Editorial Type:
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Article Type:
Research Article

Evaluation of the Aggregation Efficiency Modeling at Colder Atmospheric Temperatures in Comparison to Satellite Observations

Tatsuya Seiki aJapan Agency for Marine-Earth Science and Technology, Yokohama, Kanagawa, Japan

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Takashi M. Nagao bAtmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Chiba, Japan

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Online Publication:
30 Sep 2024
Print Publication:
01 Oct 2024
DOI:
https://doi.org/10.1175/JAS-D-23-0208.1
Page(s):
1689–1710
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Abstract

Aggregation efficiency in the upper troposphere is highly uncertain because of the lack of laboratory experiments and aircraft measurements, especially at atmospheric temperatures below −30°C. Aggregation is physically broken down into collision and sticking. In this study, theory-based parameterizations for the collision efficiency and sticking efficiency are newly implemented into a double-moment bulk cloud microphysics scheme. Satellite observations of the global ice cloud distribution are used to evaluate the aggregation efficiency modeling. Sensitivity experiments of 9-day global simulations using a high-resolution climate model show that the use of collision efficiency parameterization causes a slight increase in the cloud ice amount above the freezing level over the tropics to midlatitudes and that the use of our new sticking efficiency parameterization causes a significant increase in the cloud ice amount and a slight decrease in the snow amount particularly in the upper troposphere over the tropics. The increase/decrease in the cloud ice/snow amount in the upper troposphere over the tropics is consistent with the vertical profile of radar echoes. Moreover, the ice fraction of the cloud optical thickness is still underestimated worldwide. Finally, the cloud radiative forcing increases over the tropics to reduce the bias in the radiation budget. These results indicate that our new aggregation efficiency modeling reasonably functions even at atmospheric temperatures below −30°C; however, further improvements in the ice cloud modeling are needed.

Significance Statement

Long-standing biases in the radiative budget in climate models indicate the existence of a missing mechanism to realistically represent the ice cloud growth in the upper troposphere. This study focuses on aggregation efficiency, which has been assumed to be a tuning parameter to optimize the global radiative budget. Therefore, this study employs a theory-based parameterization to calculate the aggregation efficiency. According to the parameterization, aggregation efficiency in high clouds varies by the growth stage of the individual ice particles. As a result, small ice crystals are likely to grow more slowly, and the lifetime of cirrus clouds is prolonged to enhance cloud radiative forcing, particularly over the tropics. These results are promising for reducing the biases observed in climate models.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tatsuya Seiki, tseiki@jamstec.go.jp

Abstract

Aggregation efficiency in the upper troposphere is highly uncertain because of the lack of laboratory experiments and aircraft measurements, especially at atmospheric temperatures below −30°C. Aggregation is physically broken down into collision and sticking. In this study, theory-based parameterizations for the collision efficiency and sticking efficiency are newly implemented into a double-moment bulk cloud microphysics scheme. Satellite observations of the global ice cloud distribution are used to evaluate the aggregation efficiency modeling. Sensitivity experiments of 9-day global simulations using a high-resolution climate model show that the use of collision efficiency parameterization causes a slight increase in the cloud ice amount above the freezing level over the tropics to midlatitudes and that the use of our new sticking efficiency parameterization causes a significant increase in the cloud ice amount and a slight decrease in the snow amount particularly in the upper troposphere over the tropics. The increase/decrease in the cloud ice/snow amount in the upper troposphere over the tropics is consistent with the vertical profile of radar echoes. Moreover, the ice fraction of the cloud optical thickness is still underestimated worldwide. Finally, the cloud radiative forcing increases over the tropics to reduce the bias in the radiation budget. These results indicate that our new aggregation efficiency modeling reasonably functions even at atmospheric temperatures below −30°C; however, further improvements in the ice cloud modeling are needed.

Significance Statement

Long-standing biases in the radiative budget in climate models indicate the existence of a missing mechanism to realistically represent the ice cloud growth in the upper troposphere. This study focuses on aggregation efficiency, which has been assumed to be a tuning parameter to optimize the global radiative budget. Therefore, this study employs a theory-based parameterization to calculate the aggregation efficiency. According to the parameterization, aggregation efficiency in high clouds varies by the growth stage of the individual ice particles. As a result, small ice crystals are likely to grow more slowly, and the lifetime of cirrus clouds is prolonged to enhance cloud radiative forcing, particularly over the tropics. These results are promising for reducing the biases observed in climate models.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tatsuya Seiki, tseiki@jamstec.go.jp
Keywords: Cloud microphysics; Cloud radiative effects; Remote sensing; Satellite observations; General circulation models

1. Introduction

Ice clouds have various roles across the globe. In the midlatitudes, snow particles slowly grow along the frontal systems associated with extratropical cyclones. Cloud systems consist of broad stratiform snow clouds in the middle to upper troposphere and persistently provide rainfall (e.g., Hobbs 1978). In contrast, in the tropics, convective organization provides a humid air mass in the upper troposphere and generates tiny ice crystals near the cloud top (e.g., Yanai et al. 1973). As a result, thin anvil cirrus layers broadly form in the upper troposphere and induce strong longwave cloud radiative forcing (e.g., Liou 1986). Recently, the cloud radiative forcing of high clouds has been found to have a strong impact on the prediction of tropical cyclones (e.g., Fovell et al. 2010) and the initiation of Madden–Julian oscillations (Takasuka et al. 2018). These results indicate that detailed modeling of ice clouds could extend the predictability of atmospheric phenomena. Therefore, detailed ice cloud modeling is needed across the research fields.

Aggregation is an important growth mechanism for ice particles but is highly uncertain. In cloud microphysics schemes, aggregation is solved by assuming binary collision (e.g., Pruppacher and Klett 2010). The growth rate of a single particle is generally evaluated by counting the collected particles within its swept volume per unit time. However, aerodynamical interaction between the particles and flow modifies the actual collisional cross section (e.g., Böhm 1992b). In addition, collided particles are known to be frequently separated after the collision (cf. rigid body collision). Thus, the aerodynamical effect is represented by the collision efficiency, and the effect of separation is represented by the sticking efficiency. The aggregation efficiency between a collecting particle and a collected particle is formulated by the product of the collision efficiency and the sticking efficiency. In general, both efficiencies have values less than unity depending on the particle size and shape. The aggregation efficiency of binary collision is one of the most uncertain parameters in cloud microphysics. Thus, the efficiency can be considered as a tuning parameter.

The theoretical modeling approach partly reduces the uncertainties in the aggregation efficiency but cannot fully solve the issue. The collision efficiency of nonspherical ice particles is determined by the flow of air surrounding a collecting particle (e.g., Böhm 1992a,b,c; Wang 2002), as is determined for the drop–drop collisions. With an appropriate assumption for the particle shape and an accurate estimate of the particle size, a theory-based parameterization, which is in good agreement with measurements, has been proposed (Böhm 1992a,b,c, 1994). In contrast, the sticking efficiency originates from the condition of the surface of ice crystals. The mechanisms of sticking are not yet fully understood (cf. Pruppacher and Klett 2010). Therefore, all cloud models inevitably depend on the past observational database of the sticking efficiency that was achieved in various experimental conditions. Thus, uncertainties in the aggregation efficiency depend on the particle size, shape, and choice of the sticking efficiency database.

The lack of comprehensive observations and laboratory experiments on sticking efficiency is a crucial issue for establishing sticking efficiency modeling. In particular, the sticking efficiencies at atmospheric temperatures below 233 K have not been obtained in the literature thus far. Laboratory experiments on the sticking efficiency (e.g., Connolly et al. 2012) have been limited to atmospheric conditions at atmospheric temperatures greater than 243 K due to the difficulty in laboratory experiments. Aircraft measurements have been also utilized for estimating the aggregation efficiency in various atmospheric temperature ranges (e.g., Passarelli 1978; Kajikawa and Heymsfield 1989; Field et al. 2006). However, the estimation was also limited at atmospheric temperatures up to 228 K (Kajikawa and Heymsfield 1989). Previous studies on aggregation efficiency estimation based on aircraft measurements are limited to flight cases; hence, the estimation is reliable to a limited size range of a specific shape of ice particles. In addition, some analyses did not break down the aggregation efficiency into the collision and sticking efficiencies. For example, the aggregation efficiency of thick plate-type ice particles larger than 75 μm was estimated by Kajikawa and Heymsfield (1989). Thus, the sticking efficiencies are quite uncertain at colder atmospheric temperatures and for ice particles with very small or large sizes or with different shapes. A fitting curve to a laboratory database can be used, and then the sticking efficiencies at colder atmospheric temperatures can be extrapolated to simulate high clouds (e.g., Lin et al. 1983).

