scholarly journals On Calculating Deposition Coefficients and Aspect-Ratio Evolution in Approximate Models of Ice Crystal Vapor Growth

2019 ◽  
Vol 76 (6) ◽  
pp. 1609-1625 ◽  
Author(s):  
Jerry Y. Harrington ◽  
Alfred Moyle ◽  
Lavender Elle Hanson ◽  
Hugh Morrison
Keyword(s):  
Aspect Ratio ◽  
Free Fall ◽  
Parametric Models ◽  
Ice Crystal ◽  
Growth Data ◽  
Surface Attachment ◽  
Vapor Growth ◽  
Liquid Saturation ◽  
Cloud Models ◽  
Small Crystals

Abstract Models of ice crystal vapor growth require estimates of the deposition coefficient α when surface attachment kinetics limit growth and when ice crystal shape is predicted. Parametric models can be used to calculate α for faceted growth as long as characteristic supersaturation values are known. However, previously published measurements of are limited to temperatures higher than −40°C. Estimates of at temperatures between −40° and −70°C are provided here through reanalysis of vapor growth data. The estimated follow the same functional temperature dependence as data taken at higher temperatures. Polynomial fits to are used as inputs to a parameterization of α suitable for use in cloud models. Comparisons of the parameterization with wind tunnel data show that growth at liquid saturation and constant temperatures between −3° and −20°C can be modeled by ledge nucleation for larger (hundreds of micrometers) crystals; however, comparisons with free-fall chamber data at −7°C suggest that dislocation growth may be required to model the vapor growth of small crystals (~20 μm) at liquid saturation. The comparisons with free-fall chamber data also show that the parameterization can reproduce the measured pressure dependence of aspect-ratio evolution. Comparisons with a hexagonal growth model indicate that aspect-ratio evolution based on the theory of Chen and Lamb produces unrealistically fast column growth near −7°C that is mitigated if a theory based on faceted growth is used. This result indicates that the growth hypothesis used in habit-evolving microphysical models needs to be revised when deposition coefficients are predicted.

Semi-Analytic Functions to Calculate the Deposition Coefficients for Ice Crystal Vapor Growth in Bin and Bulk Microphysical Models.

2021 ◽  
Author(s):  
Jerry Y. Harrington ◽  
G. Alexander Sokolowsky ◽  
Hugh Morrison
Keyword(s):  
Ice Crystals ◽  
Mixing Ratio ◽  
Ice Crystal ◽  
Surface Attachment ◽  
Vapor Growth ◽  
Diffusion Limited ◽  
Cloud Models ◽  
Variable Surface ◽  
Deposition Coefficient ◽  
Relative Errors

AbstractNumerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided.

scholarly journals Estimating Surface Attachment Kinetic and Growth Transition Influences on Vapor-Grown Ice Crystals

2020 ◽  
Vol 77 (7) ◽  
pp. 2393-2410
Author(s):  
Gwenore F. Pokrifka ◽  
Alfred M. Moyle ◽  
Lavender Elle Hanson ◽  
Jerry Y. Harrington
Keyword(s):  
Diffusion Chamber ◽  
Ice Crystals ◽  
Growth Theory ◽  
Growth Data ◽  
Surface Attachment ◽  
Mass Growth ◽  
Vapor Growth ◽  
Deposition Coefficient ◽  
Direct Use ◽  
Large Decline

AbstractThere are few measurements of the vapor growth of small ice crystals at temperatures below −30°C. Presented here are mass-growth measurements of heterogeneously and homogeneously frozen ice particles grown within an electrodynamic levitation diffusion chamber at temperatures between −44° and −30°C and supersaturations si between 3% and 29%. These growth data are analyzed with two methods devised to estimate the deposition coefficient α without the direct use of si. Measurements of si are typically uncertain, which has called past estimates of α into question. We find that the deposition coefficient ranges from 0.002 to unity and is scattered with temperature, as shown in prior measurements. The data collectively also show a relationship between α and si, with α rising (falling) with increasing si for homogeneously (heterogeneously) frozen ice. Analysis of the normalized mass growth rates reveals that heterogeneously frozen crystals grow near the maximum rate at low si, but show increasingly inhibited (low α) growth at high si. Additionally, 7 of the 17 homogeneously frozen crystals cannot be modeled with faceted growth theory or constant α. These cases require the growth mode to transition from efficient to inefficient in time, leading to a large decline in α. Such transitions may be, in part, responsible for the inconsistency in prior measurements of α.

