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  • View in gallery

    Ice crystal effective density [Eq. (1)] as a function of particle maximum diameter for different habits such as hexagonal column (black), droxtal (green), bullet rosette (red), aggregate (blue), and model density in MG08 (purple dotted).

  • View in gallery

    An example of partitioning bullet rosette particles of the first-order gamma PSD (blue) and exponential PSD (black) and the solid hexagonal column particles of the first-order gamma PSD (red) for an IWC ratio of the small mode at 0.8 (dashed lines) and 0.4 (solid lines). The vertical black dashed line is the critical size (Dth1 = 100 μm). The small particle mode includes the ice crystal particles with size less than Dth1.

  • View in gallery

    (a) Simulated IWC partition ratio of hexagonal column particles assuming the first-order gamma PSDs (solid black line) and using in situ measured PSDs from TC4 (red triangles for small mode, blue plus signs for median mode, and orange diamonds for large mode). The thin black lines with vertical error bars are the mean and standard deviation of the IWC partition ratio with in situ measurement PSDs. (b) As in (a), but for .

  • View in gallery

    PDF of partitioned IWC and IWC ratio of the small, median, and large particle modes from the Rad3mom at the TWP Manus site assuming the first-order gamma PSD of hexagonal column habit (black solid contour) and bullet rosette habit (color shading with dotted contours).

  • View in gallery

    Partitioned (top) IWC and (middle) IWC ratio for small (solid), median (dotted), and large (dashed) particles from the global CloudSat 2C-ICE retrieval assuming the first-order gamma PSD of hexagonal column (black) or aggregates (red) and exponential PSD of aggregates (green) in ice clouds observed by (first column) lidar only, (second column) lidar–radar overlapped, and (third column) radar only and (fourth column) in all ice clouds. (bottom) PDFs of corresponding ice clouds normalized by the total number of all ice clouds sampled.

  • View in gallery

    Repartitioned (a) IWCs and (b) IWC ratios of the small (solid line), median (dotted line), and large particle (dashed line) modes for SWC in the model. Red represents a calculation assuming the exponential PSD and constant density of snow (ρs = 0.1 g cm−3) and Nos = 0.03 cm−4. Green represents the same calculation as the red line, except using the variable ρs in MG08. Black represents a variable Nos as approximated from double-moment schemes (Swann 1998) and the variable ρs in MG08.

  • View in gallery

    Rebuilt PSDs of snow using different PSD shapes and effective density for snow water content at (a) 0.1, (b) 1, (c) 10, and (d) 100 mg m−3. Red represents a calculation assuming the exponential PSD and a constant density of snow (ρs = 0.1 g cm−3) and Nos = 0.03 cm−4. Green represents the same calculation as the red line, except using the variable ρs in MG08. Black represents variable Nos as approximated from double-moment schemes (Swann 1998) and the variable ρs in MG08.

  • View in gallery

    Repartitioned (a) IWCs and (b) IWC ratios of small (solid), median (dotted) and large particle (dashed) modes of GWC in the model. Red represents a calculation using exponential PSD and a constant density of graupel (ρg = 0.4 g cm−3) and Nog = 0.04 cm−4. Green represents the same calculation as the solid line, except using the variable ρg in MG08. Black represents the gamma PSD and a variable Nog as defined from double-moment schemes (Swann 1998) and the variable ρg in MG08.

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Partitioning Ice Water Content from Retrievals and Its Application in Model Comparison

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  • 1 Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming
  • | 2 Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah
  • | 3 Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming
  • | 4 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
  • | 5 State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
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Abstract

Retrieved bulk microphysics from remote sensing observations is a composite of ice, snow, and graupel in the three-species ice-phase bulk microphysics parameterization. In this study, density thresholds are used to partition the retrieved ice particle size distribution (PSD) into small, median, and large particle size modes from millimeter cloud radar (MMCR) observations in the tropics and global CloudSat and CALIPSO ice cloud property product (2C-ICE) observations. It shows that the small mode can contribute to more than 60% of the total ice water content (IWC) above 12 km (colder than 220 K). Below that, dominant small mode transitions to dominant median mode. The large mode contributes to less than 10%–20% at all height levels. The PSD assumption in retrieval may cause about 10% error in the IWC partition ratio. The lidar-only region in 2C-ICE is dominated by the small mode, while the median mode dominates the radar-only region.

For the three-species ice-phase bulk microphysics parameterizations, the cloud ice mass mainly consists of the small mode. But snow and graupel in the models are not equivalent to the median and large modes in the observations, respectively. Therefore, they need to be repartitioned with rebuilt PSDs from the model assumptions using the same partition technique as the observations. The repartitioned IWCs in each mode from different ice species need to be added together and then compared with the corresponding mode from observations.

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

Corresponding author: Min Deng, mdeng2@uwyo.edu

Abstract

Retrieved bulk microphysics from remote sensing observations is a composite of ice, snow, and graupel in the three-species ice-phase bulk microphysics parameterization. In this study, density thresholds are used to partition the retrieved ice particle size distribution (PSD) into small, median, and large particle size modes from millimeter cloud radar (MMCR) observations in the tropics and global CloudSat and CALIPSO ice cloud property product (2C-ICE) observations. It shows that the small mode can contribute to more than 60% of the total ice water content (IWC) above 12 km (colder than 220 K). Below that, dominant small mode transitions to dominant median mode. The large mode contributes to less than 10%–20% at all height levels. The PSD assumption in retrieval may cause about 10% error in the IWC partition ratio. The lidar-only region in 2C-ICE is dominated by the small mode, while the median mode dominates the radar-only region.

For the three-species ice-phase bulk microphysics parameterizations, the cloud ice mass mainly consists of the small mode. But snow and graupel in the models are not equivalent to the median and large modes in the observations, respectively. Therefore, they need to be repartitioned with rebuilt PSDs from the model assumptions using the same partition technique as the observations. The repartitioned IWCs in each mode from different ice species need to be added together and then compared with the corresponding mode from observations.

