J. Meteor. Res.  2013, Vol. 28 Issue (6): 832-848   PDF    
The Chinese Meteorological Society

Article Information

LU Chunsong, LIU Yangang, NIU Shengjie, ZHAO Lijuan, YU Huaying, CHENG Muning. 2013.
Examination of Microphysical Relationships and Corresponding Microphysical Processes in Warm Fogs
J. Meteor. Res., 28(6): 832-848

Article History

Received July 30, 2013
in final form September 4, 2013
Examination of Microphysical Relationships and Corresponding Microphysical Processes in Warm Fogs
LU Chunsong1, 2, 3 , LIU Yangang3, NIU Shengjie1, ZHAO Lijuan4, YU Huaying1, CHENG Muning5    
1 Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2 State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China;
3 Atmospheric Sciences Division, Brookhaven National Laboratory, NY 11973, US;
4 Xiamen Environmental Monitoring Central Station, Xiamen 361004, China5 Second Institute of Environmental Assessment, Jiangsu Provincial Academy of Environmental Science, Nanjing 210000, China
ABSTRACT:In this paper, the microphysical relationships of 8 dense fog events collected from a comprehensive fog observation campaign carried out at Pancheng (32.2°N, 118.7°E) in the Nanjing area, China in the winterof 2007 are investigated. Positive correlations are found among key microphysical properties (cloud droplet number concentration, droplet size, spectral standard deviation, and liquid water content) in each case, suggesting that the dominant processes in these fog events are likely droplet nucleation with subsequent condensational growth and/or droplet deactivation via complete evaporation of some droplets. The abrupt broadening of the fog droplet spectra indicates the occurrence of the collision-coalescence processes as well, although not dominating. The combined effects of the dominant processes and collision-coalescence on microphysical relationships are further analyzed by dividing the dataset according to visibility or autocon-version threshold in each case. The result shows that the specific relationships of number concentration to volume-mean radius and spectral standard deviation depend on the competition between the compensation of small droplets due to nucleation-condensation and the loss of small droplets due to collision-coalescence. Generally, positive correlations are found for different visibility or autoconversion threshold ranges in most cases, although negative correlations sometimes appear with lower visibility or larger autoconversion threshold. Therefore, the compensation of small droplets is generally stronger than the loss, which is likely related to the sufficient fog condensation nuclei in this polluted area.
Keywordsfog microphysics     microphysical relationships     physical processes     observations    
1. Introduction

Fog is a severe environmental hazard that greatlyinfluences trafic, human health, and agriculturalproducts, resulting in heavy economic losses(Gultepe et al., 2007; Tardif and Rasmussen, 2007; Haeffelin et al., 2010; Niu et al., 2010a; Zhang, 2012). To reducethe losses, accurate fog forecast is necessary, and numerical forecast/simulation of fog events has attractedgreat efforts among researchers(Kong, 2002; Fu et al., 2006, 2008; Bergot et al., 2007; Gao et al., 2007;Roquelaure and Bergot, 2008; Rémy and Bergot, 2010;Shi et al., 2010, 2012; Yang et al., 2010; Zhou and Du, 2010; Kim, 2011; Porson et al., 2011; Jia and Guo, 2012; Li et al., 2012; Stolaki et al., 2012; Thoma et al., 2012; Zhou et al., 2012). Whether the numerical forecast is accurate or not depends greatly on theparameterization of complicated physical processes infog events(Croft et al., 1997; Li et al., 1997; Gultepe et al., 2007). To explore the macro and micro physicalprocesses, it is important to detect fog/cloud microphysical properties because different macro and microprocesses affect fog/cloud size distributions and hencekey microphysical properties(Li et al., 1994, 1999;Liu et al., 2008). Furthermore, microphysical properties affect visibility, an important factor in fog forecast. Many researchers related visibility to liquid water content(LWC)(e. g., Eldridge, 1971; Tomasi and Tampieri, 1976; Pinnick et al., 1978; Kunkel, 1984;Bergot and Guedalia, 1994; Stoelinga and Warner, 1999); more recently, Gultepe et al.(2006)extendedthe parameterization and related visibility to bothLWC and droplet number concentration(N). Achtemeier(2008)also discussed the relationship of visibility to fog microphysics. Therefore, studying of fogmicrophysics is necessary and important to improvement of fog forecast and reduction of losses due to fogdisasters.

