scholarly journals Determination of the Ice Particle Size Distributions Using Observations as the Integrated Constraints

2018 ◽  
Vol 75 (3) ◽  
pp. 787-804 ◽  
Author(s):  
Jun-Ichi Yano ◽  
Andrew J. Heymsfield ◽  
Aaron Bansemer
Keyword(s):  
Maximum Entropy ◽  
Particle Number ◽  
Maximum Entropy Principle ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Total Particle Number ◽  
Physically Based ◽  
Total Particle ◽  
Entropy Principle ◽  
Mean Size

Abstract The possibility is suggested of estimating particle size distributions (PSD) solely based on the bulk quantities of the hydrometeors. The method, inspired by the maximum entropy principle, can be applied to any predefined general PSD form as long as the number of the free parameters is equal to or less than that of the bulk quantities available. As long as an adopted distribution is “physically based,” these bulk characterizations can recover a fairly accurate PSD estimate. This method is tested for ice particle measurements from the Tropical Composition, Cloud and Climate Coupling Experiment (TC4). The total particle number, total mass, and mean size are taken as bulk quantities. The gamma distribution and two distributions obtained under the maximum entropy principle by taking the size and the particle mass, respectively, as a restriction variable are adopted for fit. The fitting error for the two maximum entropy–based distributions is comparable to that of a standard direct fitting method with the gamma distribution. The same procedure works almost equally well when the mean size is removed from the constraint, especially for an exponential distribution. The results suggest that the total particle number and the total mass of the hydrometeors are sufficient for determining the PSD to a reasonable accuracy when a “physically based” distribution is assumed. In addition to the in situ cloud measurements, remote sensing measurements such as those from radar as well as satellite can be adopted as physical constraints. Possibilities of exploiting different types of measurements should be further pursued.

scholarly journals What Is the Maximum Entropy Principle? Comments on “Statistical Theory on the Functional Form of Cloud Particle Size Distributions”

2019 ◽  
Vol 76 (12) ◽  
pp. 3955-3960 ◽  
Author(s):  
Jun-Ichi Yano
Keyword(s):  
Maximum Entropy ◽  
Relative Entropy ◽  
Functional Form ◽  
Maximum Entropy Principle ◽  
The Other ◽  
Standard Entropy ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Cloud Particle ◽  
Entropy Principle

Abstract The basic idea of the maximum entropy principle is presented in a succinct, self-contained manner. The presentation points out some misunderstandings on this principle by Wu and McFarquhar. Namely, the principle does not suffer from the problem of a lack of invariance by change of the dependent variable; thus, it does not lead to a need to introduce the relative entropy as suggested by Wu and McFarquhar. The principle is valid only with a proper choice of a dependent variable, called a restriction variable, for a distribution. Although different results may be obtained with the other variables obtained by transforming the restriction variable, these results are simply meaningless. A relative entropy may be used instead of a standard entropy. However, the former does not lead to any new results unobtainable by the latter.

scholarly journals Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”

2019 ◽  
Vol 76 (12) ◽  
pp. 3961-3963
Author(s):  
Wei Wu ◽  
Greg M. McFarquhar
Keyword(s):  
Particle Size ◽  
Maximum Entropy ◽  
Functional Form ◽  
Maximum Entropy Principle ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Cloud Particle ◽  
Functional Relations ◽  
Entropy Principle ◽  
Gibbs Entropy

Abstract We welcome the opportunity to correct the misunderstandings and misinterpretations contained in Yano’s comment that led him to incorrectly state that Wu and McFarquhar misunderstood the maximum entropy (MaxEnt) principle. As correctly stated by Yano, the principle itself does not suffer from the problem of a lack of invariance. But, as restated in this reply and in Wu and McFarquhar, the commonly used Shannon–Gibbs entropy does suffer from a lack of invariance for coordinate transform when applied in continuous cases, and this problem is resolved by the use of the relative entropy. Further, it is restated that the Wu and McFarquhar derivation of the PSD form using MaxEnt is more general than the formulation by Yano and allows more constraints with any functional relations to be applied. The derivation of Yano is nothing new but the representation of PSDs in other variables.

scholarly journals Urban aerosol size distributions over the Mediterranean city of Barcelona, NE Spain

2012 ◽  
Vol 12 (7) ◽  
pp. 16457-16492 ◽  
Author(s):  
M. Dall'Osto ◽  
D.C.S. Beddows ◽  
J. Pey ◽  
S. Rodriguez ◽  
A. Alastuey ◽  
...  
Keyword(s):  
Particle Number ◽  
Number Concentration ◽  
Aerosol Size Distribution ◽  
Time Variability ◽  
Small Contribution ◽  
Particle Number Concentration ◽  
Size Distributions ◽  
Total Particle Number ◽  
Total Particle ◽  
One Year