Fatigue of Drill String Connections

1995 ◽  
Vol 117 (2) ◽  
pp. 126-132 ◽  
Author(s):  
F. P. Brennan
Keyword(s):  
Aspect Ratio ◽  
Crack Growth ◽  
Empirical Model ◽  
Drill String ◽  
Full Scale ◽  
Growth Data ◽  
Service Environment ◽  
Threaded Connections ◽  
Bend Tests ◽  
Full Scale Tests

This paper reports full-scale tests on threaded connections used in drill strings. A concise background is given concerning the in-service environment and loading conditions on the connections. This details some of the reasons particular steels are used in preference to others. Crack growth data is given for ten full-scale axial and rotating bend tests. This is compared with predictions from a dedicated weight function fracture mechanics solution designed for threaded connections. Crack aspect ratio is considered with a view to development of an appropriate empirical model.

scholarly journals Aerosol-cloud interactions: The representation of heterogeneous ice activation in cloud models

2021 ◽  
Author(s):  
Bernd Kärcher ◽  
Claudia Marcolli
Keyword(s):  
Phase Transitions ◽  
Particle Number ◽  
Water Phase ◽  
Cloud Formation ◽  
Ice Formation ◽  
Ice Crystal ◽  
Nucleation Behavior ◽  
Aerosol Cloud ◽  
Cloud Models ◽  
Aerosol Cloud Interactions

Abstract. The homogeneous nucleation of ice in supercooled liquid water clouds is characterized by time-dependent freezing rates. By contrast, water phase transitions induced heterogeneously by ice nucleating particles (INPs) are described by time-independent ice-active fractions depending on ice supersaturation (s). Laboratory studies report ice-active particle number fractions (AFs) that are cumulative in s. Cloud models budget INP and ice crystal numbers to conserve total particle number during water phase transitions. Here, we show that ice formation from INPs with time-independent nucleation behavior is overpredicted when models budget particle numbers and at the same time derive ice crystal numbers from s-cumulative AFs. This causes a bias towards heterogeneous ice formation in situations where INPs compete with homogeneous droplet freezing during cloud formation. We resolve this issue by introducing differential AFs, moving us one step closer to more robust simulations of aerosol-cloud interactions.

scholarly journals Study of an ice core to the bedrock in the accumulation zone of an Alpine glacier

1976 ◽  
Vol 17 (75) ◽  
pp. 13-28 ◽  
Author(s):  
M. Vallon ◽  
J.-R. Petit ◽  
B. Fabre
Keyword(s):  
Water Content ◽  
Ice Core ◽  
Ice Crystal ◽  
Vertical Orientation ◽  
Axis Orientation ◽  
Alpine Glacier ◽  
Small Crystals ◽  
Average Water ◽  
Intermediate Size ◽  
Average Size

AbstractA water table appearing every summer where the ice begins, at a gerpth of approximately 30 m, accelerates the transformation of firn into ice during the summer (80% of the ice formed every year appears in less than 2 months). The ice formed in this way contains from 0 to 0.6% water. The average water content increases gradually with the gerpth because of the heat of gerformation. But, near bedrock, between 180 and 187 m, the permeability of the blue ice is such that the water content drops (0.3% as compared to 1.3% between 160 and 180 m).From a gerpth of 33 m, a foliation of sedimentary origin gradually gervelops in the ice. Its dip increases regularly to a gerpth of 145 m. At 145 m it jumps sudgernly freom 20° to 40°, then at 170 m freom 40° to 65°, which can be explained by old modifications in the bergschrund. This foliation disappears near bedrock (180-187 m), where there are no bubbles in the ice.The average size of an ice crystal increases slowly in the firn, shows seasonal fluctuations between 30 and 50 m, then jumps freom a diameter of 1 or 2 mm to 10 or 20 mm between 50 and 80 m. Between 180 and 187 m, the ice is mager of large crystals (3-10 cm diameter; the figure, however, is probably inexact due to a recrystallization of the samples).The very strong sub-vertical orientation of the optic axes of the firn crystals disappears quickly, and freom 66 m on, in ice with large crystals, a fabric of multiple maxima appears (generally, 3 or 4 directions, forming a triangle or a rhombus). On the other hand, in the small crystals that form bands parallel to the plane of foliation, only one direction of preferential orientation can be seen, or two close to one another. Crystals of intermediate size (10 to 50 mm) generally have two directions of preferred orientation at an angle of approximately 50° to one another. No matter how big the crystals are, the angle between the most commonc-axis orientation and the vertical does not change freom 60 to 170 m gerpth.

scholarly journals Chemistry of riming: the retention of organic and inorganic atmospheric trace constituents

2017 ◽  
Vol 17 (16) ◽  
pp. 9717-9732 ◽  
Author(s):  
Alexander Jost ◽  
Miklós Szakáll ◽  
Karoline Diehl ◽  
Subir K. Mitra ◽  
Stephan Borrmann
Keyword(s):  
Wind Tunnel ◽  
Empirical Model ◽  
Free Fall ◽  
Liquid Water Content ◽  
Growth Surface ◽  
Phase Zone ◽  
Convective Clouds ◽  
Cloud Models ◽  
Trace Constituents ◽  
Semi Empirical

