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The concentration of black carbon (BC), measured in near-surface air on the territory of the Pechora-Ilych State Natural Biosphere Reserve (PISNBR) on the western side of the Northern Ural Mountains, far from sources, is presented for two years (December 2017–November 2019). The temporal variations in BC concentration throughout a year and the location of its main sources are analyzed. The average values for two cold and two warm half-years were 128 and 62 ng/m3, respectively. The BC concentration in near-surface atmosphere was compared with MERRA-2 reanalysis data. On a monthly scale, the anomalous increase in BC concentration during short-term smoke aerosol transport across the observation area is more clearly revealed from the reanalysis data, rather than by values measured at a single point. Daily monitoring allows us to detect the specific dates of such situations.

The content and evolution of brown carbon (BrC) in smokes from Siberian forest fires were analyzed using measurements of the aerosol absorption optical depth (AAOD) at three Russian AERONET stations located in Tomsk, Zvenigorod, and Yekaterinburg. Estimates are obtained of the relative contribution of BrC in fine aerosol particles to the absorption of solar radiation at a wavelength of 440 nm (ηBrC) and, in particular, for an anomalous episode of long-range transport of smokes from Siberia to the European part of Russia in summer 2016. A considerable BrC content is found in smokes in Tomsk and Zvenigorod (where ηBrC is estimated to be 15 and 18% on average). It is noteworthy that no significant ηBrC values were revealed during passage of smokes from Siberian fires over Yekaterinburg. The ηBrC values were found to decrease with aerosol aging under sunlit conditions on the characteristic timescale of about 30 h. At the same time, the measurements in Zvenigorod indicate that the absorption properties of the organic component of smoke aerosol increase during a much longer evolution.

We present model estimates of diurnally averaged direct radiative effects of smoke aerosol in the solar spectral range obtained using observations at the Tiksi station in the period of anomalously high black carbon (ВС) concentration in the near-surface atmospheric layer (July 2014). These data are compared with the radiative effect of aerosol tipical for summer conditions in this region. It is shown that the monthly average radiative effects, caused, on the one hand, by variations in the optical characteristics of background aerosol and, on the other hand, by short-term BC outflows from forest fires to the region of observations, are comparable in value.

Measurements (2012–2014) of black carbon (BC) concentration in the surface air in the region of Tiksi International Hydrometeorological Observatory, located near the delta of the Lena River, are analyzed. Variations in the BC concentration with different magnitudes and durations are revealed. Anomalous (larger than 1000 ng/m3) peaks of BC concentration are shown to be rarely encountered, predominately in the warm season of the year (May–September), for no longer than two days. The longest episodes of high BC concentration are associated with long-range atmospheric transport of wildfire products. During such episodes, the air temperature and radiation budget significantly change in the surface atmosphere. The increases in the surface air temperature on days when smoke aerosol comes from nearby fires in July may reach 10°C (at the climatic norm 10–11°C).

The most useful format to display the gathered information did not readily present itself. An obvious choice was to arrange the applications according to the pyrolytic technique described in the report. The sample preparation procedures were similar for both studies. Smoke aerosols of the materials of interest were produced in the laboratory under non-flaming or flaming combustion conditions, and the material produced collected on glass-fiber filters. In many cases, visual inspection of the spectra from simple mixtures could lead to the identification of the fuel materials. For more complex mixtures, however, extensive “crunching” of the data was necessary using pattern recognition techniques before judgments could be made as to what fuel mixture might have produced the smoke aerosol analyzed. An analytical problem of considerable interest to the military concerns the detection of bioaerosols — specifically the need for early warning of a foreign biological presence at perimeters of military posts, stations, airfields, and battlefields.

