Evaluation of Hydrometeor Phase and Ice Properties in Cloud-Resolving Model Simulations of Tropical Deep Convection Using Radiance and Polarization Measurements

Bastiaan van Diedenhoven Center for Climate System Research, Columbia University, and NASA Goddard Institute for Space Studies, New York, New York

Search for other papers by Bastiaan van Diedenhoven in
Current site
Google Scholar
PubMed
Close
,
Ann M. Fridlind NASA Goddard Institute for Space Studies, New York, New York

Search for other papers by Ann M. Fridlind in
Current site
Google Scholar
PubMed
Close
,
Andrew S. Ackerman NASA Goddard Institute for Space Studies, New York, New York

Search for other papers by Andrew S. Ackerman in
Current site
Google Scholar
PubMed
Close
, and
Brian Cairns NASA Goddard Institute for Space Studies, New York, New York

Search for other papers by Brian Cairns in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

Satellite measurements are used to evaluate the glaciation, particle shape, and effective radius in cloud-resolving model simulations of tropical deep convection. Multidirectional polarized reflectances constrain the ice crystal geometry and the thermodynamic phase of the cloud tops, which in turn are used to calculate near-infrared reflectances so as to constrain the simulated ice effective radius, thereby avoiding inconsistencies between retrieval algorithms and model simulations. Liquid index values derived from Polarization and Directionality of the Earth’s Reflectances (POLDER) measurements indicate only ice-topped clouds at brightness temperatures (BTs) lower than −40°C, only liquid clouds at BT > −20°C, and both phases occurring at temperatures in between. Liquid index values calculated from model simulations generally reveal too many ice-topped clouds at BT > −20°C. The model assumption of platelike ice crystals with an aspect ratio of 0.7 is found consistent with POLDER measurements for BT < −40°C when very rough ice crystals are assumed, leading to an asymmetry parameter of 0.74, whereas measurements indicate more extreme aspect ratios of ~0.15 at higher temperatures, yielding an asymmetry parameter of 0.84. MODIS-retrieved ice effective radii are found to be 18–28 μm at BT < −40°C, but biased low by about 5 μm owing primarily to the assumption of pristine crystals in the retrieval. Simulated 2.13-μm reflectances at BT < −40°C are found to be about 0.05–0.1 too large compared to measurements, suggesting that model-simulated effective radii are 7–15 μm too small. Two simulations with contrasting ice nucleation schemes showed little difference in simulated effective radii at BT < −40°C, indicating that homogeneous nucleation is dominating in the simulations. Changes around −40°C in satellite observations suggest a change in cloud-top ice shape and/or size in natural deep convection possibly related to a change in the freezing mechanism.

Corresponding author address: Bastiaan van Diedenhoven, Center for Climate System Research, Columbia University, 2880 Broadway, New York, NY 10025. E-mail: bastiaan.vandiedenhoven@nasa.gov

Abstract

Satellite measurements are used to evaluate the glaciation, particle shape, and effective radius in cloud-resolving model simulations of tropical deep convection. Multidirectional polarized reflectances constrain the ice crystal geometry and the thermodynamic phase of the cloud tops, which in turn are used to calculate near-infrared reflectances so as to constrain the simulated ice effective radius, thereby avoiding inconsistencies between retrieval algorithms and model simulations. Liquid index values derived from Polarization and Directionality of the Earth’s Reflectances (POLDER) measurements indicate only ice-topped clouds at brightness temperatures (BTs) lower than −40°C, only liquid clouds at BT > −20°C, and both phases occurring at temperatures in between. Liquid index values calculated from model simulations generally reveal too many ice-topped clouds at BT > −20°C. The model assumption of platelike ice crystals with an aspect ratio of 0.7 is found consistent with POLDER measurements for BT < −40°C when very rough ice crystals are assumed, leading to an asymmetry parameter of 0.74, whereas measurements indicate more extreme aspect ratios of ~0.15 at higher temperatures, yielding an asymmetry parameter of 0.84. MODIS-retrieved ice effective radii are found to be 18–28 μm at BT < −40°C, but biased low by about 5 μm owing primarily to the assumption of pristine crystals in the retrieval. Simulated 2.13-μm reflectances at BT < −40°C are found to be about 0.05–0.1 too large compared to measurements, suggesting that model-simulated effective radii are 7–15 μm too small. Two simulations with contrasting ice nucleation schemes showed little difference in simulated effective radii at BT < −40°C, indicating that homogeneous nucleation is dominating in the simulations. Changes around −40°C in satellite observations suggest a change in cloud-top ice shape and/or size in natural deep convection possibly related to a change in the freezing mechanism.

Corresponding author address: Bastiaan van Diedenhoven, Center for Climate System Research, Columbia University, 2880 Broadway, New York, NY 10025. E-mail: bastiaan.vandiedenhoven@nasa.gov

1. Introduction

Tropical deep convection plays an important role in the climate system. The cloud net radiative forcings at the top of the atmosphere for cloud types associated with tropical convective systems can be several hundreds of watts per square meter and either positive or negative locally, although the integrated net forcing of all such clouds in the current climate may be close to zero (e.g., Hartmann et al. 2001; Kubar et al. 2007). The majority of these clouds are topped with ice, and the balance between longwave and shortwave radiative forcing by ice clouds depends in part on ice water path and the sizes and shapes of the ice constituent crystals (Stackhouse and Stephens 1991; Jensen and Toon 1994; Fu et al. 1998; Fu 2007). In addition, the temperature level at which glaciation occurs plays an important role in determining the net radiative forcing of such cloud systems since it affects convective dynamics and, ultimately, cloud macrophysical properties (Fowler et al. 1996; Baker 1997). Incomplete understanding of ice formation processes that govern the glaciation temperature, ice water path, and crystal sizes and shapes, as well as their interaction with atmospheric conditions and availability of ice nuclei, hampers the development of adequate parameterization of deep convective cloud systems in climate models (e.g., Fowler et al. 1996; Baker 1997; Wu et al. 2009; Heymsfield et al. 2009). To better constrain parameterizations of such clouds in climate models, detailed studies of ice formation processes using cloud-resolving model (CRM) simulations and observational constraints are needed (e.g., Moncrieff et al. 1997; Bechtold et al. 2000; Fridlind et al. 2004; Fan et al. 2010; Varble et al. 2011; Fridlind et al. 2012a).

Intensive field campaigns have provided a wealth of in situ measurements that can be used to constrain and evaluate cloud-resolving model simulations of tropical convective cloud systems to some extent (e.g., Brown and Heymsfield 2001; Fridlind et al. 2004; Wang et al. 2009b; Fan et al. 2010). However, some important diagnostics related to ice formation processes, such as ice crystal size and glaciation temperature, remain uncertain owing to the lack of in situ measurements in strong updraft regions, commonly poor spatiotemporal coverage of cloud sampling throughout, and issues associated with shattering of large ice crystals on aircraft probe inlets (e.g., Cober et al. 2001; Lawson et al. 2010; Korolev et al. 2011). For instance, previous studies using detailed cloud-resolving model simulations (e.g., Phillips et al. 2007; Fan et al. 2010) show that the choices between currently proposed homogeneous and heterogeneous freezing parameterizations significantly affect the simulated anvil macrophysical properties, such as anvil areal extent and convective strength, and microphysical properties, such as ice number concentrations and sizes, but that results could not be sufficiently constrained by the available in situ measurements.

Satellite remote sensing measurements have more extensive coverage than in situ measurements and obviously avoid in situ probe challenges, but radiances measured by satellite instruments are often not uniquely related to the physical parameters of interest. To extract microphysical quantities from remote sensing measurements, retrieval algorithms, including many a priori assumptions, are necessary, which often leads to retrieval products that are not straightforward to interpret. For instance, owing to the assumption of vertically uniform cloud layers in cloud particle effective radius retrieval algorithms and uncertainties in photon penetration depth estimates, it is not obvious to what cloud depth a retrieved effective radius pertains (Nakajima and King 1990; Rolland et al. 2000; Yang et al. 2001; Platnick 2000; Zhang et al. 2010). Assumptions about ice crystal shapes and small-scale surface roughness have also been shown to stongly influence the retrieved cloud optical thickness and effective radius (Yang et al. 2008a; Zhang et al. 2009, 2010). Finally, cloud phase retrieval algorithms generally classify clouds either as liquid or ice, but generally perform poorly over mixed-phase clouds and cloud consisting of separate ice and liquid layers (Nasiri and Kahn 2008; Cho et al. 2009; Riedi et al. 2010), which hampers robust retrievals of cloud properties in such cases.

Increasing attention has been given recently to the direct forward modeling of remotely sensed quantities based on numerical simulations, for instance, to evaluate the simulated cloud properties by directly comparing the forward-modeled and real measurements (e.g., Ringer et al. 2003; van Diedenhoven et al. 2009; Masunaga et al. 2010; Inoue et al. 2010; Grasso et al. 2010; Grasso and Lindsey 2011; Bodas-Salcedo et al. 2011). This approach allows partial circumvention of possible uncertainties associated with differences between (i) the a priori assumptions made in the remote sensing retrieval process and (ii) the cloud properties assumed in and/or produced by the cloud model, such as vertical profiles, particle size distributions, and ice crystal habits. This approach can also help increase our understanding of satellite retrieval products and how they might be improved (e.g., Zinner et al. 2010; Zhang et al. 2010).

In this paper we investigate how glaciation temperature and ice crystal sizes produced by detailed cloud-resolving model simulations of tropical deep convection can be evaluated with satellite observations. We combine data from the Polarization and Directionality of the Earth’s Reflectances (POLDER) instrument and the Moderate Resolution Imaging Spectroradiometer (MODIS) to obtain collocated information about thermodynamic phase and ice crystal size and shape as a function of cloud-top temperature. Using forward-modeled total and polarized reflectances, we explore how the thermodynamic phase and ice crystal size information are related to quantities computed from the model results. Thus, we establish a framework that can be used to evaluate glaciation temperatures and ice crystal sizes predicted by a cloud model. In addition, we demonstrate some of the merits and shortcomings of using retrieved effective crystal size to evaluate model simulations.

After describing the forward model in section 2, the cloud-resolving model simulations in section 3, and the data in section 4, we present results in section 5 and conclusions in section 6.