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Corresponding author: Min Deng, mdeng2@uwyo.edu

1. Introduction

Ice clouds have been identified as one of the main components in the upper troposphere because of their frequent occurrences and strong radiative effects (Liou 1986; Ackerman et al. 1988; Stephens 2005; Sassen et al. 2008; Mace 2010; Hong et al. 2016). Ice cloud occurrence frequency varies depending not only on regions and seasons but also on the types of ice clouds (Hong and Liu 2015). For example, tropical anvil clouds (Massie et al. 2002; Mace et al. 2006; Deng et al. 2016) spreading thousands of kilometers can last for days after the deep convection disappears. The microphysical processes (Mossop 1985; Jensen and Toon 1994; McFarquhar and Black 2004) such as aggregation and multiplication and secondary generation mechanism (Ackerman et al. 1988) affect the ice cloud microphysical properties and life span, which hence determine the magnitude and sign of the ice cloud radiative forcing (Hong and Liu 2015; Hartmann 2016).

To retrieve the microphysical properties of ice clouds from present satellite or ground-based remote sensing observations, usually one particle size distribution (PSD) shape is assumed and retrieved along with the ice bulk microphysical properties such as IWC and effective radius re in one sample volume, which includes both floating ice and precipitating ice (i.e., snow and graupel) if they coexist.

However, many bulk microphysics schemes (Lin et al. 1983; Krueger et al. 1995) follow the traditional three-species ice-phase scheme. It predicts the mixing ratio for each species with assumptions of a certain form of PSD, which means that in each model grid box, there are three mixing ratios or IWCs, if the three species coexist, compared to one retrieved IWC from observations. Single-moment microphysical schemes describing each species with only one model variable require coefficients to be defined so that the PSD can be determined as monotonic functions of mass mixing ratio. The subgrid microphysics processes among the species need to be parameterized (Lin et al. 1983). For example, aggregation of ice crystals to form snow or aggregation of snow crystals to form graupel is determined by an autoconversion rate and a conversion threshold. The conversion technique does not allow the ice crystals to grow gradually from cloud ice to precipitating ice, because it converts the ice to graupel immediately after a minimum mixing ratio threshold is met. Accretion of snow, ice, or graupel with other classes of hydrometeors is determined by PSD; terminal velocity of snow, ice, or graupel; and the mixing ratio of each species.

In recent years, a number of more flexible “double moment” microphysics schemes have been developed that represent both the mass and number concentration of each species (Ferrier 1994; Wang and Chang 1993; Morrison et al. 2005; Morrison and Grabowski 2008, hereafter MG08; Li et al. 2008), which allows greater flexibility in representing size distributions and hence microphysical process rates, significantly reduces the number of adjustable coefficients, and increases the physical realism. Therefore, there is a general trend toward the use of more detailed multimoment and multispecies schemes in spite of the complexity and the computational cost.

The parameterization of microphysics schemes has been shown to be crucial for simulations (Ferrier 1994; Morrison et al. 2009); however, it needs to be validated against observations to ensure that the model is physically realistic. Such model evaluation with an observation dataset is undergone with tremendous efforts (Randall et al. 2003).

First, it is difficult to separate errors in the cloud model microphysics from those related to the dynamic forcing. Therefore, the method of testing the sensitivity of model simulation results to different microphysical parameterizations is usually adopted. McCumber et al. (1991) showed that the evolution of heat and hydrometeor profiles and the radar reflectivity structure during deep convection are very sensitive to densities, fall speeds, and number concentration of precipitating ice species. Recently, this issue is partially solved by modelers (Luo et al. 2003; Blossey et al. 2007; Khairoutdinov and Randall 2003) using observational forcing data (Zhang and Lin 1997; Xie et al. 2004) during intensive operation periods to constrain models. For instance, Khairoutdinov and Randall (2003) applied a cloud-resolving model (CRM) to simulate the evolution of clouds over the Atmospheric Radiation Measurement (ARM; Ackerman and Stokes 2003) site in the Southern Great Plains (SGP) using large-scale and surface forcing data. They found out that changes to the autoconversion/accretion ratio coefficients, as well as the ice aggregation threshold, affect the ice cloud most profoundly. Blossey et al. (2007) found out during the Kwajalein Experiment (KWAJEX) simulation that the University of Utah microphysical scheme (Luo et al. 2003) can generate twice as much graupel and about half as much cloud ice as the system for atmospheric modeling microphysical scheme (Khairoutdinov and Randall 2003).

Second, direct observational retrievals corresponding to model outputs that distinguish floating ice from precipitating ice (i.e., snow and graupel) are not available. Some investigators added the water content of ice species together to generate total IWC or measurement variables such as radar reflectivity (Zhang et al. 2005; Luo et al. 2003) and compare them with observations. Blossey et al. (2007) evaluated the cloud-resolving modeling of deep convection during KWAJEX using TRMM satellite- and ground-based radar observations and found out that simulated radar reflectivity tends to be excessive in the upper troposphere, suggesting the simulated high clouds are precipitating large hydrometeors too efficiently. However, different ice species have very different characteristics, such as fall speed and mass–size relations, which affect the ice cloud occurrence frequency, lightning formation (Wang et al. 2011), and radiative effects in the model simulations. Therefore, it is imperative to develop a method to bridge the retrieved ice mass with the model simulation in a consistent way to allow one to make more meaningful comparisons between models and observations and to assess the parameterization of microphysical processes in models.

