The Radiative Effect on Cloud Microphysics from the Arctic to the Tropics

Xiping Zeng Army Research Laboratory, Adelphi, Maryland;

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Andrew J. Heymsfield National Center for Atmospheric Research, Boulder, Colorado;

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Zbigniew Ulanowski British Antarctic Survey, Cambridge, and University of Manchester, Manchester, United Kingdom;

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Ryan R. Neely III National Centre for Atmospheric Science, University of Leeds, Leeds, United Kingdom;

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Xiaowen Li NASA Goddard Space Flight Center, Greenbelt, and Morgan State University, Baltimore, Maryland;

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Jie Gong NASA Goddard Space Flight Center, Greenbelt, and Universities Space Research Association, Columbia, Maryland;

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Dong L. Wu NASA Goddard Space Flight Center, Greenbelt, Maryland

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Abstract

Cloud representation is one of the largest uncertainties in the current weather and climate models. In this article, the observations and modeling of the radiative effect on (cloud) microphysics (REM) from the Arctic to the tropics are overviewed, providing a new direction to meet the challenge of cloud representation. REM deals with the radiation-induced temperature difference between cloud particles and air. It leads to two common phenomena observed at the surface—dew and frost—and impacts clouds aloft significantly, which is noticed via the wide occurrence of horizontally oriented ice crystals (HOICs). However, REM has been overlooked by all of the operational weather and climate models. Based on the bin model of REM and the global distribution of radiative cooling/warming, the observations of REM from several platforms (e.g., aircrafts, field campaigns, and satellites) are coordinated in this article, yielding a global picture on REM. As a result, the picture is compatible with the global distribution of HOICs and other ice crystal characteristics obtained from various clouds on the globe, such as diamond dust (or clear-sky precipitation) in the Arctic, subvisual cirrus clouds in the tropical tropopause layer, and other cirrus clouds from the low to high latitudes. In addition, ice crystals possess relatively strong REM compared to liquid drops because their aspect ratio is usually not one. The global picture on REM can be used by the weather and climate modelers to diagnose their cloud representation biases. It can also be used to improve the atmospheric ice retrieval algorithm from satellite observations.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

* CURRENT AFFILIATION: University of Maryland Baltimore County, Baltimore, Maryland

Corresponding author: Dr. Xiping Zeng, xiping.zeng.civ@army.mil

Abstract

Cloud representation is one of the largest uncertainties in the current weather and climate models. In this article, the observations and modeling of the radiative effect on (cloud) microphysics (REM) from the Arctic to the tropics are overviewed, providing a new direction to meet the challenge of cloud representation. REM deals with the radiation-induced temperature difference between cloud particles and air. It leads to two common phenomena observed at the surface—dew and frost—and impacts clouds aloft significantly, which is noticed via the wide occurrence of horizontally oriented ice crystals (HOICs). However, REM has been overlooked by all of the operational weather and climate models. Based on the bin model of REM and the global distribution of radiative cooling/warming, the observations of REM from several platforms (e.g., aircrafts, field campaigns, and satellites) are coordinated in this article, yielding a global picture on REM. As a result, the picture is compatible with the global distribution of HOICs and other ice crystal characteristics obtained from various clouds on the globe, such as diamond dust (or clear-sky precipitation) in the Arctic, subvisual cirrus clouds in the tropical tropopause layer, and other cirrus clouds from the low to high latitudes. In addition, ice crystals possess relatively strong REM compared to liquid drops because their aspect ratio is usually not one. The global picture on REM can be used by the weather and climate modelers to diagnose their cloud representation biases. It can also be used to improve the atmospheric ice retrieval algorithm from satellite observations.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

* CURRENT AFFILIATION: University of Maryland Baltimore County, Baltimore, Maryland

Corresponding author: Dr. Xiping Zeng, xiping.zeng.civ@army.mil

Clouds change climate by modulating the radiative equilibrium of the Earth (Liou 1986; Stephens et al. 1990; Zeng et al. 2009; Heymsfield et al. 2017). They also change weather by modulating atmospheric stability and thus large-scale vertical circulations (Slingo and Slingo 1988, 1991; Raymond 2000; Raymond and Zeng 2000). Hence, clouds work as a key part in both the water and energy cycles of the atmosphere.

The current atmospheric models, however, do not represent clouds well. The global models have the biases of “excessive water vapor” and “too dense clouds” (Zhang et al. 2001; Nam et al. 2012; Jiang et al. 2012, 2015). The high-resolution models have similar biases even in different regions, such as the Arctic (Klein et al. 2009; Morrison et al. 2011), the midlatitudes (Zeng et al. 2007), and the tropics (Powell et al. 2012; Zeng et al. 2013; Franklin et al. 2016). All of the models perform imperfectly in cloud representation, because they overlook some cloud processes, such as the radiative effect on (cloud) microphysics (REM).

REM leads to two daily phenomena in unsaturated air: dew and frost. When radiation cools the ground surface, water vapor condenses/deposits on the ground surface even though the air is still unsaturated. Cloud particles near cloud top, just as dew/frost forms, can grow at the expense of water vapor, suggesting REM is a candidate to mitigate the bias of excessive water vapor.

REM has been studied for about six decades. Fuchs (1959) first introduced a radiative term into the diffusional drop growth equation by treating the atmosphere as a blackbody, and then concluded that REM is negligible except for large drops. In fact, the atmosphere is quasi-transparent for infrared radiation (IR) with wavelengths of 8–12 μm. Hence, REM is important in thin clouds or near the edge of thick clouds, which motivated the later studies (Heymsfield 1973; Roach 1976; Hall and Pruppacher 1976; Stephens 1983; Wu et al. 2000; Lebo et al. 2008; Zeng 2008, 2018a,b; Brewster et al. 2020).