2. Forward model

The cloud-resolving model (CRM) simulations analyzed in this paper are made with the Distributed Hydrodynamic Aerosol-Radiation-Microphysics Application (DHARMA) (Ackerman et al. 1995; Fridlind et al. 2007, 2012b; see section 3), which includes binned microphysics with 36 particle size bins. The forward calculations from CRM fields are performed using a plane-parallel doubling-adding code (Hansen and Travis 1974; De Haan et al. 1987) for the visible and near-infrared wavelengths. Complex refractive indices for ice and liquid water are taken from Warren and Brandt (2008). The refractive indices are weighted by the instrument spectral response functions and the incoming solar spectrum. To account for the highly peaked scattering phase functions, we use the δ-M approximation (Wiscombe 1977) for multiply-scattered light, whereas the contribution of single-scattered light is calculated analytically [using the TMS method described by Nakajima and Tanaka (1988)]. The weak water vapor absorption in the 2.13-μm band is accounted for using correlated-k distributions (Lacis and Oinas 1991).

For thermal infrared (11 μm) brightness temperature (BT) calculations, the two-stream code in DHARMA is used (Toon et al. 1989). The computed fluxes are converted to brightness temperatures assuming an anisotropic factor of 1.03, representing thick high clouds (Loeb et al. 2003). Longwave anisotropic factors for high clouds range from about 1 to 1.1, depending on cloud emissivity and observation geometry (Loeb et al. 2003, 2005), which translates into an uncertainty in computed brightness temperature of about 4 K. For the 11-μm brightness temperature simulations, the ice optical properties are represented by a collection of spheres that have the same total volume and surface area as the ice, obtained by adjusting the number of particles (Grenfell and Warren 1999; Neshyba et al. 2003). The optical properties for these spheres are obtained using Lorenz–Mie theory (Mie 1908). This method was shown to be accurate to within a few kelvin for ice clouds at infrared wavelengths (Fu et al. 1999; Neshyba et al. 2003).

The shortwave optical properties for spherical liquid drops are computed using Lorenz–Mie theory and are integrated over the DHARMA size bins using a uniform distribution within each bin. Obtaining appropriate optical properties for nonspherical ice crystals at visible and near-infrared wavelengths is less straightforward, given the strong sensitivity to crystal shape at these wavelengths and the myriad of naturally occurring ice crystal shapes (Baran 2009). In clouds associated with tropical deep convection, ice crystals are generally observed to be either irregular or resembling aggregates of plates with various configurations (Um and McFarquhar 2009; Baran et al. 2011). The morphology of small (D < 60 μm) particles is highly uncertain (Um and McFarquhar 2009; Baran 2009; Um and McFarquhar 2011; Nousiainen et al. 2011), though small particles can contribute significantly to integrated ice optical properties (e.g., Cooper and Garrett 2010; Protat et al. 2011). However, optical properties of ice crystals are dominated by their projected area, volume, small-scale surface roughness, and the aspect ratio of their components, with other shape characteristics having minor roles (Mitchell et al. 1996; Fu et al. 1998; Fu 2007; Um and McFarquhar 2009). Specifically, the extinction and absorption cross sections of ice crystals are determined mainly by their volume and projected area (Fu et al. 1998; Mitchell 2002), while the scattering phase matrices are dominated by the aspect ratio and small-scale surface roughness of the ice crystal components (Macke et al. 1996; Fu 2007; Yang and Fu 2009). Ice crystal projected area and volume and the aspect ratio of the crystal components are also the key parameters governing fall speeds, and capacitances, which, in turn, determine growth, evaporation, and sedimentation rates of ice crystals (Böhm 1992; Heymsfield and Iaquinta 2000; Westbrook et al. 2008; Westbrook 2008). [Although fall speeds and capacitances are usually related to ice crystal mass instead of volume, bulk volume V is directly related to mass m via V = m/ρi, where ρi is the density of solid ice (Mitchell 2002).]

Here we use these facts to compute optical properties that are consistent with the DHARMA ice microphysical properties in the following manner. For extinction and absorption cross sections, geometric optics calculations (Macke et al. 1996) are performed using equivalent hexagonal plates that match the size-dependent volume and projected area assumptions in DHARMA (see section 3). The scattering phase matrices are calculated using geometric optics calculations and a separate set of equivalent hexagonal plates that match the size-dependent projected area and aspect ratio assumptions in DHARMA. Note that, using this method, we do not assume (only) single hexagonal plates to be present in the observed clouds, but rather mixtures of complex structures with hexagonal-shaped components, and that their optical properties can be represented by equivalent hexagonal plates (cf. Fu et al. 1998; Fu 2007). We also note that although small ice crystals (D < 5 μm) are assumed to be solid spheres in DHARMA, we use hexagonal plates with an aspect ratio of unity to calculate their scattering phase matrices, as optical properties of spheres are known to be not representative of those of small ice crystals (e.g., Nousiainen et al. 2011). In section 5a we will use POLDER measurements collected during Tropical Warm Pool International Cloud Experiment (TWP-ICE) to evaluate some of these assumptions.

Small-scale surface roughness is the only parameter significantly controlling the optical properties that is not specified in DHARMA for ice microphysical processes. The geometrics optical code of Macke et al. (1996) uses a statistical distortion of the crystal facets as an efficient and realistic proxy for small-scale crystal roughness (Yang et al. 2008b). The degree of crystal distortion is indicated by the “roughness parameter” δ [see Macke et al. (1996) for its definition].

Ice crystal optical properties are calculated for maximum diameters representing the DHARMA size bin centers. Liu et al. (2012) have shown that, for ice optical properties, this approach leads to negligible errors in comparison with approaches that integrate the optical properties over size bins when more than 30 size bins are used, as is the case here.

The DHARMA simulations are run on a 0.9-km horizontal grid, whereas the combined Moderate Resolution Imaging Spectroradiometer (MODIS)–POLDER measurements used in this study are obtained on an ~6 km × 6 km grid (see section 4). The two-stream calculations for the thermal infrared (11–μm) brightness temperatures are performed on the native DHARMA grid and averaged over 7 × 7 grid points using the independent pixel approximation. To obtain the visible and near-infrared simulations with a similar resolution as the measurements, the vertical profiles of water drop and ice particle size distributions are first averaged over 7 × 7 DHARMA grid points. Compared with averaging (polarized) reflectances computed on the DHARMA native grid using the independent pixel approximation, averaging the model fields instead reduces the computational effort by a factor of nearly 50. To estimate the possible error associated with averaging before rather than after radiative calculations, we computed the 2.13-μm reflectance for 12 randomly chosen 7 × 7 blocks using the independent pixel approximation and compared the results to reflectances computed using the averaged size distributions. Differences in 2.13-μm reflectances were generally less than 8%, and were ~2% on average.

The solar zenith angle for the observations used in this study is about 22°, and scattering angles for the MODIS data range from 147° to 178°, with a mean of 158°. To be consistent with these geometries, we perform the forward simulations with a solar zenith angle of 22° and a relative azimuth angle of 0°, yielding a scattering angle of 158°. Maximum differences in 2.13-μm reflectances within the 147°–178° scattering angle range are found to be generally less than 6%, with a mean of ~3%. Since polarized reflectance is mainly determined by light with low orders of scattering, variations in the relative azimuth angle are of minor influence on it (van de Hulst 1957), and differences between observed and measured polarized reflectances owing to differences in geometry can be assumed negligible (C.-Labonnote et al. 2000; Knap et al. 2005).

3. Cloud-resolving model simulations

The DHARMA CRM simulations described in this paper are based on observations made during the TWP-ICE campaign in Darwin, Australia, in 2006 (May et al. 2008; Frederick and Schumacher 2008). Specifically, we focus on the monsoon event occurring near the Darwin Atmospheric Radiation Measurement Program (ARM) climate research facility site on 19–20 January[termed event A in Varble et al. (2011) and Fridlind et al. (2012a)], which was typical for the monsoon period during TWP-ICE.

Model initialization and forcings are taken from the specifications of a CRM intercomparison study based on TWP-ICE observations (Fridlind et al. 2010). The model domain is 176 km × 176 km × 24 km with periodic lateral boundary conditions. Horizontal grid spacing is 917 m. Vertical grid spacing is 100 m below 1.5 km, linearly increasing to 250 m between 1.5 and 3 km, uniformly 250 m between 3 and 18.5 km, and stretched above 18.5 km. Aerosol size distributions are initialized with a trimodal number size distribution profile derived from observations made between the surface and 14.5 km during the TWP-ICE active monsoon period (Fridlind et al. 2010), and assume a simplified aerosol composition of 100% ammonium bisulfate. As in the Fridlind et al. (2012a) sensitivity test, we nudge domain-mean potential temperature and water vapor concentration profiles with a 6-h time scale at all elevations above 1 km, linearly decreasing to zero nudging strength at 500 m. Since aerosol sources are not represented, we also nudge domain-mean aerosol profiles with a 6-h time scale at all elevations. Horizontally uniform nudging preserves three-dimensional structure in thermodynamic and aerosol fields. The dynamical time step varies to maintain an advective Courant number below 0.8, with a maximum length of 5 s.

Simulations employ a size-resolved (bin, spectral) microphysics scheme that imposes no size distribution assumptions on the simulated hydrometeor populations. Aerosol, water drops, and two ice particle classes are represented using 36 mass-doubling bins for number concentration and, except in the case of aerosol, for dissolved ammonium bisulfate mass. The mass of the smallest bin in the hydrometeor classes corresponds to that of a droplet with diameter 2 μm. Time substepping is employed with a minimum step of 0.2 s to locally resolve fast microphysical processes such as droplet activation and condensational growth. Following Böhm (1989, 1992), hydrometeor fall speeds are calculated based on the mass, maximum dimension, projected area, and aspect ratio assigned to each bin. To approximate the impact of ice habit on vapor deposition and sublimation rates, capacitance is calculated for oblate spheroids [Pruppacher and Klett 1997, their Eqs. (13)–(78)] with aspect ratios as specified for each bin. For several different ice crystal habits and size ranges, Mitchell (1996) reported simple power-law relationships between ice crystal maximum dimension D, mass m, and projected area Ap; that is, m = αDβ and Ap = γDσ. To obtain the relationships for the less dense (“fluffy”) ice crystal class (cloud ice and snow), coefficients and exponents of several habits from Mitchell are used at different size ranges above D = 120 μm (see Table 1). Ice crystals with maximum dimensions smaller than 5 μm are assumed to be solid ice spheres. For ice crystals with maximum dimensions in the range 5–120 μm, we use a power-law from a linear fit in log–log space between the mass of a solid sphere with D = 5 μm and the mass of assemblages of planar polycrystals with D = 120 μm. In the same manner, the ApD relation for this size range is obtained. For the dense ice class the coefficients and exponents for lump graupel cystals (R4b) reported by Mitchell (1996) are used for maximum dimension above 200 μm (see Table 2), and solid ice spheres are again assumed for maximum dimension smaller than 5 μm, and the interpolation technique described above is used to obtain the coefficients and exponents for dense ice crystals with maximum dimensions in the range 5–200 μm. Using these mD and ApD relationships and converting the mass to bulk volume via V = m/ρi allows us to relate the maximum crystal dimension D with effective dimensions for single particles, defined as deff = (3/2) V/Ap (Mitchell 2002), as shown in Fig. 1. Similar relationships between effective and maximum sizes for various crystal shapes have been reported by Yang et al. (2005).