Recently, Waliser et al. (2009) compared simulated IWC of ice, snow, and graupel from several general circulation models with CloudSat IWC products separated by precipitating or nonprecipitating clouds. Chen et al. (2011) proposed a PSD partition method to partition the retrieved atmospheric ice mass into portions of small and large particle size modes. The partitioned IWC of the small mode in observations is considered to be equivalent to cloud ice in the model, and the large mode is considered to be equivalent to the precipitating ice species in the model, assuming that there is no need to repartition the PSD of snow and graupel in the model and that the small size mode in snow or graupel is negligible in cloud ice compared with the small mode in the observation. Such a comparison for ice species in models with observations is very important to evaluate the conversion validity among them and the microphysical processes parameterization in models (Li et al. 2012). However, there are two questions not investigated in Chen et al. (2011):

  1. How sensitive is the PSD partition method to the retrieval assumptions such as the particle habits and PSD? We are interested to know whether the partition is too sensitive to those assumptions so that the partition among the different modes is not distinguishable.
  2. The size distribution assumed for the precipitating ice in models such as snow, graupel, or hail covers a broad size range (Heymsfield et al. 2002; Field et al. 2007) depending on the parameters used to determine the PSD. If we partition the retrieved PSD into three modes, would the partitioned three size modes in the observational retrieval be related to the cloud ice, snow, and graupel in the model simulations? If not, then we need to repartition the water content in the ice species and then add the repartitioned IWCs in each mode from all the ice species and compare it with the corresponding mode from the observational retrieval.

In this study, we follow the PSD partition method in Chen et al. (2011) to partition the assumed PSD function in retrieval into three particle size modes using ice crystal density (i.e., mass–size relation), and then we test the sensitivity of partitioned ice mass to the assumptions of PSD shapes and ice particle habits (density) using in situ measurement and retrieval data at the ARM tropical western Pacific (TWP) Manus site and the CloudSat 2C-ICE dataset (Deng et al. 2010, 2013, 2015). Moreover, we reconstruct the PSD of snow and graupel in the model and repartition them with the PSD method in a similar manner as the observations to explore how the partitioned three size modes in observational retrieval are related to the ice species in the model simulations.

The paper is organized as follows. The partition technique based on the ice crystal density is introduced in section 2. IWC partition sensitivity to the PSD shapes is simulated numerically with idealized PSD functions and in situ measured PSDs during the NASA Tropical Composition, Cloud, and Climate Coupling (TC4) field campaign, where tropical ice clouds are extensively sampled by in situ measurement (Deng et al. 2010; Tian et al. 2010; Lawson et al. 2010). Then in section 3, retrieved IWCs of the three modes are examined for tropical ice clouds observed by millimeter cloud radar (MMCR) only at the ARM TWP Manus site and global ice clouds from the CloudSat 2C-ICE product. The IWC partition in the CloudSat 2C-ICE product is also examined in different lidar and radar coverage regions. In section 4, we discuss how the partitioned IWCs in retrieval are related to the model-simulated ice, snow, and graupel water contents by repartitioning the rebuilt PSD of the snow and graupel water content. A discussion and a summary are given in section 5.

2. Partition methodology

a. Ice particle density and partition thresholds

The mass–size relation is complex for nonspherical ice crystals. It depends on particle habits and particle size, which evolve as the ice crystals undergo different physical or dynamical processes. According to laboratory experiments (Hallett and Mason 1958; Mason 1994), ice crystals could undergo the following transitions of habits in the temperature range from 0° to −30°C: plate to needles to hollow columns to dendrites to prismatic column dependent on microphysical processes under certain temperatures and the supersaturation of the environment. Composite habits can be produced when crystals growing in a particular temperature are suddenly transferred into a different environment. Their bulk densities range from 0.05 to 0.9 g cm−3 (Pruppacher and Klett 1978).

Seven ice crystal shapes commonly observed in ice clouds are formed using aspect ratios (the ratio of particle length to particle diameter; Auer and Veal 1970): plates, solid and hollow hexagonal columns, planar bullet rosettes, spatial bullet rosettes, aggregates, and droxtals. Their mass–size and area–size relations and scattering properties have been studied in Aydin and Walsh (1999) and Yang et al. (2000) and parameterized as a function of maximum diameter Dmax. Thus, using these parameterizations, the equivalent projected area Aeff and volume Veff of nonspherical ice crystal can be obtained directly from Dmax. Then we can define the effective density of an ice particle as
e1
where ρi ≈ 0.9 g cm−3. Equation (1) shows that if the particle is close to a solid sphere, then the density is close to the bulk ice density. We present ρe of four particle habits in Fig. 1. Droxtals have a constant large density of 0.65 g cm−3. Aggregates are less dense with ρe at about 0.15 g cm−3. Densities of solid hexagonal column particles smaller than 100 μm are constant (0.55 g cm−3) because of the assumption of constant aspect ratios in their ice crystal formations, which is observed to be the case for small pristine ice crystals in the uppermost portion of cirrus clouds (Heymsfield and Iaquinta 2000). After that, density decreases to below 0.1 g cm−3 as Dmax increases. Density of bullet rosettes is generally smaller than that of hexagonal columns with the same Dmax. Densities of plates and hollow hexagonal columns (not shown) are between of those of solid hexagonal columns and bullet rosettes.
Fig. 1.
Fig. 1.

Ice crystal effective density [Eq. (1)] as a function of particle maximum diameter for different habits such as hexagonal column (black), droxtal (green), bullet rosette (red), aggregate (blue), and model density in MG08 (purple dotted).

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

Hereafter, we drop the subscript of Dmax for simplicity. Empirical power-law-fitting relations between the mass and maximum diameter are developed from in situ observations (Mitchell et al. 1990; Heymsfield and Iaquinta 2000):
e2
where am and bm are the fitting parameters. MG08 built up one PSD in model simulations with different relationships according to rimed conditions for ice crystals (Table 1) and then partitioned the PSD into four regions referred to as small ice sphere, dense nonspherical crystals, graupel, and partially rimed crystals bounded by critical particle sizes Dth, Dgr, and Dcr. The corresponding ρe can be derived as
e3
and overplotted as a purple dotted line in Fig. 1. Similar to those of hexagonal columns and bullet rosettes, ρe of MG08 also decreases as D increases except for the solid small particles less than 25 μm. For the particles larger than about 500 μm, their densities are larger than those of hexagonal column particles because of the riming effect assumed in MG08.
Table 1.

Density of snow and graupel or the mass–size relation assumed in the bulk microphysics schemes from published literature and used in our IWP repartition calculation.