Abstract. During free fall in clouds, ice hydrometeors such as snowflakes and ice particles grow effectively by riming, i.e., the accretion of supercooled droplets. Volatile atmospheric trace constituents dissolved in the supercooled droplets may remain in ice during freezing or may be released back to the gas phase. This process is quantified by retention coefficients. Once in the ice phase the trace constituents may be vertically redistributed by scavenging and subsequent precipitation or by evaporation of these ice hydrometeors at high altitudes. Retention coefficients of the most dominant carboxylic acids and aldehydes found in cloud water were investigated in the Mainz vertical wind tunnel under dry-growth (surface temperature less than 0 °C) riming conditions which are typically prevailing in the mixed-phase zone of convective clouds (i.e., temperatures from −16 to −7 °C and a liquid water content (LWC) of 0. 9 ± 0. 2 g m−3). The mean retention coefficients of formic and acetic acids are found to be 0. 68 ± 0. 09 and 0. 63 ± 0. 19. Oxalic and malonic acids as well as formaldehyde show mean retention coefficients of 0. 97 ± 0. 06, 0. 98 ± 0. 08, and 0. 97 ± 0. 11, respectively. Application of a semi-empirical model on the present and earlier wind tunnel measurements reveals that retention coefficients can be well interpreted by the effective Henry's law constant accounting for solubility and dissociation. A parameterization for the retention coefficients has been derived for substances whose aqueous-phase kinetics are fast compared to mass transport timescales. For other cases, the semi-empirical model in combination with a kinetic approach is suited to determine the retention coefficients. These may be implemented in high-resolution cloud models.

Modeling Ice Crystal Aspect Ratio Evolution during Riming: A Single-Particle Growth Model

2015 ◽  
Vol 72 (7) ◽  
pp. 2569-2590 ◽  
Author(s):  
Anders A. Jensen ◽  
Jerry Y. Harrington
Keyword(s):  
Wind Tunnel ◽  
Growth Model ◽  
Liquid Water ◽  
Single Particle ◽  
Liquid Drop ◽  
Ice Crystals ◽  
Ice Crystal ◽  
Vapor Growth ◽  
Wind Tunnel Data ◽  
Fall Speed

This paper describes and tests a single-particle ice growth model that evolves both ice crystal mass and shape as a result of vapor growth and riming. Columnar collision efficiencies in the model are calculated using a new theoretical method derived from spherical collision efficiencies. The model is able to evolve mass, shape, and fall speed of growing ice across a range of temperatures, and it compares well with wind tunnel data. The onset time of riming and the effects of riming on mass and fall speed between −3° and −16°C are modeled, as compared with wind tunnel data for a liquid water content of 0.4 g m−3. Under these conditions, riming is constrained to the more isometric habits near −10° and −4°C. It is shown that the mass and fall speed of riming dendrites depend on the liquid drop distribution properties, leading to a range of mass–size and fall speed–size relationships. Riming at low liquid water contents is shown to be sensitive to ice crystal habit and liquid drop size. Moreover, very light riming can affect the shape of ice crystals enough to reduce vapor growth and suppress overall mass growth, as compared with those same ice crystals if they were unrimed.

The Effects of Surface Kinetics on Crystal Growth and Homogeneous Freezing in Parcel Simulations of Cirrus

2015 ◽  
Vol 72 (8) ◽  
pp. 2929-2946 ◽  
Author(s):  
Chengzhu Zhang ◽  
Jerry Y. Harrington
Keyword(s):  
Crystal Growth ◽  
Mean Free Path ◽  
Cloud Base ◽  
Ice Crystal ◽  
Surface Kinetics ◽  
Cloud Models ◽  
Cloud Development ◽  
Deposition Coefficient ◽  
Growth Rate Control ◽  
Homogeneous Freezing

Abstract The uptake of water vapor excess by ice crystals is a key process regulating the supersaturation in cold clouds. Both the ice crystal number concentration and depositional growth rate control the vapor uptake rate and are sensitive to the deposition coefficient . The deposition coefficient depends on temperature and supersaturation; however, cloud models either ignore or assume a constant . In this study, the effects of on crystal growth and homogeneous freezing of haze solution drops in simulated cirrus are examined. A Lagrangian parcel model is used with a new ice growth model that predicts the deposition coefficients along two crystal growth axes. Parcel model results indicate that predicting can be critical for predicting ice nucleation and supersaturation at different stages of cloud development. At cloud base, model results show that surface kinetics constrain the homogeneous freezing rate primarily through the growth impact of small particle sizes in comparison to the mean free path. The deposition coefficient has little effect on homogeneous freezing rates, because the high cloud-base supersaturation produces near unity. Above the cloud-base nucleation zone, decreasing supersaturation causes to decrease to values as low as 0.001. These low values of lead to higher steady-state supersaturation. Also, the low values of produce substantial impacts on particle shape evolution and particle size, both of which are dependent on updraft strength.

