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At least 649 records · Page 36

A 1D Model for Nucleation of Ice From Aerosol Particles: An Application to a Mixed‐Phase Arctic Stratus Cloud Layer

Abstract Mixed‐phase clouds (MPCs) have been identified as significant contributors to uncertainties in climate projections, attributable to model representation of processes controlling the formation and loss of supercooled water droplets and ice particles from the atmosphere. Arctic MPCs are commonly widespread and long‐lived, with sustained ice crystal formation processes that challenge current understanding. This study examines the ice‐nucleating particle (INP) reservoir dynamics governing immersion‐mode heterogeneous freezing in an observed case of Arctic MPCs using a simplified 1D aerosol‐cloud model. The model setup includes prescribed dynamical forcings and thermodynamic profiles, and represents INPs as multicomponent and polydisperse particle size distributions. Diagnostic and prognostic approaches to immersion freezing parameterization are compared, including time‐independent (singular) number‐ and surface area‐based descriptions and a time‐dependent description following classical nucleation theory (CNT). The choice of freezing parameterization defines the size of the INP reservoir. The CNT‐based description yields an orders of magnitude larger INP reservoir than the singular parameterizations, which is the dominant factor for sustained ice crystal formation. The efficiency of the freezing process and cloud cooling are of secondary importance. A diagnostic treatment neglecting INP loss is only accurate when the INP reservoir size is large and INP depletion weak. Since a larger INP reservoir sustains ice crystal formation substantially longer, and ice water path scales with ice crystal concentrations for the conditions considered, resolving the source of differences in INP reservoir dynamics due to model implementation is a high priority for advancing climate model physics.

54 ENVIRONMENTAL SCIENCES↗

Physical Processes Controlling the Distribution of Relative Humidity in the Tropical Tropopause Layer over the Pacific

The distribution of relative humidity with respect to ice (RHI) in the Boreal wintertime Tropical Tropopause Layer (TTL - about 14-19 km) over the Pacific is examined with the extensive dataset of measurements from the NASA Airborne Tropical TRopopause EXperiment (ATTREX). Multiple deployments of the Global Hawk during ATTREX provided hundreds of vertical profiles spanning the Pacific with accurate measurements of temperature, pressure, water vapor concentration, ozone concentration, and cloud properties. We also compare the measured RHI distributions with results from a transport and microphysical model driven by meteorological analysis fields. Notable features in the distribution of RHI versus temperature and longitude include (1) the common occurrence of RHI values near ice saturation over the western Pacific in the lower TTL (temperatures greater than 200 K) and in airmasses with low ozone concentrations indicating recent detrainment from deep convection; (2) low RHI values in the lower TTL over the eastern Pacific where deep convection is infrequent; (3) RHI values following a constant H2O mixing ratio in the upper TTL (temperatures below about 195 degrees Kelvin), particularly for samples with ozone mixing ratios greater than about 50-100 parts-per-billion-volume indicating mixtures of tropospheric and stratospheric air, and (4) RHI values typically near ice saturation in the coldest airmasses sampled (temperatures less than about 190 degrees Kelvin). We find that the typically saturated air in the lower TTL over the western Pacific is largely driven by the frequent occurrence of deep convection in this region. The nearly-constant water vapor mixing ratios in the upper TTL result from the combination of slow ascent (resulting in long residence times) and wave-driven temperature variability on a range of time scales (resulting in most air parcels having experienced low temperature and dehydration).

ozone↗

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; AMS 10th Satellite Symposium) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014; this conference) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end to end physical and dynamical basis for relating lightning rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relation to updraft strength, updraft volume, precipitation‐sized ice mass, etc.; however, relation specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler techniques to resolve the physical and dynamical storm characteristics specifically around the time of the lightning jump. This information will help forecasters anticipate lightning jump occurrence, or even be of use to determine future characteristics of a given storm (e.g., development of a mesocyclone, downdraft, or hail signature on radar), providing additional lead time/confidence in the severe storm warning paradigm.

Shultz, Christopher J.↗

Multirate partitioned Runge–Kutta methods for coupled Navier–Stokes equations

Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a significant challenge due to the difference in physics, temporal, and spatial scales. Further, this study explores multirate partitioned Runge-Kutta methods for the fluid-fluid interaction problem and demonstrates its parallel performance by using the PETSc library. We consider compressible Navier-Stokes equations with gravity coupled through a rigid-lid interface. Our large-scale numerical experiments reveal that multirate partitioned Runge-Kutta coupling schemes (1) can conserve total mass; (2) have second-order accuracy in time; and (3) provide favorable strong- and weak-scaling performance on modern computing architectures. We also show that the speedup factors of multirate partitioned Runge-Kutta methods match theoretical expectations over their base (single-rate) method.