Uncertainties in the aggregation efficiency at colder atmospheric temperatures particularly affect global climate simulations since high thin clouds have strong longwave cloud radiative forcing. Figure 1 shows the ice cloud fraction over the tropical ocean sorted by the cloud-base temperatures from CALIPSO, CloudSat, and ECMWF ancillary atmospheric state datasets [the EarthCARE Research A-Train Product Monitor (Okamoto et al. 2007, 2008, 2010; Hagihara et al. 2010; Yoshida et al. 2010)]. The satellite observations clearly capture the characteristics of tropical cloud systems: deep convective clouds with cloud-base temperatures near the sea surface and cloud-top temperatures reaching up to the tropopause along with thin anvil cirrus clouds that form by detrainment near the cloud top of deep convective clouds (Fig. 1a). For convenience, the ice clouds with cloud-base temperatures greater than 273 K are categorized as deep convective clouds, and those with cloud-base temperatures below 273 K are categorized as anvil cirrus clouds. Based on the categorization, most anvil clouds exist at atmospheric temperatures below 243 K, and approximately half of the anvil clouds have cloud-base temperatures below 243 K (Fig. 1b). Thus, most cirrus cloud simulations by climate models are found to be unreliable.

Fig. 1.
Fig. 1.

(a) Joint PDF of the cloud occurrence at each atmospheric temperature range sorted by the cloud-base temperatures over the tropical ocean (from 20°S to 20°N). (b) As in (a), but for the PDF of the cloud occurrence at each atmospheric temperature range. Based on the joint PDF, cirrus-type clouds (Ci) are categorized by cloud-base temperatures colder than 273 K, and convective-type clouds (Dc) are categorized by cloud-base temperatures warmer or equal to 273 K. For reference, the occurrence of the objective cirrus-type clouds, which have cloud-base temperatures colder than 243 K, is also plotted. To obtain the cloud occurrence, the radar- or lidar-detectable cloud mask [the so-called C4 mask defined by Okamoto et al. (2007, 2008) and Hagihara et al. (2010)] is used. Ice clouds are defined by successive cloudy ranges that contain at least one range with atmospheric temperatures colder than 273 K (Seiki et al. 2019).

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

This study aims to examine the impact of aggregation efficiency on various cloud systems around the globe. The aggregation efficiency in most bulk cloud microphysics schemes is quite simply formulated: The sticking efficiency is formulated as a function of atmospheric temperature based on the aforementioned database (Lin et al. 1983; Cotton et al. 1986; Karrer et al. 2021), and the collision efficiency is assumed to be a fixed value across all cloud systems and all cloud development phases (Lin et al. 1983; Cotton et al. 1986; Milbrandt and Yau 2005; Morrison et al. 2005; Seifert and Beheng 2006; Morrison and Milbrandt 2015; Karrer et al. 2021; Sulia et al. 2021; Seiki and Ohno 2023). Only a few bulk cloud microphysics schemes incorporate the effect of the collision efficiency using the lookup tables (e.g., Cotton et al. 2003; Thompson et al. 2008). Recently, Jin and Baik (2020) developed a simple parameterization for the collision efficiency between cloud droplets and snow and then applied the parameterization to a bulk cloud microphysics scheme. They found that the snow amount slightly increased in a midlatitude mesoscale convective cloud case by considering the collision efficiency. It was expected that the snow amount could more significantly change over the tropics by means of collision efficiency modeling because tropical cirrus clouds were sensitive to aggregation (e.g., Kodama et al. 2012; Seiki et al. 2015a; Roh et al. 2017; Seiki and Ohno 2023).

In this study, theory-based parameterizations for the collision efficiency and sticking efficiency were implemented in a double-moment bulk cloud microphysics scheme in the Nonhydrostatic Icosahedral Atmospheric Model [NICAM (Tomita and Satoh 2004; Satoh et al. 2008, 2014; Kodama et al. 2021)] named NDW6 (Seiki and Nakajima 2014; Seiki et al. 2014, 2015b; Seiki and Ohno 2023); then, global high-resolution simulations were evaluated in reference to satellite observations. Recently, Seiki and Ohno (2023) developed a size-resolved method to numerically integrate the collection equation with the Gauss–Legendre quadrature. With this method, the strong dependence of the collision and sticking efficiencies on the particle size were explicitly considered. The method was already implemented in NDW6, and global high-resolution simulations were effectively achieved. Thus, aggregation efficiency modeling was indirectly evaluated by comparing the global distribution of ice clouds.

In this study, spaceborne radar observations were utilized to evaluate aggregation signals in the vertical profile of radar echoes. In the case of warm clouds, rapid change in particle size through collisional growth could be clearly distinguished from slow condensation growth using radar observations because the radar reflectivity factor Ze has a strong sensitivity to the particle size D (Suzuki and Stephens 2008; Suzuki et al. 2010). The sensitivity of Ze to the particle size has also been utilized for evaluating aggregation modeling in the upper troposphere (e.g., Seiki and Ohno 2023). The change in the horizontal distribution of ice clouds was then evaluated using passive imager observations. Specifically, the retrieval products of the cloud optical thickness (COT) and ice COT fraction (Nagao and Suzuki 2021, 2022) were utilized for comparison. The retrieval products provided information on the cloud phases at greater optical depths beyond the reach of lidar signals, while passive imagers could not provide vertical profiles of the cloud phase. Any changes to slow aggregation were expected to increase the ice COT in analogy to the traditional cloud lifetime effects (e.g., Albrecht 1989). Finally, improvements in the radiative fluxes at the top of the atmosphere (TOA) were examined in reference to the broadband radiometer observations.

The aggregation efficiency modeling is described in section 2. The numerical settings and satellite products used for model evaluation are provided in section 3. The results from the sensitivity experiments are examined in section 4. The remaining biases in the NICAM simulations are discussed in section 5. Finally, section 6 briefly summarizes the modeling method and findings from the collision and sticking efficiency modeling.

2. Aggregation efficiency modeling

a. Collisional equation

Collisional growth in bulk schemes is generally evaluated by solving the collection equation. The growth rates of the mass concentration L and number concentration N are formulated by integrating the collection kernel K with the particle size distribution f and particle mass x as follows:
(∂Nj∂t)col,jk=−∫∫0∞fj(lnDj)fk(lnDk)K(Dj,Dk)dlnDjdlnDk,
(∂Lj∂t)col,jk=−∫∫0∞xjfj(lnDj)fk(lnDk)K(Dj,Dk)dlnDjdlnDk,
K(Dj,Dk)=Ejk(Dj,Dk)π4(Da,j+Da,k)2|υj(Dj)−υk(Dk)|.
Here, a hydrometeor category j is assumed to be collected by a hydrometeor category k. NDW6 predicts the hydrometeor categories of cloud water, rain, cloud ice, snow, and graupel; hereafter, the category indices are denoted as c, r, i, s, and g, respectively. The collection kernel consists of the collection efficiency Ejk, the collisional cross section with the area-equivalent diameter Da, and the sweep distance per unit time. Since the sweep distance per unit time is represented by the difference in the terminal velocities υ between the collecting and collected particles, it is difficult to analytically integrate the collection kernel in Eqs. (1) and (2). In most bulk cloud microphysics schemes, the terminal velocity used in the kernel is simplified using a power-law relation, and then, the kernel is approximately reformulated to be easily integrated. However, such a simplification is known to cause severe errors in evaluating the collisional growth term (Seifert et al. 2014; Seiki and Ohno 2023). In particular, thin cirrus clouds and intense rainfall systems over the tropics are strongly affected by this simplification (Seiki and Ohno 2023).
In our study, the collection equation is numerically solved with the Gauss–Legendre quadrature to avoid these issues, as follows:
(∂Nj∂t)col,jk=−∑nknmax∑njnmaxfj(ln⁡Dnj)fk(lnDnk)K(Dnj,Dnk)wnjwnk,
(∂Lj∂t)col,jk=−∑nknmax∑njnmaxxnjfj(lnDnj)fk(lnDnk)K(Dnj,Dnk)wnjwnk,
where wn is the quadrature weight and nmax is the number of Gauss nodes. Thus, the dependence of the aggregation efficiency in the collection kernel on the particle size is explicitly represented in this method. In our study, an nmax value of 6 is used to accurately calculate the collision efficiency and new sticking efficiency parameterizations, which are described in the following subsections.

