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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

The abundance and distribution of water vapor in Jupiter's atmosphere

The atmospheric transmission window between 1800 and 2250 cm(-1) in Jupiter's atmosphere was observed from the Kuiper Airborne Observatory (KAO) and by the infrared spectrometer (IRIS) on Voyager. The vertical distribution of H2O was derived for the 1 to 6 bar portion of Jupiter's troposphere. The spatial variation of H2O was measured using IRIS spectra of the Hot Spots in the North and South Equatorial Belts, the Equatorial Zone, and for an average of the North and South Tropical Zones. The H2O column abundance above the 4 bar level is the same in the zones as in the SEB Hot Spots, about 20 cm-amagat. The NEB Hot Spots are desiccated by a factor of 3 with respect to the rest of Jupiter. For an average between -40 to 40 deg latitude, the H2O mole fraction, qH2O, is saturated for P less than 2 bars, qH2O = 4x10 to the -6 in the 2 to 4 bar range and it increases to 3x10 to the -5 at 6 bars. A similar vertical profile applies to the spatially resolved zone and belt spectra, except that H2O falls off more rapidly at P less than 4 bars in the NEB Hot Spots. The massive H2O cloud at 5 bars, T = 273 K, proposed in solar composition models, is inconsistent with the observations. Instead, a thin H2O ice cloud would form at 2 bars, T = 200 K. The O/H ratio in Jupiter, inferred from H2O measurements in both belts and zones at 6 bars, is depleted by a factor of 50 with respect to the Sun. The implications for the origin of Jupiter of globally depleted O/H, but enhanced C/H and N/H, are discussed.

Bjoraker, Gordon L.↗
NASA NTRS1991

Properties of scatterers in the troposphere and lower stratosphere of Uranus based on Voyager imaging data

Scalar and vector radiative transfer and microphysical models are presently constructed from photometrically and geometrically corrected Voyager images of Uranus defining spatially-resolved intensities over a range of phase angles for two latitude bands. The methane ice cloud occupying 1.2-1.3 bar is of 0.7 optical depth at 22.5 deg S, rising to 2.4 at 65 deg S; the volume absorption coefficient of the cloud particles is 50 percent greater at the low latitude than at the high, assuming constant mean cloud particle size. The scattering model also includes photochemically-produced stratospheric hydrocarbon ices in the upper troposphere and stratosphere, as well as an optically thick hydrogen sulfide cloud.

Rages, Kathy↗
NASA NTRS2016

Performance of the Goddard Multiscale Modeling Framework with Goddard Ice Microphysical Schemes

The multiscale modeling framework (MMF), which replaces traditional cloud parameterizations with cloud-resolving models (CRMs) within a host atmospheric general circulation model (GCM), has become a new approach for climate modeling. The embedded CRMs make it possible to apply CRM-based cloud microphysics directly within a GCM. However, most such schemes have never been tested in a global environment for long-term climate simulation. The benefits of using an MMF to evaluate rigorously and improve microphysics schemes are here demonstrated. Four one-moment microphysical schemes are implemented into the Goddard MMF and their results validated against three CloudSat/CALIPSO cloud ice products and other satellite data. The new four-class (cloud ice, snow, graupel, and frozen drops/hail) ice scheme produces a better overall spatial distribution of cloud ice amount, total cloud fractions, net radiation, and total cloud radiative forcing than earlier three-class ice schemes, with biases within the observational uncertainties. Sensitivity experiments are conducted to examine the impact of recently upgraded microphysical processes on global hydrometeor distributions. Five processes dominate the global distributions of cloud ice and snow amount in long-term simulations: (1) allowing for ice supersaturation in the saturation adjustment, (2) three additional correction terms in the depositional growth of cloud ice to snow, (3) accounting for cloud ice fall speeds, (4) limiting cloud ice particle size, and (5) new size-mapping schemes for snow and graupel. Despite the cloud microphysics improvements, systematic errors associated with subgrid processes, cyclic lateral boundaries in the embedded CRMs, and momentum transport remain and will require future improvement.