Record wildfires affected Australia from December 2019 to early 2020. Massive plumes of fire pollutants were lifted into the upper troposphere and even into the stratosphere by pyro-convection triggered by the intense heat of the fires. Subsequently the smoke aerosol was transported over thousands of kilometres eastwards at above 20 km altitude as Lidar observations in South America and satellite imagery show. Space and ground-based remote sensing of aerosol optical thickness indicate a temporary substantial increase in aerosol loading over large parts of the Southern Hemisphere, which offset the usual hemispheric contrast in aerosol. In addition to the massive impact on air quality at Australia’s east coast, this had important effects on the hemisphere-wide radiation budget.We investigate the dispersal of the fire smoke aerosol and its radiative effects with the global aerosol-climate model ECHAM6.3-HAM2.3. Biomass burning emissions are prescribed by daily satellite-based estimates from the Global Fire Assimilation System (GFAS). As the horizontal model resolution is too coarse to explicitly resolve convection, the injection height of Australian fire smoke is set to heights between 5 and 15 km and varied in terms of sensitivity studies. The model results for late 2019 and early 2020 are evaluated with ground and satellite remote sensing measurements, as well as contrasted with smoke results for years with low Australian wildfire emissions. The sensitivity results show how the fire injection heights affect the evolution of the smoke plume but also what role radiatively induced self-lifting plays. According to the model, the 2019/20 Australian wildfires considerably perturbed the radiation budget of the Southern Hemisphere. Due to large transport heights relative to clouds and a long lifetime of smoke particles in the stratosphere, the solar irradiance at ground averaged from January to March 2020 decreased by more than 1 W m-2 for the Southern Hemisphere, which corresponds roughly to the short-term cooling caused by a large volcanic eruption, while the elevated smoke layers experienced significant absorptive heating.Considering the recent series of extreme wildfires globally and their probably further increasing occurance in a changing climate, these results indicate a need for larger attention to pyro-convection in global climate modelling.

The report presents the results of a comprehensive experiment on the study of the atmosphere over Lake Baikal, which was carried out in July - August 2019. Remote investigation of aerosol content in the troposphere was carried out using mobile lidars. One of the lidars was installed on board the research vessel «Academician Koptyug». The route of the vessel covered the entire water area of the lake. The second lidar for the entire duration of the experiment was located on the southeastern shore of Lake Baikal. The period of the experiment coincided with extensive forest fires in Eastern Siberia. The lidar data made it possible to reconstruct the spatiotemporal distribution of the smoke aerosol over the Baikal water area and estimate its optical depth, the values of which, in extreme cases, reached up to τ ≈4.

Highly frequent wildfires are observed every year in Yunnan province, China. This study investigated the smoke injection height in a wildfire event using multi-source remote sensing data in Yunnan. The wildfire event was identified and characterized by combining MODIS and Landsat-8 data. The smoke injection height of the event and the vertical profile of smoke aerosol were inferred from CALIPSO data. The results showed that although the burned areas were only 167.67 ha, the maximum smoke injection height of the wildfire event can reach approximately 4.63 km above sea level. In addition, by comparing the smoke injection height with that of other types of fire events, we found that the plumes of the wildfire event in Yunnan were the most likely candidates for injecting smoke into the free troposphere and producing smoke transport. This study has significant implications for understanding the impact of wildfire smoke plumes on air quality in Yunnan.

Shortwave-absorbing aerosols seasonally overlay extensive low-level stratocumulus clouds over the southeast Atlantic. While much attention has focused on the interactions between the low-level clouds and the overlying aerosols, few studies have focused on the mid-level clouds that also occur over the region. The presence of mid-level clouds over the region complicates the space-based remote-sensing retrievals of cloud properties and the evaluation of cloud radiation budgets. Here we characterize the mid-level clouds over the southeast Atlantic using lidar- and radar-based satellite cloud retrievals and observations collected in September 2016 during the ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) field campaign. We find that mid-level clouds over the southeast Atlantic are relatively common, with the majority of the clouds occurring between altitudes of 5 and 7 km and at temperatures between 0 and −20 ∘C. The mid-level clouds occur at the top of a moist mid-tropospheric smoke-aerosol layer, most frequently between August and October, and closer to the southern African coast than farther offshore. They occur more frequently during the night than during the day. Between July and October, approximately 64 % of the mid-level clouds had a geometric cloud thickness less than 1 km, corresponding to a cloud optical depth of less than 4. A lidar-based depolarization–backscatter relationship for September 2016 indicates that the mid-level clouds are liquid-only clouds with no evidence of the existence of ice. In addition, a polarimeter-derived cloud droplet size distribution indicates that approximately 85 % of the September 2016 mid-level clouds had an effective radius less than 7 µm, which could further discourage the ability of the clouds to glaciate. These clouds are mostly associated with synoptically modulated mid-tropospheric moisture outflow that can be linked to the detrainment from the continental-based clouds. Overall, the supercooled mid-level clouds reduce the radiative cooling rates of the underlying low-altitude cloud tops by approximately 10 K d−1, thus influencing the regional cloud radiative budget.

