scholarly journals Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

2021 ◽  
Author(s):  
J. Shen ◽  
M. Yu ◽  
A. J. Koivisto ◽  
H. Jiang ◽  
Y. Liu ◽  
...  
Keyword(s):  
Size Distribution ◽  
Atmospheric Aerosols ◽  
Cloud Droplet ◽  
Size Distribution Function ◽  
Colloid Interface ◽  
Inverse Gaussian ◽  
Cloud Droplets ◽  
Droplet Dynamics ◽  
Time Required ◽  
Small Cloud

AbstractThe inverse Gaussian distributed method of moments (IGDMOM; J. Atmospheric Sci. 77 (9): 3011-3031, 2020) was developed to analytically solve the kinetic collection equation (KCE) for the first time. Using the IGDMOM, we obtained both new analytical and asymptotic solutions to the KCE. This is shown for both the free molecular and continuum regime collision frequency functions. The new analytical solutions are highly suitable for demonstrating the self-preserving size distribution (SPSD) theory. The SPSD theory is considered one of the most elegant research works in atmospheric science for aerosols or small cloud droplets. It was initially discovered by Friedlander (J. Meteorology 17 (5): 479-483, 1960) and then developed by Lee (J. Colloid Interface Sci. 92 (2): 315-325, 1983) with an assumption of the time-dependent lognormal size distribution function. In this study, we demonstrate that the SPSD theory of coagulating atmospheric aerosols can be presented in a simpler and more rigorous theoretical way, which is realized through the introduction of the IGDMOM for describing aerosol size distributions. Using the IGDMOM, the new formulas for the SPSD, as well as the time required for aerosols to reach the SPSD, are analytically provided and verified. Furthermore, we discover that the SPSD of atmospheric aerosols undergoing coagulation is only determined using a shape factor variable, 𝛺, which is composed of the first three moments at an initial stage. This study has critical implications for developing tropospheric atmospheric aerosol or small cloud droplet dynamics models and further verifies the SPSD theory from the viewpoint of theoretical analysis.

scholarly journals Droplet Growth in Warm Water Clouds Observed by the A-Train. Part II: A Multisensor View

2010 ◽  
Vol 67 (6) ◽  
pp. 1897-1907 ◽  
Author(s):  
Takashi Y. Nakajima ◽  
Kentaroh Suzuki ◽  
Graeme L. Stephens
Keyword(s):  
Cloud Droplet ◽  
Warm Water ◽  
Droplet Growth ◽  
Growth Processes ◽  
Cloud Droplets ◽  
Cloud Particle ◽  
Moderate Resolution ◽  
Resolution Imaging ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
Small Cloud

Abstract Hydrometeor droplet growth processes are inferred from a combination of Aqua/Moderate Resolution Imaging Spectroradiometer (MODIS) cloud particle size observations and CloudSat/Cloud Profiling Radar (CPR) observations of warm water clouds. This study supports the inferences of a related paper (Part I) (i) that MODIS-retrieved cloud droplet radii (CDR) from the 3.7-μm channel (R37) are influenced by the existence of small droplets at cloud top and (ii) that the CDR obtained from 1.6- (R16) and 2.1-μm (R21) channels contain information about drizzle droplets deeper into the cloud as well as cloud droplets. This interpretation is shown to be consistent with radar reflectivities when matched to CDR that were retrieved from MODIS data. This study demonstrates that the droplet growth process from cloud to rain via drizzle proceeds monotonically with the evolution of R16 or R21 from small cloud drops (on the order of 10–12 μm) to drizzle (CDR greater than 14 μm) to rain (CDR greater than 20 μm). Thus, R16 or R21 is an indicator of hydrometeor droplet growth processes whereas R37 does not contain information about coalescence. A new composite analysis, the contoured frequency diagram, is introduced to combine CloudSat/CPR reflectivity profiles and reveals a distinct trimodal population of reflectivities corresponding to cloud, drizzle, and rain modes.

scholarly journals Relationships between particles, cloud condensation nuclei and cloud droplet activation during the third Pallas Cloud Experiment

2012 ◽  
Vol 12 (6) ◽  
pp. 13691-13732
Author(s):  
T. Anttila ◽  
D. Brus ◽  
A. Jaatinen ◽  
A.-P. Hyvärinen ◽  
N. Kivekäs ◽  
...  
Keyword(s):  
Size Distribution ◽  
Cloud Condensation Nuclei ◽  
Cloud Droplet ◽  
Droplet Surface ◽  
The Arctic ◽  
Condensation Nuclei ◽  
Cloud Droplets ◽  
The Third ◽  
Droplet Activation ◽  
Experimental Values