snow↗
NASA NTRS2011

Observations of Recent Arctic Sea Ice Volume Loss and Its Impact on Ocean-Atmosphere Energy Exchange and Ice Production

Using recently developed techniques we estimate snow and sea ice thickness distributions for the Arctic basin through the combination of freeboard data from the Ice, Cloud, and land Elevation Satellite (ICESat) and a snow depth model. These data are used with meteorological data and a thermodynamic sea ice model to calculate ocean-atmosphere heat exchange and ice volume production during the 2003-2008 fall and winter seasons. The calculated heat fluxes and ice growth rates are in agreement with previous observations over multiyear ice. In this study, we calculate heat fluxes and ice growth rates for the full distribution of ice thicknesses covering the Arctic basin and determine the impact of ice thickness change on the calculated values. Thinning of the sea ice is observed which greatly increases the 2005-2007 fall period ocean-atmosphere heat fluxes compared to those observed in 2003. Although there was also a decline in sea ice thickness for the winter periods, the winter time heat flux was found to be less impacted by the observed changes in ice thickness. A large increase in the net Arctic ocean-atmosphere heat output is also observed in the fall periods due to changes in the areal coverage of sea ice. The anomalously low sea ice coverage in 2007 led to a net ocean-atmosphere heat output approximately 3 times greater than was observed in previous years and suggests that sea ice losses are now playing a role in increasing surface air temperatures in the Arctic.

Kurtz, N. T.↗
NASA NTRS2015

Physical Models of Layered Polar Firn Brightness Temperatures from 0.5 to 2 GHz

We investigate physical effects influencing 0.5-2 GHz brightness temperatures of layered polar firn to support the Ultra Wide Band Software Defined Radiometer (UWBRAD) experiment to be conducted in Greenland and in Antarctica. We find that because ice particle grain sizes are very small compared to the 0.5-2 GHz wavelengths, volume scattering effects are small. Variations in firn density over cm- to m-length scales, however, cause significant effects. Both incoherent and coherent models are used to examine these effects. Incoherent models include a 'cloud model' that neglects any reflections internal to the ice sheet, and the DMRT-ML and MEMLS radiative transfer codes that are publicly available. The coherent model is based on the layered medium implementation of the fluctuation dissipation theorem for thermal microwave radiation from a medium having a nonuniform temperature. Density profiles are modeled using a stochastic approach, and model predictions are averaged over a large number of realizations to take into account an averaging over the radiometer footprint. Density profiles are described by combining a smooth average density profile with a spatially correlated random process to model density fluctuations. It is shown that coherent model results after ensemble averaging depend on the correlation lengths of the vertical density fluctuations. If the correlation length is moderate or long compared with the wavelength (approximately 0.6x longer or greater for Gaussian correlation function without regard for layer thinning due to compaction), coherent and incoherent model results are similar (within approximately 1 K). However, when the correlation length is short compared to the wavelength, coherent model results are significantly different from the incoherent model by several tens of kelvins. For a 10-cm correlation length, the differences are significant between 0.5 and 1.1 GHz, and less for 1.1-2 GHz. Model results are shown to be able to match the v-pol SMOS data closely and predict the h-pol data for small observation angles.

layered polar firn emission↗
NASA NTRS2019

Seasonal Variation in Martian Water Ice Cloud Particle Size

We employ the complete record of Mars limb-viewing observations by the Compact Reconnaissance Imaging Spectrometer, totaling 922 successful retrievals, to chart the seasonal variation in water ice cloud particle size. Low-latitude clouds exhibit particle size sorting with altitude at all seasons, with particles ranging from >3.0 m in effective radius to 1.01.5 m. However, at a given altitude, the ice particle size often varies through the year. Ice particle sizes in the tropics follow a different seasonal cycle than ice mixing ratio. North polar clouds have a complex seasonal cycle, with a sloped size profile with altitude as the polar hood cloud forms in early fall trending to a roughly uniform 1.5 m profile by the end of winter. These data are an important metric to validate and improve general circulation model microphysical routines and to better understand how martian water ice clouds influence the atmospheric radiative budget.