b. Terminal velocities

NDW6 employs a theory-based parameterization for the ice terminal velocity proposed by Mitchell (1996) and Böhm (1989). In the parameterization, the particle mass x, the maximum dimension D, and the particle’s area projected normal to the flow A are needed to represent the characteristics of nonspherical ice particles. These three variables are related to each other by a power law, and NDW6 uses the coefficients and exponents provided by Mitchell (1996) (see Table 1 for details). Given a particle shape and size, the ice terminal velocity is calculated according to the theory-based formulation as follows:
υ=ηaDρaδ024 {[1+4δ02C01/2(2xgρaD2Aηa2)1/2]1/2−1}2,
where ηa is the dynamic viscosity of air, ρa is the air density, g is the gravitational constant, and two parameters, δ = 5.83 and C0 = 0.6, are chosen based on Böhm (1989). This formulation was verified in realistic snowfall events in comparison with a volume scanning video disdrometer (Kondo et al. 2021) although further sophisticated formulations were recently proposed (e.g., Mitchell and Heymsfield 2005; Heymsfield and Westbrook 2010).
Table 1.

Summary of the coefficients and exponents in the power-law relationships (x=axDbx, A=aADbA). Here, the units are converted into mks from cgs, which the original work by Mitchell (1996) used. In NDW6, cloud ice is assumed to be hexagonal columns, snow is assumed to be the assemblage of planar polycrystals in cirrus clouds, and graupel is assumed to be lump graupel, as labeled in Mitchell (1996). Note that the shape of the hexagonal columns slightly transforms at sizes larger than 100 μm.
Table 1.
Moreover, NDW6 employs a fitting curve to the rain terminal velocity observation, which was proposed by Rogers et al. (1993), to represent the terminal velocity of cloud water and rain as follows:
υ={9.65−10.43exp⁡(−600D), if(D>7.45×10−4 m)4000D[1−exp⁡(−12000D)] else .
Since the original observation was conducted in the laboratory (Gunn and Kinzer 1949), the terminal velocities were corrected by the density factor [(ρ0/ρa)0.5 with ρ0 = 1.28 kg m−3] in the atmosphere. These accurate terminal velocities were directly calculated for the collision and sticking efficiencies and the collection kernel at the Gauss nodes [Eqs. (3) and (4)].

c. Collision efficiency

In this study, a theory-based parameterization for the collision efficiency was newly implemented, as proposed by Böhm (1989, 1992a,b,c, 1994, hereafter B89, B92a,b,c, B94), whereas the collision efficiency was assumed to be unity except for the collision pairs involving cloud water in the previous version of NDW6 following Seifert and Beheng (2006). Seifert and Beheng (2006) proposed a bulk collision efficiency for cloud water using the mean volume diameter of cloud water [Dc(xc¯)] and ice hydrometeors [Dj(xj¯)] as follows:
Ec,cj¯=Ec¯Ej¯,
Ec¯=max{0,min⁡[1,Dc(xc¯)−Dc,0Dc,1−Dc,0]},
Ej¯={0, Dj(xj¯)<150×10−6Emax,j¯, Dj(xj¯)≥150×10−6,
with Dc,0 = 15 × 10−6 m, Dc,1 = 40 × 10−6 m, Emax,i¯=Emax,s¯=0.8, and Emax,g¯=1.0.

This bulk collision efficiency represents the cutoff diameter of cloud water (Dc,0) and ice hydrometeors (150 μm) below which riming does not occur. This simplified formulation was empirically determined by Seifert and Beheng (2006), but the reference data were not presented.

In contrast, the theory-based parameterization for the collision efficiency was formulated based on boundary layer theory (Böhm 1989, 1992a,b,c, 1999). In addition, a correction factor based on potential flow theory (Böhm 1994, 1999) was proposed. The correction factor captured the observational fact that the collision efficiency sharply dropped to 0 when a collided particle was smaller than a certain threshold; this was the so-called cutoff radius (e.g., Wang 2002). Previously, the cutoff radius was selected as a fixed value; however, it was known to have a large impact, especially on the riming of cloud droplets onto large ice particles in low-level mixed-phase clouds (e.g., Furtado and Field 2017; Seiki and Roh 2020). Therefore, the theory-based modeling of the correction factor enabled the calculation of the intermediate values with a rapid reduction in the collision efficiencies without empirical tuning. The parameterization generally captured past observation datasets for riming and aggregation although some theoretical incorrectness was found (Böhm 2004; Posselt et al. 2004). Reproducibility of the corrected version of the parameterization degraded in reference to the observation dataset (Böhm 2004), and hence, we implemented the previous version (Böhm 1999) for practical use. Our study predominantly followed the description by Böhm (1999, hereafter B99), in which a series of works for collision efficiency parameterization (Böhm 1989, 1992a,b,c, 1994) was compiled. The characteristics of nonspherical ice shapes were generalized by using the area ratio q and the axial ratio α; representative mass, radius, and other physical parameters in the two-body system (collecting and collected particles in the flow) were characterized by appropriately weighted mean values. The assumption and formulation used in this study for the parameterization are summarized in Table 2, and the axisymmetric case (j = 2 in Böhm 1999) was selected. The formulation of the collision efficiency was omitted because of its complexity (readers should refer to the original papers for details).

Table 2.

Parameters related to the particle shape. Symbols follow B99.
Table 2.

The collision efficiencies in a typical range of particle sizes are examined assuming a tropical atmosphere; the collision efficiencies in various ranges of particle radii are summarized in appendix A. The vertical profiles of the mean atmospheric temperature, mean mixing ratios, and mode radii are obtained from global simulations using NDW6 [see the NEW experiment in Seiki and Ohno (2023), for details] and are simplified for the examination, as shown in Fig. 2. The simplified profiles are provided in appendix B.

Fig. 2.
Fig. 2.

Typical vertical profiles of (a) atmospheric temperature, (b) mixing ratios of the hydrometeors (qj), and (c) mode radii (rMj) over the tropical ocean. The simulation results are shown by dots, and the simplified profiles are shown by solid lines. Note that qs values exactly match qi values.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

The conventional assumption of Ecol as unity or a specific constant value in most bulk cloud microphysics schemes has been clearly found to be inaccurate based on the examination. The collision efficiencies involving cloud ice and snow significantly vary with their particle sizes (Fig. 3c). In particular, the aggregation of cloud ice and snow in the upper troposphere becomes much less efficient near the tropopause. In contrast, the collision efficiencies involving rain or graupel are close to unity (Figs. 3a,b,d), as is assumed in most bulk cloud microphysics schemes. The collision between the cloud water and ice hydrometeor categories (i.e., riming) is suppressed by considering the collisional efficiency (Fig. 3a). As expected, the suppression is more enhanced with the correction based on potential flow theory.

Fig. 3.
Fig. 3.

The vertical profiles of the collision efficiencies Ecol averaged with the weight of the collection kernel. (a) Collision pairs involving cloud water, (b) collision pairs involving rain, (c) collision pairs between cloud ice and snow, and (d) collision pairs with the collector of graupel are shown. Solid lines indicate the collision efficiency based on boundary layer theory with the correction based on potential flow theory, and dashed lines indicate the collision efficiency based only on boundary layer theory.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

d. Sticking efficiency

In this study, a theory-based parameterization for the sticking efficiency was newly implemented based on Phillips et al. (2015, hereafter EsP15), whereas an empirical fitting curve for the sticking efficiency proposed by Lin et al. (1983, hereafter EsL83) was used in the previous version of NDW6. The conventional formulation depends only on the atmospheric temperature as follows:
Estick(T)=exp[−astick(T−T0)],
where T0 = 273 K and astick is the empirically determined constant parameter. The parameter astick was able to be fit to laboratory experiments from −25° to −6°C (Fig. 4 in Lin et al. 1983). Thus, the previous version of NDW6 did not apply extrapolation to the sticking efficiency with the lower limit of the atmospheric temperature of −25°C (Fig. 4). Therefore, the sticking efficiency at atmospheric temperatures below −25°C was completely uncertain based on the formulation. In addition, the formulation did not capture various Estick values in the past observation dataset (Pruppacher and Klett 2010), indicating that the parameter astick had various values in the cloud systems. In particular, the strong dependence of the aggregation efficiency on the particle size, as was found by the estimates based on aircraft measurements (e.g., Field et al. 2006), should be considered.
Fig. 4.
Fig. 4.