Abstract. Differential mobility particle sizer (DMPS) aerosol concentrations (N13–800) were collected over a one-year-period (2004) at an urban background site in Barcelona, North-Eastern Spain. Quantitative contributions to particle number concentrations of the nucleation (33–38%), Aitken (39–49%) and accumulation mode (18–22%) were estimated. We examined the source and time variability of atmospheric aerosol particles by using both K-means clustering and Positive Matrix Factorization (PMF) analysis. Performing clustering analysis on hourly size distributions, nine K-means DMPS clusters were identified and, by directional association, diurnal variation and relationship to meteorological and pollution variables, four typical aerosol size distribution scenarios were identified: traffic (69% of the time), dilution (15% of the time), summer background conditions (4% of the time) and regional pollution (12% of the time). According to the results of PMF, vehicle exhausts are estimated to contribute at least to 62–66% of the total particle number concentration, with a slightly higher proportion distributed towards the nucleation mode (34%) relative to the Aitken mode (28–32%). Photochemically induced nucleation particles make only a small contribution to the total particle number concentration (2–3% of the total), although only particles larger than 13 nm were considered in this study. Overall the combination of the two statistical methods is successful at separating components and quantifying relative contributions to the particle number population.

scholarly journals Classification of aerosol population type and cloud condensation nuclei properties in a coastal California littoral environment using an unsupervised cluster model

2019 ◽  
Author(s):  
Samuel A. Atwood ◽  
Sonia M. Kreidenweis ◽  
Paul J. DeMott ◽  
Markus D. Petters ◽  
Gavin C. Cornwell ◽  
...  
Keyword(s):  
Cluster Model ◽  
Particle Number ◽  
Cloud Condensation Nuclei ◽  
Sea Breeze ◽  
Northern Coast ◽  
Size Distributions ◽  
Condensation Nuclei ◽  
Entire Study ◽  
Total Particle Number ◽  
Total Particle

Abstract. Aerosol particle and cloud condensation nuclei (CCN) measurements from a littoral location on the northern coast of California at Bodega Bay Marine Laboratory (BML) are presented for approximately six weeks of observations during the CalWater-2015 field campaign. A combination of aerosol microphysical and meteorological parameters was used to classify variability in the properties of the BML surface aerosol using a K-means cluster model. Eight aerosol population types were identified that were associated with a range of impacts from both marine and terrestrial sources. Average measured total particle number concentrations, size distributions, hygroscopicities, and activated fraction spectra between 0.08 % and 1.1 % supersaturation are given for each of the identified aerosol population types, along with meteorological observations and transport pathways during time periods associated with each type. Five terrestrially influenced aerosol population types represented different degrees of aging of the continental outflow from the coast and interior of California and their appearance at the BML site was often linked to changes in wind direction and transport pathway. In particular, distinct aerosol populations, associated with diurnal variations in source region induced by land/sea-breeze shifts, were classified by the clustering technique. A terrestrial type representing fresh emissions, and/or a recent new particle formation event, occurred in approximately 10 % of the observations. Over the entire study period, three marine influenced population types were identified that typically occurred when the regular diurnal land/sea-breeze cycle collapsed and BML was continuously ventilated by air masses from marine regions for multiple days. These marine types differed from each other primarily in the degree of cloud processing evident in the size distributions, and in the presence of an additional large-particle mode for the type associated with the highest wind speeds. One of the marine types was associated with a multi-day period during which an atmospheric river made landfall at BML. The generally higher total particle number concentrations but lower activated fractions of four of the terrestrial types yielded similar CCN number concentrations to two of the marine types for supersaturations below about 0.4 %. Despite quite different activated fraction spectra, the two remaining marine and terrestrial types had CCN spectral number concentrations very similar to each other, due in part to higher number concentrations associated with the terrestrial type.

scholarly journals Comparison between summertime and wintertime Arctic Ocean primary marine aerosol properties

2013 ◽  
Vol 13 (9) ◽  
pp. 4783-4799 ◽  
Author(s):  
J. Zábori ◽  
R. Krejci ◽  
J. Ström ◽  
P. Vaattovaara ◽  
A. M. L. Ekman ◽  
...  
Keyword(s):  
Sea Ice ◽  
Water Temperature ◽  
Arctic Ocean ◽  
Particle Number ◽  
Number Concentration ◽  
The Arctic ◽  
Particle Number Concentration ◽  
Size Distributions ◽  
Total Particle Number ◽  
Total Particle