Above-low-cloud aerosol (ACA) has important impacts on low clouds bellow. Based on the satellite data from 2007 to 2010, this study analyzed the relationship between ACA optical depth (OD), ACA occurrences and low cloud integrated color ratio (CR) over tropic Atlantic region where ACA frequently occurs. The results show that, the integrated attenuated CR (IACR) of low cloud is about 30%-50% larger over smoke region in smoke outbreak seasons than other regions or seasons. However, the IACR of low cloud over dust region shows small difference between dust outbreak seasons and other seasons. It indicates that above-low-cloud smoke aerosol can introduce stronger color effect than dust. The integrated corrected CR (ICCR) of low cloud tends to decrease with increasing above-cloud dust OD, while the low cloud ICCR shows weak relationship with above-low-cloud smoke OD. And, the above-low-cloud dust aerosol could introduce strong microphysics effect, that is, the low cloud droplet size may decrease with increasing burden of dust aerosol above.

Biomass burning emits vapors and aerosols into the atmosphere that can rapidly evolve as smoke plumes travel downwind and dilute, affecting climate- and health-relevant properties of the smoke. To date, theory has been unable to explain variability in smoke evolution. Here, we use observational data from the BBOP field campaign and show that initial smoke concentrations can help predict changes in smoke aerosol aging markers, number, and diameter. Because initial field measurements of plumes are generally > 10 minutes downwind, smaller plumes will have already undergone substantial dilution relative to larger plumes. However, the extent to which dilution has occurred prior to the first observation is not a measurable quantity. Hence, initial observed concentrations can serve as an indicator of dilution, which impacts photochemistry and aerosol evaporation. Cores of plumes have higher concentrations than edges. By segregating the observed plumes into cores and edges, we infer that particle aging, evaporation, and coagulation occurred before the first measurement, and we find that edges generally undergo higher increases in oxidation tracers, more decreases in semivolatile compounds, and less coagulation than the cores.

Multiyear (1995-2018) time series of photometer observations of characteristics of aerosol optical depth (AOD) and columnar water vapor of the atmosphere are used to analyze the specific features of their seasonal and interannual variations, taking into consideration the results, obtained in the last four years. It is noted that the annual AOD behavior persistently exhibits two maxima (in spring and summer periods), mainly attributed to the increased content of fine-mode smoke aerosol. The interannual variations in AOD and in concentration of coarse-mode particles show a statistically significant trend, with the decreases being, on the average, respectively about 0.013 and 0.006 μm3/μm2 per decade.

We present estimates of direct radiative effects (DRE) for background and smoke aerosol in the IR spectral region. The estimates are obtained using an original Monte Carlo algorithm and OPAC models for typical summer conditions and smoke haze conditions on the territory of Siberia in 2012. It is shown that the DRE value at the atmospheric boundaries in the thermal spectral region is approximately 3% of the daily mean radiation effect in the solar spectral region under background conditions, and 10–15% under conditions of strong turbidity.

We discuss the results of spectral measurements of aerosol optical depth (AOD) of the atmosphere, carried out in warm periods of 2011–2016 in the Arctic settlement Barentsburg (Spitsbergen Archipelago). The statistical characteristics of seasonal and interannual variations in atmospheric AOD in the wavelength range of 0.34–2.14 μm are presented. The average AOD (0.5 μm) over the six-year period of observations had been 0.086, and, in particular, the fine mode AOD component had been 0.062 and the coarse mode AOD component had been 0.024. It is shown that the seasonal variations were best manifested in the decrease of modal (most probable) values of fine mode AOD component from 0.055 in spring to 0.025 in autumn. As compared to the preceding (pre-2011) period, we noted a closer convergence in the average AOD values between spring and summer, primarily due to a decrease in the content of fine mode aerosol in spring and its increase in summer. The summertime AOD growth is most likely due to episodic outflows of smoke aerosol from boreal zones of Eurasia and North America.