Abstract. Concurrent measurement of aerosols, cloud condensation nuclei (CCN) and cloud droplet activation were carried out as a part of the third Pallas Cloud Experiment (PaCE-3) which took place at a ground based site located on northern Finland during the autumn of 2009. In this study, we investigate relationships between the aerosol properties, CCN and size resolved cloud droplet activation. During the investigated cloudy periods, the inferred number of cloud droplets (CDNC) varied typically between 50 and 150 cm−3 and displayed a linear correlation both with the number of particles having sizes over 100 nm and with the CCN concentrations at 0.4% supersaturation. Furthermore, the diameter corresponding to the 50% activation fraction, D50, was generally in the range of 80 to 120 nm. The measured CCN concentrations were compared with predictions of a numerical model which used the measured size distribution and size resolved hygroscopicity as input. Assuming that the droplet surface tension is equal to that of water, the measured and predicted CCN concentrations were generally within 30%. We also simulated size dependent cloud droplet activation with a previously developed air parcel model. By forcing the model to reproduce the experimental values of CDNC, adiabatic estimates for the updraft velocity and the maximum supersaturation reached in the clouds were derived. Performed sensitivity studies showed further that the observed variability in CDNC was driven mainly by changes in the particle size distribution while the variations in the updraft velocity and hygroscopicity contributed to a lesser extent. The results of the study corroborate conclusions of previous studies according to which the number of cloud droplets formed in clean air masses close to the Arctic is determined mainly by the number of available CCN.

scholarly journals CCN activation and cloud processing in sectional aerosol models with low size resolution

2005 ◽  
Vol 5 (9) ◽  
pp. 2561-2570 ◽  
Author(s):  
H. Korhonen ◽  
V.-M. Kerminen ◽  
K. E. J. Lehtinen ◽  
M. Kulmala
Keyword(s):  
Size Distribution ◽  
Large Scale ◽  
Reference Model ◽  
Cloud Model ◽  
Cloud Droplet ◽  
Anthropogenic Sources ◽  
Aerosol Size Distribution ◽  
Droplet Growth ◽  
Cloud Droplets ◽  
Cloud Processing

Abstract. We investigate the influence of low size resolution, typical to sectional aerosol models in large scale applications, on cloud droplet activation and cloud processing of aerosol particles. A simplified cloud model with five approaches to determine the fraction of activated particles is compared with a detailed reference model under different atmospheric conditions. In general, activation approaches which assume a distribution profile within the critical model size sections predict the cloud droplet concentration most accurately under clean and moderately polluted conditions. In such cases, the deviation from the reference simulations is below 15% except for very low updraft velocities. In highly polluted cases, the concentration of cloud droplets is significantly overestimated due to the inability of the simplified model to account for the kinetic limitations of the droplet growth. Of the profiles examined, taking into account the local shape of the particle size distribution is the most accurate although in most cases the shape of the profile has little relevance. While the low resolution cloud model cannot reproduce the details of the out-of-the-cloud aerosol size distribution, it captures well the amount of sulphate produced in aqueous-phase reactions as well as the distribution of the sulphate between the cloud droplets. Overall, the simplified cloud model with low size resolution performs well for clean and moderately polluted regions that cover most of the Earth's surface and is therefore suitable for large scale models. It can, however, show uncertainties in areas with strong pollution from anthropogenic sources.

scholarly journals Chemical composition and droplet size distribution of cloud at the summit of Mount Tai, China

2017 ◽  
Author(s):  
Jiarong Li ◽  
Xinfeng Wang ◽  
Jianmin Chen ◽  
Chao Zhu ◽  
Weijun Li ◽  
...  
Keyword(s):  
Chemical Composition ◽  
Size Distribution ◽  
Droplet Size ◽  
Atmospheric Aerosols ◽  
Ph Value ◽  
Inorganic Ions ◽  
Droplet Size Distribution ◽  
Dilution Effect ◽  
Water Soluble ◽  
Cloud Droplets