Sticking efficiencies calculated by Phillips et al. (2015) (solid colored lines), Lin et al. (1983) (black dashed line), and Connolly et al. (2012) (solid black line) with the reference atmosphere (Fig. 2). The subscripts EsP15 (jk) indicate the pair of hydrometeor categories, and EsP15 is averaged at each altitude with a weighting of the collection kernel. Note that EsP15ig is multiplied by 104 for visualization.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

According to Phillips et al. (2015), the sticking efficiencies are effectively expressed by the distribution of the collision kinetic energy Kc normalized by the bond energy. Here, the bond energy is assumed to be proportional to the contact area of a collided small particle in the two-body system; hereafter, smaller and larger particles are denoted as subscripts of small and large, respectively. Finally, the sticking efficiency EsP15 is formulated as follows:
Estick=exp⁡[−β*(T,RH)KcφξcAπDA,small2],
Kc=0.5xsmallxlargexsmall+xlargeυimp2,
where cA is the correction factor of the contact area, DA is the area equivalent diameter, ξ is the enhancement factor of the interlocking mechanism originating from an increase in monomers by aggregation, φ describes the bond energy originating from ostatic attraction between charged ice particles and is assumed to be unity in this study, β* is an empirical coefficient that was determined by laboratory experiments, and υimp is the impact velocity. Note that various phenomena that could affect the sticking efficiency (e.g., a transition of particle shapes by atmospheric temperature, sintering effect, and so on) are implicitly considered through the fitting of β* to the laboratory experiments (Phillips et al. 2015). The temperature dependency of β* is applied to only cloud ice and snow because the growth rate of the aspect ratio of the ice crystals changes through vapor deposition at an atmospheric temperature of −15°C (Chen and Lamb 1994; Connolly et al. 2012). This phenomenon is unlikely to be applied to graupel; hence, β* for graupel is assumed to be independent of the atmospheric temperature based on Phillips’ analyses. More details can be found in the original paper. The formula and parameters, which do not follow Phillips et al. (2015) or are not specified in Phillips et al. (2015), are described in the following paragraphs.
The impact velocity υimp is used to describe Kc and cA, and in the original paper, the parameterization of the impact velocity proposed by Rasmussen and Heymsfield (1985) was applied. Since the parameterization is based on fitting to the database in various ranges of the Reynolds number NRe and Stokes number Ns, many conditional branches were used. However, in this study, a simplifying formulation for υimp was used to avoid the conditional branches in terms of computational efficiency and readability as follows:
υimp=|υlarge−υsmall|×0.3[tanh⁡(2.0log⁡10Ns)+1.0].
This formulation approximates the impact velocities in the typical ranges of NRe and Ns (cf. Fig. 2). In addition, the formulation can remove the artificial ripples that appear in the original fitting curves in a smaller range of Stokes numbers due to a polynomial approximation.
The number of monomers nm is needed to evaluate the interlocking enhancement factor ξ. In general, interlocking is more likely to occur on the contact surface as nm increases, and hence, nm estimation has a significant impact on ξ. However, nm is not explicitly predicted in NDW6. Thus, in this study, a simple estimation of nm for cloud ice and snow based on Connolly et al. (2012) was used, as suggested by Phillips et al. (2015).
nm,j=min[100.0,1.0+ 2×max(Dj−D0,0.0)D0],
where D0 = 100.0 × 10−6 m. This formulation is based on a very limited observational case in which an aggregate particle gets two extra monomers with every 100-μm increase in the maximum dimension. Here, nm allows the use of real numbers although the number of monomers needs to be an integer because the bulk cloud microphysics schemes assume particles as an ensemble. For cloud ice, nonaggregated pristine ice crystals are assumed in NDW6, and hence, nm,i should be 1.0 in this case. However, even a nonaggregated ice crystal has some branches (e.g., bullet rosette) as the particle size grows (e.g., Bailey and Hallett 2004, 2009). In terms of practical use, EsP15 becomes too small without the interlocking enhancement factor ξ in reference to the observations by Connolly et al. (2012) (not shown). Therefore, in this study, Eq. (12) is also used for cloud ice. For graupel, Eq. (12) is used ad hoc although the diagnosis is based on the observations of pristine ice crystals and aggregates. No observational dataset is available to diagnose nm,g, as was discussed in Phillips et al. (2015).

Figure 4 shows the sticking efficiencies calculated by EsP15 and EsL83 and the sticking efficiency observations calculated by Connolly et al. (2012, hereafter EsC12). Note that the EsC12 values from 273 to 243 K were linearly interpolated, and the EsC12 values at temperatures below 243 K were fixed at 243 K because no observations were obtained in their laboratory experiments; the EsL83 values at temperatures below 253 K were fixed at 253 K in NDW6 (Seiki et al. 2022) because no reliable data were available (Pruppacher and Klett 2010). In addition, EsL83 refers to the sticking efficiency used for the i–s collision case (cf. Fig. 4 in Lin et al. 1983). We expected that the theory-based parameterization is more reliable above an altitude of 10 km than the fixed values because of the support by the physical mechanisms. In general, EsP15 varies by the hydrometeor category pairs, and its variability is mostly within the observational range (EsL83 and EsC12). For details, the characteristics of EsP15 are described in the following.

Just below the tropopause, the sticking efficiency (EsP15ii, EsP15is, and EsP15ss) decreases as the altitude decreases. Based on Eq. (1), the sticking efficiency mainly depends on the ratio of the collision kinetic energy to the surface area of a small particle Kc/(πDA,small2) in the initial stage of aggregation; here, the interlock enhancement ξ does not work sufficiently. Assuming xsmall ≪ xlarge and given an ice bulk density defined by x = (π/6)D3 ρbulk, the ratio is approximated as Kc/(πDA,small2) ∼ (1/12)Dsmallρbulk,smallυlarge. Therefore, an increase in the particle size (Fig. 2c) increases the ratio [Eq. (9)]. This reduction in the sticking efficiency is commonly observed among EsP15ii, EsP15is, and EsP15ss down to an altitude of 12 km. The variability of the sticking efficiency among the pairs (ii, is, and ss) mainly originates from the variability of the bulk density. Below the altitude, the particle sizes of cloud ice and snow become sufficiently large to enhance the interlocking mechanisms through nonspherically growing particle shapes. As a result, an increase in the enhancement factor ξ dominates the significant increase in the sticking efficiency down to an altitude of 8 km (∼253 K). The peak value of EsC12 near the atmospheric temperature of 258 K originates from the two-dimensional (plate like) growth of ice crystals through vapor deposition that effectively interlocks ice particles in a collision (Connolly et al. 2012). This inherent nature of the ice particle shapes is effectively captured by EsP15ii, EsP15is, and EsP15ss through β* in Eq. (9), and this shape effect dominates within 258 ± 4 K. Overall, EsP15ii effectively captures the transition of the sticking efficiency observed by Connolly et al. (2012) from 273 to 243 K. Note that the shape effect to ξ is not implicitly folded into β* below atmospheric temperatures colder than 243 K because of lack of the laboratory experiments.

EsP15is varies in the same range as EsL83. Since EsL83 was proposed to simulate the snow field caused by thunderstorms (cf. Lin et al. 1983), the sticking efficiency values could be optimized to reproduce snow aggregation. However, EsP15ii is much smaller than EsL83. In Lin et al. (1983), the autoconversion of cloud ice was simply formulated by the first-order homogeneous linear equation of the cloud ice mixing ratio with a tunable relaxation time. Therefore, EsL83 was not optimized for the i–i collision case.