Abstract. Primary marine aerosols (PMAs) are an important source of cloud condensation nuclei, and one of the key elements of the remote marine radiative budget. Changes occurring in the rapidly warming Arctic, most importantly the decreasing sea ice extent, will alter PMA production and hence the Arctic climate through a set of feedback processes. In light of this, laboratory experiments with Arctic Ocean water during both Arctic winter and summer were conducted and focused on PMA emissions as a function of season and water properties. Total particle number concentrations and particle number size distributions were used to characterize the PMA population. A comprehensive data set from the Arctic summer and winter showed a decrease in PMA concentrations for the covered water temperature (Tw) range between −1°C and 15°C. A sharp decrease in PMA emissions for a Tw increase from −1°C to 4°C was followed by a lower rate of change in PMA emissions for Tw up to about 6°C. Near constant number concentrations for water temperatures between 6°C to 10°C and higher were recorded. Even though the total particle number concentration changes for overlapping Tw ranges were consistent between the summer and winter measurements, the distribution of particle number concentrations among the different sizes varied between the seasons. Median particle number concentrations for a dry diameter (Dp< 0.125μm measured during winter conditions were similar (deviation of up to 3%), or lower (up to 70%) than the ones measured during summer conditions (for the same water temperature range). For Dp > 0.125μm, the particle number concentrations during winter were mostly higher than in summer (up to 50%). The normalized particle number size distribution as a function of water temperature was examined for both winter and summer measurements. An increase in Tw from −1°C to 10°C during winter measurements showed a decrease in the peak of relative particle number concentration at about a Dp of 0.180μm, while an increase was observed for particles with Dp > 1μm. Summer measurements exhibited a relative shift to smaller particle sizes for an increase of Tw in the range 7–11°C. The differences in the shape of the number size distributions between winter and summer may be caused by different production of organic material in water, different local processes modifying the water masses within the fjord (for example sea ice production in winter and increased glacial meltwater inflow during summer) and different origin of the dominant sea water mass. Further research is needed regarding the contribution of these factors to the PMA production.

Using maximum entropy approach for prediction of drop size distribution in a pilot plant multi-impeller extraction contactor

RSC Advances ◽  
2015 ◽  
Vol 5 (116) ◽  
pp. 95967-95980 ◽  
Author(s):  
Mehdi Asadollahzadeh ◽  
Meisam Torab-Mostaedi ◽  
Shahrokh Shahhosseini ◽  
Ahad Ghaemi
Keyword(s):  
Maximum Entropy ◽  
Size Distribution ◽  
Pilot Plant ◽  
Drop Size ◽  
Maximum Entropy Principle ◽  
Drop Size Distribution ◽  
Size Distributions ◽  
Entropy Principle ◽  
Drop Size Distributions ◽  
Column Extractor

In this study, the maximum entropy principle is used to predict the drop size distributions in a multi-impeller column extractor.

scholarly journals Comparison between summertime and wintertime Arctic Ocean primary marine aerosol properties

2012 ◽  
Vol 12 (12) ◽  
pp. 31153-31186 ◽  
Author(s):  
J. Zábori ◽  
R. Krejci ◽  
J. Ström ◽  
P. Vaattovaara ◽  
A. M. L. Ekman ◽  
...  
Keyword(s):  
Sea Ice ◽  
Water Temperature ◽  
Arctic Ocean ◽  
Particle Number ◽  
Rate Of Change ◽  
The Arctic ◽  
Size Distributions ◽  
Data Set ◽  
Total Particle Number ◽  
Total Particle

Abstract. Primary marine aerosols (PMA) are an important source of cloud condensation nuclei, and one of the key elements of the remote marine radiative budget. Changes occurring in the rapidly warming Arctic, most importantly the decreasing sea ice extent will alter PMA production and hence the Arctic climate through a set of feedback processes. In light of this, laboratory experiments with Arctic Ocean water during both Arctic winter and summer were conducted and focused on PMA emissions as a function of season and water properties. Total particle number concentrations and particle number size distributions were used to characterize the PMA population. A comprehensive data set from the Arctic summer and winter showed a decrease in PMA concentrations for the covered water temperature (Tw) range between −1 °C and 15 °C. A sharp decrease in PMA emissions for a Tw increase from −1 °C to 4 °C was followed by a lower rate of change in PMA emissions for Tw up to about 6 °C. Near constant number concentrations for water temperatures between 6 °C to 10 °C and higher were recorded. Even though the total particle number concentrations changes for overlapping Tw ranges were consistent between the summer and winter measurements, the distribution of particle number concentrations among the different sizes varied between the seasons. Median particle number concentrations for Dp < 0.125 μm measured during winter conditions were similar (deviation of up to 3%), or lower (up to 70%) than the ones measured during summer conditions (for the same water temperature range). For Dp > 0.125 μm, the particle number concentrations during winter were mostly higher than in summer (up to 50%). The normalized particle number size distribution as a function of water temperature was examined for both winter and summer measurements. An increase in Tw from −1 °C to 10 °C during winter measurements showed a decrease in the peak of relative particle number concentration at about Dp of 0.180 μm, while an increase was observed for particles with Dp > 1 μm. Summer measurements exhibited a relative shift to smaller particle sizes for an increase of Tw in the range 7–11 °C. The differences in the shape of the number size distributions between winter and summer may be caused by different production of organic material in water, different local processes modifying the water masses within the fjord (like sea ice production in winter and increased glacial melt water inflow during summer) and different origin of the dominant sea water mass. Further research is needed regarding the contribution of these factors to the PMA production.