Scott D. Guzewich↗
DOE OSTI2020

A New Method for Ice-Ice Aggregation in the Adaptive Habit Model

In this paper, a novel methodology for modeling ice-ice aggregation is presented. This methodology combines a modified hydrodynamic collection algorithm with bulk aggregate characteristic information from an offline simulator that collects ice particles, namely, the Ice Particle and Aggregate Simulator, and has been implemented into the Adaptive Habit Microphysics scheme in the Weather Research and Forecasting Model. Aggregates, or snow, are formed via collection of cloud ice particles, where initial ice characteristics and the resulting geometry determine aggregate characteristics. Upon implementation, idealized squall-line simulations are performed to examine the new methodology in comparison with commonly used bulk microphysics schemes. It is found that the adaptive habit aggregation parameterization develops snow and reduces ice mass and number concentrations compared to other schemes. The development of aggregates through the new methodology cascades into other interesting effects, including enhancements in ice and snow growth, as well as homogeneous freezing. Further microphysical analyses reveal varying sensitivities, where snow processes are most sensitive to the new parameterization, followed by ice, then cloud, rain, and graupel processes. Further, the new scheme results in enhancements in surface precipitation due to the persistence of snow at lower altitudes. This persistence is a result of shape-dependent melting and sublimation, increasing the residence time. Moreover, these low-level enhancements are reflected in increases in radar reflectivity at the surface and its spatial distribution. Finally, the ability to predict snow shape and density allows for the simulation of polarimetric radar quantities, resulting in signature enhancements compared to schemes that do not consider spatial and temporal variations in snow shape and density.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A new method for operating a continuous flow diffusion chamber to investigate immersion freezing: assessment and performance study

Glaciation in mixed-phase clouds predominately occurs through the immersion freezing mode where ice nucleating particles (INPs) immersed within supercooled droplets induce nucleation of ice. Currently, model representations of this process are a large source of uncertainty in simulating cloud radiative properties, and to constrain these estimates, continuous flow diffusion chamber (CFDC)-style INP devices are commonly used to assess the immersion freezing efficiencies of INPs. In this study, a new approach was explored to operating such an ice chamber that provides maximum activation of particles without droplet breakthrough and correction factor ambiguity to obtain high-quality INP measurements in a manner that has not been demonstrated as possible previously. The conditioning section of the chamber was maintained at ~ –20 °C and water relative humidity (RH w ) ~ 113 % conditions to maximize the droplet activation, and the droplets were supercooled with an independently temperature-controlled nucleation section at a steady cooling rate (0.5 °C min –1 ) to induce the freezing of droplets and evaporation of unfrozen droplets. The performance of the modified ice chamber was evaluated using four INP species: K-feldspar, illite-NX, Argentinian soil dust, and airborne arable dust that had shown ice nucleation over a wide span of supercooled temperatures. Dry dispersed and size-selected K-feldspar particles were generated in the laboratory. Illite-NX and soil dust particles were sampled during the second phase of the Fifth International Ice Nucleation Workshop (FIN-02) campaign, and airborne arable dust particles were sampled from the aerosol inlet located on the rooftop of the laboratory. The measured ice nucleation efficiencies of model aerosols with a surface active site density (n s ) metric were higher, but mostly agreed within one order of magnitude compared to literature results.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

The impact of aerosol mixing state on immersion freezing: insights from classical nucleation theory and particle-resolved simulations

Immersion freezing, initiated by ice-nucleating particles (INPs) in supercooled aqueous droplets, plays an important role in the formation of ice crystals within clouds. The efficiency of immersion freezing depends strongly on INP composition and, crucially, on the mixing state – how chemical species are distributed across the particle population. Here, we quantify the impact of aerosol mixing state on immersion freezing using a combined theoretical and particle-resolved modeling approach. We derive analytical expressions for the frozen fraction of internally and externally mixed INP populations based on classical nucleation theory, showing that the frozen fraction is sensitive to whether ice-active species are present in all particles or only in a subset of the population. We introduce a multi-species immersion freezing scheme into the particle-resolved model PartMC, using the water activity-based immersion freezing model (ABIFM) to compute freezing probabilities for mixed-composition particles. To improve computational efficiency, we implement a Binned Tau-Leaping algorithm and demonstrate an order-of-magnitude speedup with minimal accuracy loss. Simulations reproduce the analytical trends in limiting cases and extend the analysis to more general aerosol populations, where mixing state continues to exert a substantial control on frozen fraction. Sensitivity analyses across particle size, species type, and cooling condition reveal that the mixing state effect is most pronounced when small amounts of highly efficient INPs are mixed with less efficient materials. These findings underscore the need to represent aerosol mixing state explicitly in models of heterogeneous ice nucleation to reduce uncertainty in cloud-phase partitioning.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1995