Abstract. Chemical composition of 39 cloud samples and droplet size distribution in 24 cloud events were investigated at the summit of Mt. Tai from July to October 2014. Inorganic ions, organic acids, metals, HCHO, H2O2, sulfur(IV), organic carbon, element carbon as well as pH and electrical conductivity were analyzed. The acidity of the cloud water significantly decreased from a reported value of pH 3.86 in 2007–2008 (Guo et al., 2012) to pH 5.87 in the present study. The concentrations of nitrate and ammonium were both increased since 2007–2008, but the overcompensation of ammonium led to the increase of the mean pH value. The microphysical properties showed that cloud droplets were smaller than 26.0 μm and the most were in the range of 6.0–9.0 μm. The maximum droplet number concentration (Nd) was associated with droplet sizes of 7.0 μm. Cloud droplets exhibited a strong interaction with atmospheric aerosols. High PM2.5 level resulted in higher concentrations of water soluble ions and smaller sizes with more numbers of cloud droplets, and further gave rise to relatively high acidity. High degrees of relative humidity facilitated the formation of large cloud droplets and led to high liquid water contents under low PM2.5 level. The cloud droplets to wet deposition acted as an important sink of soluble material in the atmosphere and the dilution effect of the water content should be considered when estimating concentrations of soluble components in the cloud phase.

scholarly journals Relationships between particles, cloud condensation nuclei and cloud droplet activation during the third Pallas Cloud Experiment

2012 ◽  
Vol 12 (23) ◽  
pp. 11435-11450 ◽  
Author(s):  
T. Anttila ◽  
D. Brus ◽  
A. Jaatinen ◽  
A.-P. Hyvärinen ◽  
N. Kivekäs ◽  
...  
Keyword(s):  
Size Distribution ◽  
Cloud Condensation Nuclei ◽  
Cloud Droplet ◽  
Droplet Surface ◽  
The Arctic ◽  
Condensation Nuclei ◽  
Cloud Droplets ◽  
The Third ◽  
Droplet Activation ◽  
Experimental Values

Abstract. Concurrent measurement of aerosols, cloud condensation nuclei (CCN) and cloud droplet activation were carried out as a part of the third Pallas Cloud Experiment (PaCE-3) which took place at a ground based site located on northern Finland during the autumn of 2009. In this study, we investigate relationships between the aerosol properties, CCN and size resolved cloud droplet activation. During the investigated cloudy periods, the inferred number of cloud droplets (CDNC) varied typically between 50 and 150 cm−3 and displayed a linear correlation both with the number of particles having sizes over 100 nm and with the CCN concentrations at 0.4% supersaturation. Furthermore, the diameter corresponding to the 50% activation fraction, D50, was generally in the range of 80 to 120 nm. The measured CCN concentrations were compared with predictions of a numerical model which used the measured size distribution and size resolved hygroscopicity as input. Assuming that the droplet surface tension is equal to that of water, the measured and predicted CCN concentrations were generally within 30%. We also simulated size dependent cloud droplet activation with a previously developed air parcel model. By forcing the model to reproduce the experimental values of CDNC, adiabatic estimates for the updraft velocity and the maximum supersaturation reached in the clouds were derived. Performed sensitivity studies showed further that the observed variability in CDNC was driven mainly by changes in the particle size distribution while the variations in the updraft velocity and hygroscopicity contributed to a lesser extent. The results of the study corroborate conclusions of previous studies according to which the number of cloud droplets formed in clean air masses close to the Arctic is determined mainly by the number of available CCN.

scholarly journals CCN activation and cloud processing in simplified sectional aerosol models with low size resolution

2005 ◽  
Vol 5 (4) ◽  
pp. 4871-4892
Author(s):  
H. Korhonen ◽  
V.-M. Kerminen ◽  
K. E. J. Lehtinen ◽  
M. Kulmala
Keyword(s):  
Size Distribution ◽  
Large Scale ◽  
Reference Model ◽  
Cloud Model ◽  
Cloud Droplet ◽  
Aerosol Size Distribution ◽  
Droplet Growth ◽  
Distribution Profile ◽  
Cloud Droplets ◽  
Cloud Processing

Abstract. We investigate the influence of low size resolution, typical to sectional aerosol models in large scale applications, on cloud droplet activation and cloud processing of aerosol particles. A simplified cloud scheme with five approaches to determine the fraction of activated particles is compared with a detailed reference model under different atmospheric conditions. In general, activation approaches which assume a distribution profile within the critical model size sections predict the cloud droplet concentration most accurately under clean and moderately polluted conditions. In such cases, the deviation from the reference simulations is below 15% except for very low updraft velocities. In highly polluted cases, the concentration of cloud droplets is significantly overestimated due to the inability of the simplified scheme to account for the kinetic limitations of the droplet growth. Of the profiles examined, taking into account the local shape of the particle size distribution is the most accurate although in most cases the shape of the profile has little relevance. While the low resolution cloud model cannot reproduce the details of the out-of-the-cloud aerosol size distribution, it captures well the amount of sulphate produced in aqueous-phase reactions as well as the distribution of the sulphate between the cloud droplets. Overall, the simplified cloud scheme with low size resolution performs well for clean and moderately polluted regions that cover most of the Earth's surface and is therefore suitable for large scale models.

