Ice Aggregates Research Articles

Glacio and hydro-isostasy in the Mediterranean Sea: Clark’s zones and role of remote ice sheets

Solving the sea-level equation for a spherically symmetric Earth we study the relative sea-level curves in the Mediterranean Sea in terms of Clark's zones and we explore their sensitivity to the time-history of Late-Pleis- tocene ice aggregates. Since the Mediterranean is an intermediate field region with respect to the former ice sheets, glacio- and hydro-isostasy both contribute to sea-level variations throughout the Holocene. In the bulk of the basin, subsidence of the sea floor results in a monotonous sea-level rise, whereas along continental margins water loading produces the effect of «continental levering», which locally originates marked highstands followed by a sea-level fall. To describe such peculiar pattern of relative sea-level in this and other mid-latitude closed basins we introduce a new Clark's zone (namely, Clark's zone VII). Using a suite of publicly available ice sheet chronologies, we identify for the first time a distinct sensitivity of predictions to the Antarctic ice sheet. In par- ticular, we show that the history of mid to Late Holocene sea-level variations along the coasts of SE Tunisia may mainly reflect the melting of Antarctica, by a consequence of a mutual cancellation of the effects from the North- ern Hemisphere ice-sheets at this specific site. Ice models incorporating a delayed melting of Antarctica may ac- count for the observations across the Mediterranean, but fail to reproduce the SE Tunisia highstand.

Energy balance of the Deep Impact experiment

We present results on the energy balance of the Deep Impact experiment based on analysis of 180 infrared spectra of the ejecta obtained by the Deep Impact spacecraft. We derive an output energy of 16.5 (+9.1/−4.1) GJ. With an input energy of 19.7 GJ, the error bars are large enough so that there may or may not be a balance between the kinetic energy of the impact and that of outflowing materials. Although possible, no other source of energy other than the impactor or the Sun is needed to explain the observations. Most of the energy (85%) goes into the hot plume in the first few seconds, which only represents a very small fraction (<0.01%) of the total ejected mass. The hot plume contains 190 (+263/−71) kg of H 2O, 1.6 ± 0.5 kg of CO 2, 8.2 (+11.3/3.1) kg of CO (assuming a CO/H 2O ratio of 4.3%), 27.9 (+25.0/−8.9) kg of organic material and 255 ± 128 kg of dust, while the ejecta contains ∼10 7 kg of materials. About 12% of the energy goes into the ejecta (mostly water) and 3% to destroy the impactor. Volatiles species other than H 2O (CO 2, CO or organic molecules) contribute to <7% of the energy balance. In terms of physical processes, 68% of the energy is used to accelerate grains (kinetic energy), 16% to heat them, 6% to sublimate or melt them and 10% (upper limit) to break and compress dust and/or water ice aggregates into small micron size particles. For the hot plume, we derive a dust/H 2O ratio of 1.3 (+1.9/−1.0), a CO 2/H 2O ratio of 0.008 (+0.009/−0.006), an organics/H 2O ratio of 0.15 (+0.29/−0.11) and an organics/dust ratio of 0.11 (+0.30/−0.07). This composition refers to the impact site and is different from that of the bulk nucleus, consistent with the idea of layers of different composition in the nucleus sub-surface. Our results emphasize the importance of laboratory impact experiments to understand the physical processes involved at such a large scale.

On the generation of charge layers in MCS stratiform regions

We suggest a quantitative one-dimensional model treating the formation of charge layers near the 0 °C isotherm in stratiform regions of mesoscale convective systems. A number of factors principal for the field generation have been taken into account: both non-inductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °С isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. Non-inductive collisional charging near the 0 °C isotherm was not considered. It was found that both non-inductive and inductive melting mechanisms can contribute; the inductive melting charging of ice aggregates was found more preferable, while the contribution of non-inductive mechanisms might be significant depending on particular conditions. The role of light ions in the formation of the positive charge layer near the 0 °C isotherm may be important. If the advection from the convective region ensures charge inflow to the upper charged layers, the melting charging mechanisms are able to explain an observable electric field structure in the whole stratiform region. It is important that the mutual position of the zero point on the vertical air velocity profile and the point of maximum melting-charge-transfer determines the fine structure of the electric field in the vicinity of the 0 °C isotherm.