In collisions involving graupel, the sticking efficiencies are likely to be low due to the stronger collision kinetic energies of graupel. This characteristic becomes distinct as the collided particles become denser. In particular, EsP15ig is significantly smaller than EsP15sg despite similar particle sizes between the cloud ice and snow in this case (Fig. 2c). Assuming that Kc/(πDA,small2) ∝ρbulk,small, ρbulk,i is approximately 3–4 times larger than ρbulk,s in the setting [Table 1 and Eqs. (9) and (10)]. Thus, the EsP15ig values are equivalent to the EsP15sg values raised to a power of 3–4. Specifically, the bond energy, which is proportional to the surface area, is not sufficiently large to overcome the stronger collision kinetic energy due to the higher density of cloud ice. Note that this effect, which originates from the variability in the particle shapes, is highly uncertain; hence, the simulated results need to be carefully evaluated in reference to the observations. In addition, an appropriate choice of the electricity factor φ could result in more realistic representation of intense convective clouds since electricity is strongly charged by frequent collision in convective systems (e.g., Takahashi 1978).

3. Experimental designs

a. Numerical settings

In this study, the NICAM with a horizontal resolution of 14 km is used for global simulations. The NICAM has 78 vertical layers, and its model top is set at 50 km. The horizontal resolution is clearly coarse as a cloud-resolving model but is sufficient to examine the sensitivity of the cloud microphysics (e.g., Seiki et al. 2022). Global simulations were initiated on 12 September 2016, a series of 9-day integrations were performed, and the last 6 days were analyzed to examine the sensitivity of the collision and sticking efficiencies. Past studies using the NICAM have shown that the sensitivities of cloud microphysics are distinct within 2 weeks (e.g., Kodama et al. 2012; Seiki et al. 2015a; Seiki and Roh 2020; Roh et al. 2020; Seiki and Ohno 2023). Changes in cloud distributions occurred within the 4 days, and subsequently, the atmospheric temperature slowly responded to the modified cloud radiative forcing (Seiki et al. 2015a). The configuration for atmospheric physics was the same as that used for the High Resolution Model Intercomparison Project (HighResMIP) products (Kodama et al. 2021) with the exception of cloud microphysics.

The control (CTL) experiment is the same as the NEW in Seiki and Ohno (2023), in which the collision efficiency is assumed to be unity except for the collision pairs involving cloud water [Eq. (7)], and the simple formulation of the sticking efficiency (EsL83) is used. Next, a sensitivity experiment with collision efficiency modeling (EXP-Ec) was performed. Finally, a sensitivity experiment with collision efficiency modeling and the new sticking efficiency parameterization EsP15 was performed (EXP-EcEs). Calculation costs significantly increased by implementing the Ecol and new Estick parameterizations. The calculation costs of the aggregation procedure and the entire NICAM increased 140% and 30%, respectively, in EXP-Ec and 180% and 34%, respectively, in EXP-EcEs compared to those in the CTL experiment on the vector supercomputer SX-Aurora TSUBASA.

b. Observational data

The vertical profile of the ice clouds was evaluated by the CloudSat and CALIPSO satellite observation products provided by the Japan Aerospace Exploration Agency. Radar reflectivity is used to generate the contoured frequency by altitude diagram (CFAD). For clarity, cirrus clouds with cloud-base temperatures warmer than 253 K (∼8-km altitude) were excluded from the analyses because the simulation results frequently contain liquid phase particles in the atmospheric temperature range (Fig. 2). Note that in this study, the satellite data are analyzed during September 2014 because the product is available from 2006 to 2014. The simulated results were postprocessed by the Joint Simulator for Satellite Sensors (Hashino et al. 2013) to emulate radar reflectivity. In the Joint Simulator, single scattering properties were precalculated using the discrete dipole approximation and then were tabulated as a lookup table of the ice water content and effective radius (Okamoto 2002; Okamoto et al. 2003; Sato and Okamoto 2006). The shapes of ice particles were assumed as a mixture of columns, bullet rosettes, and plate-like ice (Sato and Okamoto 2011). This choice has negligible errors in the estimation of radar reflectivity in cirrus clouds, in which the ice effective radius takes a value generally smaller than 100 μm.

Global cloud distributions were evaluated based on the radiative fluxes at the top of the atmosphere. In this study, Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) TOA monthly means data edition 4.1 data product [CERES-EBAF (Loeb et al. 2018)] is used for reference.

The coverage and optical depth of cloud layers were evaluated by the Second-Generation Global Imager (SGLI) on board the Global Change Observation Mission–Climate (GCOM-C) satellite (Imaoka et al. 2010). The GCOM-C satellite was launched in 2017, and hence, the observation dataset does not exist during the simulation period. Instead, SGLI data are analyzed during September 2019. The phase discrimination product developed by Nagao and Suzuki (2021) is used and captures the ice fraction in the total cloud optical thickness in a cloudy pixel (ICOTF). The bias correction for the observed ICOTF is described in appendix C. The cloud optical properties were analyzed for cloudy pixels with a total optical thickness larger than 5 to avoid large classification errors in the satellite analysis (Nagao and Suzuki 2021). In addition, pixels with a solar zenith angle larger than 70° were excluded from the analysis for safety. Moreover, pixels over sea ice were excluded from the analysis using the sea ice concentration level 2 product of version 3 from the GCOM-W satellite (JAXA 2012; Cho et al. 2020). The vertical profiles of the simulated COT were processed by a weighting function to emulate the downward observation by the SGLI (see appendix D).

Note that we have checked that the annual variability in zonal-mean values of SGLI products and CloudSat–CALIPSO products is sufficiently low compared to the difference between the simulations and observations.

4. Results

a. Hydrometeor distribution

The zonal-mean values of the mixing ratios of the hydrometeors are shown in Fig. 5, and the vertical profiles averaged over the tropics and mid- to high latitudes are shown in Fig. 6. In general, the cloud ice increases, and correspondingly, snow decreases in EXP-Ec by suppressing the collisional growth of the small ice crystals (cf. Fig. 3). As a result, supercooled cloud water slightly decreases through enhancement of the Bergeron–Findeisen process due to the longevity of cloud ice. These characteristics in each experiment are commonly observed in both the tropics and mid- to high latitudes (Fig. 6). In EXP-EcEs, cloud ice/snow significantly increases/decreases in the upper troposphere by further suppressing aggregation among the cloud ice particles in colder temperature regions (Fig. 4). In addition, suppression of aggregation between cloud ice and graupel increases cloud ice just above the freezing level in EXP-EcEs.

Fig. 5.
Fig. 5.

Comparison of zonal-mean values of the mixing ratios (mg kg−1) of the hydrometeors from the CTL experiment, EXP-Ec, and EXP-EcEs.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

Fig. 6.
Fig. 6.

Comparison of the averaged vertical profiles of the mixing ratio of the hydrometeors. Upper figures are calculated over the mid- to high latitudes (60°–40°S and 60°–80°N), and lower figures are calculated over the tropics (0°–20°N). Here, the cloud water mixing ratio over the mid- to high latitudes is halved for visualization.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

The revisions in the collision and sticking efficiencies have minimal effect on the rain and graupel amount since the rain amount is mostly determined by the vapor amount and the graupel is basically generated by freezing and accretion of the rain droplets that are insensitive to the efficiencies (cf. Fig. 3).

b. Vertical profiles of the radar echo

Aggregation in the upper troposphere is evaluated using the CFAD in comparison with the radar echo observations. In this study, cirrus clouds over the tropical ocean were sampled since these cloud systems are dominated by cloud ice and snow (Figs. 6a–c).

In the observations, small Ze values are distributed with small variance at altitudes from 12 to 16 km (Figs. 7a,f). In the CTL experiment, the frequency of Ze is positively skewed and has a long-tailed distribution in the altitude range (Figs. 7b,g). In warm clouds, collision and coalescence are known to broaden a monomodal cloud particle size distribution and finally transform the particle size distribution into a bimodal structure (e.g., Berry and Reinhardt 1974). In analogy to warm clouds, overestimation of aggregation is considered to enhance the standard deviation and positive skewness of the Ze distribution in the CTL experiment (Figs. 7f,g). The bias is partially alleviated in EXP-Ec and clearly decreases in EXP-EcEs (Figs. 7c,d,f,g). These comparisons indicate that, in the altitude range, cloud ice rarely aggregates, which suppresses the growth of Ze. At altitudes from 8 to 12 km, the mode value of radar reflectivity increases toward the cloud base. This transition correlates to the aggregation in the altitude range and an increase in vapor deposition owing to the warmer atmospheric temperature with more water vapor. Correspondingly, the mixing ratios of cloud ice and snow have the maximum value at the altitude of approximately 10 km in the NICAM simulations (Figs. 6a–c). The increasing mode value is unclear in the CTL experiment (Fig. 7b). In contrast, the mode finally becomes distinct in EXP-EcEs.

