 5 50 mm. The surface temperature is 299 K and the surface albedo is 0.05 throughout the IR region. The viewing zenith angle is 20.08. (left) The fast model (black solid line) and 32-stream DISORT (red dashed line) (a) simulated TOA BTs, (c) upward flux at TOA, (e) downward flux at the surface, and (g) upward flux at the bottom of the upper ice cloud. (right) Simulation errors of the fast model and the DISORT in terms of (b) TOA BT errors, and (d),(f),(h) relative flux errors.

specific aspect ratios and, as described by Otto et al. (2007), use an averaged mineral dust aerosol refractive index spectrum.

4. Model comparisons In one run, the present fast RTM simulates radiances/ fluxes with a high-spectral resolution at arbitrary altitudes and directions (for radiances). The fast RTM is evaluated in comparison with the reference 32-stream DISORT in terms of numerical accuracy and computational time. A typical midlatitude summer atmosphere (McClatchey et al. 1972) with a surface temperature of 299 K is used to conduct the comparisons. The atmosphere is separated into 80 layers with a 0.5-km thickness from the surface to 30 km and a 1-km thickness for the

upper atmosphere. The clear-sky optical thickness values for each clear layer are precalculated by using the LBLRTM (Clough et al. 2005) and are used as input for both the fast RTM and DISORT. Figure 3 compares the simulations associated with multiple ice cloud layers from the fast model and the 32-stream DISORT. An upper ice cloud consisting of small ice particles (Deff 5 30 mm) with optical thickness 1.0 and cloud-top height (CTH) of 12.5 km and a lower ice cloud consisting of large ice crystals (Deff 5 50 mm) with optical thickness of 2.0 and CTH of 7.5 km are used. A Lambertian surface with an albedo of 0.05 is assumed in the calculation. The left column of Fig. 3 shows the two model simulations of TOA BT at a 208 viewing zenith angle, the TOA upward flux, the downward flux at the surface, and the upward flux at the higher ice cloud

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FIG. 4. Comparisons between the fast RTM and the 32-stream DISORT. An upper ice cloud (CTH 5 12.5 km, Deff 5 30 mm, t 5 1.0) and an underlying water cloud (CTH 5 5 km, Deff 5 24 mm, t 5 5.0) are assumed in the model atmosphere. The other conditions are as in Fig. 3.

bottom, respectively. The right column of Fig. 3 shows simulation errors of the fast RTM in terms of BT difference and relative flux errors. Under multilayered ice cloud conditions, the TOA BT errors of the fast RTM are generally smaller than 0.1 K, and the relative errors of the simulated flux on different levels are limited to 0.3%. Figure 4 is similar to Fig. 3 but shows comparisons between the two models for a scene consisting of a high cirrus cloud (t 5 0.5, Deff 5 30 mm, CTH 5 12.5 km) above an optically thick water cloud (t 5 5, Deff 5 24 mm, CTH 5 5 km). Note that in the first case, the lower cloud consists of relatively large ice crystals with a Deff of 50 mm, and in the second case, Deff of the lower water cloud layer is 24 mm, which results in a higher cloud albedo and larger reflection impact. Therefore, the fast model simulated upward fluxes (Figs. 4b,d) have some biases, and the relative errors reach 0.5% at wavenumbers larger than 1100 cm21. A typical case with

a high cirrus cloud (t 5 0.5, Deff 5 30 mm, CTH 5 12.5 km) existing above a lower mineral dust aerosol layer with an optical thickness of 2.0, and an aerosol layer top height (ATH) of 2.5 km is tested (Fig. 5). The assumed full aerosol particle size distribution is contributed by two lognormal distributions including a finemode diameter of 0.4 mm and a coarse-mode diameter of 3.0 mm. The standard deviations for the two distributions are 1 mm. For small aerosol particles in comparison with the thermal IR wavelength, the aerosol optical thickness values are generally smaller than 0.2 in the spectral region between 1100 and 1300 cm21, when the 0.64-mm optical thickness is 2. In this spectral region, more emitted or reflected energy by the upper ice cloud layer can reach the surface, leading to a slight decrease in model accuracy. In conclusion, we test a more complicated scene with optically thin ice and aerosol layers and an optically thick water cloud simultaneously existing at three levels (Fig. 6). With the increase in transparent