The Capacitance of Pristine Ice Crystals and Aggregate Snowflakes

Abstract A new method of accurately calculating the capacitance of realistic ice particles is described: such values are key to accurate estimates of deposition and evaporation (sublimation) rates in numerical weather models. The trajectories of diffusing water molecules are directly sampled, using random “walkers.” By counting how many of these trajectories intersect the surface of the ice particle (which may be any shape) and how many escape outside a spherical boundary far from the particle, the capacitances of a number of model ice particle habits have been estimated, including hexagonal columns and plates, “scalene” columns and plates, bullets, bullet rosettes, dendrites, and realistic aggregate snowflakes. For ice particles with sharp edges and corners this method is an efficient and straightforward way of solving Laplace’s equation for the capacitance. Provided that a large enough number of random walkers are used to sample the particle geometry (∼104) the authors expect the calculated capacitances to be accurate to within ∼1%. The capacitance for the modeled aggregate snowflakes (C/Dmax = 0.25, normalized by the maximum dimension Dmax) is shown to be in close agreement with recent aircraft measurements of snowflake sublimation rates. This result shows that the capacitance of a sphere (C/Dmax = 0.5), which is commonly used in numerical models, overestimates the evaporation rate of snowflakes by a factor of 2. The effect of vapor “screening” by crystals growing in the vicinity of one another has also been investigated. The results clearly show that neighboring crystals growing on a filament in cloud chamber experiments can strongly constrict the vapor supply to one another, and the resulting growth rate measurements may severely underestimate the rate for a single crystal in isolation (by a factor of 3 in this model setup).

Radar Backscattering Computations for Fractal-Shaped Snowflakes

We propose a model for large snowflakes based on the fractal nature of their particle shapes. Monte Carlo simulations were conducted to make particles with a fractal dimension of 1.8 to 2.4. The roundness parameter for the projected images of the modeled particles was derived, and an average roundness of approximately 0.4 for particles with fractal dimension 2.1 was indicated; this average roundness matched reported values measured for large ice aggregates. The finite difference time domain method was used to calculate the backscattering cross-sections of ice particles with a fractal dimension of 2.1 and a particle diameter of up to ∼20 mm at microwave frequencies of 95 GHz, 35 GHz, and 9.8 GHz. The results were compared with those of equivalent-volume spheres and randomly oriented equivalent-volume hexagonal columns. Our snowflake model had smaller values of radar backscattering cross-sections than did the equivalent-volume spheres in the size range out of the Rayleigh regime. Furthermore, large differences in backscattering cross-sections between the snowflake model and the equivalent-volume hexagonal column were confirmed, in particular at a frequency of 35GHz.

Numerical Simulation of Dust Aggregate Collisions. I. Compression and Disruption of Two‐Dimensional Aggregates

We carry out numerical simulations of dust aggregate collisions to study the compression and disruption processes of aggregates in their growth. To compare with the pioneering studies of Dominik & Tielens, we focus on two-dimensional head-on collisions, in which we obtain similar results for compression and disruption to theirs. In addition to the similarities, we examine the dependence of the collisional outcomes on the aggregate size and the parameters relevant to the particle interaction in detail by treating large aggregates that consist of up to 2000 particles. Compression of aggregates by collisions reduces the radius of gyration and increases the number of contacts between the constituent particles. Our results show that the changes in the gyration radius and the number of contacts after impact depend on the impact energy and that the dependence is scaled by the energy necessary to roll all contacts. We provide empirical formulae for the changes in the gyration radius and the number of contacts. Furthermore, we find that the degree of maximum compression is determined by the ratio of rolling energy to breaking energy. This indicates that ice aggregates become more compact than quartz aggregates in the same impact conditions. Any aggregates are catastrophically disrupted when the impact energy exceeds approximately 10 times the energy necessary to break all contacts. Our results, however, suggest that it becomes harder to disrupt the aggregates with an increasing number of particles.

Problems in large-scale modeling of sea ice cover evolution

Results of large-scale mathematical modeling of sea ice cover evolution are analyzed. Special attention is given to formalization of the thermal effect of the atmosphere on ice cover evolution. A model of sea ice cover evolution is developed in which thermal effects of the environment on ice cover and aggregation, fragmentation, and hummocking of ice are taken into account. The model adequacy is estimated by sample distribution of area and thickness of ice cover in the Sea of Japan.