REM was previously neglected partly because it is complicated for radiation transfer and ice crystal habit and orientation. Mathematically, it is a process in a geometric space with 10 dimensions (i.e., 4 for space and time; 2 for radiation direction; 1 for radiation wavelength; and 3 for ice crystal size, shape, and orientation), and thus its simulations usually need high-performance computing. Physically, REM entangles macroscale variables of radiation transfer in the atmosphere with microscale variables of individual ice crystals. Moreover, the REM process is nonlocal: an ice crystal in the tropical tropopause layer, for example, can receive IR emitted by the clouds far below and/or by the ground surface. Hence, it is a challenge to represent REM in the weather and climate models with limited computational resources.

To simplify REM, the radiative ratio of ηz was introduced to separate the macroscale and microscale variables in REM (Zeng 2008, 2018a) [see Eq. (5) for its definition]. The ratio was used to classify REM (see section “Three modes of REM”), suggesting that REM be split into three subtopics: 1) microscale study of individual ice crystals and ice crystal spectrum with a given ηz (Fuchs 1959; Heymsfield 1973), 2) macroscale study for the spatial and temporal variations of ηz (Stephens 1983; Harrington et al. 2000; Zeng 2008; Klinger et al. 2019), and 3) the interaction between the microscale and macroscale processes (or the interaction between ηz and clouds; Bott et al. 1990). In reference to the three subtopics, the major studies over the past decades are reviewed in Tables 1 and 2 for ice and warm clouds, respectively, with their clouds studied, methodology used, and conclusions obtained.

Table 1.

Models and observations of REM for ice particles.

Table 1.
Table 2.

Models and observations of REM for liquid drops.

Table 2.

With the bin model of REM becoming mature (Zeng 2018a) and new observations available (Neely et al. 2013; Goerke et al. 2017; Zeng et al. 2019), REM is evaluated with specific observations (Zeng et al. 2021). In this article, the prediction of REM is compared to the ice crystal observations from the Arctic to the tropics, beginning with the physics of frost formation and REM.

Physics of frost formation

Frost (or water vapor deposition) forms on particles because radiative cooling decreases particle temperature. Consider a spherical particle aloft with radius r and temperature Ts. It is immersed in an air parcel with temperature T and relative humidity Hi with respect to ice. Its critical relative humidity is defined as
Hic=Esi(Ts)/Esi(T),
where Esi(T) denotes the saturation vapor pressure over ice at temperature T. When Hic < Hi, water vapor diffuses inwards and then deposits on it, bringing about frost. Otherwise, it has no frost and sublimates if it is composed of ice.
Radiation changes Ts, bringing about TsT and thus Hic ≠ 1. Consider the particle at its ­critical case of Hic = Hi. It exchanges energy with its environment via two processes: conduction and radiation. It receives conductive energy from its environment with a rate (Mason 1971)
Qc4πr(TTs)
Meanwhile, it emits and absorbs IR, losing energy with a rate (Zeng 2008)
Qr4πr2(1η),
where η denotes the ratio of infrared flux incident on particle surface to the radiative flux emitted by the same particle at ambient temperature T.
At the critical case, the two rates reach a balance or Qr = Qc. Substituting Eqs. (2) and (3) into Qr = Qc yields
TsTr(η1),
which shows that TsT, the particle–air temperature difference, is directly proportional to r. A similar expression for a nonspherical particle was derived, which still holds a positive correlation between TsT and particle size (or equivalent ­radius r)1 (Zeng 2008).
Equation (4) also shows that TsT is proportional to η − 1. Since η varies with particle shape and orientation, another radiative ratio
ηz=F++F2σT4
is introduced that is independent of particles, where σ is the Stefan–Boltzmann constant, and F+ and F are the upward and downward IR fluxes in the atmosphere with positive magnitudes, respectively (Zeng 2008, 2018a). Clearly, ηz varies from one air parcel to another but does not change with particles inside. It determines η of a particle inside as (Zeng 2018a)
(η1) =α(ηz1),
where 0 ≤ α ≤ 1, and α depends on particle size, shape, and orientation [see Eqs. (13)–(17) of Zeng (2018a) for the expression of α]. In general, the particle with horizontal orientation possesses larger α than the same particle with vertical orientation.
Substituting Eq. (6) into Eq. (4) yields2
TsTαr(ηz1),
which exhibits particle temperature Ts versus particle size, shape, and orientation for a given ηz. When ηz < 1 (radiative cooling), the larger the particle, the lower its Ts (or Hic) is, which explains the daily phenomenon: frost forms more frequently on wide grass leaves than on narrow ones. Moreover, a horizontally oriented particle possesses lower Ts (or Hic) than a vertically oriented one when ηz < 1, which explains the phenomenon that frost forms more frequently on car front windows than on side windows, for the former loses energy to space more efficiently than the latter.

Three modes of REM

The analytic expression of Hic is derived via Ts (Zeng 2008, 2018a). It is computed with the observed ice crystal shape, mass, terminal velocity, and dimensional relationship (Auer and Veal 1970; Heymsfield 1972; Heymsfield and Iaquinta 2000). Figure 1 displays Hic versus ice crystal size, shape, and orientation as well as ηz. To be specific, Hic increases with ηz; Hic of a horizontally oriented ice crystal (HOIC) is lower than that of a vertically oriented one; and Hic of a plate-like HOIC at ηz = 0.8 starts its dramatic decrease against crystal size at half crystal size of ∼500 μm, which is attributed to the dendritic extensions at crystal size > 200 μm.

Fig. 1.
Fig. 1.

Critical relative humidity Hic vs half crystal size (or semi-major axis length) at T = −30°C and p = 680 hPa for (left) horizontally oriented plate-like crystals with different ηz and (right) ice crystals with different shape and orientation at ηz = 0.8.

