The Behavior of Number Concentration Tendencies for the Continuous Collection Growth Equation Using One- and Two-Moment Bulk Parameterization Schemes

2007 ◽  
Vol 46 (8) ◽  
pp. 1264-1274
Author(s):  
Jerry M. Straka ◽  
Katharine M. Kanak ◽  
Matthew S. Gilmore
Keyword(s):  
Growth Process ◽  
Number Concentration ◽  
Mathematical Explanation ◽  
Growth Equation ◽  
Parameterization Schemes ◽  
Distribution Shape ◽  
Bulk Parameterization

Abstract This paper presents a mathematical explanation for the nonconservation of total number concentration Nt of hydrometeors for the continuous collection growth process, for which Nt physically should be conserved for selected one- and two-moment bulk parameterization schemes. Where possible, physical explanations are proposed. The assumption of a constant no in scheme A is physically inconsistent with the continuous collection growth process, as is the assumption of a constant Dn for scheme B. Scheme E also is nonconservative, but it seems this result is not because of a physically inconsistent specification; rather the solution scheme’s equations simply do not satisfy Nt conservation and Nt does not come into the derivation. Even scheme F, which perfectly conserves Nt, does not preserve the distribution shape in comparison with a bin model.

scholarly journals The Lognormal-Like Distributions in the Linear Growth Equations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4300-4307
Author(s):  
Ning-Ning Pang ◽  
Wen-Jer Tzeng
Keyword(s):  
Growth Process ◽  
Linear Growth ◽  
Growth Equation ◽  
Two Dimensional ◽  
Exponential Distributions ◽  
One Dimensional ◽  
The Social ◽  
Exponential Random Variables ◽  
Growth Equations ◽  
The One

The distributions of the global interfacial widths, correlation functions, and the local interfacial widths of the growth process described by the one-dimensional Edward-Wilkinson equation are shown to be denumerable convolutions of exponential distributions. The same conclusions can also be extended to the distributions of the global interfacial widths for another linear growth equation, describing some super-rough growth processes, in both one- and two-dimensional cases. Most of these distributions display the lognormal-like behavior. We propose that the mechanism provided by the accumulation of exponential random variables may contribute to a lot of the lognormal-like behavior observed in the social and natural sciences.

scholarly journals Enhancement of nanoparticle formation and growth during the COVID-19 lockdown period in urban Beijing

2020 ◽  
Author(s):  
Xiaojing Shen ◽  
Junying Sun ◽  
Fangqun Yu ◽  
Xiaoye Zhang ◽  
Junting Zhong ◽  
...  
Keyword(s):  
Sulfuric Acid ◽  
Growth Process ◽  
Anthropogenic Activities ◽  
Nucleation And Growth ◽  
Number Concentration ◽  
Aerosol Formation ◽  
Reduction Of Nox ◽  
Primary Emissions ◽  
Novel Coronavirus ◽  
Available Information

Abstract. Influenced by the spread of the global 2019 novel coronavirus (COVID-19) pandemic, primary emissions of particles and precursors associated with anthropogenic activities decreased significantly in China during the Chinese New Year of 2020 and the lockdown period (January 24–February 16, 2020), as indicated by approximately 50 % reduction of NOx emission nation-wide based on the open literature. Two-month measurements of the number size distribution of neutral particles and charged ions showed that during the lockdown (LCD) period, the number concentration of particles smaller than 100 nm decreased by approximately 40 % compared to the pre-LCD period in January. However, the accumulation mode particles increased by approximately 20 % as several polluted episodes contributed to secondary aerosol formation. In this study, new particle formation (NPF) events were found to be enhanced in the nucleation and growth processes during the LCD period, as indicated by higher formation (J2) and growth rate (GR), even as NPF occurrence frequency slightly decreased. The condensing vapors controlling the nucleation and growth process, sulfuric acid, and oxidation product of volatile organic compounds were estimated based on available information. The proxy values showed that sulfuric acid and organic oxidized vapors increased during the LCD period by approximately 35 % and 133 % on NPF days, respectively. Higher J2 and GR during the LCD period were favored by the increased concentration level of condensing vapors and decreased condensation sink. Several heavy haze episodes have been reported by other studies during the LCD period; however, the increase in nanoparticle number concentration should also be considered. Some typical NPF events produced a high number concentration of nanoparticles that intensified in the following days to create severe aerosol pollution. Our study confirms a significant enhancement of the nucleation and growth process of nanoparticles during the COVID-19 LCD in Beijing and highlights the necessity of controlling nanoparticles in current and future air quality management.