Table 1.

Coefficients and exponents for mass- and area-dimensional power laws (see text) for the fluffy ice class used in this study. Relations are in cgs units and taken from, or based on, those from Mitchell (1996).

Table 1.
Table 2.

As in Table 1, but for the dense ice class used in this study.

Table 2.
Fig. 1.
Fig. 1.

Relationships between effective and maximum diameters assumed for the dense (dashed) and fluffy (solid) ice crystal classes. Spheres with the density of solid ice are shown for comparison (dotted).

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

The information on ice crystal aspect ratios from remote sensing and in situ measurements is rather sparse, especially for crystal shapes more complex than columns and plates. Here, we use aspect ratios based on the observations of Korolev and Isaac (2003). By analyzing numerous measurements of the cloud particle imager (CPI) instrument, they found average aspect ratios of about 0.7–0.8 for particles larger than 60 μm at temperatures between −35° and −40°C and aspect ratios closer to 1 for smaller particles. Based on their analysis, for the aspect ratio of the fluffy and dense ice with crystals with maximum dimensions larger than 120 μm, we use aspect ratios of 0.7 and 0.8, respectively. Ice crystals with maximum dimension smaller than 5 μm are assumed spherical, and between 5 and 120 μm the aspect ratios are linearly interpolated. Here the CRM uses a maximum diameter of 120 μm to transition to an aspect ratio that is constant with size, rather than the 60 mm found by Korolev and Isaac since the m–D and ApD relations also have a break point at D = 120 μm, although the forward calculations do transition to an aspect ratio that is constant with size at 60 μm. We note, however, that both the DHARMA simulations and the forward calculations were negligibly affected by this difference. Furthermore, we note that the study of Korolev and Isaac (2003) did not include tropical convective clouds, but was instead focused on midlatitude and polar stratiform clouds associated with frontal systems and temperatures warmer than −40°C. However, other in situ and lidar measurements suggest particles with aspect ratios near 1 dominate cloud tops associated with deep convection (e.g., Noel et al. 2004; Lawson et al. 2010; Nousiainen et al. 2011). Similar aspect ratios (0.65 ± 0.05) were theoretically derived for large crystal aggregates in cirrus by Westbrook et al. (2004). In section 5a, we evaluate our assumptions on aspect ratio using POLDER measurements collected during TWP-ICE.

The bin microphysics simulations here are restarted from time 36 h in a simulation with one-moment parameterized microphysics (Grabowski 1999) with full nudging (Fridlind et al. 2012b). To reduce microphysical persistence from the parameterized scheme, during the restart all ice is simply discarded, while all liquid water in each grid cell is placed in a single size bin determined by the mixing ratio and an assumed droplets concentration of 100 cm3. This restart procedure allowed spinup of the dynamics field using an inexpensive bulk microphysics scheme.

For the purposes of this study, we consider only two simulations, referred to asprognostic and diagnostic treatments. In one simulation, we use a relatively simple prognostic scheme for ice nuclei (IN) as in Fridlind et al. (2007). An IN array is initialized to a total concentration of 30 L−1 at all elevations, which is a feasible value (Meyers et al. 1997) adopted in the absence of measurements during TWP-ICE. The IN are consumed by deposition, condensation, immersion, and contact modes as described by Fridlind et al. (2007, see their Table 1 and appendix A), and the domain-mean profiles of IN concentration are nudged to the initial concentrations with a 6-h time scale to crudely account for unknown sources. In the second simulation, IN are treated using a simple diagnostic scheme as in Morrison et al. (2011). Diagnostic IN number concentration is initialized to 30 L−1 at all elevations. All IN are activated to ice crystals if the supersaturation exceeds 5% with respect to ice, and the number concentration of available IN is simply the initial concentration minus the concentration of any ice crystals present. The objective of these two simulations is simply to provide a contrast in ice nucleation treatments. In both simulations, all other processes that affect liquid and ice hydrometeors remain the same. Homogeneous aerosol and droplet freezing are represented as in Fridlind et al. (2004). Hallett–Mossop rime splintering and shattering of large droplets when freezing, and all other microphysical processes, are represented as in Fridlind et al. (2007).

Figure 2 shows horizontally averaged liquid and ice mixing ratios as a function of time modeled using the diagnostic IN and prognostic IN treatments. The figures also show horizontally averaged mean, minimum, and maximum thermal infrared (11 μm) brightness temperatures (see section 2). At the beginning of the simulations ice crystals form at temperatures lower than −4°C, resulting in mean brightness temperatures of around −35° to −25°C. These ice clouds then largely dissipate over the next 10 h, leading to mean brightness temperatures increasing to about −20°C (diagnostic IN) or −10°C (prognostic IN). This initial ice is formed owing to the high relative humidities and IN availability at the initialization of the simulations. Therefore, we consider the period before simulation time t = 43 h as model spinup and exclude it from further analysis. At around t = 43 h substantial convective cores start to develop, topped with an increasingly thicker ice top. Unfortunately, the simulations in this developing stage appear to be contaminated by cloud associated with spinup of the bin microphysics. After this period high liquid water contents appear at temperatures warmer than 0°C, and ice is produced mainly in two temperature ranges, between 0° and −20°C and between about −40° and −60°C, while the mean brightness temperature rapidly decreases to about −75°C, owing to developing deep convection. Interestingly, small amounts of supercooled liquid appear at temperatures down to about −38°C at this stage. Ice water mixing ratios peak at around t = 55 h after which they start to decrease along with the mean and especially the minimum brightness temperatures, suggesting an onset of the dissipating stage of the system. However, the full dissipating stage characterized by strongly increasing brightness temperatures (Futyan and Del Genio 2007) is not completed in these simulations because of the high computational expense. The time series of ice and liquid mixing ratios and brightness temperatures are similar using the diagnostic and prognostic IN, although the mean ice water mixing ratio values below −40°C are greater with the diagnostic approach. Also, somewhat higher mean ice mixing ratios are present in the spinup phase of the simulations using the diagnostic approach.

Fig. 2.
Fig. 2.

Domain averages of (left) liquid and (right) ice water mixing ratios as a function of simulation time and horizontal mean temperature, for simulations using the (top) diagnostic and (bottom) prognostic IN treatments. The red solid and dotted lines show the domain mean and extremes, respectively, of the simulated 11-μm brightness temperature.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

The spatial resolution and particle size bins used in these model simulations can be considered rather coarse. For this reason, and because of possible influence on the available time slices of microphysical spinup, we consider these simulations as preliminary but sufficient to demonstrate how ice formation in such CRM simulations of tropical deep convection can be evaluated with satellite observations.

4. Data

For this study we combine data from MODIS and POLDER (Fougnie et al. 2007) instruments on the Aqua and Polarization and Anisotropy of Reflectances for Atmospheric Sciences Coupled with Observations from a Lidar (PARASOL) satellite platforms, respectively, which were both in the A-train constellation during the investigated period. Aqua has a local equatorial crossing time around 1338 UTC, with PARASOL lagging 3 min behind. The swath of MODIS completely overlaps that of POLDER.

Here, MODIS level-1 2.13-μm and 11-μm radiance measurements are used as proxies for particle size and cloud-top height, respectively. The 11-μm radiance measurements are converted to brightness temperatures for an equivalent blackbody source. MODIS level-2 retrievals (collection 5) of ice crystal effective radius and optical thickness are also used (Platnick et al. 2003; King et al. 2004; Baum et al. 2005b). The 1.6-μm and 3.7-μm channels are also sensitive to particle size (Rolland et al. 2000; Minnis et al. 2011), but are not used in this study because of shortcomings in the MODIS–Aqua 1.6-μm channel and to avoid complications owing to the presence of thermal emission in the 3.7-μm channels. Moreover, the 2.13-μm channel is also used in the standard collection five retrieval product analyzed in this study. We use polarization measurements from POLDER to obtain information on thermodynamic cloud phase (cf. Goloub et al. 2000). Furthermore, we use POLDER polarization measurements to evaluate the ice crystal geometry assumed in the model simulations and radiative transfer calculations (cf. C.-Labonnote et al. 2000; Knap et al. 2005; Baran and C.-Labonnote 2006; Baran 2009; Ottaviani et al. 2012).

The MODIS measurements have a spatial resolution of about 1 km at nadir, while POLDER measurements are provided on an ~6 km × 6 km grid (Bréon 2006; Fougnie et al. 2007). To obtain combined MODIS and POLDER measurements, here we average all MODIS measurements and products for which the pixel center is within the corresponding POLDER pixel boundaries. Only pixels with centers within 5° of Darwin, Australia (12°30′S, 131°53′E), and with a land fraction lower than 5% are selected. The data is not filtered by cloud fraction. All combined POLDER and MODIS data obtained in the active monsoon phase (16–25 January 2006) and that comply with the selection criteria described above are included. Nearly 14 000 combined MODIS–POLDER pixels are selected. The diurnal cycle of maritime tropical convection is relatively weak (e.g., Yang and Slingo 2001). Hence, by collecting polar-orbiting satellite data from several daily overpasses and over a large area, it is expected that the various developmental stages of tropical deep convection over ocean are sampled sufficiently to compare to model results that also include these stages.

a. Statistics of brightness temperature and optical thickness

Several studies (e.g., Rossow and Schiffer 1991; Johnson et al. 1999; Sherwood and Wahrlich 1999; Kubar et al. 2007) classify cloud types jointly by their optical thickness τ and cloud-top temperature (or height). To statistically analyze our data as a function of temperature and optical thickness, we sample them in 4°C intervals of 11-μm brightness temperatures ranging from −93° to 27°C (180–300 K) and within the optical thickness ranges 5–10, 10–30, 30–90, and >90. These optical thickness ranges are roughly similar to the ranges used in the International Satellite Cloud Climatology Project (ISCCP) cloud classification scheme (Rossow and Schiffer 1991, 1999). To minimize the influence of thin in situ cirrus on our analysis, and to ensure the 11-μm brightness temperature measurements are a good proxy for cloud-top temperature (Rossow and Schiffer 1999; Minnis et al. 2008), we exclude cloud with optical thickness less than 5 from this study.