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Consider multiple ice particles in an air parcel with relative humidity Hi. Since their Hic varies with crystal size, shape, and orientation, some of them with Hic > Hi shrink via sublimation, whereas the others with Hic < Hi grow via deposition. As a result, radiation alters the particle size distribution, which is referred to as REM.

REM is classified into two types: radiative cooling and warming, which are represented by ηz <1 and >1, respectively, because Hic −1 ∝ TsTηz −1. The two types of REM function oppositely in the evolution of ice crystal spectrum, which is discussed below in turn.

REM with radiative cooling.

An air parcel with ηz < 1 is colloidally unstable (Zeng 2008), which exhibits as three modes:

  • Mode I deals with the water transfer between water vapor and ice crystals, where radiative cooling enhances (or slows) ice crystal deposition (or sublimation) (Heymsfield 1973; Hall and Pruppacher 1976; Stephens 1983). The mode causes the dew/frost formation at the surface. It also impacts clouds with low ice crystal number concentration, which is noticed by the aircraft observations of ice crystals in clear air. Braham and Spyers-Duran (1967) observed the ice crystals falling from cirrus trails and found that the cirrus crystals with length ∼850 μm survived a fall of ∼6 km in a dry environment. Such a long fall of kilometers is not explained well by the classic ice crystal sublimation rate with no REM (i.e., Hic = 1). After introducing REM, the ice crystal sublimation rate is decreased by (Hi − 1)/(HiHic) times. For example, (Hi − 1)/(HiHic) ≈ 1.4 when Hi = 0.3, ηz = 0.7 (over the lower-tropospheric clouds; Zeng 2018b), and Hic = 0.8 (for HOICs in Fig. 1). Hence, REM can increase the computed fall distance significantly to match the observed one, supporting the mode.

  • Mode II deals with the water transfer from small to large ice crystals; from vertically ­oriented (or spherical rosette) to horizontally oriented ice crystals, which resemble the Wegener–Bergeron–Findeisen process on the water transfer from supercooled drops to ice crystals (Zeng 2008, 2018a). The mode happens in an almost stationary air ­parcel, where Hi is modulated mainly by the sublimation/deposition of ice crystals, and ­consequently, large HOICs form at the expense of small (or vertically oriented) ice crystals. Figure 2 displays the formation of precipitating HOICs in a stationary air parcel with ηz = 0.5, ­temperature T = −30°C, and pressure p = 680 hPa, given the same initial spectra of vertically and ­horizontally oriented ice crystals.

  • Mode III happens in an ascending air parcel near cloud top, where large HOICs grow fast while small ones need no sublimation to supply water vapor because additional water vapor for deposition is furnished via the adiabatic temperature decrease of ascending air (Zeng et al. 2021). The mode can be treated mathematically as a superimposition of modes I and II.

Fig. 2.
Fig. 2.

REM-induced evolution of the spectrum dM(lna)/dlna of (top) vertically and (bottom) ­horizontally oriented plate crystals, where M(lna) denotes the mass of ice crystals with semi-major axis length shorter than a. Thick line denotes the initial spectrum; time interval between lines is 1 h. The simulation employs ηz = 0.5, T = −30°C, and p = 680 hPa (from Zeng 2018a).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

REM with radiative warming.

An air parcel with ηz > 1 is colloidally stable. When ηz > 1, Ts > T and thus Hic > 1 [see Eq. (7)]. Hence, radiative warming slows (or enhances) the deposition (or sublimation) of individual ice crystals. Consider multiple ice crystals in a stationary air parcel with ηz > 1. Their spectrum evolution relies on Hic. Since (Hic − 1)/(ηz − 1) is a function of ice crystal size, shape, and orientation (Zeng 2008, 2018a), Hic with ηz > 1 and < 1 is symmetric with respect to Hic = 1 in Fig. 1. Hic − 1 with ηz = 1.5, for example, is equal to 1 − (Hic − 1) with ηz = 0.5. Hence, Fig. 1 (or Fig. 1 of Zeng 2018a) shows that Hic with ηz > 1 increases with ice crystal size. The dependence of Hic on crystal size at ηz > 1 explains the phenomenon in a stationary air parcel with ηz > 1: large ice crystals shrink via sublimation whereas small ones grow via deposition, narrowing the ice crystal spectrum (Wu et al. 2000; Zeng 2008).

Global distribution of radiative cooling/warming.

Radiative cooling/warming plays a key role in REM and is measured by ηz. It has two contributors: clouds and their background. To distinguish the contributor of clouds from the other, ηz is decomposed into two parts:
ηz=(ηz)background+(ηz)cloud ,
where (ηz)background represents ηz with no cloud and (ηz)cloud a perturbation of ηz imposed by clouds (Zeng et al. 2021).

The two parts in Eq. (8) are computed using Eq. (5), a two-stream radiation package for F+ and F, and the observational data of the atmosphere, underlying surface, and clouds (Fu and Liou 1992; Chou et al. 1995; Zeng et al. 2021). The first part, (ηz)background, is computed herein using the National Oceanic and Atmospheric Administration reanalysis data (see supplemental material for details). Its results are displayed in Fig. 3. Generally speaking, ηz < 1 in the lower and middle troposphere in the low and middle latitudes; ηz < 1 through the troposphere in the high latitudes, especially in Antarctica.

Fig. 3.
Fig. 3.

Vertical cross section of the radiative ratio ηz with no clouds (ηz)background for the four seasons of 2019: (from top to bottom) December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON). Blue and red represent radiative cooling and warming, respectively; the yellow solid contour line denotes ηz = 1; the interval of ηz between the two contour lines is 0.2. Black solid and dashed lines denote the contour lines of air temperature T = 0° and −40°C, respectively.