54 ENVIRONMENTAL SCIENCES↗

Biological particles and aerosol-cloud interactions in the Southern Great Plains (Final Report)

The United States Southern Great Plains (SGP) is the genesis for much of the warm season precipitation in the central and eastern United States. While atmospheric thermodynamics and large-scale dynamics play an important role in formation of precipitation, precipitation mechanisms are also sensitive to aerosols. Aerosols can suppress precipitation as cloud condensation nuclei (CCN) or act as ice nucleating particles (INP) in deep convective clouds. This project focused on understanding the role of primary biological aerosol particles (PBAP) in the region and its influence on cloud formation. Specifically, we focused on biological aerosol in the form of pollen, one type of PBAP that is emitted in large yet variable quantities from vegetation in the mid latitudes. Field observations provide evidence of pollen in the planetary boundary layer and pollen components in cloud droplets and fine particulate matter. Further, pollen grains can easily rupture when wet, forming smaller, sub pollen particles with sizes less than one micron. We evaluated the potential for PBAP events at the Department of Energy (DoE) SGP Atmospheric Radiation Measurement (ARM) research facility due to the rich dataset available. We also developed model simulations that accounted for pollen emission and the generation of sub pollen particles, which have been shown to be both cloud condensation nuclei and ice nucleating particles. The proposed work was designed to address the following questions: 1. What are the physical and chemical signatures of biological aerosol such as pollen in SGP ARM measurements? 2. What is the role of pollen-derived particles on deep convection and precipitation in the Central US? Using measurements from the DoE SGP ARM site and recent airborne campaigns, we evaluated the signatures of pollen and pollen-derived aerosols on optical properties, cloud properties and precipitation (Subba et al., 2021). We identified pollen-driven events over the data record and used the Weather Research and Forecasting Model with fully coupled chemistry (WRF-Chem) to conduct chemically realistic simulations of aerosols during and summer mesoscale convective events in the Southern Great Plains (Subba et al., in review). This work improved our understanding of the role of biological aerosol on clouds and precipitation in the Central United States and placed these results in context with anthropogenically-driven processes.

54 ENVIRONMENTAL SCIENCES↗

Biological particles and aerosol-cloud interactions in the Southern Great Plains

The United States Southern Great Plains (SGP) is the genesis for much of the warm season precipitation in the central and eastern United States. While atmospheric thermodynamics and large-scale dynamics play an important role in formation of precipitation, precipitation mechanisms are also sensitive to aerosols. Aerosols can suppress precipitation as cloud condensation nuclei (CCN) or act as ice nucleating particles (INP) in deep convective clouds. This project focused on understanding the role of primary biological aerosol particles (PBAP) in the region and its influence on cloud formation. Specifically, we focused on biological aerosol in the form of pollen, one type of PBAP that is emitted in large yet variable quantities from vegetation in the mid latitudes. Field observations provide evidence of pollen in the planetary boundary layer and pollen components in cloud droplets and fine particulate matter. Further, pollen grains can easily rupture when wet, forming smaller, sub pollen particles with sizes less than one micron. We evaluated the potential for PBAP events at the Department of Energy (DoE) SGP Atmospheric Radiation Measurement (ARM) research facility due to the rich dataset available. We also developed model simulations that accounted for pollen emission and the generation of sub pollen particles, which have been shown to be both cloud condensation nuclei and ice nucleating particles. The proposed work was designed to address the following questions: 1. What are the physical and chemical signatures of biological aerosol such as pollen in SGP ARM measurements? 2. What is the role of pollen-derived particles on deep convection and precipitation in the Central US? Using measurements from the DoE SGP ARM site and recent airborne campaigns, we evaluated the signatures of pollen and pollen-derived aerosols on optical properties, cloud properties and precipitation (Subba et al., 2021). We identified pollen-driven events over the data record and used the Weather Research and Forecasting Model with fully coupled chemistry (WRF-Chem) to conduct chemically realistic simulations of aerosols during and summer mesoscale convective events in the Southern Great Plains (Subba et al., in review). This work improved our understanding of the role of biological aerosol on clouds and precipitation in the Central United States and placed these results in context with anthropogenically-driven processes.

