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At least 469 records · Page 26

Improved Convective Ice Microphysics Parameterization in the NCAR CAM Model

Partitioning deep convective cloud condensates into components that sediment and detrain, known to be a challenge for global climate models, is important for cloud vertical distribution and anvil cloud formation. In this study, we address this issue by improving the convective microphysics scheme in the National Center for Atmospheric Research Community Atmosphere Model version 5.3 (CAM5.3). The improvements include: (1) considering sedimentation for cloud ice crystals that do not fall in the original scheme, (2) applying a new terminal velocity parameterization that depends on the environmental conditions for convective snow, (3) adding a new hydrometeor category, “rimed ice,” to the original four-class (cloud liquid, cloud ice, rain, and snow) scheme, and (4) allowing convective clouds to detrain snow particles into stratiform clouds. Results from the default and modified CAM5.3 models were evaluated against observations from the U.S. Department of Energy Tropical Warm Pool-International Cloud Experiment (TWP-ICE) field campaign. The default model overestimates ice amount, which is largely attributed to the underestimation of convective ice particle sedimentation. By considering cloud ice sedimentation and rimed ice particles and applying a new convective snow terminal velocity parameterization, the vertical distribution of ice amount is much improved in the midtroposphere and upper troposphere when compared to observations. The vertical distribution of ice condensate also agrees well with observational best estimates upon considering snow detrainment. Further, comparison with observed convective updrafts reveals that current bulk model fails to reproduce the observed updraft magnitude and occurrence frequency, suggesting spectral distributions be required to simulate the subgrid updraft heterogeneity.

54 ENVIRONMENTAL SCIENCES↗

Improving GCM Representation of Convective Cloud Microphysics by Using ARM Raman Lidar and Cloud Radar Observations

The overall objective of this Department of Energy (DOE) Atmospheric System Research (ASR) funded project is to improve the representation of convective cloud microphysics in global climate models (GCMs) and check it by comparing the model simulations with observations. We have derived the cloud ice water content by synthesizing ARM Raman lidar (RL) and cloud radar observations at the Atmospheric Radiation Measurement (ARM) sites. Noting that the simulated anvil clouds in terms of their macro- and micro-physical properties are sensitive to the parameterization of convective microphysical processes, observed ice water content in anvil clouds provides a useful constraint on these parameterizations. We have improved the convective microphysics parameterization scheme by (1) considering sedimentation for cloud ice crystals that do not fall in the original scheme, (2) applying a new terminal velocity parameterization that depends on the environmental conditions for convective snow, (3) adding a new hydrometeor category, “rimed ice,” to the original four-class (cloud liquid, cloud ice, rain, and snow) scheme, and (4) allowing convective clouds to detrain snow particles into stratiform clouds. We have examined the impact of improved convective cloud microphysics parameterization on the simulated global climate from GCM simulations.

54 ENVIRONMENTAL SCIENCES↗

Aircraft Engine Icing Event Avoidance and Mitigation Through Real-Time Simulation and Controls

A process for mitigating or proactively avoiding an aircraft engine icing event may include detecting ice crystals in the atmosphere using one or more sensors on board an aircraft in real time. The process may also include modulating one or more engine operating conditions to proactively change an ice accretion location, to avoid the occurrence of an icing event. The process may further include implementing one or more modulated engine operating conditions in engine controls software, hardware, or both.

Veres, Joseph P.↗

Improved Convective Ice Microphysics Parameterization in the NCAR CAM Model

Partitioning deep convective cloud condensates into components that sediment and detrain, known to be a challenge for global climate models, is important for cloud vertical distribution and anvil cloud formation. In this study, we address this issue by improving the convective microphysics scheme in the National Center for Atmospheric Research Community Atmosphere Model version 5.3 (CAM5.3). The improvements include: (1) considering sedimentation for cloud ice crystals that do not fall in the original scheme, (2) applying a new terminal velocity parameterization that depends on the environmental conditions for convective snow, (3) adding a new hydrometeor category, “rimed ice,” to the original four-class (cloud liquid, cloud ice, rain, and snow) scheme, and (4) allowing convective clouds to detrain snow particles into stratiform clouds. Results from the default and modified CAM5.3 models were evaluated against observations from the U.S. Department of Energy Tropical Warm Pool-International Cloud Experiment (TWP-ICE) field campaign. The default model overestimates ice amount, which is largely attributed to the underestimation of convective ice particle sedimentation. By considering cloud ice sedimentation and rimed ice particles and applying a new convective snow terminal velocity parameterization, the vertical distribution of ice amount is much improved in the midtroposphere and upper troposphere when compared to observations. The vertical distribution of ice condensate also agrees well with observational best estimates upon considering snow detrainment. Comparison with observed convective updrafts reveals that current bulk model fails to reproduce the observed updraft magnitude and occurrence frequency, suggesting spectral distributions be required to simulate the subgrid updraft heterogeneity.