The 2D histograms in Fig. 3 show frequencies of occurrence of cloud optical thickness and brightness temperatures in the combined POLDER–MODIS data. Since the observed cold clouds are expected to be mostly associated with tropical convective systems, we interpret the cold, extremely optically thick (τ > 90) clouds to be the cores of the systems; cold (T < −40°C), optically thick (30 > τ > 90) clouds to be less thick cores and stratiform areas around cores; and cold, moderately thick (10 > τ > 30) and thin (5 > τ > 10) clouds to be stratiform areas, parts of (precipitating) anvils or detached anvil clouds. Furthermore, clouds of midrange temperatures (−40° < T < 0°C) with optical thicknesses below 30 generally represent developing systems or terminal cumulus congestus, while marine boundary layer clouds are characterized by warmer temperatures (Houze 1993; Johnson et al. 1999; Kubar et al. 2007; Luo et al. 2009; Bacmeister and Stephens 2011). The convective cores, stratiform areas, and anvils are evident in Fig. 3 at temperatures between about −40° and −75°C with brightness temperature generally decreasing with increasing optical thickness. Furthermore, developing convection or cumulus congestus appears at brightness temperatures colder than 0°C and optical thickness values below 30. Very few pixels (<0.2%) with optical thicknesses above 30 and brightness temperatures warmer than −40°C occur in the data. These statistics are comparable with the statistics gathered by others in tropical regions (Johnson et al. 1999; Kubar et al. 2007) and suggest that the expected developmental stages of deep convection are reasonably well sampled here.

Fig. 3.
Fig. 3.

Observed joint BT–τ histogram from MODIS data described in text. Optical thickness bins are given in text; BT bins are 4°C wide. Dashed regions indicate cloud-type interpretations as indicated.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

To investigate the effects of different treatments of IN on different cloud types in the CRM simulations of deep convection described in section 3, for each CRM time slice all simulated quantities are averaged within each 11-μm BT and optical thickness range, as described in section 5. To obtain a simple relationship between model and observational samples, we aggregate the MODIS and POLDER data into blocks that have the same size as the domain of the CRM simulations (and TWP-ICE observational domain), that is, 176 km × 176 km, and subsequently average the level-1 and level-2 data within each block and within each 11-μm BT and optical thickness bin, as is done for the simulations. Added advantages of this aggregation of the satellite data over the 176 km × 176 km blocks include that it improves the angular sampling of the POLDER polarized reflectance (cf. Bréon and Goloub 1998) and it is expected to decrease possible 3D radiative transfer effects (Marshak et al. 1999). Stratifying the observations and simulations at different cloud-top temperatures, the glaciation levels, and particle size profiles of convective cloud systems can be evaluated, assuming the time–space interchangeability of satellite retrieved relations discussed by Lensky and Rosenfeld (2006) is applicable (cf. Yuan and Li 2010).

b. Thermodynamic phase information from POLDER

The POLDER directional polarization measurements are used to determine the thermodynamic phase of the cloud tops. The analysis is based on the method used in the operational level-2 POLDER thermodynamic phase algorithm (Goloub et al. 2000). This method utilizes the prominent difference in directional polarized reflectance from spherical cloud drops, which produce a strong rainbow feature around 140° scattering angle, versus nonspherical ice particles, which show little or no structure in directional polarized reflectance at these scattering angles. Part of the POLDER thermodynamic phase algorithm involves determining whether the main rainbow feature from spherical cloud drops is significantly detectable in the measured directional polarized reflectance (Goloub et al. 2000), leading to either a liquid-phase or ice-phase classification. Recognizing that the thermodynamic phase of the cloud top is not a digital quantity—that is, observed radiation can have encountered several cloud layers with different phase and/or mixed-phase layers (Riedi et al. 2010)—here we define a liquid index, which indicates to what degree the rainbow feature from spherical drops is detectable in the directional polarized reflectance. This liquid index is directly derived from the measurements and can be simply simulated from cloud model simulations by using a vector radiative transfer model so as to evaluate the cloud model results by comparing real and simulated liquid index values.

The liquid index is derived from POLDER’s level 1 directional polarized reflectance Rp in the 0.86-μm channel. For each footprint, measurements are obtained by POLDER at up to 16 different viewing angles (Fougnie et al. 2007). The calculation of the liquid index is illustrated in Fig. 4, which shows simulated Rp (solid lines) for a liquid-topped versus an ice-topped cloud. For this illustration, Rp values are calculated with the forward-model described in section 2 for two profiles arbitrarily chosen from the CRM simulations. Note that the decrease of polarized reflectance at scattering angles between 100° and 120° in the liquid-topped example suggests that these simulations are still affected by some ice crystals in cloud top (cf. Riedi et al. 2010). To calculate the liquid index, first a straight line, defined by slope a and offset b, is fit through all available Rp measurements in the 120°–130° and 150°–160° scattering angle ranges, using a least squares fit (dashed lines in Fig. 4). The liquid index (LI) is then defined as the mean difference between all available polarized reflectance measurements Rpi) at scattering angles Θi in the range 135°–145° and the values of the fit at scattering angles Θi (shaded area in Fig. 4), normalized by the value of the fit at Θ1 (dotted line); that is,
e1
where Ndir is the number of measurements available at directions between 135° and 145° scattering angles and a and b are defined above. When using POLDER data, LI is calculated for all cases for which Ndir ≥ 2 and at least four measurements are available for the least squares fit. The LI is near zero when the observed radiation is dominated by scattering from nonspherical ice crystals and increases with increasing contribution of light scattered from spherical liquid drops. Considering a simplistic two-layered cloud consisting of a liquid layer topped with an ice layer, the LI of such a cloud will be near zero if the ice layer is optically thick and increases with decreasing ice layer optical thickness. For example, the LI for the liquid-topped cloud shown in Fig. 4 is 2.2, while the LI for the ice-topped cloud is 0.003. Also, LI values near zero will be obtained for single-layer optically thin ice clouds. The LI can be readily calculated using Eq. (1) from POLDER measurements for which enough measurements at the required scattering angles are available, and from simulated polarized reflectance measurements using CRM output.
Fig. 4.
Fig. 4.

Simulated polarized reflectance as a function of scattering angle illustrating the definition of the liquid index (LI) for (a) liquid-topped cloud and (b) ice-topped cloud. See text for explanation.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

A quantitative interpretation of the liquid index can be obtained using simulated measurements. To simulate POLDER measurements we use forward-model simulations described in detail in section 2. These calculations are based on the CRM simulation using the diagnostic IN approach described in section 3. Figure 5 shows simulated LI as a function of the total optical thickness of the ice particles above the liquid-phase part of the cloud. The top of the liquid-phase part of the cloud is defined here as the altitude where the water drop optical depth, vertically integrated from the top of the model domain, exceeds 0.1. Only clouds with a total optical thickness larger than 5 are included in this figure and our further study. As shown by Riedi et al. (2010), the rainbow feature is increasingly attenuated with increasing optical depth of the overlying ice layer. Figure 5 shows that the LI is near 2.5 when ice optical thickness is less than about 0.1, and LI decreases with increasing ice layer optical thickness until it levels off near zero for ice layer optical thicknesses larger than about 2. Note that cases with less than 0.1 optical thickness from water drops within the vertical column are not included in Fig. 5. These cases will lead to LI near zero since we only include clouds with optical thickness above 5 and thus at least 4.9 optical thickness of ice is present in such clouds. In the case of multilayer situations where warm liquid clouds are overlaid by cold thin cirrus clouds (τ < 05), which are potentially undetected by the 11-μm channel, Fig. 5 indicates that LI values will be ~1 or greater. In the evaluation of ice crystal size and geometry that follows, we limit the analysis to the subsample in which ice crystals dominate the polarized and near-infrared reflectances by selecting all pixels with LI < 0.3 since these represent clouds that are topped with more than about two optical depths of ice, as indicated by Fig. 5.

Fig. 5.
Fig. 5.

Simulated LI values as a function of ice optical depth above the level where the integrated optical depth of liquid water exceeds 0.1. The parameterization discussed in the text is shown in gray.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

For the calculations shown in Fig. 5, roughened compact plates are assumed with a roughness parameter δ of 0.6. However, the LI is minimally affected by the assumed roughness parameter. For example, using near-pristine compact plates (δ = 0.2) yields minimum LI values of around 0.2 for ice-topped clouds, and differences between LI calculated with near-pristine and rough plates decrease with decreasing ice optical depth above the liquid part of the cloud. The lower limit of LI is further discussed in section 5b.

The trend seen in Fig. 5 suggests a simple relationship of LI based on the total optical thickness of the ice particles above the liquid part of the cloud (τice↑). A least squares linear fit through the data points with total optical thickness of the ice particles above the liquid part of the cloud greater than 0.1 and less than 2.6 gives LI = 0.7 − 1.7log(τice↑). At values of τice↑ for which this fit exceeds 2.6, or is less than zero, the parameterized LI is set to 2.6 or 0, respectively. If found to be robust across a wide range of conditions, such a relationship could be used to estimate LI values from values of τice↑ derived from model results for direct comparison with measurements, without the need for more complex radiative transfer model calculations.