Table 1.
We can partition the retrieved PSD like MG08 using the critical size or the corresponding size of constant density thresholds of 0.9, 0.1, and 0.4 g cm−3 for cloud ice, snow, and graupel, respectively, which are assumed in some microphysics schemes (Tao et al. 2003; Kuang et al. 2005; Lin et al. 1983). However, because of the variation of densities shown in Fig. 1, the corresponding D of a density threshold Dth for different particle habits varies by twofold to tenfold. For example, the corresponding Dth at densities equal to 0.1 and 0.4 g cm−3 for the hexagonal column particles are around 400 and 100 μm, respectively, while those for the aggregates should be 50 and 0 μm. In this study, we choose two thresholds (Dth1 = 100 μm and Dth2 = 800 μm), define the size boundaries, and then partition the PSD into three modes referred to as small mode (D < Dth1), median mode (Dth1 < D < Dth2), and large mode (D > Dth2). The two thresholds seem arbitrarily chosen even though the consideration of particle density is given here. Shifting the thresholds monotonically affects the IWC partition in observations as shown in Chen et al. (2011). If those thresholds are fixed and consistent for both observations and model simulations, then the comparison between observations and model simulations would be unambiguous. From the retrieved PSD and the assumed effective density in Eq. (1), we can calculate the IWC for each mode as
e4
or as the following with the mass–size relation in Eq. (3):
e5
where i represents small, median, and large modes and Di1 and Di2 represent the particle size boundaries for each mode. Whether the particle is floating or precipitating depends on the particle fall velocity and the ambient air motion. Here, we can calculate the mass-weighted fall velocity for each mode as
e6
In Eq. (6), Vf is the particle fall velocity calculated from the mass–size and area–size relations and drag theory (Mitchell 1996; Heymsfield and Iaquinta 2000; Mitchell and Heymsfield 2005), and n(D) is the PSD function for our study. Here, we assume a modified gamma function PSD:
e7
where No is the magnitude of PSD, Dm is the size where the function n(D) maximizes, and α indicates the breadth of the spectrum. If α equal 0, then it turns to an exponential PSD. For the first-order gamma PSD, where α equals 1, the total bulk IWC with the mass–size relation in Eq. (5) is calculated as
e8
The bulk re can be calculated as
e9
where aa and ba are the fitting parameters in the area–size relation (MG08). IWC partition ratio is defined as the ratio of IWC of each mode in Eq. (4) to the total bulk IWC in Eq. (8). By definition, No cancels in the IWC partition ratio, which means that the partition ratio is determined by the PSD slope and width or the bulk re of the PSD and independent of the magnitude of PSD (i.e., No in the PSD), which we will illustrate later.

Figure 2 shows an example of partitioning bullet rosette particles of the first-order gamma (blue) and the exponential PSD (black) and hexagonal column particles of the first-order gamma PSD (red) with the PSD parameters listed in Table 2. The set of dashed lines has 80% of IWC ratio in the small mode, while the set of solid lines has 40% of IWC ratio in the small mode. Those PSDs of 80% are dominated by small particles less than 100 μm, while the mass contribution of median and large particles increases because of the larger volume of larger particles. To decrease the IWC ratio of the small mode from 80% (dashed lines) to 40% (solid lines) in Fig. 2, the PSD has to increase the number concentration of particles larger 100 μm, thus increasing the bulk re. The change of No would only shift the PSD upward or downward in parallel but not change the IWC ratio since the No is cancelled out by definition and so is bulk re in Eq. (7). Therefore, the IWC partition ratio is a function of the bulk re.

Fig. 2.
Fig. 2.

An example of partitioning bullet rosette particles of the first-order gamma PSD (blue) and exponential PSD (black) and the solid hexagonal column particles of the first-order gamma PSD (red) for an IWC ratio of the small mode at 0.8 (dashed lines) and 0.4 (solid lines). The vertical black dashed line is the critical size (Dth1 = 100 μm). The small particle mode includes the ice crystal particles with size less than Dth1.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

Table 2.

Lists of parameters assumed in PSDs in Eq. (7) and the corresponding re for IWC partition examples of the small mode at 40% and 80% as shown in Fig. 2. Note that the magnitude of the PSD is assumed to be 1 for the three examples.

Table 2.

b. Partition in situ measured PSD from TC4

As indicated by in situ measurements (Mace et al. 2002; Heymsfield et al. 2002; Mitchell et al. 1990; Deng et al. 2010), actual PSDs are quite varying in terms of inverse exponential or bimodal shape or others. As a sensitivity study, we calculate the IWC partition ratio using 3500 in situ measured PSDs by 2D stereo probe (2DS) during the TC4 experiment on 22 July 2007. Early in the flight, the DC-8 sampled a thick anvil outflow between about 7.6 and 11.6 km that was streaming southwestward from dissipating convective sources over the eastern Pacific. After sampling the anvil clouds over the eastern Pacific, the DC-8 headed northbound, flying through a persistent thin cirrus layer over the southwestern Caribbean Sea. The 2DS-observed PSDs (Deng et al. 2010) show that for the thick anvil case, there are more large particles than in the high-cirrus case, so the PSD suggests some bimodality in the distribution. For the thin-cirrus case, there is a higher concentration of small particles with little evidence of bimodal particle spectra.

Using those in situ–measured PSDs of solid hexagonal column particles, the calculated IWC partition ratios of the three modes as a function of bulk re are plotted in Fig. 3a along with the calculation of the first-order gamma PSD of hexagonal column particles as the solid black line. First, it shows that the partition ratios from in situ PSDs have a very similar re dependence with those from gamma PSD. It is scattered with about 20% deviation. Second, it shows the mean partition ratios (dashed lines with error bars) from the in situ PSD are a little biased compared with those from the gamma PSD (solid lines): the IWC ratio of the small mode using a gamma PSD is generally overestimated by about 10%, while that of the median mode is underestimated by about 10% when re is less than 100 μm. When re is larger than 100 μm, the IWC ratio of the median mode is overestimated but that of the large mode is underestimated by about 10%.

Fig. 3.
Fig. 3.