Fig. 7.
Fig. 7.

CFAD of the 94-GHz radar echo from (a) CloudSat satellite observations, (b) CTL experiment, (c) EXP-Ec, and (d) EXP-EcEs. The analysis domain is limited to the tropical ocean (0°–20°N), and the cirrus clouds are sampled. Here, the cirrus clouds are defined by cloud bottom temperatures colder than 253 K following Seiki et al. (2019), and CFADs are plotted where the cirrus cloud coverage exceeds 0.01. For reference, the tropical mean atmospheric temperature is indicated on the right side of the y axis. In addition, statistics of the Ze distribution at each altitude are shown in the bottom row: (e) mean, (f) std dev, and (g) skewness.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

Based on these comparisons, the empirical parameterization for the sticking efficiency [Eq. (8)] cannot sufficiently suppress the cloud ice particle growth by aggregation near the tropopause. In contrast, the theory-based parameterization of the sticking efficiency [Eq. (9)] reasonably functions even in the upper troposphere (Fig. 7d). In particular, the transition of the nonaggregation growth mode to the aggregation growth mode is captured by using parameterization.

c. Verification of the ice fraction

The changes in cloud coverage and COT by the implementation of Ecol and new Estick modeling were evaluated by using ICOTF. The satellite observations showed that COT was distributed in a narrow value range from 15 to 20 over the globe (Fig. 8a). The retrieved COT values vary by the fraction of ice due to the different backscattering characteristics between spherical liquid droplets and nonspherical ice particles. Thus, the maximum uncertainties of the retrieved COT values can be examined by assuming all particles as liquid or ice.

Fig. 8.
Fig. 8.

Zonal-mean values of (a) the total COT and ice optical thickness and (b) ICOTF. These optical properties were averaged over the ocean. For reference, COT retrievals assuming all particles as ice or liquid were obtained using the 1.05- and 2.21-μm channels and are shown by the dashed and dotted lines, respectively.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

The NICAM simulations generally capture the value range of COT except for tropical regions. The simulated COT over the tropics is certainly overestimated since the simulated COT values are larger than the COT retrieval assuming liquid droplets. By considering the collision efficiency, the COT slightly decreased, mostly due to the decrease in the cloud water mixing ratio in low-level clouds (Fig. 6). In contrast to the agreement of COT between the simulations and SGLI observations, the simulated ICOTF is generally underestimated in reference to SGLI observations. The increase in cloud ice amount by the revisions (Fig. 6) resulted in improvements in the ICOTF over the tropics (Fig. 8b). The remaining biases in the simulated COT over the tropics and ICOTF over the globe are discussed in section 5.

Figure 9 shows the cloud coverages by cloud type. Following Nagao and Suzuki (2021), in this study, the four-type classification by ICOTF and cloud-top temperatures is used and includes warm liquid clouds, supercooled liquid clouds, mixed-phase clouds, and ice clouds. All simulations effectively capture the zonal-mean values of the cloud coverage with COTs larger than 5 (Figs. 9a–d). However, an analysis of the breakdown indicates that the ice clouds and mixed-phase clouds are underestimated in the midlatitudes to high latitudes, whereas the supercooled water clouds are overestimated in the region. In the simulation, more than half of the simulated ice clouds have a COT of less than 1 (not shown). This result indicates that the ice cloud coverage is effectively represented by our simulations; however, the ice cloud optical thickness is underestimated, as was also found in Fig. 8b. The bias is partially alleviated in EXP-EcEs but is not sufficiently solved.

Fig. 9.
Fig. 9.

Zonal-mean cloud coverage values of each cloud type over the ocean. Definition of the four cloud types follows Nagao and Suzuki (2021): The “warm water” type is defined as clouds with CTT warmer than 273 K and ICOTF smaller than 0.2; the “supercooled water” type is defined as clouds with the CTT equal to or colder than 273 K and with ICOTF smaller than 0.2; the “mixed-phase” type is defined as clouds with the ICOTF equal to or larger than 0.2 and smaller than 0.8; “ice” type is defined as the other clouds. Cloudy pixels where the retrieval method does not work are indicated by “uncertain.” Note that the cloud cover is accumulated by the cloud types.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

d. Radiative fluxes

The collision and sticking efficiency modeling was evaluated by comparing the radiative budget. Figures 10 and 11 show the comparison of outgoing longwave radiation and outgoing shortwave radiation at the top of the atmosphere (OLR and OSR, respectively) in reference to the CERES satellite observations. In the CTL experiment, longwave and shortwave cloud radiative forcings are underestimated over the tropics. In terms of the zonal-mean average values over the tropics (0°–20°N), the underestimation of OLR and OSR in the CTL experiment (11.1 and −19.6 W m−2, respectively) is much alleviated in EXP-Ec (6.6 and −17.6 W m−2, respectively) and in EXP-EcEs (−4.6 and −9.2 W m−2, respectively). The improvements in OLR and OSR mostly originate from the most convective region over the Indian Ocean to the western Pacific Ocean. In the domain from 70° to 170°E and 0° to 20°N, the OLR and OSR changes from the CTL experiment by the revisions are 7.8 and 4.3 W m−2 in EXP-Ec and 26.2 and 18.9 W m−2 in EXP-EcEs, respectively.

Fig. 10.
Fig. 10.

Horizontal distribution of the OLR from (a) CTL experiment, (b) EXP-Ec, (c) EXP-EcEs, and (d) CERES satellite observations. (e) Zonal-mean averaged values. Note that monthly mean values of the CERES satellite observations are used for reference, whereas the simulated results are averaged during the last 6 days in the simulation period.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for OSR.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

The ICOTF increase by the revisions strongly modifies the shortwave radiation (Figs. 8b and 11) since ice clouds have a greater backscattering effect than liquid clouds due to nonsphericity (e.g., Fu 2007). In addition to the ICOTF change, cirrus cloud coverage increases by the revisions due to the longevity of cirrus clouds (Fig. 9). This results in an increase in the cloud radiative forcing, with a decrease in OLR and an increase in OSR. The effects are more prominent in convective regions (e.g., the north Indian Ocean to the western Pacific Ocean) through the abundant vapor supply into the upper troposphere. Thus, the revisions are expected to sufficiently contribute to improvements in tropical climate simulations even though ICOTF remains underestimated.

5. Discussion

a. Bias in the simulated COT

The bias in the simulated COT over the tropics has two possibilities: underestimation of the retrieved COT and overestimation of the simulated COT.

An idealized cloud structure (e.g., single layer and single phase) is generally assumed in cloud retrieval algorithms for passive imagers (e.g., Nakajima and King 1990; Platnick et al. 2017; Nakajima et al. 2019). The assumptions are known to cause non-negligible biases in COT retrieval. For example, a single-layer ice cloud requires smaller COT values than multilayered ice and liquid clouds to achieve the same cloud albedo in the visible spectrum (Kato et al. 2011). As a result, the retrieved COT values for multilayered high thin cirrus and low-level cumuli, which are commonly observed in the tropical region (cf. Figs. 6a–c), tend to be underestimated. This underestimation bias is partially mitigated by incorporating a mixed-phase structure parameterized by the ICOTF (Nagao and Suzuki 2021). Nevertheless, other issues, such as subpixel-scale inhomogeneity of cloud properties, including clear-sky contamination (Cahalan et al. 1994; Oreopoulos and Davies 1998) and three-dimensional radiative transfer effects (Várnai and Marshak 2002; Kato et al. 2006), have not yet been addressed. Therefore, uncertainties in the retrieved COT values inherently remain. Irrationally darkened cloudy pixels are expected to be found especially near the cloud edge because of small-scale variability (e.g., Koren et al. 2008). These problematic cloudy pixels mostly have COTs less than 5 (not shown). Sampling of thick cloud pixels with COTs larger than 5 significantly reduces the systematical biases, and processing of zonal mean eliminates the random errors in comparison.