A Test of Ice Self-Collection Kernels Using Aircraft Data

Abstract Aircraft observations from the Cirrus Regional Study of Tropical Anvils and Cirrus Layers (CRYSTAL)–Florida Area Cirrus Experiment (FACE) campaign obtained in the anvil of a large convective storm from 26 July 2002 are presented. During this flight a Lagrangian spiral descent was made, allowing the evolution of the ice particle size distribution to be followed. Relative humidities during ∼1 km (from −11° to −3°C) of the descent were within 4% of ice saturation. It was assumed that the ice particle size distribution was evolving through the process of aggregation alone. Three idealized ice–ice collection kernels were used in a model of ice aggregation and compared to the observed ice particle size distribution evolution: a geometric sweep-out kernel, a Golovin (sum of particle masses) kernel, and a modified-Golovin kernel (sum of particle masses raised to a power). The Golovin kernel performed worst. The sweep-out kernel produced good agreement with the observations when a constant aggregation efficiency of 0.09 was used. The modified-Golovin kernel performed the best and implied that the aggregation efficiency of sub-300-μm particles was greater than unity when compared with a geometric sweep-out kernel.

On the scattering phase‐function of non‐symmetric ice‐crystals

AbstractTheoretical phase‐functions representing randomly oriented fractal ice‐crystals, bullet‐rosettes, ice aggregates, and an ensemble of ice crystals are compared to measured phase‐functions using a Polar Nephelometer located in the Antarctic. The Polar Nephelometer operated at a wavelength of 0.80 µm and measured the scattering phase‐functions of individual ice‐crystals between the scattering angles of 5.86° and 167°. The Polar Nephelometer was operated in tandem with a Cloud Particle Imager (supplied by SPEC Inc.) both were situated at the South Pole Amundsen–Scott base station during January 2002. In this paper we report on a sample of Polar Nephelometer data obtained over a time interval of 2000 seconds consisting of 3256 phase‐functions measured from individual ice‐crystals. The 3256 measured phase‐functions were averaged to produce an ensemble‐averaged phase‐function. The theoretical phase‐functions have been compared to the measured ensemble‐averaged phase‐function. The paper demonstrates that phase functions representing single ice‐crystal geometries do not reproduce the measured data well. However, the theoretical phase‐function representing scattering from an ensemble of ice crystals is found to be the best description of the measured phase‐function over all scattering angles. Copyright © 2005 Royal Meteorological Society.

Isostatic rebound following the Alpine deglaciation: impact on the sea level variations and vertical movements in the Mediterranean region

SUMMARY The present-day sea level variations and geodetically observed ground deformations in the Mediterranean area are normally ascribed to the combined effect of tectonic or human-driven subsidence and postglacial uplift as a result of the melting of the major Pleistocene ice sheets. However, another potential cause of deformation, only marginally considered to date, is the melting of the glacier that covered the Alps during the last glacial maximum (LGM). The aim of this paper is to predict the long-term sea level variations induced by the melting of both the late-Pleistocene and Alpine ice sheets and compare our results with the relative sea level (RSL) observations available in the Mediterranean region. This task is accomplished solving the sea level equation (SLE) for a spherically symmetric viscoelastic Earth. Our analysis shows that the melting of the Alpine glacier has marginally affected the Holocene sea level variations in the near-field sites in southern France (Marseilles and Roussillon) and the central Tyrrhenian sea (Civitavecchia), and that the RSL predictions are significantly sensitive to the chronology of the remote ice aggregates. The computations, which are performed using a specific mantle viscosity profile consistent with global observations of RSL rise, show that the uplift rate driven by the Alpine isostatic readjustment may account for up to 1 of the rates observedatGPSstationsinthewesternportionofthechain.Ourresultssuggestthatathorough modelization of both near- and far-field ice sheets is necessary to gain a better insight into the present-day deformations and sea level variations in the Mediterranean region.

The origin, ultrastructure, and microbiology of the sediment accumulating in liquid nitrogen storage vessels

During long-term cryopreservation, ice sediment accumulates in storage Dewars and poses a risk of microbial contamination to stored samples. Ice accumulates in liquid nitrogen via two general processes: (1) ice forming in the atmosphere above an open Dewar falls into the vessel; and (2) ice forming on cold surfaces of the Dewar or inventory system enters the liquid nitrogen. These ice crystals aggregate and entrap other materials, such as bacteria, fungal spores, and general laboratory debris present within the liquid nitrogen. Measured changes in the ultrastructure of ice aggregates following long-term storage are consistent with transient warming events to temperatures of −100 °C. Bacteria were identified in all samples and filamentous fungi in 9 out of 10 samples. These micro-organisms are commonly found in the environment and would not be expected to have been derived from IVF samples. Some of the bacteria identified are associated with nosocomial infections in humans. The implications that the association of microbial contamination with ice crystals has on cryopreservation procedures are discussed.