54 ENVIRONMENTAL SCIENCES↗

Does a continuous solid nucleus exist in comets.

The implication of actual cometary observations for the physical nature of comets is briefly reviewed, bringing out the complete conflict with observation of the ice-dust solid nucleus model put forward in recent years as representing the fundamental structure of comets. That under increasing solar heat the nucleus develops an expanding atmosphere is inconsistent with the well-established phenomenon that the coma contracts with decreasing distance from the sun. Several comets remaining always beyond Mars have nevertheless been strongly active and produced fine tails. That some comets show at times a star-like point of light is readily explicable on the dust-cloud structure and by no means establishes that a solid nucleus exists. With the nucleus-area corresponding not to a small solid mass but to an optical phenomenon, there would be no reason to expect that it would describe a precise dynamical orbit. On the hypothesis of a nucleus, it is necessary to postulate further some internal jet-propulsion mechanism to account for the orbital deviations.

Lyttleton, R. A.↗

The Goddard Cumulus Ensemble Model (GCE): Improvements and Applications for Studying Precipitation Processes

Convection is the primary transport process in the Earth's atmosphere. About two-thirds of the Earth's rainfall and severe floods derive from convection. In addition, two-thirds of the global rain falls in the tropics, while the associated latent heat release accounts for three-fourths of the total heat energy for the Earth's atmosphere. Cloud-resolving models (CRMs) have been used to improve our understanding of cloud and precipitation processes and phenomena from micro-scale to cloud-scale and mesoscale as well as their interactions with radiation and surface processes. CRMs use sophisticated and realistic representations of cloud microphysical processes and can reasonably well resolve the time evolution, structure, and life cycles of clouds and cloud systems. CRMs also allow for explicit interaction between clouds, outgoing longwave (cooling) and incoming solar (heating) radiation, and ocean and land surface processes. Observations are required to initialize CRMs and to validate their results. The Goddard Cumulus Ensemble model (GCE) has been developed and improved at NASA/Goddard Space Flight Center over the past three decades. It is amulti-dimensional non-hydrostatic CRM that can simulate clouds and cloud systems in different environments. Early improvements and testing were presented in Tao and Simpson (1993) and Tao et al. (2003a). A review on the application of the GCE to the understanding of precipitation processes can be found in Simpson and Tao (1993) and Tao (2003). In this paper, recent model improvements (microphysics, radiation and land surface processes) are described along with their impact and performance on cloud and precipitation events in different geographic locations via comparisons with observations. In addition, recent advanced applications of the GCE are presented that include understanding the physical processes responsible for diurnal variation, examining the impact of aerosols (cloud condensation nuclei or CCN and ice nuclei or IN) on precipitation processes, utilizing a satellite simulator to improve the microphysics, providing better simulations for satellite-derived latent heating retrieval, and coupling with a general circulation model to improve the representation of precipitation processes.

GCE↗

Design and Performance of McRas in SCMs and GEOS I/II GCMs

The design of a prognostic cloud scheme named McRAS (Microphysics of clouds with Relaxed Arakawa-Schubert Scheme) for general circulation models (GCMs) will be discussed. McRAS distinguishes three types of clouds: (1) convective, (2) stratiform, and (3) boundary-layer types. The convective clouds transform and merge into stratiform clouds on an hourly time-scale, while the boundary-layer clouds merge into the stratiform clouds instantly. The cloud condensate converts into precipitation following the auto-conversion equations of Sundqvist that contain a parametric adaptation for the Bergeron-Findeisen process of ice crystal growth and collection of cloud condensate by precipitation. All clouds convect, advect, as well as diffuse both horizontally and vertically with a fully interactive cloud-microphysics throughout the life-cycle of the cloud, while the optical properties of clouds are derived from the statistical distribution of hydrometeors and idealized cloud geometry. An evaluation of McRAS in a single column model (SCM) with the GATE Phase III and 5-ARN CART datasets has shown that together with the rest of the model physics, McRAS can simulate the observed temperature, humidity, and precipitation without many systematic errors. The time history and time mean incloud water and ice distribution, fractional cloudiness, cloud optical thickness, origin of precipitation in the convective anvil and towers, and the convective updraft and downdraft velocities and mass fluxes all show a realistic behavior. Performance of McRAS in GEOS 11 GCM shows several satisfactory features but some of the remaining deficiencies suggest need for additional research involving convective triggers and inhibitors, provision for continuously detraining updraft, a realistic scheme for cumulus gravity wave drag, and refinements to physical conditions for ascertaining cloud detrainment level.