(a) Simulated IWC partition ratio of hexagonal column particles assuming the first-order gamma PSDs (solid black line) and using in situ measured PSDs from TC4 (red triangles for small mode, blue plus signs for median mode, and orange diamonds for large mode). The thin black lines with vertical error bars are the mean and standard deviation of the IWC partition ratio with in situ measurement PSDs. (b) As in (a), but for .

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

The small mode dominates when the bulk re is less than 40 μm, the median mode dominates when re is between 40 and 100 μm, and the large mode dominates when re is larger than 100 μm. The value of from the in situ PSD is very similar to that from the gamma PSD. For the small mode, the mean fall velocity is below 20 cm s−1, the median mode has a fall velocity of 30–80 cm s−1, and the large mode fall velocity is 1 m s−1.

In cloud-resolving model simulations, Luo et al. (2003) assumed re of cloud ice to be 20 μm, while Blossey et al. (2007) assumed that re changes substantially from 10 to 30 μm. Compared to those model assumptions of density and re for ice in bulk microphysics schemes, the partitioned small mode from observation seems to have a consistently small re and fall velocity. However, whether the partitioned three modes are correspondingly related to the three species in the bulk microphysics scheme still remains a question, which will be discussed in section 4.

3. IWC partition distribution from ground and satellite observations

a. IWC partition distribution using ARM MMCR retrieval

In this section, we examine the partitioned IWC and ratios with two different retrieval datasets. The first retrieval algorithm is developed in Deng and Mace (2006) using the first three Doppler moments of the ARM MMCR observation (Rad3mom). It assumes the first-order gamma PSD in one radar sample volume. Rad3mom utilizes the physical fact that the observed Doppler spectrum is a convolution between a spectrum of air motions and a radar reflectivity spectrum from cloud particles that exist in air without mean motion or turbulence. For more algorithm details, please refer to Deng and Mace (2006). Rad3mom has been applied to the MMCR Doppler moments measurement at the ARM TWP C3 site during 2005–08. This dataset includes relatively thick anvil clouds and high thin cirrus clouds with cloud bases higher than the freezing level but excludes those ice clouds in the precipitating profiles because of the radar signal attenuation in rain. Because the ARM MMCR has a sensitivity of −50 dBZ at 15 km, it can observe most cirrus clouds up to 15 km if it is not attenuated. Rad3mom has recently been compared with three other radar-only and radar–lidar algorithms in Comstock et al. (2013). The IWC probability density functions (PDFs) and its height dependence in the radar–lidar-overlapped region are similar among four algorithms, the IWC above 12 km from Rad3mom and the other radar-only method in the radar-only region tends to be constant with height, and the IWC from the other two methods increases only a little with increasing height. These differences in the vertical distribution contribute to the heating-rate differences.

To study the IWC partition sensitivity to habits, the retrieval algorithm and the IWC partition are performed twice assuming hexagonal column (HC) and bullet rosette (BR) particles, respectively. We are aware that neither habit would be the reality; a closer-to-reality crystal habit composite is most desired in this research area. However, the sensitivity study sheds some insights on the IWC partition ratio error due to habit assumptions.

The vertical distributions of partitioned IWCs and ratio among the three modes of BR ice particles are shown in Fig. 4 in color contours and black dotted lines. As the temperature increases from 200 to 270 K, the IWC ratio of the small mode decreases from about 0.65 to less than 0.1, while the IWC ratio of the median mode increases from about 0.25 to 0.7, and the IWC ratio of the large mode increases a little from less than 0.1 to 0.3. The vertical distributions of partitioned IWC ratio from the HC ice particles retrieval (solid lines) have similar temperature dependences with the BR ice particle retrieval. Compared to the BR retrieval, the IWC ratio of the small mode of HC retrieval in clouds colder 220 K is slightly larger. The IWC ratio of the median mode of HC retrieval in clouds warmer than 240 K is slightly larger, while the IWC ratio of the large mode is slightly smaller.

Fig. 4.
Fig. 4.

PDF of partitioned IWC and IWC ratio of the small, median, and large particle modes from the Rad3mom at the TWP Manus site assuming the first-order gamma PSD of hexagonal column habit (black solid contour) and bullet rosette habit (color shading with dotted contours).

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

The partitioned IWC of the small mode varies little with temperature despite the large vertical variation of its IWC ratio for both HC and BR retrievals. The partitioned IWCs of the median and large modes increase with increasing temperature. Even though the IWC ratios of both small and large modes in ice clouds warmer than 240 K (between 10 and 6 km) are around 0.2, the partitioned mean IWC of the large mode is 5–10 times larger than that of the small mode. This is because the IWC partition ratio is positively correlated to the retrieved bulk re and IWC: both IWC and re increase with increasing temperature (Deng and Mace 2008), and the IWC partition ratio is a strong function of re, as shown in Fig. 2a. Therefore, larger IWC ratios of the small mode are associated with smaller bulk IWCs, while larger IWC ratios of the large mode are tied with larger bulk IWCs, thus resulting in larger partitioned IWC of the large mode than that of the small mode at the same IWC ratio in clouds warmer than 240 K.

To explain the difference due to particle habits in Fig. 4, let us refer to the density distribution of HC and BR particles in Fig. 1. The density of HC particles with size between 10 and 800 μm is several times larger than BR particles of the same size; therefore, partitioned IWC and IWC ratios of the small and median modes assuming HC habits are slightly larger than those with BR habits. This comparison indicates the assumption of particle density or particle habits is important in the ice mass partition. In Chen et al. (2011), a solid ice density is assumed for all size particles in the CloudSat 2B-CWC retrieval algorithm. If in reality, the large particles have relatively smaller density than solid ice, then the IWC ratio of the large mode in Chen et al. (2011) would be overestimated and that of the small mode would be underestimated. This speculation seems consistent with the finding in Fig. 7 of Chen et al. (2011) that the partitioned IWC ratio of the small mode with Dth1 equal to175 μm is still smaller than the precipitating flag technique in the work of Waliser et al. (2009). Of course, the consistency between the partition method and the flag technique still needs further investigation.