Figure 6 shows the LI values derived from the POLDER measurements as a function of 11-μm BT, and for the different optical thickness ranges. For each 176 km × 176 km block, as described in section 4a, level-1 data within each 11-μm BT and optical thickness range are averaged before LI values are derived. Thus, data from each spatial block can contribute one data point at each combination of BT and optical thickness interval. As shown in Fig. 6, LI is near or below zero for BT lower than −40°C, indicating ice-topped clouds. Between −40° and −20°C, liquid index values ranging from below zero to larger than 2 are observed, indicating that both ice and liquid cloud tops are present at these temperatures. For BT warmer than −20°C, LI is near or greater than 1, indicating liquid-topped clouds. The relatively moderate values for BT warmer than 0°C might indicate very thin ice clouds (τ < 0.5) overlying lower-level liquid water clouds, as discussed above, although few measurements are available for these BT values. No simple relation between optical thickness and LI is apparent.

Fig. 6.
Fig. 6.

Measured LI values vs infrared brightness temperature . Dashed lines denote the envelope of the measurements. The dotted line indicates the threshold LI value of 0.3 used to separate liquid- and ice-topped clouds. Different ranges of total cloud optical thickness are denoted by different colors as indicated.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

To assess the general variation of the LI within the sampled spatial blocks and within each BT and optical thickness interval, we calculate LIupper and LIlower from the upper and lower quartiles, respectively, of the level-1 data contributing to each single data point in Fig. 6 and define the interquartile range (IQR) of the LI as the difference LIupper − LIlower. Mean values of the IQR are 0.06 for clouds below a temperature of −40°C, and increase to 0.5 for clouds with tops between −20° and −40°C and to 0.7 for warmer clouds.

The results shown here are consistent with glaciation levels ranging from −40° to −20°C reported in previous studies using POLDER (Riedi et al. 2001; Giraud et al. 2001), MODIS (Yuan et al. 2010; Mitchell and d’Entremont 2011), Advanced Very High Resolution Radiometer (AVHRR), Geostationary Operational Environmental Satellite (GOES) (Rosenfeld et al. 2008), Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) (Yoshida et al. 2010; Naud et al. 2010), and ground-based lidar and radar (Riedi et al. 2001; Ansmann et al. 2009; Westbrook and Illingworth 2011). Interestingly, these observations show a significant amount of supercooled liquid at temperatures down to about −35°C. Although some studies find no indication of liquid drops at temperatures less than about −20°C (e.g., Lawson et al. 2010), supercooled liquid at such low temperatures has been measured in situ in convective clouds (Rosenfeld and Woodley 2000), and has been inferred from remote sensing measurements down to −36°C (Ansmann et al. 2009; Mitchell and d’Entremont 2011). Modeling studies also indicate that supercooled liquid may be sustained at temperatures down to about −35°C in strong updrafts (Khain et al. 2001; Rosenfeld et al. 2008). In section 5 we evaluate the glaciation temperatures produced by the DHARMA simulations.

c. Effective radius and 2.13-μm reflectance from MODIS

The MODIS team retrieves an ice effective radius Reff from visible and near-infrared measurements (King et al. 2004). In the case of ice clouds, the effective radius is usually defined as
e2
where V, Ap, and N are the total volume, total orientation-averaged projected area, and the number density of the ice crystals of maximum dimension D, respectively (Francis et al. 1994; Baum et al. 2005a). Although there are other definitions (McFarquhar and Heymsfield 1998), the effective radius as defined in Eq. (2) is consistent with the general definition of effective radius for cloud droplets given by Hansen and Travis (1974) and is also directly related to the effective photon pathlength within a collection of ice crystals (Mitchell 2002).

Figure 7a shows MODIS-retrieved effective radius Reff versus BT. The data are aggregated as described above for LI (section 4b). To focus on ice-dominated cloud tops, only cases with LI values less than 0.3 are included. As seen in Fig. 7, for cloud tops colder than about −40°C, retrieved effective radii are about 18–28 and about 23–36 μm for warmer cloud tops. The mean IQR of the effective radii within the sampled spatial blocks and within each BT and optical thickness interval is 1.7 μm for cloud tops colder than −40°C, and 5.1 μm for warmer clouds. At temperatures lower than −40°C, effective radii slightly increase with temperature with a slope of 0.09 ± 0.007 μm K−1, while the slope increases significantly for warmer temperatures to 0.4 ± 0.15 μm K−1. The relation between cloud-top temperature and particle size is commonly explained by size-sorting processes owing to ice fall speeds that increase with size (Heymsfield 1975; McFarquhar and Heymsfield 1997; Yuan et al. 2010), although increasing water vapor available for ice particle growth with temperature and ice crystal aggregation during sedimentation may also play a role (Heymsfield and Donner 1990; Pruppacher and Klett 1997), among other possible factors. The apparent increase in slope for temperatures warmer than −40°C, as seen in Fig. 7a, is interesting since this is roughly the temperature above which only heterogeneous freezing occurs (Pruppacher and Klett 1997). At colder temperatures, small ice particles formed by homogeneous freezing of droplets and aerosols may contribute to the smaller effective radii (Brown and Heymsfield 2001; Heymsfield et al. 2009; Cooper and Garrett 2010; Hendricks et al. 2011). This trend would appear to be consistent with the increase in bimodality of the ice size distributions measured during the Tropical Composition, Cloud and Climate Coupling (TC4) campaign for temperatures higher than −40°C, although no sudden increase in in situ–measured effective particle size is seen corresponding to this onset of bimodality (Lawson et al. 2010; Mitchell et al. 2011b). However, this apparent change in the effective radius profile at −40°C retrieved by MODIS may also be a retrieval artifact caused by a change in ice particle shape as a function of temperature, as discussed in section 5 (cf. Mitchell et al. 2011a).

Fig. 7.
Fig. 7.

MODIS-retrieved (a) effective radii and (b) measured 2.13-μm reflectances for ice-topped clouds (LI < 0.3), colors as in Fig. 6.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

Similar ice effective radii (15–35 μm) were retrieved with the aircraft-mounted MODIS Airborne Simulator (MAS) over tropical clouds during the TC4 campaign (Kindel et al. 2010). The decrease of ice particle sizes with decreasing temperatures below −40°C in MODIS retrievals over tropical deep convection were recently discussed by Yuan and Li (2010). Likewise, in situ measurements also generally show positive correlations between ice crystal effective radii and temperature, although the reported relations strongly vary (Rolland et al. 2000; Garrett et al. 2003; Gayet et al. 2006). Although such in situ measurements are known to suffer from issues related to ice crystal shattering on the probes inlets and other problems (Field et al. 2003; McFarquhar et al. 2007; Korolev et al. 2011), measurements using improved probes that aim to mitigate ice shattering problems show similar results (Lawson et al. 2010; Mitchell et al. 2011b). We note also that the DHARMA relation between maximum and effective dimension seen in Fig. 1 and the retrieved ice effective radii around 25 μm shown in Fig. 7 would correspond to near-IR radiative absorption dominated by crystals with maximum dimensions around 100–200 μm, which is roughly consistent with in situ size distribution measurements obtained during the TC4 and the National Aeronautics and Space Administration African Monsoon Multidisciplinary Analyses (NAMMA) campaigns (Lawson et al. 2010). However, caution is warranted when comparing satellite-retrieved effective radii with those derived from local in situ measurements observed at different levels within clouds, since effective radii obtained by remote sensing retrievals represent a weighted average of the effective radii in the first few optical depths of the cloud tops and the weighting depends on the near-IR channel used in the retrieval (Wang et al. 2009a; Zhang et al. 2010).

Interestingly, at any given temperature, the observed range in effective radius is quite narrow, and no simple relationship between effective radius and optical thickness is found: optically thick convective cores, cold stratiform areas, and anvil outflow (τ > 5) with similar cloud-top temperatures all have comparable effective radii in this dataset, consistent with the observation that variations of ice-effective radii measured in situ are mainly a function of temperature in tropical convective clouds (e.g., Garrett et al. 2003). However, since cloud-top temperature generally increases slightly with distance from convective cores (see Fig. 3), particle sizes could correspondingly increase with distances from convective cores, although the opposite has also been observed (Garrett et al. 2005; Bedka and Minnis 2010).

In the MODIS retrieval procedure over ocean, ice effective radius and cloud optical thickness are simultaneously retrieved by determining the closest match between measurements in bands centered at 0.864 and 2.13 μm and the corresponding simulated values using a lookup table (King et al. 2004). The lookup table is calculated assuming a vertically uniform cloud layer, and an ice size and shape distribution derived from numerous in situ measurements (Baum et al. 2005a,b). For clouds with retrieved optical thickness above 5, as sampled in this study, the 2.13-μm reflectances are nearly a direct proxy for retrieved particle effective radius, as is apparent from Figs. 7a, 7b, and 8. For most of the observed range in 2.13-μm reflectance (R2.13), the relation between reflectances and effective radii (Fig. 8) can be approximated well by
e3
(with Reff in microns and R2.13 dimensionless), although for lower reflectances a more nonlinear relation is expected (cf. Zhang et al. 2010). However, recent studies point out possible biases in the retrieved effective radius owing to limitations of the used ice size and shape distributions and the assumption of pristine ice crystals in the retrieval algorithm (Yang et al. 2008a; Baum et al. 2011), as well as interpretation issues related to the assumption of a single vertically uniform cloud layer (Zhang et al. 2010). To partly bypass such issues, here we directly compare the observed 2.13-μm reflectances (Fig. 7b) with the corresponding values calculated from the CRM simulations, assuming an optical ice model that is consistent with the observations and the CRM microphysics, as discussed in section 5. For optical thickness values less than 5, the 2.13-μm reflectances also depend significantly on optical thickness (Rolland et al. 2000). For this reason, among others, we exclude clouds with optical thickness lower than 5 from this study.
Fig. 8.
Fig. 8.

Relation between MODIS-retrieved effective radii and measured 2.13-μm reflectances for ice-topped clouds (LI < 0.3). The dashed line shows a least squares fit [see Eq. (3)].