terminal velocity↗

Habit–Dependent Vapor Growth Modulates Arctic Supercooled Water Occurrence

We present an analysis of long-term data collected at Utqiagvik, Alaska, to explore the impacts of cloud processes on the probability of finding supercooled water given cloud temperature, P(L|T), in the topmost unseeded liquid-bearing layers. P(L|T) has local minima at temperatures around –6°C and –15°C. Simulations using habit-evolving ice microphysics models suggest that these minima are the result of efficient vapor growth by non-isometric habits found at these temperatures. Here, we conclude that habit-dependent vapor growth of ice crystals modulates the macrophysical occurrence of supercooled water in polar clouds, the effect of which should be included in model parametrizations to avoid biases and/or error compensation. Our methodology is adaptable for spherical ice treatments implemented in models (example parametrizations provided), amenable for use with satellite measurements to give global impartial observational targets for model evaluations, and may allow empirical characterization of bulk responses to seeding and possibly secondary ice effects.

54 ENVIRONMENTAL SCIENCES↗

Modeling the Deterioration of Engine and Low Pressure Compressor Performance During a Roll Back Event Due to Ice Accretion

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

Veres, Joseph P.↗

Modeling the Deterioration of Engine and Low Pressure Compressor Performance During a Roll Back Event Due to Ice Accretion

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

Jorgenson, Philip C. E.↗

Ice Nucleation in the Tropical Tropopause Layer: Implications for Cirrus Occurrence, Cirrus Microphysical Properties, and Dehydration of Air Entering the Stratosphere

Recent laboratory experiments have advanced our understanding of the physical properties and ice nucleating abilities of aerosol particles atlow temperatures. In particular, aerosols containing organics will transition to a glassy state at low temperatures, and these glassy aerosols are moderately effective as ice nuclei. These results have implications for ice nucleation in the cold Tropical Tropopause Layer (TTL; 13-19 km). We have developed a detailed cloud microphysical model that includes heterogeneous nucleation on a variety of aerosol types and homogeneous freezing of aqueous aerosols. This model has been incorporated into one-dimensional simulations of cirrus and water vapor driven by meteorological analysis temperature and wind fields. The model includes scavenging of ice nuclei by sedimenting ice crystals. The model is evaluated by comparing the simulated cloud properties and water vapor concentrations with aircraft and satellite measurements. In this presentation, I will discuss the relative importance of homogeneous and heterogeneous ice nucleation, the impact of ice nuclei scavenging as air slowly ascends through the TTL, and the implications for the final dehydration of air parcels crossing the tropical cold-point tropopause and entering the tropical stratosphere.

tropopause↗

High Ice Water Concentrations in the 19 August 2015 Coastal Mesoconvective System

During August 2015, NASA's DC-8 research aircraft was flown into High Ice Water Content (HIWC) events as part of a three-week campaign to collect airborne radar data and to obtain measurements from microphysical probes. Goals for this flight campaign included improved characterization of HIWC events, especially from an airborne radar perspective. This paper focuses on one of the flight days, in which a coastal mesoscale convective system (MCS) was investigated for HIWC conditions. The system appears to have been maintained by bands of convection flowing in from the Gulf of Mexico. These convective bands were capped by a large cloud canopy, which masks the underlying structure if viewed from an infrared sensing satellite. The DC-8 was equipped with an IsoKinetic Probe that measured ice concentrations of up to 2.3 g m(exp -3) within the cloud canopy of this system. Sustained measurements of ice crystals with concentrations exceeding 1 g m(exp -3) were encountered for up to ten minutes of flight time. Airborne Radar reflectivity factors were found to be weak within these regions of high ice water concentrations, suggesting that Radar detection of HIWC would be a challenging endeavor. This case is then investigated using a three-dimensional numerical cloud model. Profiles of ice water concentrations and radar reflectivity factor demonstrate similar magnitudes and scales between the flight measurements and model simulation. Also discussed are recent modifications to the numerical model's ice-microphysics that are based on measurements during the flight campaign. The numerical model and its updated ice-microphysics are further validated with a simulation of a well-known case of a supercell hailstorm measured during the Cooperative Convective Precipitation Experiment. Differences in HIWC between the continental supercell and the coastal MCS are discussed.