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

The other part, (ηz)cloud, is determined by optically thick clouds, where thick and thin clouds are distinguished with a threshold of IR cloud optical depth of ∼0.5 approximately. Figure 4, for example, displays ηz around a thick cloud, exhibiting a dipole structure of ηz: ηz < 1 near cloud top and ηz > 1 near bottom. The dipole structure is clear in physics. The ice crystals near cloud top and bottom receive almost the same upward and downward IR (or ∼σT4) from a thick cloud, respectively. However, the former receives little IR from the space and the air above, whereas the latter receives strong upwelling IR from the underlying surface, bringing about ηz < 1 near cloud top and ηz > 1 near bottom (Zeng 2008).

Fig. 4.
Fig. 4.

Vertical cross sections of ηz in the cloudy atmosphere over the tropical Atlantic Ocean at 1506 UTC 11 Feb 2017. Blue and red represent radiative cooling and warming, respectively. Yellow, green, and black contour lines indicate the ice and liquid water content of 0.5 × 10−3, 5 × 10−3, and 50 × 10−3 g kg−1, respectively. All data used come from the CloudSat and CALIPSO observations.

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Although the accurate ηz of a specific cloud is obtained with in situ observational data (Zeng et al. 2021), Fig. 3 approximately represents the global distribution of ηz for thin clouds or clear sky and Fig. 4 for single-layer thick clouds when cloud bottom temperature is lower than the underlying surface temperature.

Global observations of REM

Since large and/or horizontally oriented ice crystals form at ηz < 1 via REM [see Eq. (7) for reason and Fig. 2 for crystal orientation selection], their observations are used to evaluate REM. The observations of polar clouds are discussed first, because ηz < 1 occurs frequently in the polar regions (Fig. 3).

Polar clouds.

Diamond dust (or clear-sky precipitation) is common, especially in polar winter (Curry et al. 1996; Intrieri and Shupe 2004; Schlenczek et al. 2017). It consists of large ice crystals with diameters between 50 and 250 μm and occasionally near 1,000 μm (Shimizu 1963; Kikuchi and Hogan 1979; Walden et al. 2003; Lawson et al. 2006). In addition, its crystal number concentration and extinction are quite low. Thus, looking through diamond dust toward the Sun, an observer can see ice crystals falling just like diamonds—and away from the Sun, nothing except for blue sky. Hence, diamond dust differs from ice fog for its large crystal diameter and low crystal number concentration, because ice fog is “composed of suspended particles of ice, partly ice crystals 20–100 μm in diameter, but chiefly, especially when dense, droxtals 12–20 μm in diameter” (American Meteorological Society 2022).

Diamond dust and ice fog share two processes: REM and the overall cooling of air, where the latter process includes the heat flow from air to cooled crystals (Gotaas and Benson 1965). However, they are dominated by the two processes, respectively, because REM varies with crystal size (Fig. 1). In ice fog, all ice crystals have relatively weak REM because of their small size, and thus the overall cooling of air brings about Hi > 1 (or the air is supersaturated with respect to ice). In contrast, in diamond dust, ice crystals have strong REM for their large size, and larger crystals grow at the expense of water vapor so that Hi < 1, bringing about sublimation of smaller ice crystals (Zeng 2018a; see the modeled difference between ice fog and diamond dust in the supplemental material).

REM explains the thin column crystals of length ∼1,000 μm (or the Shimizu crystals) observed in unsaturated environment. Consider an air parcel with relative humidity Hi < 1. Its ice crystals at equilibrium with half crystal size a* satisfy Hic = Hi. Figure 5 shows that a* increases with decreasing Hi.

Fig. 5.
Fig. 5.

Plot showing that an air parcel with ηz < 1 is colloidally unstable. Red line represents the critical relative humidity Hic vs half crystal size (or semi-major axis length) a for horizontally oriented column-like crystals at ηz = 0.5, T = −30°C, and p = 680 hPa; it also represents the critical half crystal size a* vs relative humidity Hi. Consider an air parcel with two ice crystals, Hi = 95%, and a*=235μm μm (green lines). One crystal with a (e.g., 235.5 μm) > a* grows via deposition and then maintains Hic < Hi, becoming a precipitating particle eventually. In contrast, the other crystal with a (e.g., 234.5 μm) < a* shrinks via sublimation and then maintains Hic > Hi, vanishing eventually. As a result, the two crystals deviate from their initial size oppositely, showing the air parcel is colloidally unstable.

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

The magnitude of a* is used to separate all ice crystals in the parcel into two subpopulations: small crystals with half crystal size a<a* that sublimate for their Hic > Hi, and large ones with a>a* that grow for Hic < Hi. Hence, in a special unsaturated environment with high Hi (or small a*), an ice crystal grows and maintains a>a* during its descent. Once its size reaches ∼100 μm, it grows rapidly to become a Shimizu crystal of length ∼1,000 μm, because the Hic of large ice crystals is far below 100% and decreases significantly with crystal size (Fig. 5).

REM also explains the vertical structure of diamond dust. Ice crystals of diamond dust usually originate in thin cirrus clouds above (Hogan 1975). After they fall into an unsaturated environment (or their mother cloud becomes dissipated), their spectrum is broadened and their number concentration is decreased by REM. This model of REM is consistent with the airborne observations of diamond dust: the ice crystals at 900-m altitude above the ground were smaller and their number concentration was higher than toward lower altitudes (Ohtake et al. 1982).

Two-dimensional reflections of a lidar beam were used to measure ice crystal properties, providing direct evidence to support REM (Goerke et al. 2017). When an ice crystal reflects a beam from a ground lidar onto the snow surface below, its specular reflection pattern is captured as an image by a camera. The image pattern, in turn, is used to retrieve its shape, size, orientation, roughness, and altitude, based on scattering theory (Ulanowski et al. 2012).

Figure 6, for example, displays three image patterns observed at the Summit Station in Greenland on 6 December 2016 (Goerke et al. 2017). The three patterns, as retrieved with the technique based on laser speckle (Ulanowski et al. 2012), are caused by three HOICs: a hexagonal plate with diameter 150 μm, a slightly rounded hexagonal plate with diameter 130 μm, and a strongly rounded hexagonal plate with diameter 120 μm, respectively. The retrieved shapes of the crystals reveal their histories: the hexagonal plate had undergone deposition; rounded crystals, sublimation (Nelson 1998).