scholarly journals The importance of interstitial particle scavenging by cloud droplets in shaping the remote aerosol size distribution and global aerosol-climate effects

2015 ◽  
Vol 15 (11) ◽  
pp. 6147-6158 ◽  
Author(s):  
J. R. Pierce ◽  
B. Croft ◽  
J. K. Kodros ◽  
S. D. D'Andrea ◽  
R. V. Martin
Keyword(s):  
Size Distribution ◽  
Droplet Size ◽  
Indirect Effect ◽  
Cloud Droplet ◽  
Aerosol Size Distribution ◽  
Cloud Physics ◽  
Cloud Droplets ◽  
Aerosol Indirect Effect ◽  
Ice Cloud ◽  
Coagulation Process

Abstract. In this paper, we investigate the coagulation of interstitial aerosol particles (particles too small to activate to cloud droplets) with cloud drops, a process often ignored in aerosol-climate models. We use the GEOS-Chem-TOMAS (Goddard Earth Observing System-Chemistry TwO-Moment Aerosol Sectional) global chemical transport model with aerosol microphysics to calculate the changes in the aerosol size distribution, cloud-albedo aerosol indirect effect, and direct aerosol effect due to the interstitial coagulation process. We find that inclusion of interstitial coagulation in clouds lowers total particle number concentrations by 15–21% globally, where the range is due to varying assumptions regarding activation diameter, cloud droplet size, and ice cloud physics. The interstitial coagulation process lowers the concentration of particles with dry diameters larger than 80 nm (a proxy for larger CCN) by 10–12%. These 80 nm particles are not directly removed by the interstitial coagulation but are reduced in concentration because fewer smaller particles grow to diameters larger than 80 nm. The global aerosol indirect effect of adding interstitial coagulation varies from +0.4 to +1.3 W m−2 where again the range depends on our cloud assumptions. Thus, the aerosol indirect effect of this process is significant, but the magnitude depends greatly on assumptions regarding activation diameter, cloud droplet size, and ice cloud physics. The aerosol direct effect of the interstitial coagulation process is minor (< 0.01 W m−2) due to the shift in the aerosol size distribution at sizes where scattering is most effective being small. We recommend that this interstitial scavenging process be considered in aerosol models when the size distribution and aerosol indirect effects are important.

scholarly journals Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment

2019 ◽  
Vol 77 (1) ◽  
pp. 337-353 ◽  
Author(s):  
Xiang-Yu Li ◽  
Axel Brandenburg ◽  
Gunilla Svensson ◽  
Nils E. L. Haugen ◽  
Bernhard Mehlig ◽  
...  
Keyword(s):  
Size Distribution ◽  
Droplet Size ◽  
Early Stage ◽  
Droplet Size Distribution ◽  
Energy Dissipation Rate ◽  
Cloud Droplets ◽  
Navier Stokes Equation ◽  
Droplet Dynamics ◽  
Condensational Growth ◽  
Rain Formation

Abstract We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high-resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water vapor mixing ratio, and the resulting supersaturation fields together with the Navier–Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation.

scholarly journals Cloud-droplet growth due to supersaturation fluctuations in stratiform clouds

2018 ◽  
Author(s):  
Xiang-Yu Li ◽  
Gunilla Svensson ◽  
Axel Brandenburg ◽  
Nils E. L. Haugen
Keyword(s):  
Reynolds Number ◽  
Size Distribution ◽  
Cloud Droplet ◽  
Energy Dissipation Rate ◽  
Droplet Growth ◽  
Size Distributions ◽  
Cloud Droplets ◽  
Stratiform Clouds ◽  
Water Vapor Mixing Ratio ◽  
Condensational Growth

Abstract. Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets being modeled as Lagrangian particles. We find that the width of droplet size distributions increases with time, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower size distributions. Nevertheless, in agreement with earlier Lagrangian stochastic models of the condensational growth, the standard deviation of the surface area of droplets increases as t1/2. Also, we numerically confirm that the time evolution of the size distribution depends strongly on the Reynolds number and only weakly on the mean energy dissipation rate. This is shown to be due to the fact that temperature fluctuations and water vapor mixing ratio fluctuations increases with increasing Reynolds number, therefore the resulting supersaturation fluctuations are enhanced with increasing Reynolds number. Our simulations may explain the broadening of the size distribution in stratiform clouds qualitatively, where the updraft velocity is almost zero.

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