Moreover, the overestimation of the simulated COT values over the tropics is explained by the long-standing bias in convective strength in the NICAM. NICAM simulations are likely to produce sporadic convection that is too strong over the tropics (Kodama et al. 2015, 2021). The bias cannot be solved even with the use of a horizontal grid resolution of up to 3.5 km (Takasuka et al. 2024). Recently, Takasuka et al. (2024) successfully reduced the bias by using a subgrid parameterization of horizontal turbulent diffusion; this is the so-called Leonard term (Leonard 1975) proposed by Moeng et al. (2010). The Leonard term functions to selectively suppress strong convective updrafts; consequently, intense precipitation systems over the ITCZ are weakened. Thus, a COT value that is too large over the tropics is expected to be partially improved by using the Leonard term. The reduction in intense precipitation can result in an increase in high cloud thickness (ICOTF) through further moisture supply to the upper troposphere as well.

b. Bias in the simulated ICOTF

The remaining biases in the ice cloud thickness could be alleviated by revising ice cloud modeling: aerosols, breakup, and subgrid processes. Subpixel inhomogeneity also affects the accuracy of satellite retrieval but was effectively excluded by sampling thick cloudy pixels with COTs larger than 5. The sources of the uncertainties in the satellite product and the correction method for a systematical bias in ICOTF are provided in appendix C.

In this study, the double-moment bulk cloud microphysics scheme, NDW6, is not coupled with the aerosol transport model implemented in the NICAM (Goto et al. 2015, 2020). Thus, the homogeneous and heterogeneous ice nucleation processes in NDW6 are assumed to have globally uniform background aerosols. As a result, this setting could result in biases in ice nucleation by region. Recently, NDW6 has been coupled with the aerosol transport model (Goto et al. 2024). Aerosol cloud interactions could partially solve the remaining biases.

The ice breakup process (e.g., Phillips et al. 2017b), which is not implemented in NDW6, is known to drastically increase the formation of ice particles (e.g., Phillips et al. 2017a). This process suppresses the aggregate growth and produces many tiny ice crystals after breakup. Therefore, a reduction in snow and graupel and a significant increase in the ice crystal number concentration occur. A significant increase in Ni is expected to significantly increase the ice cloud optical thickness.

Subgrid processes are also non-negligible to reproduce the cirrus cloud structure. Due to strong vertical wind shear in the upper troposphere, cirrus clouds have very fine-scale structures. Heymsfield (1975) schematically illustrates the structure of cirrus uncinus and its generating cells based on observations: Individual streaks in a cirrus cloud system have a horizontal scale of less than 1 km, and strong updraft and downdraft alternately occur in the entire cirrus cloud system. This kind of cirrus cloud system can be resolved by using large-eddy simulations (e.g., Sölch and Kärcher 2010, 2011). In addition to structural subgrid effects, turbulent effects on ice clouds are not well understood (e.g., Ohno et al. 2020). Regional simulations with much finer spatial resolution can supplement the understanding of the impact of subgrid dynamics on the ICOTF.

6. Summary

In our study, collision efficiency modeling was newly implemented in the double-moment bulk cloud microphysics scheme in NICAM, and also, the empirical formulation of the sticking efficiency was replaced with theory-based parameterization in the scheme. The new efficiencies were evaluated in reference to the satellite observations. For comparison, global simulations were performed, and the following results were found:

  1. Implementation of the collision efficiency caused an increase in the cloud ice amount over the midlatitudes and tropics due to a decrease in the aggregation growth. Correspondingly, the snow and cloud water mixing ratio slightly decreased above the freezing level.

  2. With the theory-based sticking efficiency, the cloud ice amount significantly increased by up to approximately 200% above the freezing level by suppressing self-aggregation of cloud ice and aggregation between cloud ice and graupel.

  3. The reduction in the aggregation efficiency at colder atmospheric temperatures was evaluated by comparing CFAD to the CloudSat observations: the standard deviation and skewness of the Ze distribution were reasonably suppressed above the altitude of 10 km to match the observed CFAD.

  4. The simulations globally underestimated the thickness of the ice clouds even using the theory-based sticking efficiency parameterization in comparison with the SGLI observations.

  5. Finally, OLR decreased by 15.7 W m−2 and OSR increased by 10.4 W m−2 over the tropics; moreover, the radiation biases in the NICAM were alleviated. The change was beneficial for CMIP6 GCMs because the GCMs had long-standing underestimation biases in the cloud radiative forcing over the tropics by 10–20 W m−2 (Li et al. 2013, 2020).

Thus, the theory-based parameterizations for Ecol and Estick reasonably functioned in global climate simulations. The next challenge is to investigate the impact of aggregation efficiency modeling on individual atmospheric disturbances (e.g., MJO and tropical cyclones) because the new modeling specifically increased the cloud radiative forcing over the north Indian Ocean to the western Pacific Ocean where tropical cyclones and intraseasonal oscillation are the most active. In addition, further improvements in ice cloud microphysics are needed to increase the ice cloud optical thickness (e.g., breakup of aggregates).

Finally, the implementation of Ecol and the new Estick parameterizations significantly increased the computational cost; the NICAM global simulations consumed approximately 34% more computational resources. Thus, simplification of the parameterizations to be cheaper in terms of the computational cost is desired. The use of a lookup table for aggregation efficiency is a simple solution in practice.

Acknowledgments.

The CERES-EBAF satellite products were obtained from the NASA Langley Research Center Atmospheric Science Data Center. The combined CloudSat–CALIPSO products were obtained from the EarthCARE Research Product Monitor (http://www.eorc.jaxa.jp/EARTHCARE/research_product/ecare_monitor.html) by the Japan Aerospace Exploration Agency (JAXA). The GCOM-C/SGLI products (top-of-atmosphere radiance, cloud flag, and land surface reflectance) and the GCOM-W/AMSR2 L2 Sea Ice Concentration product were obtained from the JAXA Global Portal System (https://gportal.jaxa.jp/gpr/?lang=en). This study was supported by the MEXT program for the Advanced Studies of Climate Change Projection (SENTAN) (Grant JPMXD0722680395) and the JAXA/GCOM-C project. Tatsuya Seiki was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant JP21K03674 and Third Research Announcement on the Earth Observations of JAXA. Takashi Nagao was supported by JSPS KAKENHI Grant JP19H05699. The simulations in this study were performed using the Earth Simulator. The authors are grateful to Kentaroh Suzuki for providing valuable discussions. The authors are grateful to the reviewers for their comments.

Data availability statement.

The satellite products are available on the website of the individual satellites, except for the GCOM-C/SGLI products. The model output and the GCOM-C/SGLI products used in this study were not archived in public data storage but will be curated for 5 years and are available upon request by contacting the corresponding author. The source code availability of the NICAM and the experimental settings are documented by Kodama et al. (2021) in detail.

APPENDIX A

Collision Efficiencies

The mean collision efficiencies weighted by the particle size distributions and the collection kernel without the sticking efficiency [Eq. (3)] are shown in Fig. A1. In NDW6, for simplicity, cloud water is assumed to be collected particles in all pairs; cloud ice is assumed to be collected particles in the collision between cloud ice and snow; cloud ice and snow are assumed to be collected particles in the collision between rain and cloud ice and between rain and snow; and graupel is assumed to be collecting particles. The fixed relationship is valid in typical cases (cf. Fig. 2c).

Fig. A1.
Fig. A1.