Proctor, Fred H.↗

The Dependence of Cirrus Gamma Size Distributions Expressed as Volumes in N(sub 0)-Lambda-Mu Phase Space and Bulk Cloud Properties on Environmental Conditions: Results from the Small Ice Particles in Cirrus Experiment (SPARTICUS)

The variability of cirrus ice microphysical properties is investigated using observations obtained during the Small Particles in Cirrus (SPARTICUS) campaign. An existing approach that represents a size distribution (SD) as a single gamma function using an ellipsoid of equally realizable solutions in (N(sub 0), lambda, mu) phase space is modified to automatically identify multiple modes in SDs and characterize each mode by such an ellipsoid. The modified approach is applied to ice crystals with maximum dimension D greater than15 micrometers collected by the 2-D stereo and 2-D precipitation probes on the Stratton Park Engineering Company Learjet. The dependencies of N(sub 0), mu, and lambda from each mode, total number concentration, bulk extinction, ice water content (IWC), and mass median maximum dimension D(sub mm) as a function of temperature T and cirrus type are then analyzed. The changes in the observed codependencies between N(sub 0), mu, and lambda, bulk extinction, IWC, and D(sub mm) with environmental conditions indicate that particles were larger at higher T during SPARTICUS. At most two modes were observed in any SD during SPARTICUS, with the average boundary between them at 115 micrometers, similar to past studies not using probes with shatter mitigating tips and artifact removal algorithms. The bimodality of the SDs increased with T. This and the differences in N(sub 0), mu, and lambda between the modes suggest that particles with smaller D nucleated more recently than particles with larger D, which grew via vapor deposition and aggregation. Because smaller crystals, whose concentrations are uncertain, make marginal contributions to higher order moments, the use of higher moments for evaluating model fields is suggested.

Ellipsoids↗

Polarimetric scattering from layered media with multiple species of scatterers

Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies-layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost-covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.

Nghiem, S. V.↗

Feasibility of sea ice typing with synthetic aperture radar (SAR): Merging of Landsat thematic mapper and ERS 1 SAR satellite imagery

Earth Remote-Sensing Satellite (ERS) 1 synthetic aperture radar (SAR) and Landsat thematic mapper (TM) images were acquired for the same area in the Beaufort Sea, April 16 and 18, 1992. The two image pairs were colocated to the same grid (25-m resolution), and a supervised ice type classification was performed on the TM images in order to classify ice free, nilas, gray ice, gray-white ice, thin first-year ice, medium and thick first-year ice, and old ice. Comparison of the collocated SAR pixels showed that ice-free areas can only be classified under calm wind conditions (less than 3 m/s) and for surface winds greater than 10 m/s based on the backscattering coefficient alone. This is true for pack ice regions during the cold months of the year where ice-free areas are spatially limited and where the capillary waves that cause SAR backscatter are dampened by entrained ice crystals. For nilas, two distinct backscatter classes were found at -17 dB and at -10 dB. The higher backscattering coefficient is attributed to the presence of frost flowers on light nilas. Gray and gray-white ice have a backscatter signature similar to first-year ice and therefore cannot be distinguished by SAR alone. First-year and old ice can be clearly separated based on their backscattering coefficient. The performance of the Geophysical Processor System ice classifier was tested against the Landsat derived ice products. It was found that smooth first-year ice and rough first-year ice were not significantly different in the backscatter domain. Ice concentration estimates based on ERS 1 C band SAR showed an error range of 5 to 8% for high ice concentration regions, mainly due to misclassified ice-free and smooth first-year ice areas. This error is expected to increase for areas of lower ice concentration. The combination of C band SAR and TM channels 2, 4, and 6 resulted in ice typing performance with an estimated accuracy of 90% for all seven ice classes.