Indonesia has experienced frequent fires due to the lowering of groundwater levels caused by drainage via extensive canal networks for agricultural development since the 1970s. However, the impact of canals on fire emissions is still poorly understood. Here we investigate canal impacts on smoke aerosol emissions for Indonesian peatland and non-peatland fires by quantifying the resulting changes of smoke aerosol emission coefficient (Ce) that represents total aerosol emissions released from per unit of fire radiative energy. First, we quantified the impacts of canal drainage and backfilling on water table depth (WTD) variations using field data and then expanded such impacts from field to regional scales by correlating field WTD to satellite terrestrial water storage (TWS) anomalies from Gravity Recovery and Climate Experiment. Second, we estimated Ce from fire radiative power and smoke-aerosol emission rates based on Moderate Resolution Imaging Spectroradiometer active fire and multi-angle implementation of atmospheric correction aerosol products. Finally, we evaluated the Ce variation with TWS anomalies. The results indicate: (a) Ce is larger in peatland fires than in non-peatland fires; (b) Ce increases significantly as TWS anomalies decrease for both peatland and non-peatland fires; and (c) Ce changes at nearly twice the rate in peatland for a given TWS anomaly range as in non-peatland. These phenomena likely result from the different fuel types and combustion phases prevalent under different moisture conditions. These findings support the Indonesian government’s recent peatland restoration policies and pave the way for improved estimation of tropical biomass burning emissions.

The paper presents the results of studies of air mass and smoke aerosol transport using the HYSPLIT, NAAPS models and data of remote sensing CALIPSO during the forest fires in 2016 in Baikal region. In June 2016 the homogeneous filling of the atmosphere by smoke aerosol over the Baikal region up to 2 km was observed. It is revealed that in the spectra of particle size distribution the large particles of the submicron aerosol fraction with a diameter exceeding 200 nm are observed, typical for smoke particles. The results of trajectories calculation have shown that in June influence of local fire on air quality in Ulan-Ude was observed under the general northwest transport of a smoke aerosol, in July downwind was mainly from the Irkutsk, Krasnoyarsk and the Yamalo-Nenets regions.

A technique is proposed for determining of the large-scale smoke aerosol fluxes using a wind field reanalysis data and the satellite monitoring data of the aerosol optical depths and the vertical profile of the attenuation coefficient. The directions of the long-range transport of the Siberian smoke haze fragments were determined in July 2016. The maximum large-scale mass fluxes and the total mass of the smoke aerosol during the transfer of air masses through the Ural meridian to the west (0.38*106 ton/day and 1.38*106 tons) and through the 115ºE meridian to the east (0.26*106 ton/day and 0.72*106 tons) were estimated.

Comprehensive observational experiments on atmospheric aerosol particles were conducted over Nanjing. Aerosol particles were detected vertically in real time by polarization micro pulse lidar (PMPL). To improve the accuracy of the lidar ratio, we combined observational data from ground-based polarization lidar and a sun photometer. Furthermore, the influence of meteorological conditions on vertically-resolved aerosol optical properties was analyzed. On the other hand, sources of aerosol pollution were analyzed using backward air mass trajectory, the potential and source contribution function (PSCF) and concentration weighted trajectory (CWT) models. Aerosol types were identified from PMPL data, sun photometer and cloud-aerosol lidar and infrared pathfinder satellite observations (CALIPSO). Accordingly, a large number of coarse-mode aerosol particles (pure sand-dust particles predominate) from North China appeared in spring, and smoke aerosol particles were generated from biomass combustion in autumn. The study shows that the local emission and regional transport are both important contributors to aerosol pollution events.

The results of measurements of the aerosol optical depth (AOD) of the atmosphere carried out in 66th and 67th cruises of RV “Akademik Mstislav Keldysh” (Kara and Barents Seas) and at Russian scientific center in Barentsburg (Svalbard) during polar summer of 2016 are analyzed. It is shown that the level of aerosol turbidity of the atmosphere was close to the long-term average data in arctic latitudes. The mean value of AOD(0.5 μm) obtained from shipborne measurements is 0.065±0.056 and analogous value in Barentsburg is 0.072±0.040. The smoke plumes of forest fires on the continent significantly affected the atmospheric turbidity during measurements. For example, the contribution of smoke aerosol in the mean value of AOD (0.5 μm) obtained onboard the ship is about 44%.