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FIG. 5. Comparisons between the fast RTM and the 32-stream DISORT. An upper ice cloud (CTH 5 12.5 km, Deff 5 30 mm, t 5 1.0) and an underlying mineral dust aerosol layer [ATH 5 2.5 km, fine mode (specified in terms of diameter) 5 0.4 mm, coarse mode (specified in terms of diameter) 5 3.0 mm, standard deviation 5 1.0 mm, t 5 2.0] are defined in the model atmosphere. The other conditions are as in Fig. 3.

layers, the accuracy of the upward radiance simulation decreases, which may be caused by simplifications associated with cloud/aerosol-layer reflection. For this case, the TOA BT errors exceed 0.1 K in some regions and the overall BT RMSE is 0.05 K, higher than in the two cases without an aerosol layer. We also investigate the model performance when the surface is more reflective. Figure 7 shows the comparisons between the two models with a surface albedo of 0.1. The other model inputs are the same as the ones used to plot Fig. 4. Figure 7g shows the comparison between the upwelling fluxes at the bottom of the lower water cloud. Increasing the surface albedos seems to have little impact on the model accuracy. We also compare the computational time for 100 runs by the two models using a single 2.93-GHz CPU on a Linux sever. For the single-cloud-layer case, the DISORT takes 28 522 s, while the fast RTM takes only 2.7 s, more than 10 000 times faster than the DISORT. With an increase in the number of cloud and aerosol

layers, the computational time of the DISORT does not significantly increase: however, the computational time of the fast RTM is almost doubled in the two-layer case (4.6 s) and tripled in the three-layer case (6.6 s), suggesting that the fast RTM spends most of the computational time in conjunction with scattering layers. Generally speaking, the fast RTM is four orders of magnitude faster than the DISORT under singlescattering-layer conditions and three orders of magnitude faster under multiple-scattering-layer conditions. Note that simulations related to a specific sensor can be performed by integrating SRF-weighted results. More importantly, the current model can be combined with various clear-sky models designed for specific sensors, such as the correlated-k distribution (CKD) method (e.g., Kratz 1995; Shi et al. 2009), the principal component method (Liu et al. 2006), and the clear-sky module of the community radiative transfer model (Han et al. 2006). For example, instead of conducting

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FIG. 6. Comparisons between the fast RTM and the 32-stream DISORT. Three scattering layers are specified in the model atmosphere. The upper ice cloud (CTH 5 12.5 km) and lower water cloud (CTH 5 2.0 km) have the same properties as the ice and water clouds in Fig. 4. The aerosol layer (ATH 5 3.5 km) has the same properties as in the aerosol layer in Fig. 5. The other conditions are as in Fig. 3.

simulation at a 0.1-cm21 spectral resolution, the CKD method reduces computational burden by providing several gas transmittance profiles with different weightings for a specific band. With a CKD clear-sky module, only a small number of forward computations are required to calculate radiances by using different weighted transmittance profiles and cloud–aerosol LUTs. Note, SRF can be incorporated into the CKD method (Edwards and Francis 2000). The band-based simulation can be averaged with these radiances and CKD weightings, which significantly reduces computational time for applications to remote sensing with observations by high-spectral sensors such as the AIRS, and by narrowband sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Visible Infrared Imaging Radiometer Suite (VIIRS). With these advantages, the present cloud–aerosol module can be applied to various remote sensing implementations.

5. Model applications With the highly accurate and computationally efficient RTM, various remote sensing applications in realistic atmospheres are expected. In this section, we demonstrate the present RTM’s capability for cloud property retrieval and cloud radiative forcing studies involving a multiple-cloud-layer atmosphere. A cloudy case off the western coast of South America on 10 August 2008 (around 0710 UTC, local nighttime) is presented. Collocated Aqua MODIS observations (MYD02 Level 1B), CloudSat 2B-GEOPROF-lidar product (version 004), and CloudSat 2B-CLDCLASSlidar product (version 1.0) are used to conduct the case study (both CloudSat products are available from http:// www.cloudsat.cira.colostate.edu/dataHome.php). Lidar is a powerful, active instrument with inherent advantages in optically thin cloud detection. However, the lidar backscattering signals attenuate rapidly with the