scholarly journals Ice-nucleating particle versus ice crystal number concentration in altocumulus and cirrus embedded in Saharan dust: A closure study

2019 ◽  
Author(s):  
Albert Ansmann ◽  
Rodanthi-Elisavet Mamouri ◽  
Johannes Bühl ◽  
Patric Seifert ◽  
Ronny Engelmann ◽  
...  
Keyword(s):  
Terminal Velocity ◽  
Number Concentration ◽  
Saharan Dust ◽  
Ice Crystal ◽  
Aerosol Cloud ◽  
Parameterization Schemes ◽  
Microphysical Properties ◽  
Before And After ◽  
Order Of Magnitude ◽  
Mixed Phase Clouds

Abstract. For the first time, a closure study of the relationship between ice-nucleating particle concentration (INPC) and ice crystal number concentration (ICNC) in altocumulus and cirrus layers, solely based on ground-based active remote sensing, is presented. Such aerosol-cloud closure experiments are required (a) to better understand aerosol-cloud interaction in the case of mixed-phase clouds, (b) to explore to what extend heterogeneous ice nucleation can contribute to cirrus formation which is usually controlled by homogeneous freezing, and (c) to check the usefulness of available INPC parameterization schemes, applied to lidar profiles of aerosol optical and microphysical properties up to tropopause level. The INPC-vs-ICNC closure studies were conducted in Cyprus (Limassol and Nicosia) during a six-week field campaign in March–April 2015 and during the 17-month CyCARE (Cyprus Clouds Aerosol and Rain Experiment) campaign. Focus is on altocumulus and cirrus layers which developed in pronounced Saharan dust layers at heights from 5–11 km. Cloud top temperatures ranged from −20 °C to −57 °C. INPC was estimated from polarization/Raman lidar observations in combination with published INPC parameterization schemes for immersion and deposition nucleation. ICNC was estimated from combined Doppler lidar, aerosol lidar, and cloud radar observations of the terminal velocity of falling ice crystals, radar reflectivity and lidar backscatter in combination with modeling of backscattering at 532 nm and 8.5 mm wavelength. Good to acceptable agreement between INPC (observed before and after the occurrence of the cloud layer under investigation) and ICNC values was found in three proof-of-concept closure experiments. In these case studies, INPC and ICNC values matched within an order of magnitude (i.e., within the uncertainty ranges of the INPC and ICNC estimates), and ranged from 0.1–10 per liter in the altocumulus layers and 1–50 per liter in the cirrus layers observed between 8–11 km height.

scholarly journals The Berry and Reinhardt Autoconversion Parameterization: A Digest

2008 ◽  
Vol 47 (2) ◽  
pp. 375-396 ◽  
Author(s):  
Matthew S. Gilmore ◽  
Jerry M. Straka
Keyword(s):  
Number Concentration ◽  
Shape Parameters ◽  
Cloud Droplets ◽  
Relative Variance ◽  
Model Solutions ◽  
Distribution Shape ◽  
Mean Diameter ◽  
Important Time

Abstract The simplified version of the Berry and Reinhardt parameterization used for initiating rain from cloud droplets is presented and is compared with 12 other versions of itself from the literature. Many of the versions that appear to be different from each other can be brought into agreement with the original parameterization by making the same assumptions: a mean diameter based upon mass or volume and distribution shape parameters chosen to give the same cloud mass relative variance as the original Berry and Reinhardt parameterization. However, there are differences in how authors have chosen to parameterize the cloud number concentration sink and rain number concentration source, and those choices, along with model limitations, have important impacts on rain development within the scheme. These differences among versions are shown to have important time-integrated feedbacks upon the developing initial rain distribution. Three of 12 implementations of the bulk scheme are shown to be able to reproduce the original Berry and Reinhardt bin-model solutions very well, and about 6 of 12 do poorly.