b. IWC partition distribution using CloudSat 2C-ICE dataset

A-Train satellite data provide an unprecedented global vertically resolved ice cloud observation. The CloudSat 2C-ICE product is a synergetic ice cloud retrieval created by optimally combining the CloudSat radar and the CALIPSO lidar measurements using a variational method to provide the profiles of extinction coefficient, IWC, and re for ice particles (Deng et al. 2010, 2013, 2015). It provides ice cloud microphysical properties in ice clouds and the ice part in some mixed-phase clouds identified by the CloudSat cloud classification product. For mixed-phase clouds where the supercooled water layer is identified by CALIPSO lidar observation, 2C-ICE treats the clouds below that water layer as ice clouds using radar only to perform the retrieval. For mixed-phase clouds in deep convection, where the lidar signal is usually attenuated, 2C-ICE retrieves clouds above −6°C mainly relying on CloudSat radar only (Deng et al. 2010). Attenuation due to ice particle distributions is included in the radar and lidar forward model. The Mie scattering effect of nonspherical large particles is calculated in the forward model lookup table according to a discrete dipole approximation (DDA) by Hong (2007).

Since the combination of CALIPSO lidar and CloudSat radar measurement are used in CloudSat 2C-ICE retrieval data, they form three unique lidar–radar regions. Because of the diminished sensitivity to small particles of radar signal and the decreasing ice particle size with decreasing temperature, there is a lidar-only region at colder temperatures. Because of the strong attenuation of lidar signal, there is a radar-only region at warmer temperatures. The lidar–radar-overlap region is in between. The PDFs of ice clouds observed in the three regions normalized by the total number of all ice clouds sampled are plotted in Fig. 5. We can see that peaks are around 215, 235, and 255 K for lidar-only, radar–lidar, and radar-only regions, respectively.

Fig. 5.
Fig. 5.

Partitioned (top) IWC and (middle) IWC ratio for small (solid), median (dotted), and large (dashed) particles from the global CloudSat 2C-ICE retrieval assuming the first-order gamma PSD of hexagonal column (black) or aggregates (red) and exponential PSD of aggregates (green) in ice clouds observed by (first column) lidar only, (second column) lidar–radar overlapped, and (third column) radar only and (fourth column) in all ice clouds. (bottom) PDFs of corresponding ice clouds normalized by the total number of all ice clouds sampled.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

The 2C-ICE data have been compared with in situ data and other retrieval datasets such as CloudSat 2B-CWC_RVOD (Austin et al. 2009) and radar–lidar (DARDAR; Delanoë and Hogan 2008) in Deng et al. (2013). It has been found that the mean ratios of the retrieved IWC and re in 2C-ICE to those estimated from in situ data are 1.12 and 1.05, respectively. The 2C-ICE retrieval agrees reasonably well with the DARDAR results in the radar region, which includes the radar–lidar overlap and radar-only regions, while the 2C-ICE retrieval in the lidar-only region has somewhat better agreement with in situ measurement than DARDAR since 2C-ICE takes the extra constraint that the effective reflectivity Ze is below the detection threshold of the CloudSat radar near −30 dBZe. In addition, an additional constraint is applied using a parameterization of Ze in the lidar-only region compiled from a climatology of ground-based cloud radar and lidar data (Deng et al. 2015).

To test the partition sensitivity to PSD and ice particle habits, we performed the 2C-ICE retrieval and IWC partition for three runs with 2007 data:

  1. Assuming the first-order gamma PSD of hexagonal column habit (Gamma_HC)
  2. Assuming the first-order gamma PSD of aggregate habit (Gamma_agg)
  3. Assuming the exponential PSD of aggregate habit (EXP_agg)

In situ measurements in the midlatitudes or tropics (Heymsfield et al. 2002; Mitchell 1996) showed that there is a vertical dependence of particle size and density. Small ice crystals at the cloud top are close to solid spheres with effective densities equal to bulk ice, often regarded as “quasi spherical.” In the middle layer, which contains growing ice crystals via aggregation, accretion, and collision, the ice clouds are dominated by solid or hollow columns, pristine plates, and bullet rosettes. Near the cloud base, crystals are composed primarily of irregular polycrystals or aggregates with low effective density. Given the vertical distributions of ice particles from in situ measurements and the lidar–radar coverages in the 2C-ICE product, it is a preparatory step for making a distinction between cloud ice and precipitating ice to assume that the lidar-only region is mainly associated with suspended small ice particles. In the following, we examine the partitioned IWC among the three modes for all ice clouds and the ice clouds observed in these three radar–lidar regions as well.

The temperature dependence of partitioned IWC ratio and IWC of all ice clouds in Fig. 5 is very similar to that from the MMCR retrieval in Fig. 4, while more ice clouds are observed above 200 K because of the CALIPSO lidar contribution. Figure 5 shows the IWC ratio of the small mode in the lidar-only region can reach 0.7. The IWC of the small mode is around 1 mg m−3. In the lidar–radar-overlap region, the IWC ratio of the small mode decreases from about 0.4 to 0.1 as the temperature increases, while the IWC ratio of the median mode increases from 0.5 to 0.8. The range of IWC of the small mode is still on the order of ~1 mg m−3.

In the radar-only region, the median mode remains dominant. The IWC ratio of the large mode increases from 0.05 to 0.2 as the temperature increases. The partitioned IWC of the median and large modes are orders larger than that of the small mode.

The comparison among three tests shows that the partition ratio is relatively more sensitive to particle density or particle habits than to the PSD shapes. Nevertheless, the difference of IWC ratio and IWC among the three modes is larger than the difference due to the assumptions of particle habits and PSD shapes, which means that this PSD method can clearly partition the retrieved PSD into three size modes. Moreover, the partitioned IWC and IWC ratios of the three modes from the CloudSat 2C-ICE dataset are consistent with those from the ARM MMCR retrieval in Fig. 4 though the two datasets are from two independent measurements and retrieval algorithms. The small particle mode dominates in the lidar-only region, and the median particle mode dominates in the radar-only region. However, we need to be cautious because the definition of the three lidar–radar coverage regions depends on the sensitivities of the instruments deployed in the projects.