Considered are the conditions of the natural illuminance of Moscow during the period of smoke haze caused by forest and peat-bog fires in summer 1972,2002, and 2010. Assessed is the impact of such extreme conditions on total, scattered, and direct illuminance. The main attention is paid to the illuminance attenuation due to the smoke haze in the case of few-cloud weather. It is demonstrated that if smoke aerosol is present, direct illuminance decreases by 70% on average and total illuminance, by 30% as compared with similar conditions on the days with typical aerosol. Small increase in scattered illuminance is observed (by 45–90%). The analysis of illuminance in the cases of the haze of various intensity demonstrated that in the case of very intensive smoke screening, direct illuminance decreased to zero, total illuminance, by 70%, and increase in scattered illuminance slowed down. On such days horizontal visibility was equal to 100–200 m like under the conditions of thick fog.

In vitro test methods may be vital in understanding tobacco smoke, the main toxicants responsible for adverse health effects, and elucidating disease mechanisms. There is a variety of ‘whole smoke’ exposure systems available for the generation, dilution and delivery of tobacco smoke in vitro; these systems can be procured commercially from well-known suppliers or can be bespoke set-ups. These exposure technologies aim to ensure that there are limited changes in the tobacco smoke aerosol from generation to exposure. As the smoke aerosol is freshly generated, interactions in the smoke fractions are captured in any subsequent in vitro analysis. Of the commercially available systems, some have been characterised more than others in terms of published scientific literature and developed biological endpoints. Others are relatively new to the scientific field and are still establishing their presence. In addition, bespoke systems are widely used and offer a more flexible approach to the challenges of tobacco smoke exposure.In this review, the authors present a summary of the major tobacco smoke exposure systems available and critically review their function, set-up and application for in vitro exposure scenarios. All whole smoke exposure systems have benefits and limitations, often making it difficult to make comparisons between set-ups and the data obtained from such diverse systems. This is where exposure and dose measurements can add value and may be able to provide a platform on which comparisons can be made. The measurement of smoke dose, as an emerging field of research, is therefore also discussed and how it may provide valuable and additional data to support existing whole smoke exposure set-ups and aid validation efforts.

Smoke transport patterns over the Maritime Continent (MC) are studied through a combination of approaches, including a) analyzing AODs obtained from satellite products; b) aerosol transport modeling with AOD assimilation along with the atmospheric flow patterns; c) analyzing smoke wet deposition distributions; and d) examining forward trajectories for smoke events defined in this study. It is shown that smoke transport pathways are closely related to the low-level atmospheric flow, i.e., during June–Sept, smoke originating from the MC islands with a dominant source over central and southern Sumatra, and southern and western Borneo, is generally transported northwestward south of the equator and northeastward north of the equator with the cross-equatorial flow, to the South China Sea (SCS), the Philippines and even further to the western Pacific. During the October–November transitional period, smoke transport paths are more zonally oriented compared to June–September. Smoke originating from Java, Bali, Timor etc, and southern New Guinea, which are in the domain of easterlies and southeasterlies during the boreal summer (June–November), is generally transported westward. It is also found that smoke transport over the MC exhibits multi-scale variability. Smoke typically lives longer and can be transported farther in El Nino years and later MJO phases compared with non El Nino years and earlier MJO phases. During El Nino periods there is much stronger westward transport to the east tropical Indian Ocean. Finally, orographic effect on smoke transport over the MC is also clearly discernable.

The paper presents the results of investigations of temporal variations of the vertical structure of aerosol fields in the mountain valley of Lake Baikal, in the presence of smokes from both far and local wildfires. The measurements were carried out using the "LOSA-M2" lidar arranged on the eastern coast of Lake Baikal, during the expeditions of 2013 and 2015, when the extremely high values of the aerosol content in the troposphere due to forest fires were observed. A significant difference exists between the spatial-temporal structure of the smoke aerosol fields of local forest fires in the lake water area and the case when the sources of admixtures are located at a considerable distance.

Research has shown that cigarette smoke changes chemically and physically after it is released into indoor air, that these changes can increase secondhand smoke (SHS) toxicity, and that acute exposures to even low levels of SHS increase the risk of cardiopulmonary disease. We designed a system to reproduce realistic SHS exposures in the laboratory for use in controlled human exposure studies. We generated cigarette smoke with a smoking machine, diluted it and conducted it through a 6 m3 stainless steel flow reactor at rates equivalent to the upper ranges of normal residential air exchange rates, to create aged cigarette smoke as a model for secondhand cigarette smoke. We observed that approximately 50% of the particle mass deposited within the system and that particle deposition percentage was higher when absorbent materials were placed within the system. The particle size ranges and deposition percentages, coefficients and velocities observed for this smoke aerosol are in good agreement with published va...