scholarly journals A Two-Moment Bulk Parameterization of the Drop Collection Growth in Warm Clouds

2020 ◽  
Vol 77 (3) ◽  
pp. 797-811 ◽  
Author(s):  
Xiping Zeng ◽  
Xiaowen Li
Keyword(s):  
Time Delay ◽  
Analytic Solution ◽  
Liquid Water Content ◽  
Number Concentration ◽  
The Self ◽  
Cloud Drop ◽  
Final Version ◽  
Warm Rain ◽  
Drop Number ◽  
Bulk Parameterization

Abstract To improve the modeling of warm rain initiation, a two-moment bulk parameterization of the drop collection growth in warm clouds is developed by two steps: (i) its prototype is first derived based on the analytic solution of the stochastic collection equation (SCE) with the Golovin kernel, and (ii) the prototype is then revamped empirically to fit the numerical solution of SCE with the real hydrodynamic collection kernel, reaching the final version of the parameterization. Since the final version represents the self-collection of cloud drops explicitly, it replicates warm rain initiation well even when liquid water content (cloud-drop number concentration) is very low (high). It also replicates the autoconversion threshold and time delay of rain initiation via a small autoconversion rate.

Fundamental Research into Thin Films in a Developing Country

1972 ◽  
Vol 30 ◽  
pp. 500-501
Author(s):  
J.A. Eades ◽  
E. Grünbaum
Keyword(s):  
Thin Films ◽  
Growth Process ◽  
Empirical Process ◽  
Nucleation And Growth ◽  
Research Groups ◽  
Film Research ◽  
Fundamental Research ◽  
Controlled Deposition ◽  
The One ◽  
The University

In the last decade and a half, thin film research, particularly research into problems associated with epitaxy, has developed from a simple empirical process of determining the conditions for epitaxy into a complex analytical and experimental study of the nucleation and growth process on the one hand and a technology of very great importance on the other. During this period the thin films group of the University of Chile has studied the epitaxy of metals on metal and insulating substrates. The development of the group, one of the first research groups in physics to be established in the country, has parallelled the increasing complexity of the field.The elaborate techniques and equipment now needed for research into thin films may be illustrated by considering the plant and facilities of this group as characteristic of a good system for the controlled deposition and study of thin films.

UHV-STM studies of silicon nano-pyramid growth on silicon surface at high temperature

1992 ◽  
Vol 50 (2) ◽  
pp. 1144-1145
Author(s):  
T. Sato ◽  
S. Kitamura ◽  
T. Sueyoshl ◽  
M. Iwatukl ◽  
C. Nielsen
Keyword(s):  
High Temperature ◽  
Relaxation Process ◽  
Thermal Effect ◽  
Bias Voltage ◽  
Silicon Surface ◽  
Growth Process ◽  
Tunneling Current ◽  
Fabrication Technique ◽  
Nano Fabrication ◽  
Electromigration Effect

Recently, the growth process and relaxation process of crystalline structures were studied by observing a SI nano-pyramid which was built on a Si surface with a UHV-STM. A UHV-STM (JEOL JSTM-4000×V) was used for studying a heated specimen, and the specimen was kept at high temperature during observation. In this study, the nano-fabrication technique utilizing the electromigration effect between the STM tip and the specimen was applied. We observed Si atoms migrated towords the tip on a high temperature Si surface.Clean surfaces of Si(lll)7×7 and Si(001)2×l were prepared In the UHV-STM at a temperature of approximately 600 °C. A Si nano-pyramid was built on the Si surface at a tunneling current of l0nA and a specimen bias voltage of approximately 0V in both polarities. During the formation of the pyramid, Images could not be observed because the tip was stopped on the sample. After the formation was completed, the pyramid Image was observed with the same tip. After Imaging was started again, the relaxation process of the pyramid started due to thermal effect.

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