Diabatic forcing and intialization with assimilation of cloud water and rainwater in a forecast model

In this study, diabatic forcing, and liquid water assimilation techniques are tested in a semi-implicit hydrostatic regional forecast model containing explicit representations of grid-scale cloud water and rainwater. Diabatic forcing, in conjunction with diabatic contributions in the initialization, is found to help the forecast retain the diabatic signal found in the liquid water or heating rate data, consequently reducing the spinup time associated with grid-scale precipitation processes. Both observational Special Sensor Microwave/Imager (SSM/I) and model-generated data are used. A physical retrieval method incorporating SSM/I radiance data is utilized to estimate the 3D distribution of precipitating storms. In the retrieval method the relationship between precipitation distributions and upwelling microwave radiances is parameterized, based upon cloud ensemble-radiative model simulations. Regression formulae relating vertically integrated liquid and ice-phase precipitation amounts to latent heating rates are also derived from the cloud ensemble simulations. Thus, retrieved SSM/I precipitation structures can be used in conjunction with the regression-formulas to infer the 3D distribution of latent heating rates. These heating rates are used directly in the forecast model to help initiate Tropical Storm Emily (21 September 1987). The 14-h forecast of Emily's development yields atmospheric precipitation water contents that compare favorably with coincident SSM/I estimates.

Raymond, William H.↗
NASA NTRS1980

The albedo of snow for partially cloudy skies

The input parameters of the model are atmospheric precipitable water, ozone content, turbidity, cloud optical thickness, size and shape of ice crystal of snow and surface pressure. The model outputs spectral and integrated solar flux snow reflectance as a function of solar elevation and fractional cloudcover. The model is illustrated using representative parameters for the Antarctic coastal regions. The albedo for a clear sky depends inversely on the solar elevation. At high elevation the albedo depends primarily upon the grain size; at low elevation this dependence is on grain size and shape. The gradient of the albedo-elevation curve increases as the grains get larger and faceted. The albedo for a dense overcast is a few percent higher than the clear sky albedo at high elevations. A simple relation between the grain size and the overcast albedo is obtained. For a set of grain size and shape, the albedo matrices (the albedo as a function of solar elevation and fractional cloudcover) are tabulated.

Choudhury, B. J.↗
NASA NTRS2012

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

Korkin, Sergey V.↗
DOE OSTI2022

Combined Effect of the Wegener–Bergeron–Findeisen Mechanism and Large Eddies on Microphysics of Mixed-Phase Stratiform Clouds

Abstract The process of glaciation in mixed-phase stratiform clouds was investigated by a novel Lagrangian–Eulerian model (LEM) in which thousands of adjoining Lagrangian parcels moved within a turbulent-like velocity field with statistical parameters typical of the Arctic boundary layer. We used detailed bin microphysics to describe the condensation/evaporation processes in each parcel, in which droplets, aerosols, and ice particles were described using size distributions of 500 mass bins. The model also calculated aerosol mass inside droplets and ice particles. Gravitational sedimentation of droplets and ice particles was also accounted for. Assuming that droplet freezing is the primary source of ice particles, the Arctic clouds observed in Indirect and Semi-Direct Aerosol Campaign (ISDAC) were successfully simulated. The model showed that at a low ice particle concentration typical of ISDAC, large vortices (eddies) led to a quasi-stationary regime, in which mixed-phase St existed for a long time. The large eddies controlled the water partitioning in the mixed-phase clouds. Droplets formed and grew in updrafts, typically reaching the cloud top, and evaporated in downdrafts. Ice particles grew in updrafts and downdrafts. The Wegener–Bergeron–Findeisen (WBF) mechanism was efficient in downdrafts and some parts of updrafts, depending on ice concentration and vertical velocity. At low ice concentrations, the effect of ice on the phase partitioning was negligible. In this regime, liquid droplets were found near the cloud top, whereas ice particles precipitated through the cloud base. When ice concentration exceeded about 10 L −1 , the WBF mechanism led to glaciation of almost the entire cloud, with the exception of narrow cloud regions associated with strong updrafts. At ice particle concentrations of a few tens per liter, the oscillatory regime took place due to the ice–liquid interaction. The microphysical structure of mixed-phase St forms as a combined effect of cloud dynamics (large eddies) and the WBF mechanism.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1984