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FIG. 7. Comparisons between the fast RTM and the 32-stream DISORT. The surface albedo is 0.1. The other conditions are as in Fig. 4. (g) Upwelling fluxes at the bottom of the lower water cloud simulated by the fast RTM and the DISORT and (h) the corresponding fast RTM errors.

increase of t and cannot penetrate optically thick clouds with t larger than 3 (Sassen and Cho 1992; Protat et al. 2006). In contrast, radar signals always miss very thin cirrus clouds but are able to penetrate optically thick clouds that are opaque to lidar (Comstock et al. 2004). Therefore, the Cloudsat 2B-GEOPROF-lidar product incorporated both the CALIPSO lidar and CloudSat radar-detected cloud-layer boundary information to provide full vertical atmospheric column structures. The CloudSat 2B-CLDCLASS-lidar product provides the thermodynamic phase of each layer. Figures 8a and 8b show cloud boundary altitudes and temperatures along the CALISPO/CloudSat track, respectively. In the region of interest, the CALIPSO track ranges from 58N, 808W to 48S, 838W. The cloud scenes are complicated: warm and broken lower-level water clouds (red) are covered by a cold, high-level ice cloud layer (blue) located between 10 and 16 km. The clear-sky profiles are extracted from a 3-h instantaneous National Aeronautics

and Space Administration (NASA) Global Modeling and Assimilation Office (GMAO) Modern-Era Retrospective Analysis for Research and Applications (MERRA) product (Rienecker et al. 2008). The ocean surface emissivity values throughout the spectral region are assumed to be a constant: 0.98. First, we apply a simple retrieval method to estimate cloud optical thickness values with the assumed effective diameter values of a lower-level water cloud; specifically, the lower water cloud has droplets with a constant effective diameter of 20 mm. We need to emphasize that the present study is focused on the RTM, rather than on the retrieval technique. In the future, sophisticated retrieval methods can be developed, based on the present RTM, to simultaneously retrieve the microphysical and optical properties of both ice and water clouds. By using different ice cloud t ice (varying between 0.1 and 10), Deff,ice (10– 150 mm), and water cloud t wat (1.0–5.0) combinations, the RTM calculates TOA BTs at a 0.1-cm21 spectral

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longwave radiative forcing (CRFice) spectra with the present RTM and retrieved cloud properties. The TOA longwave CRFice,n is defined as the difference between the TOA OLRs with and without the upper-level ice cloud: CRFn 5 OLRwithout_ice,n 2 OLRwith_ice,n .

FIG. 8. A multiple-cloud-layer case study using the collocated MODIS, CALIPSO, and CloudSat data on 10 Aug 2008. (a) The lidar- and radar-detected cloud boundaries (top and base) of the upper ice cloud (blue) and lower water cloud (red). (b) The cloud boundary temperatures and the MODIS-observed 11-mm BTs. (c) Comparisons between CALIPSO t and RTM-retrieved t. (d) The RTM-simulated TOA ice CRF (integrated from 700 to 1300 cm21) using retrieved cloud properties.

resolution and subsequently simulates MODIS observations at bands 29, 31, and 32 (8.5, 11, and 12 mm) with the MODIS SRFs. The appropriate t ice–Deff,ice–t wat combination, in which the simulations are closest to the MODIS observations, is recorded. Figure 8c shows the CALIPSO optical thickness values for both ice (blue) and water (red) clouds, as well as the RTM-based retrievals for ice (black) and water (green) clouds. Although the RTM-based retrievals differ from their CALIPSO counterparts in some regions if cloud boundaries have obvious variations (e.g., latitudes 48– 58N, 08–18N, and 18–28S), the two cloud t products are consistent when the cloud boundaries are at approximately the same height. By trapping upwelling emission from the surface and lower atmospheric and emitting energy at a colder temperature, clouds significantly reduce the OLR. To better understand the radiative impact of clouds on climate, analyzing cloudy-sky OLRs is important. In our case study, we analyze TOA ice cloud instantaneous