Aircraft observations of the influence of electric fields on the aggregation of ice crystals

Aircraft observations of ice-crystal size and habit distributions in the cirrus outflow from deep convection at several geographic locations are reported. In situ measurements were made in the outflow from maritime thunderstorms near Kwajalein, part of the Marshall Islands and of thunderstorms with more continental aerosol concentrations both in the United States and near Darwin, Australia over the Tiwi Islands. Images of chain-like aggregates of small ice crystals, some with plate-like shapes were observed with a state-of-the-art microphysics probe in the outflow regions of continental storms that were typically highly electrified, displaying lightning. The ‘chains’ were not found in the outflow regions of maritime storms that are typically less electrically active. The striking similarity between these images and previous laboratory measurements of ice aggregation in electric fields are remarked upon. This evidence is used to support the theory that chain aggregates of ice crystals may be common in fully glaciated regions of continental thunderstorms, where ice-particle number densities are high, and their presence is due to the electric field alignment of ice crystals with subsequent enhancement of the aggregation process by dipole induction resulting in short-range attractive inter-particle forces. It is not confirmed where in the storm the aggregates were typically formed; however, in the Darwin thunderstorms they were noted to occur with the highest frequency towards the cirrus outflow base when the cirrus base altitude was high, and generally decreased in frequency with increasing distance from the storm. The potential consequences of electrically enhanced aggregation in continental storms and related electric field mechanisms along with the role of homogeneous freezing in intense thunderclouds are discussed. Copyright © 2005 Royal Meteorological Society

Charge sign reversal in irregular ice particle‐graupel collisions

Laboratory measurements of the sign of electric charge transfer separated in rebounding collisions between large ice crystals and a graupel pellet growing by riming are analyzed. In these experiments, the usual negative rimer charging regime noted at temperatures below about −10°C at moderate liquid water contents is reversed to positive when the crystals have grown larger. The experiments were performed with an impact velocity of 5.5 m s−1, the ambient temperature was varied in the range −15 to −26°C with an effective water content from 0.5 to 3 g m−3. A cloud particle imager shows a clear correlation between the rimer charge sign reversal to positive and the presence of a high proportion of irregular and large ice crystals or aggregates in the cloud. The results suggest that in collisions between graupel and these ice particles the graupel will charge positively while the irregular particles carry away a negative charge. These are the first measurements of this kind of collision and the findings may have important implications in the thunderstorm electrification process.

The dependence of retrieved cirrus ice‐crystal effective dimension on assumed ice‐crystal geometry and size‐distribution function at solar wavelengths

AbstractThe dependence of retrieved ice‐crystal effective dimension on assumed ice‐crystal shape and size‐distribution function is investigated at solar wavelengths (0.87, 1.6 and 3.7 µm). The dual viewing Along Track Scanning Radiometer is used to retrieve ice‐crystal effective dimension using a method of Optimal Estimation over semi‐transparent cirrus located in the tropics and mid‐latitudes. The ice‐crystal effective dimension is defined in terms of the effective diameter and it is retrieved assuming roughened hexagonal ice aggregates, pristine hexagonal ice columns, and four‐branched bullet rosettes. It is shown that if a phase function that well represents the scattering properties of cirrus is applied to each crystal type then the retrieved ice‐crystal effective diameter is only weakly dependent on ice‐crystal shape and size‐distribution function. Absolute differences between retrieved ice‐crystal effective diameter assuming hexagonal ice columns and ice aggregates combined with a representative phase function are generally well within ±5 µm. The findings of this paper have the important implication that, in climate models, simulation of cirrus cloudy radiances at solar wavelengths might be made to be independent of assumed ice‐crystal shape and size‐distribution function. © Crown copyright, 2004.