Microwave radiances from precipitating clouds containing aspherical ice, combined phase, and liquid hydrometeors

A numerical algorithm based on Eddington's second approximation to the equation of radiative transfer has been developed in order to compute the radiances with horizontal and vertical polarization that emerge from precipitating clouds. This algorithm yields a rapid solution to problems pertaining to clouds with vertically inhomogeneous structure. Precipitating clouds containing liquid, mixtures of phases, and ice hydrometeors are modelled. It is shown that the lower-frequency radiances are sensitive to liquid precipitation at low altitudes while the higher-frequency radiances are more sensitive to the ice hydrometeors at the cloud tops. The extinction coefficients of aspherical hydrometeors are presented as a function of rainfall rates. The fact that vertically polarized radiances are warmer than horizontally polarized ones at high rainfall rates, with the difference diminishing at lower frequencies, is due to aspherical ice hydrometeors in the upper regions of precipitating clouds.

Wu, R.↗
NASA NTRS2016

Modeling of Highly Instrumented Honeywell Turbofan Engine Tested with Ice Crystal Ingestion in the NASA Propulsion System Laboratory

The Propulsion Systems Laboratory (PSL), an altitude test facility at NASA Glenn Research Center, has been used to test a highly instrumented turbine engine at simulated altitude operating conditions. This is a continuation of the PSL testing that successfully duplicated the icing events that were experienced in a previous engine (serial LF01) during flight through ice crystal clouds, which was the first turbofan engine tested in PSL. This second model of the ALF502R-5A serial number LF11 is a highly instrumented version of the previous engine. The PSL facility provides a continuous cloud of ice crystals with controlled characteristics of size and concentration, which are ingested by the engine during operation at simulated altitudes. Several of the previous operating points tested in the LF01 engine were duplicated to confirm repeatability in LF11. The instrumentation included video cameras to visually illustrate the accretion of ice in the low pressure compressor (LPC) exit guide vane region in order to confirm the ice accretion, which was suspected during the testing of the LF01. Traditional instrumentation included static pressure taps in the low pressure compressor inner and outer flow path walls, as well as total pressure and temperature rakes in the low pressure compressor region. The test data was utilized to determine the losses and blockages due to accretion in the exit guide vane region of the LPC. Multiple data points were analyzed with the Honeywell Customer Deck. A full engine roll back point was modeled with the Numerical Propulsion System Simulation (NPSS) code. The mean line compressor flow analysis code with ice crystal modeling was utilized to estimate the parameters that indicate the risk of accretion, as well as to estimate the degree of blockage and losses caused by accretion during a full engine roll back point. The analysis provided additional validation of the icing risk parameters within the LPC, as well as the creation of models for estimating the rates of blockage growth and losses.