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

5. Results

In this section we compare the simulated liquid index, effective radii, and 2.13-μm reflectances to the corresponding measured values. For each model time slice, the simulated quantities are binned in the same manner as the observations (see section 4). As discussed in section 4, we assume that the observations sample all evolutionary stages of marine deep convection during the active phase of the TWP-ICE campaign. Thus, we can evaluate the simulated quantities by analyzing whether the simulated LI, effective radius, and 2.13-μm reflectances fall within the envelopes of the observations shown in Figs. 6 and 7. To evaluate the assumptions of ice crystal geometry in the model simulations and to constrain the ice crystal roughness in the forward simulations, first the angular variation of POLDER polarized reflectances is analyzed.

a. Evaluation of ice crystal geometry and roughness

As discussed in section 3, the DHARMA simulations assume cloud ice crystals composed of components with a planar geometry and an aspect ratio of 0.7. As demonstrated by, for example, C.-Labonnote et al. (2000), Chepfer et al. (2001), and Knap et al. (2005), the directional polarized reflectances measured by POLDER contain information about ice particle shape in the observed clouds, and we can use these to evaluate the ice shape assumptions. Figure 9 shows the distributions of polarized reflectances measured during the active monsoon phase period for high and low ice-topped clouds compared to calculated polarized reflectances for an ice cloud containing plates with two different aspect ratios and with several degrees of small-scale surface roughness δ. The calculations shown here are based on one particular vertical column of one time slice of the DHARMA simulations discussed in section 3, chosen to have a substantial optical thickness of fluffy ice type at cloud top. Since the calculated polarized reflectances do not vary significantly with cloud optical thickness or particle size distributions, these calculations are assumed representative for all simulated ice-topped clouds in our study. Note that the observed polarized reflectance at angles larger than ~160° level off at around 0.0015, whereas the simulations approach zero here. For these angles, measured polarized reflectances are likely dominated by instrument noise, estimated to be of order 0.002 above clouds (Fougnie et al. 2007).

Fig. 9.
Fig. 9.

Dark and light gray areas and white lines show full range, middle half, and median, respectively, of polarized reflectance measurements as a function of single-scattering angle for clouds with liquid index (LI) below 0.3 and brightness temperature (a),(b) lower and (c),(d) higher than −38°C. Simulations are overlaid assuming plates with aspect ratio AR = (left) 0.7 and (right) 0.15. Different line styles are for different small-scale roughness values, as shown.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

Calculations assuming plates with an aspect ratio of 0.7 fit the polarized reflectance measurements for the cold clouds reasonably well with a root-mean-squared difference (RMSD) of 3.2 × 10−4 for scattering angles larger than 160° when a roughness parameter of δ = 0.6 is used (Fig. 9a). However, platelike crystals with a more extreme aspect ratio of 0.15 but stronger roughening (δ ≈ 0.8) appear also to be able to fit most of the data for the cold clouds (Fig. 9b), with RMSD = 7.4 × 10−4, although in this case the calculations have a somewhat stronger upward curvature than observed. Thus, the polarized reflectance measurements in this angular range are apparently not sufficient to constrain both aspect ratio and small-scale surface roughness of the ice crystals. However, we can conclude that the assumed crystals with platelike components with an aspect ratio of 0.7 are at least not inconsistent with the measurements. The RMSD for all other considered combinations of aspect ratio and roughness parameter are larger than 1.5 × 10−3 for the cold clouds. As described in section 2, the aspect ratio 0.7 corresponds well with the in situ measurements gathered by Korolev and Isaac (2003) and is also consistent with the compact particles commonly assumed to be present in tops of cold clouds (Baran 2009; Nousiainen et al. 2011). Furthermore, Noel et al. (2004) showed that lidar depolarization values observed in cold tops of deep convection indicate irregular particles with an aspect ratio between 0.7 and 1.05. The rather strong roughening needed to fit the data also agrees well with the severely rough ice model found to best fit CALIPSO backscatter and depolarization measurements over tropical deep convection (Baum et al. 2010). Aside, we note that somewhat less roughened ice crystals were found to better fit global POLDER observations and CALIPSO measurements over midlatitude cirrus (Knap et al. 2005; Baran and C.-Labonnote 2006; Baum et al. 2010).

Plates with an aspect ratio 0.7 and a roughness parameter 0.6 have an asymmetry parameter of 0.74, which is in good agreement with values measured in situ, although such measurements may suffer from undersampling of the phase function forward peak and crystal shattering on probe inlets (Garrett et al. 2003; Baran 2009). Interestingly, plates with a more extreme aspect ratio of 0.15 and stronger roughening (δ = 0.8) that also overlap the middle half of the measurements (Fig. 9b) have an asymmetry parameter of 0.74 as well. Thus, although the polarized reflectance measurements cannot uniquely constrain the crystal shape or aspect ratio for cold clouds (cf. Baran 2009), they appear to provide an effective constraint on the asymmetry parameter of the ice crystals, which is important for the analyses of crystal size discussed in section 5c.

For warmer ice clouds (BT > −38°C), crystals with an aspect ratio AR = 0.7 do not fit the data well (RMSD > 1.5 × 10−3; see Fig. 9c), whereas an excellent fit to the measurements with scattering angles smaller than 160° is achieved by assuming plates with an aspect ratio 0.15 and a roughness parameter 0.6 (RMSD = 2.7 × 10−4). This match corresponds well with lidar observations by Noel et al. (2004), showing a decrease of irregular particles and an increase of low aspect ratio platelike particles with temperature. Since the retrieved ice effective radii at temperatures warmer than −38°C are somewhat larger than at colder temperatures, these more extreme aspect ratios are apparently consistent with the general assumption that larger ice particles have aspect ratios increasingly deviating from unity (e.g., Auer and Veal 1970; Baum et al. 2010). However, in situ measurements gathered by Korolev and Isaac (2003) show no, or only weak, dependence of aspect ratio on maximum diameter at a given temperature, but do show a significant dependence of the ice aspect ratio on temperature. Thus, these POLDER measurements might also indicate a general habit or aspect ratio transition around −38°C in the sampled clouds. This interpretation may be consistent with a distinct drop in ice crystal area ratios and other abrupt microphysical changes observed in situ at temperatures higher than −40°C in synoptic cirrus clouds as reported by Mitchell et al. (2011a), although a drop in area ratios was not apparent in their limited sample of anvil cirrus. A transition of particle shape at cloud tops around −38°C could possibly be related to the presence of homogeneously frozen drops with aspect ratios closer to unity at lower temperatures, compared to ice formed solely by heterogeneous freezing processes at temperatures higher than −38°C (Heymsfield et al. 2009; Cooper and Garrett 2010; Mitchell et al. 2011a). The asymmetry parameter of plates with AR = 0.15 and δ = 0.6 is 0.84, which is significantly greater than that of the particles found to fit the data for colder clouds.

We note that polarized reflectances are essentially not influenced by cloud at an optical depth larger than about 2 (Chepfer et al. 2001), making them insensitive to possible horizontal variations of ice shape deeper in the clouds. However, the small IQR in the polarized reflectances for cold clouds in Fig. 9 suggests that there is little variation of ice shape with temperature lower than −40°C, assuming that the time–space interchangeability of satellite observables (Lensky and Rosenfeld 2006) is valid. Thus, we assume that the ice model found to be consistent with the polarized reflectances is at least applicable throughout the top four optical depths that dominate the 2.13-μm reflectances analyzed in section 5c (Wang et al. 2009a; Zhang et al. 2010).

Note that here we have assumed that the optical properties of ice cloud tops are generally dominated by cloud ice represented by the fluffy category in DHARMA, although dense ice (graupel) can sometimes significantly contribute to the top few optical depths of the simulated ice clouds, as discussed below. The optical properties of graupel are computed by assuming plates with an aspect ratio AR = 0.8 and a roughness parameter δ = 0.4, consistent with the roughness parameter found to correspond best to global POLDER data by Baran and C.-Labonnote (2006).

b. Thermodynamic phase transition evaluation

Adopting a roughness value of 0.6 for fluffy ice based on the foregoing analysis, Fig. 10 shows the simulated liquid index values for the diagnostic and prognostic IN treatments compared to the envelope of the measured values shown in Fig. 6. Similar to the measurements, the simulations show LI values close to zero for all cloud tops colder than −40°C. For warmer cloud tops, some differences between measurements and simulations are observed. Using diagnostic IN (Fig. 10a), very few LI values greater than 0.3 are observed at temperatures lower than −25°C, indicating too few cloud tops containing supercooled liquid water. Moreover, for temperatures between −20° and 0°C, too many simulated LI values are close to zero, indicating too many ice-topped clouds in this temperature range. The implied overly efficient ice formation is somewhat reduced in the simulations using prognostic IN shown in Fig. 10b, where significantly more large LI values are seen warmer than −40°C, although still some LI values close to zero appear at temperatures higher than −20°C.

Fig. 10.
Fig. 10.

Simulated LI values vs infrared BT for simulations using the (a) diagnostic IN and (b) prognostic IN treatment, colors as in Fig. 6.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

The minimum LI is approximately zero in the simulations, while values down to LI = −0.28 are observed. Such negative LI values are obtained for multidirectional polarized reflectances that curve upward at scattering angles below 160° (see Fig. 4b). Figure 9 shows that such upward-curving polarized reflectance functions can occur when ice crystals with platelike components have rougher surfaces and/or more extreme aspect ratios than used in our simulations. Thus, the negative LI values seen in the observation might result from clouds that contain such particles, which are not included in our simulations. By extension, natural particles appear to be more diverse than in the simulations.

Note that the simulated LI values shown in Fig. 10 are derived from the relatively computationally intensive polarized forward-model calculations described in section 2. However, similar results (not shown) are obtained using the simple relationship between LI and the ice optical thickness above the liquid part of the cloud, as described in section 4b. If it were found to be robust over a wide range of simulation results in future studies, this relationship could be used for future evaluation of glaciation temperatures produced by models using polarized reflectance measurements, significantly reducing the computational effort.

c. Ice particle size evaluation

Here we evaluate the particle sizes produced by the model by comparing retrieved and modeled effective radii, and by comparing measured and modeled 2.13-μm reflectances. To obtain cloud-top effective radii that correspond to the effective radii retrieved by MODIS, knowledge is required about the dependence of MODIS-retrieved values on vertical variation within layers. The contribution of the effective radius at a particular optical depth within a cloud to the retrieved effective radius can be expressed by vertical weighting functions, as estimated by Wang et al. (2009a) and Zhang et al. (2010), based on the maximum photon penetration principle (Platnick 2000). They show vertical weighting functions for the 2.13-μm MODIS channel peaking somewhere within the first two optical depths, although the functions depend on the vertical profile of effective radius. Furthermore, the vertical weighting may depend on the size and shape distribution of the ice crystals (e.g., McFarquhar and Heymsfield 1998).