Sud, Yogesh C.↗

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. In this study, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Additionally, several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32,K processor cores (8,K MPI ranks and 4 OpenMP threads) and 566,M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4,K processor cores (and MPI ranks) and 68,M degrees of freedom for the coupled problem.

97 MATHEMATICS AND COMPUTING↗

Systematic Relationships Between Lidar Observables and Sizes And Mineral Composition Of Dust Aerosols

The physical and chemical properties of soil dust aerosol particles fundamentally affect their interaction with climate, including shortwave absorption and radiative forcing, nucleation of cloud droplets and ice crystals, heterogeneous formation of sulfates and nitrates on the surface of dust particles, and atmospheric processing of iron into bioavailable forms that increase the productivity of marine phytoplankton. Lidar measurements, such as extinction-to-backscatter, color and depolarization ratios, are frequently used to distinguish between aerosol types with different physical and chemical properties. The chemical composition of aerosol particles determines their complex refractive index, hence affecting their backscattering properties. Here we present a study on how dust aerosol backscattering and depolarization properties at wavelengths of 355, 532 and 1064 nm are related to size and complex refractive index, which varies with the mineral composition of the dust. Dust aerosols are represented by collections of spheroids with a range of prolate and oblate aspect ratios and their optical properties are obtained using T-matrix calculations. We find simple, systematic relationships between lidar observables and the dust size and complex refractive index that may aid the use of space-based or airborne lidars for direct retrieval of dust properties or for the evaluation of chemical transport models using forward simulated lidar variables. In addition, we present first results on the spatial variation of forward-simulated lidar variables based on a dust model that accounts for the atmospheric cycle of eight different mineral types plus internal mixtures of seven mineral types with iron oxides, which was recently implemented in the NASA GISS Earth System ModelE2.

Dust↗

Human adaptation to isolated and confined environments: Preliminary findings of a seven month Antarctic winter-over human factors study

This field study was conducted during the last decade of an austral winter-over at Palmer Station in the Antarctic. The purpose of the study was to understand temporal patterns in physiological arousal and psychological mood over the course of the mission. The investigators were principally interested in how people adapted over time to chronic and acute stressors, and how people use and modify their built environment. Physiological and psychological data were collected several times a week, and information on behavior and the use of physical facilities was collected monthly. Physiological and psychological data were compared with social changes in the setting toward the development of a sequential model of human-environment transactional relationships. Based on the study results, guidelines for design of future isolated and confined environments (ICEs) included: plan space for items which make people feel at home, provide materials to allow people to personalize their environment, allow for flexible environments, provide areas for visual and auditory privacy, equip areas for socializing and remove them from private areas, and provide facilities for exercise and for projects involving physical activity. The study offers guidelines about patterns of adaption that could be expected in an ICE, discusses how these settings can be programmed to facilitate successful adjustment, and provides information about how to design future ICE habitats to maximize a healthy living environment.

Evans, Gary W.↗

Northern Hemisphere Gullies on Mars: Analysis of Spacecraft Data and Implications for Formation Mechanisms

The origin of geologically recent gullies on Mars has remained controversial since the discovery of these features by Malin and Edgett in 2000. Numerous models have been proposed which invoke various physical processes as well as various agents of erosion to explain the origin of the Martian gullies. Hypotheses to explain the formation of the gullies invoke shallow liquid water aquifers, deep liquid water aquifers, melting ground ice, snowmelt, dry landslides, and carbon dioxide aquifers. We test the validity of such gully formation mechanisms by analyzing data from the Mars Global Surveyor and Mars Odyssey spacecrafts to uncover trends in the dimensional and physical properties of the gullies and their surrounding terrain. A similar study has previously been completed for gullies located in the southern hemisphere of Mars. The work presented here focuses exclusively on gullies in the northern hemisphere based on the identification of 136 Mars Orbiter Camera (MOC) images containing clear evidence of gully landforms, distributed in the northern mid and high latitudes. These sites have been analyzed in combination with Mars Orbiter Laser Altimeter (MOLA), Thermal Emission Spectrometer (TES), and Gamma Ray Spectrometer (GRS) data to provide quantitative measurements of numerous gully characteristics. Parameters measured include apparent source depth and distribution, vertical and horizontal dimensions, slopes, compass orientations, near-surface ice content, and factors controlling present-day climatic conditions.