Fig. 6.
Fig. 6.

Reflection images of three horizontally oriented ice crystals aloft on a grounded-based camera, which are (left) hexagonal plate with diameter 150 μm, (center) slightly rounded hexagonal plate with diameter 130 μm, and (right) strongly rounded hexagonal plate with diameter 120 μm. The images were photographed at the Summit Station in Greenland on 6 Dec 2016. Adapted from Goerke et al. (2017).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Of all the ice crystals observed in Goerke et al. (2017), about half of the plates had evidence of rounding (implying sublimation). Other, larger ones, displayed pronounced optical speckle. The population was bimodal: small plates between 125 and 530 μm in size had undergone sublimation; large plates from 0.7 to 4.0 mm, deposition. Recent research has indicated that ice crystals producing significant speckle are characterized by the presence of geometric irregularities (“roughness”) that are likely to be the result of fast and/or repeated (cyclic) growth (Voigtländer et al. 2018). Thus, the coexistence of two distinct subpopulations supports the separation of small and large crystals in Fig. 5 or mode II of REM.

The Cloud, Aerosol Polarization, and Backscatter Lidar (CAPABL) was developed to measure HOICs by implementing new polarization methods (Neely et al. 2013). CAPABL measures the particle backscatter ratio, the linear depolarization ratio, and a new data product called diattenuation through the combination of three polarization channels. The diattenuation, representing a polarization-dependent scattering efficiency, is contributed by HOICs instead of randomly oriented particles when viewed at oblique scattering angles (Hayman and Thayer 2012).

CAPABL was used to measure diattenuation with a beam zenith angle of 32° at Summit on 6 December 2016 (Neely et al. 2013, 2018; Goerke et al. 2017). Figure 7 displays its diattenuation, where strong diattenuation (red color) is contributed by HOICs. The figure also displays the corresponding radar reflectivity collected by the collocated Doppler, 35-GHz, millimeter cloud radar (MMCR) (Shupe et al. 2013). Although CAPABL rarely observed the cloud top (∼5-km altitude) due to attenuation, its observed diattenuation still shows the existence of HOICs in the middle of the cloud (∼2.5 km) that either form there or sediments from the upper portion of the cloud (or 3–5 km), supporting that REM is strong near the top or in the upper portion of thick clouds (or Fig. 4).

Fig. 7.
Fig. 7.

(top) CAPABL diattenuation and (bottom) MMCR radar reflectivity at the Summit Station from 1200 to 2400 UTC 6 Dec 2016. Black box highlights the period of camera imaging in Fig. 6, and red denotes the contribution of HOICs. Adapted from Goerke et al. (2017).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Optically thin ice clouds.

Subvisual cirrus clouds are common in the tropical tropopause layer (TTL) (Heymsfield 1986). They consist of small ice crystals with low temperature (or ∼−80°C) and low number concentration (McFarquhar et al. 2000). They are physically separated from cirrus below but tend to occur with cirrus below (Heymsfield 1986; Winker and Trepte 1998; Schwartz and Mace 2010). They can persist for weeks or months in clear skies in the equatorial regions (Lynch and Sassen 2002).

A challenging question is why the crystal number ­concentration in TTL is so low (Fig. 8; Heymsfield et al. 2013). Since ice nuclei (IN) become active with decreasing air temperature (Demott et al. 2010), it is expected that the number concentration of active IN at ∼−80°C is very high. However, the observed crystal number concentration in TTL is quite low (Fig. 8). This significant discrepancy in number concentration between ice crystals and active IN suggests that most active IN do not grow up,3 providing room for REM as an explanation.

Fig. 8.
Fig. 8.

Observed total ice crystal number concentrations Nt above 2–10 μm for T < −60°C (blue) and approximately 50 μm for T > −60°C (green) vs air temperature T, where solid lines represent data fitting, and the dotted line the average curve developed by Demott et al. (2010). Adapted from Heymsfield et al. (2013).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

REM with ηz < 1 can bring about the growth/shrinkage of relatively large/small crystals and subsequently a decrease in crystal number concentration, where active IN do not grow just like small ice crystals (Fig. 5; Zeng 2008). As a result, REM breaks the connection in number concentration between ice crystals and active IN, explaining why the number concentration of ice crystals is much lower than that of active IN in TTL.

On the other hand, ηz < 1 in TTL occurs only in company with thick clouds below because thick clouds block the strong upwelling IR from the surface (Fig. 9). The dependence of ηz < 1 in TTL on thick clouds below explains the correlation between subvisual cirrus clouds and thick clouds below.

Fig. 9.
Fig. 9.

As in Fig. 4, but for distance, where ηz < 1 (blue) near TTL occurs in company with the upper-tropospheric thick clouds below (enclosed by black lines).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Thin cirrus clouds are observed globally by a spaceborne lidar: the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) on the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) platform (Winker et al. 2010). Their HOICs are retrieved with CALIOP layer-integrated backscatter and depolarization ratio. Their CALIOP data reveal that HOICs are rare in optically thin ice clouds. Specifically, ∼6% of optically thin ice cloud layers contain HOICs; within those layers, less than 5% of crystals are horizontally oriented (Noel and Chepfer 2010).

Furthermore, the percentage of clouds with HOICs increases with latitude (Noel and Chepfer 2010; Kikuchi et al. 2021). Most HOICs are found in thin cirrus clouds with temperatures warmer than −30°C (or altitude below 10 km); almost none with temperatures colder than −30°C (or altitude above 10 km) (Noel and Chepfer 2010; Zhou et al. 2012; Kikuchi et al. 2021). REM explains these phenomena with the spatial distribution of ηz. Since thin clouds below 10 km usually undergo radiative cooling (or ηz < 1) (Fig. 3), HOICs form via REM; above 10 km, no HOICs form for radiative warming (or ηz > 1). In addition, the increase of HOICs with latitude is explained by the decrease of ηz with latitude (Fig. 3).