Application of such weighting functions is only important when the particle effective radii significantly vary over the first few optical depths of the cloud top. Alternatively, the numerator and denominator of Eq. (2) can be integrated separately without weighting down to a threshold optical depth into the cloud τthresh. Differences between effective radii obtained with different values of τthresh can be used as a measure of vertical variation near the cloud tops. Effective radii calculated for vertically nonuniform cloud tops must be interpreted with caution when comparing to retrieved values, as discussed below. Based on the results of Wang et al. (2009a) and Zhang et al. (2010), an appropriate value of τthresh is expected to be in the range from 1 to 4 for measurements at 2.13-μm.

Using three different values of τthresh, Figs. 11a and 11c show the effective radii of ice-topped clouds (LI < 0.3) simulated with the diagnostic IN and prognostic IN approaches, respectively, compared to the envelope of the MODIS-retrieved ice particle effective radii, shown in Fig. 7a. In this study, the particle size distributions are averaged over 7 × 7 DHARMA grid points, consistent with the forward-model calculations described in section 2 and the spatial resolution of the satellite retrievals discussed in section 4. For all BT bins, Figs. 11a and 11c show the full range and mean values of effective radii obtained using τthresh = 2 across all model time slices and optical thickness bins, as well as the mean values using τthresh = 1 or τthresh = 4. For both simulations, the effective radii for clouds with tops colder than about −40°C are generally about 5–10 μm smaller than the retrieved values. Note that most observed effective radii are on the large end of the envelope (Fig. 7a). Similar to the observations, the simulated effective radii increase slightly with temperature above −40°C. At the coldest tops, little variation within the first four optical depths is seen, but the vertical variation increases with temperature.

Fig. 11.
Fig. 11.

(a),(c) Effective radii and (b),(d) 2.13-μm reflectances vs brightness temperature for ice-topped clouds (LI < 0.3) in simulations using (top) diagnostic IN and (bottom) prognostic IN. In the left panels, circles and downward and upward triangles indicate mean effective radii obtained using τthresh equal to 2, 4, and 1, respectively. Dotted lines show the full range of effective radii obtain with τthresh = 2. Gray dashed lines indicate the envelope of the MODIS retrievals shown in Fig. 7a. In the right panels, circles and diamonds indicate mean 2.13-μm reflectances obtained using rough ice crystals with AR = 0.7 and 0.15, respectively. Dotted lines show full range of 2.13-μm reflectances using AR = 0.7. Gray dashed lines indicate the envelope of the MODIS measurements shown in Fig. 7b.

Citation: Journal of the Atmospheric Sciences 69, 11; 10.1175/JAS-D-11-0314.1

For cloud tops with temperatures lower than −40°C, the simulated effective radii increase more strongly with temperature. Furthermore, the variation of effective radius within the first four optical depths is significantly greater than for colder clouds. Using τthresh = 2, simulated effective radii are generally about 5–10 μm too large, while they are generally within or close to the envelope of the retrievals when τthresh = 1. For cloud tops between −40° and −20°C, effective radii simulated with the prognostic approach are somewhat larger than those obtained with the diagnostic approach. Large effective radii (>50 μm) appear at temperatures higher than −20°C, although no ice is seen in the observations at these higher temperatures.

As discussed above, the vertical weighting function needed to relate a MODIS effective radius retrieval to the actual vertically integrated effective radius in the case of a nonuniform cloud layer is not known a priori. Such weighting functions may be estimated from CRM simulations using forward-model calculations (McFarquhar and Heymsfield 1998; Wang et al. 2009a; Zhang et al. 2010). However, the effective radii currently retrieved from MODIS are also likely significantly underestimated, owing to the assumption of a mixture of mainly pristine ice crystals in the retrieval algorithm (Rolland et al. 2000; Baum et al. 2005b; Yang et al. 2008a), which is inconsistent with the polarized reflectances observed by POLDER [see section 5a and, e.g., C.-Labonnote et al. (2000); Knap et al. (2005); Baran and C.-Labonnote (2006)]. To make a more robust evaluation of particle size produced by DHARMA, in Figs. 11b and 11d we directly compare the measured and forward-modeled μm reflectances. For clouds with tops colder than about −40°C, this comparison shows that simulated reflectances are generally about 0.05–0.1 greater than those observed, when we assume rough ice crystals (δ = 0.6) with an aspect ratio AR = 0.7, which were found to be consistent with POLDER measurements (Fig. 9). This overestimation of 2.13-μm reflectances again indicates that simulated ice crystals are too small. For cloud tops warmer than −40°C, simulated 2.13-μm reflectances using AR = 0.7 are generally closer to the observations, although still about 0.02–0.07 too great. Moreover, for these temperatures the assumption of an aspect ratio of 0.7 is found inconsistent with the POLDER measurements (section 5a), and rough plates with an aspect ratio of 0.15 were found to best fit the mean polarized reflectances. To indicate the influence of particle geometry on these calculations, Figs. 11b and 11d also show the mean 2.13-μm reflectances calculated using optical properties of rough plates with an aspect ratio AR = 0.15. Owing to the higher asymmetry parameter of the plates with an aspect ratio of 0.15, the calculated 2.13-μm reflectances are generally about 0.02–0.05 lower than those obtained using plates with an aspect ratio of 0.7 and generally fall within the envelope of measured values at temperature higher than −40°C. Some cases, most notably the ones occurring at temperature higher than −20°C, are substantially affected by dense ice in the top optical depths and therefore show reduced sensitivity to the ice crystal geometry of the fluffy ice.

These simulations illustrate the utility of constraining the ice particle geometry, or at least the asymmetry parameter, for the evaluation of ice crystal effective radii, as near-infrared reflectances are shown to be sensitive to both the effective radius and the ice crystal geometry. Consequently, variations in near-infrared reflectances owing to changes in ice crystal shape can be wrongly interpreted as resulting from changes in crystal size. Interestingly, the simulations suggest that the statistically significant increase in slope of the vertical profile of 2.13-μm reflectances observed for cloud warmer than −40°C (Fig. 7b) may be caused in part by a change in aspect ratio (habit or shape) rather than a change in effective radius. The use of particle habit mixtures in the MODIS collection 5 retrieval algorithm that depend only on size but not on altitude or temperature would lead to an erroneously enhanced increase in slope of the retrieved effective radii if the 2.13-μm reflectances decrease because of an increase in asymmetry parameter as suggested by the POLDER measurements (Fig. 9).

As shown in Figs. 11a and 11c the simulated clouds with tops colder than about −40°C generally show little vertical variation in effective radius within the top four optical depths. Based on the relation between 2.13-μm reflectances and retrieved effective radius given by Eq. (3), the reflectance bias of 0.05–0.1 for cold clouds implies that the effective radii in the simulated cold tops are about 7–15 μm too small. As expected, this implied effective radius bias is somewhat larger (by ~5 μm) than from direct comparison between retrieved and simulated effective radii, since the use of ice crystals with smooth surfaces in the MODIS collection 5 retrieval algorithm yields effective radii that are too small in the case of ice clouds containing rough irregular ice crystals (Rolland et al. 2000; Yang et al. 2008a; Baum et al. 2011). Although cloud tops with brightness temperature higher than −40°C show more vertical structure in their tops than colder clouds, 2.13-μm reflectances calculated using optical properties of rough plates with an aspect ratio of 0.15, which are found to be consistent with the POLDER measurements (Fig. 9), indicate little or no bias in the simulated ice size for both simulations for these clouds.

Little difference is seen in Fig. 11 between ice crystal effective radii (and 2.13-μm reflectances) simulated with the diagnostic and prognostic IN treatment, especially for the cold clouds. The lack of difference suggests that homogeneous ice formation dominates at low temperatures in the simulations, while the low bias in simulated effective radii (and high bias in 2.13-μm reflectances) likely indicates too small crystals are produced by the homogeneous freezing scheme in the model. More variation and stronger vertical variation is seen for cloud tops at temperatures between −40° and −20°C although, again, the differences between the two IN treatments are relatively small, suggesting that the ice present at the tops of these simulated clouds is also dominated by crystals formed from homogeneous freezing of drops, which subsequently grew and descended to warmer levels. This inference is consistent with past model analysis (Phillips et al. 2007) and further supported by an additional (limited) simulation performed here that does not include IN (not shown), yielding similar effective radii as found in the diagnostic and prognostic IN treatments. In contrast, the observed differences in polarized reflectances between temperatures lower and higher than −38°C shown in Fig. 9, and the observed increase in slope of 2.13-μm reflectances versus temperature for clouds warmer than about −38°C shown in Fig. 7 suggest a change in ice shape and/or size in natural deep convection for the conditions occurring during TWP-ICE, possibly related to a change in the freezing mechanism around this temperature. Studying the intertwined roles of various ice formation mechanisms will be the subject of future work.

6. Conclusions

In this paper, we demonstrated how satellite observations of multidirectional total and polarized reflectances can be used to evaluate cloud-resolving model simulations of tropical deep convection in terms of ice crystal sizes and glaciation temperature. We used a framework that avoids inconsistencies between assumptions made in retrieval algorithms and cloud-resolving simulations by forward-calculating total and polarized reflectances in a manner consistent with the model assumptions, and output and can be compared directly with observed reflectances.

The preliminary cloud-resolving model calculations used in this paper represent a moderate monsoon event observed during the TWP-ICE campaign near Darwin, Australia, and were compared to combined MODIS and POLDER measurements. Two simulations are included in this study: one uses a diagnostic IN approach, which assumes a constant total number of ice crystals and nuclei, and the other uses a prognostic IN approach, which allows for local consumption and removal of IN. Both simulations use aerosol size distribution profiles and large-scale forcings derived from observations. We note that an analysis of the particular differences between the two model simulations considered here is not the primary objective of this study. Rather, our objective is to demonstrate the utility of an analysis framework for evaluating cloud-resolving model results more generally.

A straightforward evaluation of modeled glaciation levels used liquid index (LI) values derived from the observed and simulated multidirectional polarized reflectances, which are closely related to the optical depth of ice above any liquid-dominated depth of the cloud. LI values calculated from the model simulations using the diagnostic IN treatment indicate only glaciated tops for temperatures lower than −40°C, consistent with the observations, but reveal too many ice-topped clouds at temperatures higher than −20°C and substantially fewer supercooled cloud tops colder than −25°C than observed. The simulations using the prognostic IN treatment produced significant supercooled liquid water at temperatures down to −30°C and fewer ice-topped clouds at warmer temperatures, making them more consistent with the observations.