Steffen, Konrad↗

Sensitivity of Cirrus and Mixed-phase Clouds to the Ice Nuclei Spectra in McRAS-AC: Single Column Model Simulations

The salient features of mixed-phase and ice clouds in a GCM cloud scheme are examined using the ice formation parameterizations of Liu and Penner (LP) and Barahona and Nenes (BN). The performance of LP and BN ice nucleation parameterizations were assessed in the GEOS-5 AGCM using the McRAS-AC cloud microphysics framework in single column mode. Four dimensional assimilated data from the intensive observation period of ARM TWP-ICE campaign was used to drive the fluxes and lateral forcing. Simulation experiments where established to test the impact of each parameterization in the resulting cloud fields. Three commonly used IN spectra were utilized in the BN parameterization to described the availability of IN for heterogeneous ice nucleation. The results show large similarities in the cirrus cloud regime between all the schemes tested, in which ice crystal concentrations were within a factor of 10 regardless of the parameterization used. In mixed-phase clouds there are some persistent differences in cloud particle number concentration and size, as well as in cloud fraction, ice water mixing ratio, and ice water path. Contact freezing in the simulated mixed-phase clouds contributed to transfer liquid to ice efficiently, so that on average, the clouds were fully glaciated at T approximately 260K, irrespective of the ice nucleation parameterization used. Comparison of simulated ice water path to available satellite derived observations were also performed, finding that all the schemes tested with the BN parameterization predicted 20 average values of IWP within plus or minus 15% of the observations.

Betancourt, R. Morales↗

A scheme for parameterizing cirrus cloud ice water content in general circulation models

Clouds strongly influence th earth's energy budget. They control th amount of solar radiative energy absorbed by the climate system, partitioning the energy between the atmosphere and the earth's surface. They also control the loss of energy to space by their effect on thermal emission. Cirrus and altostratus are the most frequent cloud types, having an annual average global coverage of 35 and 40 percent, respectively. Cirrus is composed almost entirely of ice crystals and the same is frequently true of the upper portions of altostratus since they are often formed by the thickening of cirrostratus and by the spreading of the middle or upper portions of thunderstorms. Thus, since ice clouds cover such a large portion of the earth's surface, they almost certainly have an important effect on climate. With this recognition, researchers developing climate models are seeking largely unavailable methods for specifying the conditions for ice cloud formation, and quantifying the spatial distribution of ice water content, IWC, a necessary step in deriving their radiative characteristics since radiative properties are apparently related to IWC. A method is developed for specifying IWC in climate models, based on theory and measurements in cirrus during FIRE and other experiments.

Heymsfield, Andrew J.↗

Small field campaign: aerosol – ice formation closure pilot study. Final Report

Prediction of atmospheric ice formation from aerosol particles by heterogeneous nucleation represents one of the grand challenges in atmospheric science. Our insufficient predictive understanding of primary ice formation is the reason that climate models typically do not include heterogeneous ice nucleation with subsequent effects on climate uncertainty. Mixed-phase clouds, where supercooled water droplets and ice crystals coexist play globally an important role regulating climate. This is especially the case for the Arctic region that experiences the greatest warming due to climate change compared to other regions in the world. Immersion freezing initiated by ice-nucleating particles (INPs) in supercooled water droplets is recognized as the dominant primary ice formation pathway in mixed-phase cloud regimes. For this reason, it is crucial to evaluate our capability to predict immersion freezing for a given ambient aerosol population. The goal of this project is conducting a field-based pilot study at the U.S. DOE Atmospheric Radiation Measurement (ARM) user facility at Southern Great Plains (SGP) to evaluate our capability to predict the number concentration of aerosol particles that serve as INPs in the immersion freezing mode. Successful prediction of INP number concentrations is also termed “closure”. This field-observational approach represents a first-of-its kind attempt of an aerosol–ice formation closure study (AEROICESTUDY). Very few closure studies related to INPs have been conducted, and to our knowledge, none using robust size-resolved ambient aerosol composition measurements as a starting point. Achievement of aerosol–ice formation closure relies on our ability to characterize the ambient aerosol population with respect to particles size and composition and to determine INP number concentrations for specified freezing temperatures. This requires numerous online and offline instrumentation resulting in this pilot field campaign being a multi-institutional and community-collaborative effort. We chose the ARM SGP megasite for this first aerosol-ice formation closure pilot study due to its significant measurement capabilities available to obtain detailed physical characterization of the local aerosol population including size distribution, mass loading, and chemical composition of non-refractory aerosol particles. The overall objective of this project is to identify ice nucleation parameterizations that produce the most robust predictions of INP numbers and thus are best suited to be included in cloud and climate models. This objective includes the following goals for this field and laboratory-based project: i) What are the crucial aerosol physicochemical property measurements needed to accurately guide ice nucleation representations in models and long-term INP measurements? ii) What level of parameter details needs to be known to achieve aerosol–ice formation closure? iii) What are the leading causes for climate model bias in INP predictions? We found that the advances in our understanding of immersion freezing garnered over the last 20 years allowed us to yield partial and full closures of atmospheric immersion freezing from ambient aerosol particles. When the aerosol population is physicochemically complex and parameterizations for representative INP types are not yet available, we still struggle to accurately predict INP number concentrations. This project clearly demonstrates that with more laboratory and field measurements that are accompanied by particle composition analysis, the necessary datasets to achieve aerosol–ice formation closure for various locations will emerge, thus providing a robust foundation for guiding the representation of INPs in cloud and climate models.