REM also explains why HOICs are rare in thin cirrus clouds but not in thick anvil clouds (Zeng et al. 2021). When ηz < 1, HOICs grow faster and faster because Hic decreases with crystal size (Fig. 5). After becoming large, HOICs stay in their cloud if the cloud has a strong vertical velocity to support them; otherwise, they fall off their cloud. Since thin clouds usually possess small vertical velocity, they retain rare HOICs because most HOICs grow and then fall off, which explains the CALIOP observations of rare HOICs in thin cirrus clouds.

Optically thick ice clouds.

HOICs in thick clouds are observed globally with a spaceborne microwave imager: the Global Precipitation Measurement (GPM) Microwave Imager (GMI) (Skofronick-Jackson et al. 2015). GMI uses 13 microwave channels to sense clouds, 10 of which take both horizontally (H) and vertically (V) polarized measurements at frequencies 10.65, 18.7, 36.5, 89, and 166 GHz. Its high-frequency channels of 166H and 166V are sensitive to ice crystal scattering, and its polarization difference at 166 GHz (or 166PD) is caused mainly by the ice crystal orientation near cloud top, where 166PD is defined as the difference in brightness temperature (TB) between vertically and horizontally polarized channel radiance measurements (Skofronick-Jackson et al. 2008; Roberti and Kummerow 1999; Adams et al. 2008; Defer et al. 2014). In other words, the magnitude of 166PD represents the contribution of HOICs near cloud top, given that other ice microphysical properties (e.g., size, habit) are statistically homogeneous on a pixel scale of 4.4 × 7.2 km2 (Gong et al. 2018; Zeng et al. 2019). Figure 10, for example, displays GMI TB and PD at 166 GHz over a midlatitudinal winter frontal system, showing that HOICs are common. The inconsistency in spatial variation between TB and PD indicates that the percentage of HOICs varies highly in space.

Fig. 10.
Fig. 10.

Spatial distributions of (left) GMI TB and (right) PD at 166 GHz over a midlatitude winter frontal system at ∼2000 UTC 25 Nov 2018, where TB represents average of the horizontally and vertically polarized measurements at 166 GHz. The inconsistency in spatial variation between TB and PD indicates that the percentage of HOICs varies spatially.

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Statistical analyses of GMI 166PD also show that HOICs in thick clouds are common from the low to high latitudes. Figure 11 displays the probability distribution functions (PDFs) of GMI 166PD over thick clouds and no clouds. Since the difference in PDF between thick clouds and no clouds is caused by thick clouds, the figure shows that thick clouds contribute ∼3 K to 166PD from the low to high latitudes, indicating HOICs are common in thick clouds. This result is supported by the recent Polarimetric Radio Occultation observations (Padullés et al. 2021) and is consistent with the prediction of REM (or Fig. 4) concerning the latitude independence of HOICs in thick clouds.

Fig. 11.
Fig. 11.

PDF of the GMI 166PD (or polarization difference ΔTb at 166 GHz) over land. Thick lines represent columns with the maximum radar reflectivity at 5–20 dBZ and thin ones with the maximum radar reflectivity below −20 dBZ (referred to as background) in the (left) low, (center) middle, and (right) high latitudes. Adapted from Zeng et al. (2019).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

In addition, GMI 166PD decreases with increasing cloud top height (or decreasing TB from 180 to 90 K in Fig. 12; Gong et al. 2018; Zeng et al. 2021). This phenomenon is explained by the sensitivity of REM to altitude in Fig. 13. GMI 166PD also exhibits a clear diurnal variation over tropical land (Fig. 12). It reaches the maximum at 0900 LST and minimum at 1500 LST, which is out of phase with cloud fraction (or the maximum at 1800 LST and minimum at 1100 LST). REM explains its diurnal variation with the diurnal variation of ηz. To be specific, the diurnal variation of ηz is caused by the diurnal variation of land surface temperature via F+, reaching the lowest near dawn and highest after noon. After considering a delay of ∼2 h for ice crystal growth, ηz coincides with GMI 166PD in phase. In contrast, GMI 166PD exhibits no obvious diurnal variation over the tropical oceans, because the sea surface temperature and thus ηz have weak diurnal variations. These coincidences in phase and magnitude between ηz and GMI 166PD suggest that REM brings about HOICs near cloud top.

Fig. 12.
Fig. 12.

Diurnal variation of GMI 166 PD over the (a) oceans and (b) land in the tropics (or between 30°S and 30°N), where the horizontal axis is TB from the vertically polarized channel radiance measurement at 166 GHz. A curve at a local solar time (LST), denoted by one color, connects the mean values of GMI 166PD in the TB bins at a given LST. The part to the left of the vertical dash–dotted line represents the contribution of the underlying surface; the part between the two vertical lines represents the contribution of the surface and thin clouds (from Gong et al. 2018).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Fig. 13.
Fig. 13.

Time scale of REM vs height at ηz = 0.86 (black) and 0.93 (blue) in the tropics. Red circles denote the results from the numerical experiments with explicit bin model simulation. The time scale represents a period for ice crystals to double their average size, and thus measures the REM-induced broadening of ice crystal spectrum (from Zeng et al. 2021).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Moreover, REM explains the strongest diurnal variation of GMI 166PD at TB ≈ 200 K over tropical land (Fig. 12). The coincident data of GMI and CloudSat reveal that the diurnal variation is contributed mainly by the clouds at ∼7-km altitude (Gong et al. 2021); theoretical studies reveal the time scale of REM increases greatly with altitude and is about 24 h at ∼7 km (Fig. 13). When the time scale of REM is close to the period of ηz, REM becomes strongest (Zeng 2008), which explains why the diurnal variation of GMI 166PD is strong at TB ≈ 200 K.