scholarly journals The Theory of Ice Nucleation by Heterogeneous Freezing of Deliquescent Mixed CCN. Part II: Parcel Model Simulation

2005 ◽  
Vol 62 (2) ◽  
pp. 261-285 ◽  
Author(s):  
Vitaly I. Khvorostyanov ◽  
Judith A. Curry
Keyword(s):  
Large Scale ◽  
Model Simulation ◽  
Cloud Condensation Nuclei ◽  
Ice Nucleation ◽  
Crystal Nucleation ◽  
Ice Crystal ◽  
Diffusional Growth ◽  
Ice Nuclei ◽  
Cloud Models ◽  
Bin Microphysics

Abstract The new theory of ice nucleation by heterogeneous freezing of deliquescent mixed cloud condensation nuclei (CCN) presented in Part I is incorporated into a parcel model with explicit water and ice bin microphysics to simulate the process of ice nucleation under transient thermodynamic conditions. Simulations are conducted over the temperature range −4° to −60°C, with vertical velocities varying from 1 to 100 cm s−1, for varying initial relative humidities and aerosol characteristics. These simulations show that the same CCN that are responsible for the drop nucleation may initiate crystal nucleation and can be identified as ice nuclei (IN) when crystals form. The simulated nucleation rates and concentrations of nucleated crystals depend on temperature and supersaturation simultaneously, showing good agreement with observations but with noticeable differences when compared with classical temperature-only and supersaturation-only parameterizations. The kinetics of heterogeneous ice nucleation exhibits a negative feedback via water supersaturation, whereby ice nucleation depends on the water supersaturation that is diminished by ice crystal diffusional growth. This feedback is stronger than the corresponding feedback for drop nucleation, and may explain discrepancies between observed ice nuclei concentrations and ice crystal concentrations, the very small fraction of CCN that may serve as IN, and the much smaller crystal concentrations as compared to drop concentrations. The relative importance of heterogeneous versus homogeneous nucleation is examined for a variety of cloud conditions. Based on these calculations, a simple parameterization for ice crystal concentration is suggested for use in cloud models and large-scale models.

scholarly journals Relationship between temperature and apparent shape of pristine ice crystals derived from polarimetric cloud radar observations during the ACCEPT campaign

2016 ◽  
Vol 9 (8) ◽  
pp. 3739-3754 ◽  
Author(s):  
Alexander Myagkov ◽  
Patric Seifert ◽  
Ulla Wandinger ◽  
Johannes Bühl ◽  
Ronny Engelmann
Keyword(s):  
Free Fall ◽  
Crystal Shape ◽  
Ice Crystal ◽  
Ambient Conditions ◽  
Axis Ratio ◽  
Microwave Scattering ◽  
Cloud Radar ◽  
Ice Particles ◽  
Rapid Changes ◽  
Good Agreement

Abstract. This paper presents first quantitative estimations of apparent ice particle shape at the top of liquid-topped clouds. Analyzed ice particles were formed under mixed-phase conditions in the presence of supercooled water and in the temperature range from −20 to −3 °C. The estimation is based on polarizability ratios of ice particles measured by a Ka-band cloud radar MIRA-35 with hybrid polarimetric configuration. Polarizability ratio is a function of the geometrical axis ratio and the dielectric properties of the observed hydrometeors. For this study, 22 cases observed during the ACCEPT (Analysis of the Composition of Clouds with Extended Polarization Techniques) field campaign were used. Polarizability ratios retrieved for cloud layers with the cloud-top temperatures of  ∼ −5,  ∼ −8,  ∼ −15, and  ∼ −20 °C were 1.6, 0.9, 0.6, and 0.9, respectively. Such values correspond to prolate, quasi-isotropic, oblate, and quasi-isotropic particles, respectively. Data from a free-fall chamber were used for the comparison. A good agreement of detected apparent shapes with well-known shape–temperature dependencies observed in laboratories was found. Polarizability ratios used for the analysis were estimated for areas located close to the cloud top, where aggregation and riming processes do not strongly affect ice particles. We concluded that, in microwave scattering models, ice particles detected in these areas can be assumed to have pristine shapes. It was also found that even slight variations of ambient conditions at the cloud top with temperatures warmer than  ∼ −5 °C can lead to rapid changes of ice crystal shape.

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