On the radiative properties of cirrus cloud at solar and thermal wavelengths: A test of model consistency using high‐resolution airborne radiance measurements

AbstractTwo models describing the single‐scattering properties of cirrus cloud are tested for physical consistency at solar and thermal wavelengths using airborne high‐resolution radiance data. The data were obtained from a case of semi‐transparent cirrus cloud, which occurred north of Scotland during October 2000. The single‐scattering models tested are randomly oriented hexagonal ice columns and randomly oriented ice aggregates. High‐spectral resolution radiances were measured from above the cirrus at a number of wavelengths between 0.3 and 16.7 µm, thereby covering a large range of ice crystal size parameter space and complex refractive index. It is shown that consistency between retrieved optical thickness and ice crystal effective radius at both solar and infrared wavelengths could only be achieved if the ice aggregate model was assumed. Moreover, differences between the ice aggregate model and spectrally resolved brightness temperature measurements were generally well within ±1 K between the wavelengths of 3.3 and 16.0 µm in the clean atmospheric window regions. The paper shows that it is important to have simultaneous radiance measurements from both the solar and thermal spectral regions so that ice crystal scattering models and cirrus retrievals can be rigorously tested. © Crown copyright 2004.

Simulation of infrared scattering from ice aggregates by use of a size-shape distribution of circular ice cylinders.

The scalar optical properties (extinction coefficient, mass extinction coefficient, single-scattering albedo, and asymmetry parameter) of a distribution of randomly oriented ice aggregates are simulated generally to well within 4% accuracy by use of a size-shape distribution of randomly oriented circular ice cylinders at wavelengths in the terrestrial window region. The single-scattering properties of the ice aggregates are calculated over the whole size distribution function by the finite-difference time-domain and improved geometric optics methods. The single-scattering properties of the size-shape distribution of circular ice cylinders are calculated by the T-matrix method supplemented by scattering solutions obtained from complex-angular-momentum theory. Moreover, radiative-transfer studies demonstrate that the maximum error in brightness temperature space when the size-shape distribution of circular ice cylinders is used to represent scattering from ice aggregates is only approximately 0.4 K The methodology presented should find wide applicability in remote sensing of ice cloud and parameterization of cirrus cloud scalar optical properties in climate models.

A Numerical Study of Cirrus Clouds. Part II: Effects of Ambient Temperature, Stability, Radiation, Ice Microphysics, and Microdynamics on Cirrus Evolution

Using the numerical cirrus cloud model developed in Part I of this study, the development of cirrus is examined for four different environmental regimes: warm unstable, cold unstable, warm stable, and cold stable. Despite similar initial saturation conditions, the clouds in the warm and cold cases develop very differently. As summarized below, these four simulations suggest that homogeneous freezing of haze particles and cold temperatures are two major reasons for persistent cirrus clouds. The numerical model is also used here to investigate the roles of several other physical factors in cirrus evolution for a selected environmental regime. These additional factors are radiation, ice crystal habit, latent heat, and ice crystal aggregation. In the warm unstable case, ice particles quickly grow large enough to fall out of the initially supersaturated cloud generation region into the subsaturated lower region. But in the cold unstable case, due to slow growth of cold temperatures, sedimentation is greatly postponed. Thus the cold cirrus tends to persist longer than the warm cirrus. In the unstable cases, diabatic heating tends to slightly destabilize the upper part of the cloud, whose circulation thus is most persistent near the cloud top. The circulation transports water vapor upward to enable long-lasting new ice particle generation. The solar heating tends to be concentrated near the cloud top in both unstable cases, but with quite different IR heating profiles. The IR heating warms the warm cloud near the base and cools it near the top, whereas the cold cloud is radiatively warmed throughout, mostly because it is optically thinner than the warm cloud. In the stable cases, homogeneous nucleation (the homogeneous freezing of haze solution droplets, as parameterized in Part I of this paper) does not occur for the parameterization of heterogeneous nucleation used, leaving the number concentration of ice much smaller than in the unstable cases. However, the individual crystals can grow larger, due to less competition for water vapor, so that they fall out of the initial saturated layer faster than in the unstable cases. The sedimentation rate is slower in the cold stable case than in the warm stable one, again due to slower growth rates at cold temperatures. In neither stable case does the induced diabatic heating destabilize the cloud layer. In this numerical study, it is found that cirrus cloud becomes much less persistent in the simulation without any radiative processes. For warm cirrus, the growth is slightly more vigorous in the daytime than at night, while the opposite is true for cold cirrus. It is found that latent heating plays two opposite roles in the evolution of cirrus. First, it augments the initial perturbation in the growing stage of the cloud, but then tends to stabilize the cloud layer, limiting the development of cirrus at later stages of the cloud evolution. Ice crystal habit has great impact on the evolution of cirrus, especially in an unstable atmosphere. The radiative heating rates are also found to be very sensitive to the type of ice crystal in the cloud. Finally, the role of ice aggregates in the evolution of cirrus is also explored. It is found that the aggregates reduce the volume absorption coefficient, thus decreasing the optical depth and tending to reduce the radiative destabilization.