(a)–(l) Collision efficiency in a typical range of the mean area-equivalent diameter Da. Typical size is used for cloud water in (a)–(c), rain in (d)–(f), cloud ice in (h) and (i), and snow in (k). The collision efficiencies are calculated in the range where the collecting particles are larger than the collected particles. The solid lines indicate the collision efficiency based on boundary layer theory with the correction based on potential flow theory, and the dashed lines indicate the collision efficiency based only on boundary layer theory.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

APPENDIX B

Typical Vertical Profiles of the Tropical Atmosphere

The typical vertical profiles of the atmosphere used for the single-column model are simplified as follows:
Ta=300−6min(z,17.5),
qc={9z, (z≤ 2km){−185(z−2)+18}, (2km<z≤7km),
qr=max⁡[−(z−2)2+20, 0], (z≤7km),
qi={76(z−4), (4≤z<10)−76(z−10)+7, (10≤z<16),
qs=qi,
qg=−(z−6)2+18 ,
x¯c=10−11,
x¯r=10−[(z−6)/4]−0, (z<7),
x¯i=10−0.05[max(z,5)−7]2−8, (Ta≤273),
x¯s=2x¯i, (Ta≤273),
x¯g=10−{[max⁡(z,5)−6]/6}−6, (Ta≤273).
Here, the unit of the altitude z is kilometers, the unit of the mixing ratio q is milligrams per kilogram, and the unit of the mean particle mass x¯ is kilograms. The vertical profiles of the pressure and air density are derived under the hydrostatic balance with a surface pressure of 1000 hPa and a surface air density of 1.15 kg m−3. For the conversion from the mean particle mass to the maximum dimension, the power-law relationships provided in Table 1 are used.

APPENDIX C

Bias Correction for the Observed ICOTF

The retrieval method for ICOTF is based on the plane-parallel approximation which assumes a horizontally homogeneous cloud layer. Thus, the retrieved ICOTF values are known to suffer from the errors caused by inhomogeneity of a cloud layer; some examples are the three-dimensional scattering near the cloud edge (Zinner et al. 2010; Zhang et al. 2012), subpixel-scale horizontal heterogeneity of clouds (Zhang et al. 2016), and in-cloud vertical inhomogeneity (Platnick 2000; Nagao et al. 2013; Nakajima et al. 2010). Among the error sources, the heterogeneity of clear skies and cloudy skies in a pixel is particularly crucial for retrieval accuracy. Hence, errors are clearly found in the case of low-level clouds since small cumuli frequently have spatial sizes smaller than the satellite footprint size (e.g., Koren et al. 2008). This issue is partly resolved by sampling sufficiently thick clouds, but this does not fully solve the issue (Nagao and Suzuki 2021); our study used the threshold for COT of 5. Therefore, in this study, an ad hoc correction method was applied to the retrieved ICOTF values following Nagao and Suzuki (2021) with a slight modification.

Assuming that low-level clouds have an ICOTF of 0, the mean ICOTF for clouds with a cloud-top temperature (CTT) larger than 273 K (fLIQ) is processed as the systematic bias of the ICOTF for low-level clouds. The mean bias fLIQ was initially stored as a lookup table of COT (τc) and cloud effective radii (re) using the monthly global dataset and then substituted from the retrieved ICOTF values (ficot) as follows:
corrected ficot=max{ficot−min⁡[max⁡(CTT,243),273]−243273−243fLIQ(τc,re),0},
where the lower limit of CTT is determined because the retrieved ICOTF values asymptotically approach unity at a CTT of 243 K (Nagao and Suzuki 2021).

Figure C1 shows the frequency of the ICOTF occurrence at each CTT range. The median ICOTF is 1 at CTTs colder than 245 K and then decreases as CTT increases. The systematic bias fLIQ was found to be approximately 0.1 (Fig. C1b), and the bias was clearly removed by the correction (Fig. C1a). ICOTF biases related to the uncertainties have a small impact on ICOTF values of organized convective cloud systems since such clouds generally have CTTs colder than 243 K. This indicates that zonal-mean values of ICOTF over the tropics are relatively reliable.

Fig. C1.
Fig. C1.

The frequency of the ICOTF occurrence in each CTT range over the global ocean. The histograms were obtained using (a) corrected ICOTF values and (b) retrieved ICOTF values. The black solid line indicates the median of ICOTF, and the dashed two lines indicate the 25 percentile and 75 percentile. Here, cloudy pixels with solar zenith angles larger than 70° were excluded from the analysis.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

It is not obvious that corrected ICOTF values of cloudy pixels with CTTs colder than 243 K are not systematically biased. However, we considered that it does not significantly affect the comparison between simulations and observations. Given the fact that ICOTF is almost 1 at CTTs colder than 245 K, ICOTF values cannot be overestimated at the colder range. In the CTT range, the sensitivity of the SGLI channels to the ice fraction is considered to be saturated (i.e., sufficiently thick ice cloud layers generally overlie liquid cloud layers). It was found that the sensitivity of the SGLI channels to ice clouds is saturated at cloud optical depths of 20 from the cloud top (see Fig. D1 in appendix D). This characteristic is emulated in the simulated ICOTF using the weighting function (appendix D).

APPENDIX D

The Weighting Function

Retrievals using the water-absorbing short-wavelength infrared (SWIR) channels of passive imagers, such as MODIS and SGLI, are known to be sensitive to the cloud-top properties. This sensitivity was quantified by the vertical weighting function proposed by Platnick (2000). In this study, the weighting function was applied to simulated cloud optical properties to emulate the retrieved values of ICOTF with the SWIR channels.

The weighting function W at an optical depth from the cloud top τ was defined as follows:
W(τ;τc)=[R(τ+δτ)−R(τ)]/δτR(τc),
where R is the reflectance of the radiance at the top of the atmosphere and τc is the total cloud optical depth of the objective cloud. The weighting function was calculated with a plane-parallel radiative transfer model RSTAR (Nakajima and Tanaka 1986, 1988) with the assumptions of a black surface (surface albedo of 0), no gas absorption, and no Rayleigh scattering of the atmosphere. The SGLI satellite retrieval used three channels at wavelengths of 1.05, 1.63, and 2.21 μm (Nagao and Suzuki 2021).

Figure D1 shows the weighting function of the 1.63-μm channel assuming spherical liquid droplets and hexagonal ice crystals (Wliq and Wice, respectively). The SGLI sensor is most sensitive to a cloud layer near the cloud optical depth of 1–3; it is still sufficiently sensitive to cloud layers deeper than the cloud optical depth (COD) of 5, which CALIPSO cannot detect. Therefore, the use of the SGLI sensor is appropriate for evaluating the ice fraction in optically thick clouds. The weighting functions indicate that the SGLI sensor channels are sensitive to shallower range near the cloud top in the ice cloud cases than to those in warm cloud cases because of the difference in the phase function; ice crystals of nonspherical shapes are more likely to scatter radiance backward (e.g., Fu 2007; Seiki et al. 2014). In this study, Wice is used for the ICOTF analyses over the globe since the ice cloud layers generally overlap liquid cloud layers.

Fig. D1.
Fig. D1.

Weighting function of the 1.63-μm channel assuming spherical liquid droplets (red line) and hexagonal ice crystals (blue line).

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

The analyzed ICOTF values are expected to be biased depending on the condition of the cloud overlap. To determine the overlapping effect, ICOTF with Wice is examined via the typical vertical profile over the tropics (cf. Fig. 2). Figure D2a shows the condition of the objective cloud overlapping. An ice cloud layer with a COD of approximately 1 overlaps a liquid cloud layer distributed from the low to the middle troposphere. Below the COD level of 2, the liquid cloud layer dominates, and then, the liquid cloud layers have a COD of approximately 5. Figure D2b shows the estimated ICORF values at each τ level. The ICOTF with Wice has very close values to the true ICOTF in most parts of the cloud layer. In detail, the ICOTF with Wice is slightly underestimated when τc is smaller than 3 since ice clouds with a COD of approximately 1 are semitransparent. On the other hand, the ICOTF is slightly overestimated when τc is larger than 5.

Fig. D2.
Fig. D2.

(a) Vertical profiles of the optical depth from the cloud top of liquid and ice components with the typical atmospheric profile over the tropics (cf. Fig. 2). Here, the optical depth from the cloud top is used as the vertical axis. (b) ICOTF with the vertical profile of (a) and the weighting function. For reference, the true ICOTF from the model input data is also plotted with a black line.

Citation: Journal of the Atmospheric Sciences 81, 10; 10.1175/JAS-D-23-0208.1

Regarding the ICOTF analyses by the SGLI satellite, cloud pixels with τc values larger than 5 are sampled. Thus, the retrieved ICOTF values are expected to be always overestimated. Therefore, the model results should be processed with the Wice in comparison with the SGLI observations.

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