REM in warm clouds

Physics in warm clouds.

REM is effective in warm fog/clouds just as in ice clouds because the atmosphere is quasi-transparent for IR with wavelengths of 8–12 μm (see Table 2; Roach 1976; Barkstrom 1978). On the other hand, REM in warm clouds is weaker than in ice clouds, because ice crystals usually have aspect ratio away from one compared to liquid drops (see footnote 1 for the connection between size and aspect ratio of a nonspherical ice crystal; Zeng 2008).

REM in warm clouds, following Eq. (1), is measured by the critical relative humidity for a drop with radius r and salt mass ms or
Hwc=Eswn(Ts,r,ms)/Esw(T),
where Esw(T) is the saturation vapor pressure over water at air temperature T and Eswn(Ts, r, ms) is the saturation vapor pressure around a drop at drop temperature Ts. Figure 14 displays Hwc against r and ηz, showing Hwc decreases with r when ηz < 1 and r is so large that the solute and surface effects are negligible.
Fig. 14.
Fig. 14.

Critical relative humidity Hwc of drops with different salt (NaCl) mass ms vs radius at T = 15°C, p = 800 hPa, and ηz = 0.8.

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

Consider multiple drops in an air parcel with ηz < 1 and relative humidity with respect to water Hw. Suppose that one of the drops with radius r* satisfies Hwc = Hw. Thus, all the drops are separated into two subpopulations: small drops with radius r<r* that evaporate for their Hwc > Hw, and large ones with r>r* that grow for Hwc < Hw. As a result, their spectrum is broadened by REM (Guzzi and Rizzi 1980), which is displayed in Fig. 15.

Fig. 15.
Fig. 15.

REM-induced broadening of drop spectrum in an air parcel with ηz = 0.8, T = 15°C, and p = 800 hPa. The vertical axis is the mass density dM(lnr)/dlnr, where M(lnr) is the mass of drops with radius shorter than r. Thick line denotes the initial drop spectrum, and the time interval between lines is 10 min. The continuous spectrum shifting to larger sizes generates numerous large droplets (or drops with radius larger than 28 μm) eventually (from Zeng 2018b).

Citation: Bulletin of the American Meteorological Society 103, 9; 10.1175/BAMS-D-21-0039.1

The broadening of the drop spectrum is replicated recently in an experimental apparatus, where droplet mist is accommodated in a vertically oriented tube that is cooled artificially (Brewster et al. 2020). The mist in the tube undergoes two processes: REM and the overall cooling of air, where the latter includes the radiative cooling of vapor constituents (e.g., water vapor) of air and the heat flow from air to cooled droplets. Since the former broadens the drop spectrum and the latter narrows the spectrum (see supplemental materials for their opposite effects on drop spectrum), the observed broad drop spectrum indicates that the former is important or REM is responsible for the observed broadening of the drop spectrum.

The broadening of the drop spectrum is also supported by the field observations of shallow cumulus. Small and Chuang (2008) used the phase Doppler interferometer to measure the drop spectrum at different levels of shallow cumulus and found that the drop spectrum near cloud top is quite broad. The observed broad drop spectrum at cloud top is consistent with the prediction of REM near cloud top, because ηz < 1 always occurs near cumulus cloud top (Fig. 4; Zeng 2018b).4

In addition, solar radiation (SR) affects drop spectrum via REM and partially offsets the effect of IR (Hartman and Harrington 2005a,b; Marquis and Harrington 2005). To address its REM, SR can be introduced into Eq. (1) just as IR via ηz (Zeng 2018b). In warm clouds, SR heating dominates over IR cooling at larger drop radius (>200 μm), causing large drops to evaporate (Hartman and Harrington 2005a). Its REM decreases with solar zenith angle (Hartman and Harrington 2005b). In ice clouds, SR heating can cause large HOICs to sublimate and thus decrease the percentage of large HOICs, bringing about a diurnal variation of GMI 166PD with a minimum after noon, especially in the tropics. Figure 12 displays the diurnal variations of GMI 166PD over the tropical oceans and land, showing that the two diurnal variations are almost out of phase. Suppose that the diurnal variation over the tropical oceans is caused mainly by SR and the diurnal variation over tropical land by both IR and SR. The figure thus suggests that the SR-induced REM is about 1/6 (or less) of the IR-induced REM in magnitude.

Interaction between REM and other cloud processes.

Clouds change ηz that in turn changes themselves and other clouds, which exhibits as an interaction between REM and other cloud processes. The interaction can be simulated using multiple-dimensional cloud models with bin microphysics, which is exampled below for fog and clouds, respectively.

The interaction between REM and gravitational drop settling impacts the life cycle of fog, which is replicated in the one-dimensional fog model of Bott et al. (1990). REM induces large droplets near fog top that in turn fall to the ground quickly, bringing about a strong reduction of liquid water content and therefore a change of radiative cooling rate. The phase shift between large droplet growth and radiative cooling rate then brings about an oscillation in liquid water content and radiative fluxes, which resembles an oscillation observed in fog with a period of 10–30 min (Bott et al. 1990).

REM near cloud top cooperates with drop collection, accelerating the rain initiation in warm clouds (Austin et al. 1995). Nevertheless, the effect of REM on rain initiation in an air parcel depends on the residence time of the parcel near cloud top or edge (Harrington et al. 2000; Klinger et al. 2019), which becomes complicated by involving condensation nuclei and turbulent mixing (Ackerman et al. 1995).

Outlook

REM predicts that large and/or horizontally oriented ice crystals form at ηz < 1.5 Since its prediction is consistent with the plentiful observations of HOICs and other particle characteristics from different platforms (e.g., aircrafts, field campaigns, and satellites), it is inferred that REM exists from the Arctic to the tropics.