scholarly journals Urban aerosol number size distributions

2003 ◽  
Vol 3 (5) ◽  
pp. 5139-5184 ◽  
Author(s):  
T. Hussein ◽  
A. Puustinen ◽  
P. P. Aalto ◽  
J. M. Mäkelä ◽  
K. Hämeri ◽  
...  
Keyword(s):  
Particle Number ◽  
Number Concentration ◽  
Building Construction ◽  
Traffic Density ◽  
Urban Aerosol ◽  
Size Distributions ◽  
Accumulation Mode ◽  
Total Particle Number ◽  
Total Particle ◽  
Aitken Mode

Abstract. Aerosol number size distributions were measured continuously in Helsinki, Finland from 5 May 1997 to 28 February 2003. The daily, monthly and annual patterns were investigated. The temporal variation of the particle number concentration was seen to follow the traffic density. The highest total particle number concentrations were usually observed during workdays; especially on Fridays, and the lower concentrations occurred during weekends; especially Sundays. Seasonally, the highest total number concentrations were usually observed during winter and spring and the lowest during June and July. More than 80\\% of the particle number size distributions were tri-modal: nucleation mode (Dp < 30 nm), Aitken mode (20–100 nm) and accumulation mode (Dp > 90 nm). Less than 20% of the particle number size distributions have either two modes or consisted of more than three modes. Two different measurement sites are used; in the first place (Siltavuori, 5 May 1997–5 March 2001), the overall means of the integrated particle number concentrations were 7100 cm−3, 6320 cm−3, and 960 cm−3, respectively, for nucleation, Aitken, and accumulation modes. In the second site (Kumpula, 6 March 2001–28 February 2003) they were 5670 cm−3, 4050 cm−3, and 900 cm−3. The total number concentration in nucleation and Aitken modes were usually significantly higher during weekdays than during weekends. The variations in accumulation mode were less pronounced. The smaller concentrations in Kumpula were mainly due to building construction and also slight overall decreasing trend during these years. During the site changing a period of simultaneous measurements over two weeks were performed showing nice correlation in both sites.

scholarly journals Urban aerosol size distributions over the Mediterranean city of Barcelona, NE Spain

2012 ◽  
Vol 12 (22) ◽  
pp. 10693-10707 ◽  
Author(s):  
M. Dall'Osto ◽  
D.C.S. Beddows ◽  
J. Pey ◽  
S. Rodriguez ◽  
A. Alastuey ◽  
...  
Keyword(s):  
Particle Number ◽  
Number Concentration ◽  
Aerosol Size Distribution ◽  
Time Variability ◽  
Small Contribution ◽  
Particle Number Concentration ◽  
Size Distributions ◽  
Total Particle Number ◽  
Total Particle ◽  
One Year

Abstract. Differential mobility particle sizer (DMPS) aerosol concentrations (N13-800) were collected over a one-year-period (2004) at an urban background site in Barcelona, North-Eastern Spain. Quantitative contributions to particle number concentrations of the nucleation (33–39%), Aitken (39–49%) and accumulation mode (18–22%) were estimated. We examined the source and time variability of atmospheric aerosol particles by using both K-means clustering and Positive Matrix Factorization (PMF) analysis. Performing clustering analysis on hourly size distributions, nine K-means DMPS clusters were identified and, by directional association, diurnal variation and relationship to meteorological and pollution variables, four typical aerosol size distribution scenarios were identified: traffic (69% of the time), dilution (15% of the time), summer background conditions (4% of the time) and regional pollution (12% of the time). According to the results of PMF, vehicle exhausts are estimated to contribute at least to 62–66% of the total particle number concentration, with a slightly higher proportion distributed towards the nucleation mode (34%) relative to the Aitken mode (28–32%). Photochemically induced nucleation particles make only a small contribution to the total particle number concentration (2–3% of the total), although only particles larger than 13 nm were considered in this study. Overall the combination of the two statistical methods is successful at separating components and quantifying relative contributions to the particle number population.

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