4. Model applications

a. Simulated IWC repartition for model simulations

To examine how the partitioned three modes in retrieval are related to the subspecies in the model, we rebuild and repartition the PSD of snow and graupel in model simulations in this section.

The PSDs of snow and graupel (or hail) in most single-moment microphysics schemes are taken to be inverse exponential with respect to the particle maximum diameter such that
e10
where No is the intercept parameter (or the magnitude of the PSD) and λ is the slope of the PSD. It is inversely related to Dm in Eq. (7). The typical intercept parameters of snow and graupel used in the single-moment scheme are assumed to be constant, as listed in Table 3. In the double-moment ice microphysical scheme, the number concentrations of snow and graupel are predicted instead of diagnosed in the single-moment scheme. Swann (1998) found out that the number concentrations of snow or graupel are related to its water content, though it can vary by order for a given snow or graupel water content. They approximated No in the gamma PSD in Eq. (7) as a function of λ for snow and graupel derived from the double-moment scheme simulation (Swann 1998) as
e11
e12
The densities of snow ρs and graupel ρg in models are usually assumed to be constant or variable, as listed in Table 1.
Table 3.

PSD of snow and graupel assumed in the bulk microphysics schemes from published literature and used in our IWP repartition calculation.

Table 3.

In the following, we repartition the PSDs of the snow water content (SWC) and graupel water content (GWC) from the model simulation based on the PSD assumptions and the density assumption in the model so that the partitioned IWCs from observations are compared consistently with model output. Then we can find out to what extent the IWC of the small mode counts in snow and graupel mass so that it can be addressed and whether the median and large modes in observations correspond to snow and graupel in the models, respectively.

Here, we do not analyze actual model simulation outputs but define an array of SWC and GWC ranging from 0.1 mg m−3 to 1 g m−3, which correspond to Ze ranging from about −40 to 10 dBZe according to Ze–IWC relations in Liu and Illingworth (2000). For PSDs with constant No, we can calculate λ from Eq. (4). Then with Eq. (10), we can rebuild the PSD. For the estimated gamma PSD from the double-moment scheme, we can rebuild PSD with Eqs. (4), (7), (10), and (12). From the rebuilt PSD, we repartition SWC and GWC into three particle modes according to the Dth1 (100 μm) and Dth2 (800 μm) as in the observational data.

For these snow and graupel repartitions, we perform three sensitivity tests with the different assumptions of density and PSD used in model simulations (Tables 1 and 3):

  1. Test 1 (constant density and constant intercept): the exponential PSD with constant particle density (ρs = 0.1 g cm−3 and ρg = 0.4 g cm−3) and constant PSD intercept (Nos = 0.03 cm−4 and Nog = 0.0004 cm−4)
  2. Test 2 (variable density and constant intercept): the exponential PSD with variable particle density (ams = 0.001 42, bms = 2.02 and amg = 0.49, bmg = 2.8) and constant PSD intercept (Nos = 0.03 cm−4 and Nog = 0.0004 cm−4)
  3. Test 3 (variable density and variable intercept): the first-order gamma PSD with variable particle density (ams = 0.001 42, bms = 2.02 and amg = 0.49, bmg = 2.8) and variable PSD intercept in Eqs. (11) and (12) as a proxy of double-moment scheme.

b. Repartitioned IWC of snow water content in models

The partitioned IWC and IWC ratio of the three modes of SWC for three sensitivity tests are shown in Fig. 6. For the constant density and constant intercept PSD test 1 (red lines), the IWC ratio of the small mode decreases from about 0.4 to 0 as SWC increases. For the variable density but constant intercept PSD test 2 (green lines), it quickly decreases from about 0.8 to 0. It is larger than that with the constant density test because the density decreases as size increases in the variable density test. For these two tests, when SWC is less than 10 mg m−3, it is mainly partitioned between the small and median modes; when SWC is larger than 10 mg m−3, the contribution of the large mode increases from 0% to 80%.

Fig. 6.
Fig. 6.

Repartitioned (a) IWCs and (b) IWC ratios of the small (solid line), median (dotted line), and large particle (dashed line) modes for SWC in the model. Red represents a calculation assuming the exponential PSD and constant density of snow (ρs = 0.1 g cm−3) and Nos = 0.03 cm−4. Green represents the same calculation as the red line, except using the variable ρs in MG08. Black represents a variable Nos as approximated from double-moment schemes (Swann 1998) and the variable ρs in MG08.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

For the variable PSD intercept test 3 (black lines), SWC is partitioned between the small and median modes. The IWC ratio of the small mode decreases gradually from 0.6 to 0, and the IWC ratio of the median mode increases from 0.4 to 1.0 as SWC increases from 0.1 mg m−3 to 1 g m−3. The mean IWC of the small mode for these three tests is around 1 mg m−3. It might seem small in the SWC range in model simulation; however, it is on the same order of the partitioned IWC of the small mode in the observation in Figs. 4 and 5, which means the repartitioned IWC of the small mode from SWC in the model could be important in the model and observation comparison.

It is surprising to see such a big difference between the tests with constant and variable PSD intercepts, which corresponds to single- and double-moment schemes, respectively. Figure 7 shows the rebuilt PSDs of three tests at four different values of SWC. For constant No, increasing SWC directly causes increasing particle size, which increases the IWC ratio of larger particles. The IWC of the small mode still increases, but it increases at a slower rate than those of the median and large modes. Such excessively large particles generate excessively large reflectivities in the single-moment bulk microphysics parameterization. This bias has been noticed in the modeling community. Some improvement has been made by mapping the snow and graupel intercepts as functions of temperature and mass (Thompson et al. 2004; Tao et al. 2010). For variable No, increasing IWC means increasing number concentration and particle size; therefore, it slowly increases the IWC ratios of the median and large modes.

Fig. 7.
Fig. 7.