A Numerical Study of Cirrus Clouds. Part I: Model Description

Abstract This article, the first of a two-part series, presents a detailed description of a two-dimensional numerical cloud model directed toward elucidating the physical processes governing the evolution of cirrus clouds. The two primary scientific purposes of this work are (a) to determine the evolution and maintenance mechanisms of cirrus clouds and try to explain why some cirrus can persist for a long time; and (b) to investigate the influence of certain physical factors such as radiation, ice crystal habit, latent heat, ventilation effects, and aggregation mechanisms on the evolution of cirrus. The second part will discuss sets of model experiments that were run to address objectives (a) and (b), respectively. As set forth in this paper, the aforementioned two-dimensional numerical model, which comprises the research tool for this study, is organized into three modules that embody dynamics, microphysics, and radiation. The dynamic module develops a set of equations to describe shallow moist convectio...

A Process Study of the Dependence of Ice Crystal Absorption on Particle Geometry: Application to Aircraft Radiometric Measurements of Cirrus Cloud in the Terrestrial Window Region

Abstract The processes that contribute to the absorption of infrared radiation by atmospheric ice crystals are studied. The processes are separated into the geometric optics (i.e., refraction, internal, and external reflection) and above-edge (i.e., the capture of photons beyond the physical cross section of the particle via tunneling through an inertial barrier) contributions. The geometric optics and above-edge contributions to ice crystal absorption are compared and contrasted assuming ice spheres, randomly oriented hexagonal ice columns, and randomly oriented ice aggregates (i.e., systematically increasing particle complexity). The geometric optics and above-edge absorption coefficients have been calculated using the complex angular momentum approximation applied to the ice sphere, and a composite method has been used to calculate the two sets of absorption coefficients for the hexagonal ice column and ice aggregate based on the finite difference time domain and improved geometric optics methods. The ...

A consistent set of single-scattering properties for cirrus cloud: tests using radiance measurements from a dual-viewing multi-wavelength satellite-based instrument

In this paper a consistent set of single-scattering properties is presented for radiative transfer calculations and remote sensing of cirrus cloud. The single-scattering properties consist of the extinction coefficient, single-scattering albedo and phase function. A randomly oriented randomized hexagonal ice aggregate is assumed to derive the extinction coefficient and single-scattering albedo. The phase function is an extension of the Henyey–Greenstein model called the “analytic” phase function, which is generated from the asymmetry parameter at non-absorbing and absorbing wavelengths. The satellite-based dual-view along track scanning radiometer (ATSR-2) instrument is utilized to test the single-scattering properties for consistency at scattering angles between about 60° and 170°, using a method of Optimal Estimation. Optimal Estimation is applied to a set of cloud parameters and radiance measurements, which are made simultaneously at the wavelengths of 0.87, 1.6, 3.7, 11.0 and 12.0 μm , over cases of cirrus cloud located in the tropics and mid-latitudes. If the single-scattering properties and assumed model parameters were a perfect representation of the radiative properties of cirrus then the measurement residuals (i.e., differences between measurements and simulated measurements) would be identically equal to zero at each of the wavelengths for all scattering angles. It is found that the randomized ice aggregate combined with the analytic phase function minimizes the measurement residuals to generally well within ±1% (reflectance) and ±1 K (brightness temperature) at 0.87, 11.0 and 12.0 μm and to within ±3% and ±3 K at 1.6 and 3.7 μm , respectively. This compares to measurement residuals of about 8% and 10 K if the single-scattering properties are based on the randomly oriented hexagonal ice column. It is recommended that single-scattering properties based on the randomized ice aggregate combined with the analytic phase function (or a very similar phase function) should be applied to remote sensing and radiative transfer studies of cirrus cloud.