The current operational weather and climate models overlook REM, although they have represented the overall cooling of air, including the heat flow from air to cooled cloud particles (that is equal to the radiative cooling of cloud particles). If they incorporate REM in terms of ηz, their water cycle will be improved with the following scenarios:

  • Excessive water vapor is mitigated by the REM-induced formation of precipitating ice crystals (e.g., diamond dust). The process is important in the polar regions, especially in Antarctica during wintertime.

  • Excessive water vapor is mitigated by the REM-inhibited sublimation and enhanced sedimentation of precipitating ice crystals in subsaturated air. One example is the long survival of precipitating ice crystals in a dry environment observed by Braham and Spyers-Duran (1967).

  • Variations of subvisual cirrus clouds in TTL are associated with cirrus clouds below via REM. As a result, REM can reduce the amount of water vapor that ascends from the troposphere to the stratosphere.

  • Optically thick clouds are converted to thin ones via REM. Since ηz < 1 near thick cloud top, precipitating ice crystals form there and then fall off until thick clouds become thin ones (or their dipole structure of ηz is gone). This interaction between REM and clouds is similar to that described in Bott et al. (1990).

  • REM broadens the drop spectrum near the top of small cumulus that in turn helps the rain initiation of small cumulus (Austin et al. 1995; Harrington et al. 2000; Small and Chuang 2008; Zeng 2018b; Klinger et al. 2019).

In addition, HOICs have a smaller fall speed than other crystals (Heymsfield and Iaquinta 2000) and increase cloud albedo (Takano and Liou 1989).

In bulk, REM removes water vapor, liquid water, and ice from the atmosphere, working as a sink of water. It thus can impact climate change just as the release of carbon dioxide (CO2) via greenhouse gas accumulation. Consider, for example, an ideal climate model that represents all processes accurately. If it excluded REM, its water content would become too high via accumulation and thus its predicted global warming too strong, which is estimated in comparison to CO2. CO2 increases its concentration from 360 ppm in 1995 to 410 ppm in 2019 (IPCC 2021), corresponding to a relative increase of 5.7 × 10−7% day−1. Thus, an equivalent change of water vapor in a vertical column is 2.9 × 10−4 g m−2 day−1 (if the precipitable water is represented with a tropical value of ∼50 kg m−2). Since dew/frost can remove water vapor from the atmosphere on the order of 2.9 × 10−4 g m−2 day−1 (or higher), REM is as important as the release of CO2 in climate modeling.

To remove the excessive water and spurious warming, the current models usually introduce artificial sinks of water (e.g., the artificial adjustment of water vapor to observed relative humidity, the autoconversion of cloud ice to precipitating water), causing distortion of the water cycle. Specifically, the models maintain a quasi-balance between water sources and sinks by tuning the parameterization of clouds (or water sources), and consequently pass the errors of the sink representation into the parameterization of clouds. As a result, they generate water biases in one form or another, such as the low bias in supercooled liquid water in mixed-phase clouds (Klein et al. 2009; Komurcu et al. 2014) that may also be caused by lacking the subgrid parameterization of the Wegener–Bergeron–Findeisen process (Tan and Storelvmo 2016). If the models represented the water sink properly via REM, their parameterization of clouds could be improved or constrained “easily” by observations, because one side of the water balance was anchored. Hence, introducing REM will greatly improve the accuracy of the water and energy cycles of the atmosphere in the models.

1

The equivalent radius of a nonspherical particle is defined as r = S/(4πC), where S and C denote the surface area and stationary diffusion shape factor of the particle, respectively. Since it degenerates into radius for a spherical particle, it is used to measure ice particle size as well.

2

Once an ice particle deviates from the critical case, it sublimates or water vapor deposits on its surface, producing latent heating. After incorporating the latent heating, Eq. (7) becomes complicated while it still contains the factor of αr(ηz − 1). A complete equation of TsT with latent heating was presented in Zeng (2008).

3

An active IN can initiate the ice phase at its active sites on a substrate surface. In spite of the capability for nucleation, it remains its original size if HiHic. In an air parcel in TTL with ηz < 1, relatively large ice crystals grow at the expense of water vapor so that Hi < Hic for active IN, bringing about no growth of active IN. As a result, the active IN look like inactive ones.

4

The observations of Small and Chuang (2008) were also explained by the entrainment-mixing processes and stochastic condensation (e.g., Telford 1996; Liu et al. 2002; Desai et al. 2019, 2021; Luo et al. 2020).

5

Since REM favors the growth of HOICs and therefore increases the percentage of HOICs, it changes the percentage of HOICs independently of turbulence (Klett 1995), crystal shape (Stoelinga et al. 2007), and the process of Jayaweera and Mason (1965; hereafter JM), which is illustrated as follows. JM released cylinders into a liquid tank with random perturbation and then found the dominance of horizontally oriented cylinders. Suppose that JM knew the details of initial cylinder releasing and grouped the initial releasing into two kinds: one for horizontally oriented cylinders and the other for vertically oriented cylinders (even though the first kind has much more cylinders than the second kind). If JM redid two experiments with the two kinds of cylinder releasing, respectively, then they would see different cylinder orientations in the two experiments: all cylinders with the first kind of releasing are horizontally oriented and all cylinders with the second kind of releasing are vertically oriented. The difference in cylinder orientation between the two ideal experiments suggests that initial cylinder releasing can change the percentage of horizontally oriented cylinders. In clouds, REM functions similarly as the initial cylinder releasing while it does not affect the process of JM.

Acknowledgments.

The authors thank Dr. Manfred Wendisch (editor), Dr. Xianglei Huang, and three anonymous reviewers for their kind and constructive comments. They also thank Eric Mark and Jessica Schultheis for reading the manuscript.

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