Multidirectional polarized reflectances were used to partially constrain the ice particle shapes used in the simulations and forward model. The cloud ice crystals with platelike components with an aspect ratio 0.7, which are assumed in the cloud-resolving model microphysics, were shown to be consistent with the observations for clouds with 11-μm brightness temperatures lower than −38°C if the crystals are roughened. The asymmetry parameters for the ice crystals that lead to simulated polarized reflectances consistent with the observations are about 0.74, similar to values found elsewhere. For ice cloud tops warmer than −38°C, by contrast, the observed multidirectional polarized reflectances indicate the presence of such roughened ice crystals with more extreme aspect ratios of ~0.15 and asymmetry parameters closer to unity (~0.84).

Ice effective radii retrieved from these MODIS measurements are about 18–36 μm and generally increase slightly with increasing brightness temperature. However, at cold cloud tops, retrieved effective radius values were estimated to be about 5 μm too small, owing to the use of only pristine ice crystals in the retrieval algorithm. The slope of the relation between brightness temperature and retrieved effective radius appears to increase somewhat for temperatures higher than −38°C. However, using forward-modeled 2.13-μm reflectances, we showed that a change in ice crystal shape around −38°C, as indicated by multidirectional polarized reflectances, could also lead to a difference in bias in retrieved effective radius between colder and warmer ice cloud tops, owing to the assumption of ice crystal mixtures that do not depend on temperature in the retrieval algorithm.

Evaluation of simulated effective radius using MODIS retrievals was found to be hampered by vertical variation of ice size distributions, especially for cloud tops at brightness temperature higher than −40°C. By forward-simulating 2.13-μm reflectances using the ice crystal geometry most consistent with polarized reflectances, the ice crystal sizes produced by the cloud-resolving model were evaluated more robustly, namely, bypassing complications associated with retrieval assumptions. Comparing simulated and observed 2.13-μm reflectances and assuming rough plates with an aspect ratio AR = 0.7, simulated values were found to be about 0.05–0.1 too high for cold clouds, implying effective radius values 7–15 μm too small. For cloud tops warmer than −40°C, the simulated 2.13-μm reflectances, if assuming rough plates with an aspect ratio AR = 0.15, generally agree quite well with the observations.

The small differences between modeled effective radius simulated with the diagnostic and prognostic IN treatments at brightness temperature lower than −40°C indicate that homogeneous ice formation dominates in both model simulations. Also for cloud tops between −20° and −40°C, the effective radius differences between the two IN treatments are relatively minor. It is important to note that changes at −38°C in satellite observations of polarized reflectance and 2.13-μm reflectances, however, suggest a change in ice shape and/or size in natural deep convection for the conditions occurring during TWP-ICE, possibly related to a change in the freezing mechanism around this temperature.

This study illustrates how a combination of total reflectances in a moderately absorbing channel and multidirectional polarized reflectances can be used to help constrain the glaciation, particle shape, and effective radius in model simulations. The polarized reflectance constrains the thermodynamic phase of the cloud tops and the geometry of the ice crystals, which in turn can be used to forward-model reflectances in an absorbing near-infrared band so as to constrain the ice crystal effective radius.

We note that the effects of crystal roughness and aspect ratio on retrieved effective radius found in this study are of the same order of magnitude (~5 μm) as the variability that has been observed in satellite retrievals and sometimes associated with aerosol effects (e.g., Sherwood et al. 2006; Yuan et al. 2010; Jiang et al. 2011). This equivalence emphasizes the need to disentangle the effects of natural variations in ice crystal size, shape, and small-scale crystal roughness on global satellite retrievals of ice cloud properties. The combination of multidirectional polarization measurements and near-infrared observations shows great potential for making progress on these issues.

Acknowledgments

This material is based on work supported by the National Aeronautics and Space Administration under Grant 06-EOS/06-100 issued through the Earth Observing System Program of NASA’s Earth Science Division. AMF and ASA received computational support from the DOE’s National Energy Research Scientific Computing Center, and the NASA Advanced Supercomputing Division. The authors are grateful to Centre National d’Études Spatiales (CNES) and NASA for providing the POLDER and MODIS data. We thank the ICARE Data and Services Center for providing access to the POLDER data used in this study. We are grateful for the contributions from three anonymous reviewers.

REFERENCES

  • Ackerman, A. S., P. V. Hobbs, and O. B. Toon, 1995: A model for particle microphysics, turbulent mixing, and radiative transfer in the stratocumulus-topped marine boundary layer and comparisons with measurements. J. Atmos. Sci., 52, 12041236.

    • Search Google Scholar
    • Export Citation
  • Ansmann, A., and Coauthors, 2009: Evolution of the ice phase in tropical altocumulus: SAMUM lidar observations over Cape Verde. J. Geophys. Res., 114, D17208, doi:10.1029/2008JD011659.

    • Search Google Scholar
    • Export Citation
  • Auer, A., and D. Veal, 1970: The dimension of ice crystals in natural clouds. J. Atmos. Sci., 27, 919926.

  • Bacmeister, J. T., and G. L. Stephens, 2011: Spatial statistics of likely convective clouds in CloudSat data. J. Geophys. Res., 116, D04104, doi:10.1029/2010JD014444.

    • Search Google Scholar
    • Export Citation
  • Baker, M., 1997: Cloud microphysics and climate: Tropospheric processes. Science, 276, 10721078.

  • Baran, A. J., 2009: A review of the light scattering properties of cirrus. J. Quant. Spectrosc. Radiat. Transfer, 110, 12391260.

  • Baran, A. J., and L. C.-Labonnote, 2006: On the reflection and polarisation properties of ice cloud. J. Quant. Spectrosc. Radiat. Transfer, 100, 4154.

    • Search Google Scholar
    • Export Citation
  • Baran, A. J., P. J. Connolly, A. J. Heymsfield, and A. Bansemer, 2011: Using in situ estimates of ice water content, volume extinction coefficient, and the total solar optical depth obtained during the tropical ACTIVE campaign to test an ensemble model of cirrus ice crystals. Quart. J. Roy. Meteor. Soc., 137, 199218.

    • Search Google Scholar
    • Export Citation
  • Baum, B. A., A. J. Heymsfield, P. Yang, and S. T. Bedka, 2005a: Bulk scattering properties for the remote sensing of ice clouds. Part I: Microphysical data and models. J. Appl. Meteor., 44, 18851895.

    • Search Google Scholar
    • Export Citation
  • Baum, B. A., P. Yang, A. J. Heymsfield, S. Platnick, M. D. King, Y.-X. Hu, and S. T. Bedka, 2005b: Bulk scattering properties for the remote sensing of ice clouds. Part II: Narrowband models. J. Appl. Meteor., 44, 18961911.

    • Search Google Scholar
    • Export Citation
  • Baum, B. A., P. Yang, Y.-X. Hu, and Q. Feng, 2010: The impact of ice particle roughness on the scattering phase matrix. J. Quant. Spectrosc. Radiat. Transfer, 111, 25342549.

    • Search Google Scholar
    • Export Citation
  • Baum, B. A., P. Yang, A. J. Heymsfield, C. G. Schmitt, Y. Xie, A. Bansemer, Y.-X. Hu, and Z. Zhang, 2011: Improvements in shortwave bulk scattering and absorption models for the remote sensing of ice clouds. J. Appl. Meteor. Climatol., 50, 10371056.

    • Search Google Scholar
    • Export Citation
  • Bechtold, P., and Coauthors, 2000: A GCSS model intercomparison for a tropical squall line observed during TOGA-COARE. II: Intercomparison of single-column models and a cloud-resolving model. Quart. J. Roy. Meteor. Soc., 126, 865888.

    • Search Google Scholar
    • Export Citation
  • Bedka, K. M., and P. Minnis, 2010: GOES 12 observations of convective storm variability and evolution during the Tropical Composition, Clouds and Climate Coupling Experiment field program. J. Geophys. Res., 115, D00J13, doi:10.1029/2009JD013227.

    • Search Google Scholar
    • Export Citation
  • Bodas-Salcedo, A., and Coauthors, 2011: COSP: Satellite simulation software for model assessment. Bull. Amer. Meteor. Soc., 92, 10231043.

    • Search Google Scholar
    • Export Citation
  • Böhm, J., 1989: A general equation for the terminal fall speed of solid hydrometeors. J. Atmos. Sci., 46, 24192427.

  • Böhm, J., 1992: A general hydrodynamic theory for mixed-phase microphysics. Part I: Drag and fall speed of hydrometeors. Atmos. Res., 27, 253274.

    • Search Google Scholar
    • Export Citation
  • Bréon, F. M., 2006: PARASOL level-1 product: Data format and user manual. CNES, 33 pp. [Available online at http://www.icare.univ-lille1.fr/products/download/Parasol_Level-1_format.pdf.]

  • Bréon, F. M., and P. Goloub, 1998: Cloud droplet effective radius from spaceborne polarization measurements. Geophys. Res. Lett., 25, 18791882.

    • Search Google Scholar
    • Export Citation
  • Brown, P. R. A., and A. J. Heymsfield, 2001: The microphysical properties of tropical convective anvil cirrus: A comparison of models and observations. Quart. J. Roy. Meteor. Soc., 127, 15351550.

    • Search Google Scholar
    • Export Citation
  • Chepfer, H., P. Goloub, J. Riedi, J. F. De Haan, J. W. Hovenier, and P. H. Flamant, 2001: Ice crystal shapes in cirrus clouds derived from POLDER/ADEOS-1. J. Geophys. Res., 106 (D8), 79557966.

    • Search Google Scholar
    • Export Citation
  • Cho, H.-M., S. L. Nasiri, and P. Yang, 2009: Application of CALIOP measurements to the evaluation of cloud phase derived from MODIS infrared channels. J. Appl. Meteor. Climatol., 48, 21692180.

    • Search Google Scholar
    • Export Citation
  • C.-Labonnote, L., G. Brogniez, M. Doutriaux-Boucher, J.-C. Buriez, J.-F. Gayet, and H. Chepfer, 2000: Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. Comparison with in-situ and ADEOS-POLDER measurements. Geophys. Res. Lett., 27, 113116.