Rebuilt PSDs of snow using different PSD shapes and effective density for snow water content at (a) 0.1, (b) 1, (c) 10, and (d) 100 mg m−3. Red represents a calculation assuming the exponential PSD and a constant density of snow (ρs = 0.1 g cm−3) and Nos = 0.03 cm−4. Green represents the same calculation as the red line, except using the variable ρs in MG08. Black represents variable Nos as approximated from double-moment schemes (Swann 1998) and the variable ρs in MG08.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

c. Repartitioned IWC of graupel water content in models

Figure 8 shows the repartition among the three particle modes of GWC in the model. With constant No tests (red and green lines), the IWC of the small modes is around 0.01 mg m−3, orders smaller than the median and large particle modes, which means that the IWC of the small mode from GWC is negligible. The IWC and IWC ratio of the small particle mode in the variable No test 3 are larger than those with constant No tests but is still smaller than the median and large modes when GWC is larger than 1 mg m−3.

Fig. 8.
Fig. 8.

Repartitioned (a) IWCs and (b) IWC ratios of small (solid), median (dotted) and large particle (dashed) modes of GWC in the model. Red represents a calculation using exponential PSD and a constant density of graupel (ρg = 0.4 g cm−3) and Nog = 0.04 cm−4. Green represents the same calculation as the solid line, except using the variable ρg in MG08. Black represents the gamma PSD and a variable Nog as defined from double-moment schemes (Swann 1998) and the variable ρg in MG08.

Citation: Journal of the Atmospheric Sciences 75, 4; 10.1175/JAS-D-17-0017.1

For the variable No test, GWC seems dominated by the median mode, and the IWC and IWC ratios of the large mode in the variable No test are negligible. For the two constant No tests, a dominant median mode transitions to a dominant large mode as GWC increases, and the IWC and IWC ratios of the large mode are larger than those of the median mode when GWC is larger than 5 mg m−3, which is not observed in the ARM MMCR retrieval and CloudSat 2C-ICE retrievals in Figs. 4 and 5.

5. Discussion and summary

Retrieved bulk IWC from observation corresponds to the superimposed three IWCs, if the three species coexist, in the traditional three-species ice-phase scheme in Lin et al. (1983), which predicts the mixing ratio for each species with assumptions of a certain form of PSD in each model gird box. To ensure a consistent comparison between model simulations and observations, we proposed to partition the assumed PSD in both model outputs and observational retrievals into three modes, referred as small, median, and large particle modes, using the mass–size relationship and density thresholds. The small mode has a bulk mass-weighted fall velocity less than 20 cm s−1, while that for the median mode is around 20–80 cm s−1, and the large mode falls around 1 m s−1. Numerical simulation study shows that the partition ratios for the three modes are well correlated with the retrieved bulk re. For a sample volume with bulk re less than 40 μm, the retrieved PSD mainly consists of the small particle mode, which contributes more than 50% of the bulk IWC. As the PSD increases the number concentration of the median and large modes, it also increases the bulk re and the water contribution of the median and large modes. The variation of the PSD shape assumption, according to in situ measured PSDs at TC4, may cause about ~10% error in IWC partition ratio.

The partition method has been applied to two independent retrieval datasets. The three-Doppler-moment retrieval dataset from 5 years of MMCR observations at the ARM TWP Manus site includes thick anvil clouds and thin cirrus clouds in the tropics. The 2C-ICE retrieval from CloudSat includes global ice clouds as well as ice in the mixed-phase clouds in the deep convective profiles and in some stratiform mixed-phase clouds. Retrieval analysis from these datasets shows similar and distinguishable IWC partition results among the three modes, even though they are from two separate measurements and algorithms. The small mode can contribute to more than 60% of the IWC in clouds colder than 220 K. Below that, the dominant small mode transitions to the dominant median particle mode. Its IWC partition ratio decreases to about 0.15, while the IWC ratio of the median mode increases from 0.1 at about 200 K to 0.7 at about 240 K. The large mode contributes to less than 10%–20% in the clouds warmer than 240 K. The mean IWC of the small mode is on the order of 1 mg m−3 despite the large vertical variation of the IWC ratio. The mean IWC of the median mode increases from 1 to about 10 mg m−3, while the mean IWC of the large mode increase from 0.1 to 10 mg m−3 from 200 to 270 K. The habit assumption in the retrieval algorithm may cause up to about 30% uncertainty in the partitioned IWCs.

In the lidar-only region from the CloudSat 2C-ICE product, IWC is dominated by the small particle mode, and the large mode is negligible, while in the radar-only region, the median particle mode dominates, and the small mode is negligible. However, we need caution that this result may not be exactly applicable to other datasets since the definition of lidar–radar regions depends on the sensitivities of instruments used in different projects.

For the three-species ice-phase scheme in models, the cloud ice mass is generally contributed by the small particles, given the small size assumption of cloud ice. However, snow and graupel are not equivalent to the median and large modes in observations, respectively. Therefore, they need to be repartitioned with a rebuilt PSD from the model assumptions using the same partition technique in Eq. (4) as the observation, and then the repartitioned IWCs in each mode from different ice species need to be added together and compared with the corresponding mode from observation. The repartition analysis of SWC and GWC with the rebuilt PSD from the model assumptions shows that the contribution of the three particle modes to snow and graupel can vary by orders depending on the value of SWC and GWC, the assumption of particle density, and the PSD parameters. The small mode can contribute up to 50% of snow water contents when SWC is less than 1 mg m−3 and its IWC is on the same order of the partitioned IWC of the small mode in the observation. Therefore, the particle density and parameters in the rebuilt PSD for the repartition need to follow the model assumption in the microphysics schemes so that we can further analyze the microphysical process parameterization for the cause of the possible simulation discrepancy from observations. The proposed PSD partition method is effectively applicable to model simulations with either multispecies rather than the three-species or one-PSD assumption as in MG08 so that they can be compared with observations in a consistent way.

Acknowledgments

The A-Train data were acquired from the CloudSat Data Processing Center at Colorado State University. The MMCR measurements were acquired from ARM data center. This work was supported by National Aeronautics and Space Administration Grant 1002940. The research was also partly funded by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

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