54 ENVIRONMENTAL SCIENCES↗

Characterization and application of a high-resolution microfluidic device in atmospheric ice nucleation research and integrated science teaching

Ambient ice-nucleating particles (INPs) represent an important subset of aerosol particles that facilitate heterogeneous formation of ice crystals in the atmosphere, which can impact Earth system and energy. In this work, we developed an affordable high-resolution platform to replicate atmospheric immersion freezing through the unique capabilities of microfluidics to measure INP concentration of known ice nucleation active materials, as well as high-latitude soil samples. The new instrument produced comparable and extended freezing efficiency data for a multitude of samples over the temperature range of -5 to -35 °C as compared to an existing freezing assay within known uncertainties. Moreover, the new assay was integrated into science teaching at a primarily undergraduate and Hispanic-serving institute, contributing to fostering a deeper understanding of ice nucleation processes among college students, instilling their enthusiasm for science, and addressing the critical need for a well-informed citizenry. Student research assistants were involved in both research and pedagogical development processes. Three students from our team visited the Pacific Northwest National Laboratory to help characterize physicochemical properties of our test samples and to test modeling of atmospheric ice nucleation using a box model as well as a global climate model (E3SM) for the regional-scale conditions over the North Slope of Alaska (NSA) and Southern Great Plains (SGP). We also assessed student learning experience via hands-on training, research processes, and development of educational materials. On pre- and post-participation surveys and in exit interviews, students reported personal growth as advancements in breadth of experience, research-related skill sets, and regarding their educational and career goals. They also affirmed that the methods enacted incorporated the NASA Minority University Research and Education Program (MUREP) STEM Engagement Best Practices.

58 GEOSCIENCES↗

Cirrus Parcel Model Comparison Phase 2

The Cirrus Parcel Model Comparison (CPMC) project, a project of the GEWEX Cloud System Study Working Group on cirrus clouds (GCSS WG2), is an international effort to advance our knowledge of numerical simulations of cirrus cloud initiation. This project was done in two phases. In Phase 1 of CPMC, the critical components determining the predicted cloud microphysical properties were identified using parcel models in which the aerosol and ice crystal size distributions are explicitly resolved, the formulation of the homogeneous freezing of aqueous solution droplets, especially the gradient of nucleation rate with respect to solution concentration; aerosol growth modeling; and the mass accommodation coefficient of water vapor on ice surface (the deposition coefficient). In Phase 1, all simulations were conducted using a given background aerosol distribution. To complete the comparison study, participant model responses to a range of background aerosol distributions are investigated in Phase 2.

Lin, Ruei-Fong↗

Light scattering by cirrus cloud layers.

The properties of the reflection, transmission, and absorption of the cirrus cloud layers are calculated under the assumption that the ice crystals in cirrus clouds may be approximated long circular cylinders randomly oriented in space. The phase function, the single scattering albedo, and the extinction cross section are obtained on the basis of Liou's (1972) calculations of light scattering by ice clouds in the visible and infrared. A modified two-stream approximation for radiative transfer is developed and is used to evaluate the radiative properties of the cirrus cloud layers.

Liou, K.-N.↗