(19)

The spectrally integrated (from 700 to 1300 cm21) TOA CRFice values are shown in Fig. 8d. The figure illustrates the dependence of the TOA CRFice on the ice cloud properties and the existence of a lower-level water cloud. The ice cloud forcing is weak if t ice is small (e.g., latitudes 08–18N). In single-layer ice cloud scenes (e.g., latitudes 48–58N), the TOA CRFice is large because of the significant temperature difference between the surface and the ice cloud. The existence of water cloud (e.g., latitudes 18–28N) also decreases the TOA CRFice by reducing the first term on the right-hand side of Eq. (19). Figure 9 shows the spectral breakdown of the TOA upwelling flux with and without the ice cloud layer (left column) and corresponding TOA CRFice spectra (right column) of three typical profiles with latitudes at 4.68, 2.28, and 1.08N, respectively. Note that the present work does not study the entire longwave emission region, but the longwave CRF is dominated by the IR window CRF (Huang 2013). Furthermore, many other clear-sky transmission models (e.g., the CKD method) can be used to substitute for the present clear-sky module, enhancing the flexibility of the model in theoretical studies and practical applications.

6. Summary Based on a hybrid method, we develop an IR RTM to consider scattering-layer reflection and transmission. Since the reflection effect of a scattering layer is much smaller than the transmission and emission in the thermal IR spectral region, we generate local albedo LUTs for different scattering layers. The use of local albedo LUTs assumes an isotropic incident field rather than fully considering the directional variance of the incident radiance. Furthermore, higher orders of scattering-layer reflection are neglected to increase the computational efficiency without significantly reducing accuracy. Radiance that transmits diffusely through a scattering layer is calculated using the bidirectional transmissivity LUT, which, for higher accuracy, fully considers the zenith dependence of the incident field. Comparison against a reference model, the 32-stream DISORT, shows that the fast model RMSE of TOA BTs are generally smaller than 0.05 K, and the relative flux errors for atmospheres with multiple scattering layers

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FIG. 9. (a)–(c) Spectral breakdown of TOA upwelling flux with and without the ice cloud layer and (d)–(f) corresponding TOA ice CRF of three typical profiles near 4.68, 2.28, and 1.08N. The spectrally integrated TOA ice CRFs are 82.5, 28.6, and 9.2 W m22, respectively.

are less than 1%. Furthermore, the fast model is more than 10 000 times faster than the DISORT for singlelayer scenes and over 6000 and 4000 times faster than the DISORT for two- and three-layer scenes. The present fast RTM is much more flexible than its counterpart described in Wang et al. (2013b). In the previous RTM, TOA radiance is the only output applicable to satellite-based remote sensing. The new version calculates radiances and fluxes at arbitrary levels and in various directions, resulting in a wider variety of applications. For example, this model can be applied to the simulations of measurements from space, the surface, or any location within the atmosphere. Furthermore, the model capability is significantly enhanced, allowing the simultaneous occurrence of three different types of scattering layers (ice cloud, water cloud, and mineral dust aerosols) in an atmospheric column. Atmospheres consisting of more complicated scattering layers can be simulated and retrieved. By replacing the current clear-sky transmittance module with other clear-sky modules designed for specific sensors or broad bands,

the computing time of the RTM can be reduced by a factor of 10 for high-spectral sensors, such as the AIRS, and by a factor of several hundred for narrowband sensors, such as the MODIS and the VIIRS. With its flexibility, accuracy, and computational efficiency, the present IR RTM has the potential to be applied not only to atmospheric radiative transfer simulation and remote sensing implementations, but also to the data assimilation in operational NWP systems and cloud– aerosol–gas radiative forcing studies. A limitation of the present model is the fixed 0.1-cm21 spectral resolution, which leads to relatively large errors in strongly absorptive bands, such as the CO2 band (600–700 cm21) and the H2O band (1300–1600 cm21). However, as described in section 4, it is convenient to replace the present clear-sky module with other models that perform better for spectral bands with strong absorption. Acknowledgments. This study was partly supported by NASA grants (NNX12AL90G and NNX11AK37G) and the endowment funds related to the David Bullock

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