Estimates of some aerosol and radiation characteristics of the atmosphere in the summer of 2010 are obtained according to the results of the measurements made at the Meteorological Observatory (MO) at Moscow State University and are compared with the results of the measurements performed in 2002 and 1972 during the forest and peat fires. In contrast to 1972 and 2002, the period under study in 2010 is characterized by a greater frequency of the highest class of fire danger according to Nesterov, higher aerosol optical depths of the atmosphere up to 4.6, and a more significant weakening of solar radiation in different spectrum regions. In 2010 the smoke aerosol caused losses of the total shortwave radiation of 33%, visible radiation of 39%, ultraviolet radiation of 300–380 nm of 51%, and erythemal radiation of 63%. At the same time, an increase in the downward long-wave radiation to 40–50 W/m2 under extreme aerosol optical depths is recorded.

In early May 2006 a record high air pollution event was observed at Ny-Ålesund, Spitsbergen. An atypical weather pattern established a pathway for the rapid transport of biomass burning aerosols from agricultural fires in Eastern Europe to the Arctic. Atmospheric stability was such that the smoke was constrained to low levels, within 2 km of the surface during the transport. A description of this smoke event in terms of transport and main aerosol characteristics can be found in Stohl et al. (2007). This study puts emphasis on the radiative effect of the smoke. The aerosol number size distribution was characterised by lognormal parameters as having an accumulation mode centered around 165–185 nm and almost 1.6 for geometric standard deviation of the mode. Nucleation and small Aitken mode particles were almost completely suppressed within the smoke plume measured at Ny-Ålesund. Chemical and microphysical aerosol information obtained at Mt. Zeppelin (474 m a.s.l) was used to derive input parameters for a one-dimensional radiation transfer model to explore the radiative effects of the smoke. The daily mean heating rate calculated on 2 May 2006 for the average size distribution and measured chemical composition reached 0.55 K day−1 at 0.5 km altitude for the assumed external mixture of the aerosols but showing much higher heating rates for an internal mixture (1.7 K day−1). In comparison a case study for March 2000 showed that the local climatic effects due to Arctic haze, using a regional climate model, HIRHAM, amounts to a maximum of 0.3 K day−1 of heating at 2 km altitude (Treffeisen et al., 2005).

For many decades dioctyl phthalate (DOP), a common industrial material, has been used by the U.S. Army and other agencies to simulate aerosol behavior in nondestructive gas mask and filter serviceability testing, and for related test purposes. Techniques are completely standardized. But DOP is now considered to be a potentially hazardous material. The research reported here, which was performed using ATI Q-127 and TDA-100 “hot smoke” aerosol penetrometer test machines, identified relatively innocuous, inexpensive replacement materials for DOP. One of these, a synthetic hydrocarbon (poly-alpha olefin [PAO]), can be used to replace DOP directly with minimum impact upon existing hardware and procedures. Of more than two dozen candidate replacement materials that were tested, isostearic acid and oleic acid also performed well as DOP replacements. All three materials also show promise for cold smoke testing applications

The endurance of fog oil (FO) as a choice training smoke is credited to its advantageous characteristics, which lead to optimum obscuration of troops and mechanized equipment as well as its cost efficiency, safety, and ease of handling. Fog oil's popularity, however, has been impacted by environmental regulation of smoke aerosol emissions under the Clear Air Act (CAA). Potential violation of the CAA by use of FO has lead to a request for further understanding of technical data describing the characteristics and behavior of FO droplets/particles and plumes. Selected sources of Army-funded research have been reviewed and summarized in this report.

For the purpose of understanding the smoke detector's response to enclosure fires, a computational model for predicting the evolution of the local concentration and size distribution of smoke aerosol is presented. The model util izes the characteristic of smoke aerosol that the large size part of the size distribution is not significantly affected hy coagulation and that its size distribution takes a virtually time-independent reduced form. B, numerically solving the conservation equations of total particle volume and total particle number, the size distribution of the smoke aerosol is determined by the reduced expression of the size distribution where the total particle volume and the total particle number are the parameters. The results of sample calculations and relevant experiments showed a reasonable agreement.