Simulation↗
DOE OSTI2026

E3SMv3 ‘Nephele’ Perturbed Parameter Ensemble Value-Added Product for ENA, SGP, NSA, and Global Means

Processed output from the E3SMv3 Nephele perturbed parameter ensemble (PPE). This product contains global means of present-day (using 2010 aerosol forcings) and preindustrial (using 1850 aerosol forcings) monthly and daily global-mean quantities, as well as hourly mean quantities at the E3SMv3 model grid cell closest to the ENA, SGP, and NSA ARM sites. In this PPE, the E3SMv3 model was run for 27 months in an atmosphere-only configuration with free tropospheric winds nudged to reanalysis. Each ensemble member represents a unique combination of 25 model parameter values (in the microphysics, convective microphysics, and aerosol schemes) that were perturbed randomly and simultaneously. The E3SMv3 default configuration is included as member 0. See https://doi.org/10.22541/essoar.174907165.57104591/v1 (in review) for more information on the Nephele PPE and the perturbed parameters.

Model atmospheric temperature↗
DOE OSTI2024

Sea Ice and Cloud Processes Mediating Compensation between Atmospheric and Oceanic Meridional Heat Transports across the CMIP6 Preindustrial Control Experiment

Abstract Bjerknes compensation (BJC) refers to the anticorrelation observed between atmospheric and oceanic heat transport (AHT/OHT) variability, particularly on decadal to longer time scales that may be important to the predictability of the climate system. This study investigates the spread in BJC across fully coupled simulations of phase 6 of the Coupled Model Intercomparison Project (CMIP6) and critical processes (particularly related to sea ice and clouds) that may contribute to that spread. BJC on decadal to longer time scales is confirmed across all the simulations evaluated, and it is strongest in the Northern Hemisphere (NH) between 60° and 70°N. At these latitudes, BJC appears to be primarily driven by the exchange of turbulent fluxes (sensible and latent) in the Greenland, Iceland, and Barents Seas. Metrics to break down how sea ice and clouds uniquely modify the radiative balance of the polar atmosphere during anomalous OHT events are presented. These metrics quantify the impacts of sea ice and clouds on surface and top of atmosphere (latent, sensible, longwave, and shortwave radiative) energy fluxes. Cloud responses tend to counter the clear sky impacts over the Marginal Ice Zone (MIZ). It is further shown that the degree of BJC present in a simulation at high latitudes is heavily influenced by the sensitivity of the sea ice to OHT, which is most influential over the MIZ. These results are qualitatively robust across models and explain the intermodel spread in NH BJC in the preindustrial control experiment.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2000

The Cirrus Parcel Model Comparison Project

The cirrus Parcel Model Comparison Project involves the systematic comparison of current models of ice crystal nucleation and growth for specified, typical, cirrus cloud environments. In Phase 1 of the project reported here, simulated cirrus cloud microphysical properties are compared for situations of "warm" (-40 C) and "cold" (-60 C) cirrus subject to updrafts of 4, 20 and 100 centimeters per second, respectively. Five models are participating in the project. These models employ explicit microphysical schemes wherein the size distribution of each class of particles (aerosols and ice crystals) is resolved into bins. Simulations are made including both homogeneous and heterogeneous ice nucleation mechanisms. A single initial aerosol population of sulfuric acid particles is prescribed for all simulations. To isolate the treatment of the homogeneous freezing (of haze drops) nucleation process, the heterogeneous nucleation mechanism is disabled for a second parallel set of simulations. Qualitative agreement is found amongst the models for the homogeneous-nucleation-only simulations, e.g., the number density of nucleated ice crystals increases with the strength of the prescribed updraft. However, non-negligible quantitative differences are found. Systematic bias exists between results of a model based on a modified classical theory approach and models using an effective freezing temperature approach to the treatment of nucleation. Each approach is constrained by critical freezing data from laboratory studies. This information is necessary, but not sufficient, to construct consistent formulae for the two approaches. Large haze particles may deviate considerably from equilibrium size in moderate to strong updrafts (20-100 centimeters per second) at -60 C when the commonly invoked equilibrium assumption is lifted. The resulting difference in particle-size-dependent solution concentration of haze particles may significantly affect the ice nucleation rate during the initial nucleation interval. The uptake rate for water vapor excess by ice crystals is another key component regulating the total number of nucleated ice crystals. This rate, the product of ice number concentration and ice crystal diffusional growth rate, partially controls the peak nucleation rate achieved in an air parcel and the duration of the active nucleation time period.

Lin, Ruei-Fong↗