Heldmann, J. L.↗

On Spectral Invariance of Single Scattering Albedo for Water Droplets and Ice Crystals at Weakly Absorbing Wavelengths

The single scattering albedo omega(sub O lambda) in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength lambda and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio omega(sub O lambda)(r)/omega(sub O lambda)(r (sub O)) of two single scattering albedo spectra is a linear function of omega(sub O lambda)(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum omega(sub O lambda)(r) via one known spectrum omega(sub O lambda)(r (sub O)). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.

single scattering albedo↗

Chasing Gamma-Ray Signals from Binary Neutron Star Coalescences with the Cherenkov Telescope Array: Prospects and Observing Strategies

The detection of gravitational waves (GWs) from a binary neutron star (BNS) merger by Advanced LIGO and Advanced Virgo (GW170817), together with its electromagnetic counterpart, the short gamma-ray burst GRB 170817A, heralded the birth of multimessenger astronomy. The detection of TeV emission from GRBs motivates follow-up observations with the Cherenkov Telescope Array Observatory (CTAO), which is ideal for detecting such signals due to its unprecedented sensitivity, rapid response, and wide-field survey capabilities. The aim of this work is to evaluate GeV–TeV GW follow-up strategies for CTAO using a multistep simulation pipeline and to estimate the expected rate of joint GW–GRB detections during observing run O5. Using a simulated sample of BNS systems with corresponding GW detections, gamma-ray emission is simulated through phenomenological prescriptions based on the observed population of short GRBs, including off-axis jet scenarios. CTAO observations are simulated to account for instrument response, sky tiling strategies, integration times, and varying observing conditions. Strategies with variable and constant integration times are investigated. We find that, via an optimized follow-up strategy, about 5% of simulated GW-associated short GRBs produce GeV–TeV radiation detectable by CTAO. Detectability is strongly influenced by the jet opening angle and viewing angle, suggesting that even rough estimates of the viewing angle in GW alerts could enhance targeting. This framework motivates future follow-ups of GW-detectable events, including neutron star–black hole mergers, and further supports the development of advanced strategies incorporating galaxy distributions and synergies with future detectors such as the Einstein Telescope.

Abe, S. [University of Tokyo] (ORCID:0000000172503↗

A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part 2: Dependence of absorption and extinction on ice crystal morphology

This study builds upon the microphysical modeling described in Part 1 by deriving formulations for the extinction and absorption coefficients in terms of the size distribution parameters predicted from the micro-physical model. The optical depth and single scatter albedo of a cirrus cloud can then be determined, which, along with the asymmetry parameter, are the input parameters needed by cloud radiation models. Through the use of anomalous diffraction theory, analytical expressions were developed describing the absorption and extinction coefficients and the single scatter albedo as functions of size distribution parameters, ice crystal shapes (or habits), wavelength, and refractive index. The extinction coefficient was formulated in terms of the projected area of the size distribution, while the absorption coefficient was formulated in terms of both the projected area and mass of the size distribution. These properties were formulated as explicit functions of ice crystal geometry and were not based on an 'effective radius.' Based on simulations of the second cirrus case study described in Part 1, absorption coefficients predicted in the near infrared for hexagonal columns and rosettes were up to 47% and 71% lower, respectively, than absorption coefficients predicted by using equivalent area spheres. This resulted in single scatter albedos in the near-infrared that were considerably greater than those predicted by the equivalent area sphere method. Reflectances in this region should therefore be underestimated using the equivalent area sphere approach. Cloud optical depth was found to depend on ice crystal habit. When the simulated cirrus cloud contained only bullet rosettes, the optical depth was 142% greater than when the cloud contained only hexagonal columns. This increase produced a doubling in cloud albedo. In the near-infrared (IR), the single scatter albedo also exhibited a significant dependence on ice crystal habit. More research is needed on the geometrical properties of ice crystals before the influence of ice crystal shape on cirrus radiative properties can be adequately understood. This study provides a way of coupling the radiative properties of absorption, extinction, and single scatter albedo to the microphysical properties of cirrus clouds. The dependence of extinction and absorption on ice crystal shape was not just due to geometrical differences between crystal types, but was also due to the effect these differences had on the evolution of ice particle size spectra. The ice particle growth model in Part 1 and the radiative properties treated here are based on analytical formulations, and thus represent a computationally efficient means of modeling the microphysical and radiative properties of cirrus clouds.

Mitchell, David L.↗