In the past several decades, great efforts havebeen devoted to in situ observational studies on fog microphysics(Pilié et al., 1975; Roach et al., 1976; Meyer et al., 1986; Gerber, 1991; Fuzzi et al., 1992; Wendisch et al., 1998; Gultepe et al., 2006; Lu and Niu, 2008;Haeffelin et al., 2010; Niu et al., 2010c; Price, 2011;Yue et al., 2012, 2013; Zhang et al., 2013). In mostfog cases, LWC is lower than 0. 5 g m-3(e. g., Wobrock et al., 1992; Niu et al., 2010b); N is from a fewtens to several hundreds per cubic centimetre(García-García and Montañez, 1991; Klemm and Wrzesinsky, 2007; Gultepe et al., 2009; Liu et al., 2011; Zhao et al., 2013; Zhou et al., 2013), but N larger than1000 cm-3 is also found in some polluted areas(Li, 2001; He et al., 2003; Niu et al., 2010b); both unimodal(García-García and Montañez, 1991; Li, 2001;Niu et al., 2010c; Gonser et al., 2012) and bimodal(Hong and Huang, 1965; Pilié et al., 1975; Roach et al., 1976; Meyer et al., 1980; Gerber, 1991; Wendisch et al., 1998; Huang et al., 2000; Gultepe et al., 2009;Niu et al., 2012)size distributions have been observedin different fog cases. Furthermore, during individual fog events, remarkable spatial and temporal variations of microphysical properties have been widely reported. Spatially, similar to inhomogeneity in clouds(e. g., Baumgardner et al., 1993; Burnet and Brenguier, 2007; Haman et al., 2007), García-García et al.(2002)found inhomogeneous fog microphysical structures on a fine scale(less than 1 m). Temporally, inaddition to evident lifecycle variation, quasi-periodicoscillations of the microphysical properties and otherrelated meteorological elements(e. g., temperature and wind speed)have been observed and simulated; different mechanisms for the quasi-periodic oscillationswere proposed by different scholars, such as a cycleof fog dissipation and redevelopment processes associated with radiative cooling and turbulence(Welch et al., 1986), interaction between radiation-induceddroplet growth and subsequent depletion of dropletsdue to gravitational settling(Bott et al., 1990; Huang et al., 2000), advection of fog inhomogeneous spatialstructure(Roach et al., 1976), and effect of gravitywave(Roach, 1976; Duynkerke, 1991). Fog dropletsize distributions also have significant variability dueto the effects of different processes, such as activation, diffusional growth of droplets, turbulent mixing, gravitational settling(Niu et al., 2010b), etc. For example, explosive broadening of droplet size distributions havebeen found in observations(Pu et al., 2008; Lu et al., 2010a; Niu et al., 2012), which is directly relatedto microphysical processes, and is further related tomacro conditions, such as cooling due to invasion ofweak cold air, cooling due to long wave radiation, and water vapor advection.

Although the importance of fog microphysics and related processes has been recognized and considerableprogress has been made, much remains elusive. For example, it is still unclear what processes are the mainprocesses in determining fog droplet size distributions. To fill this gap, 8 fog events observed at Pancheng(32°12'N, 118°42'E), Nanjing, China in 2007 are studied to examine the microphysical relationships and main and minor physical processes. The results willbe helpful to improve theoretical underst and ing of fogphysics and parameterization of fog/cloud physics inmodels.

In addition, past fog observations in China werelargely based on gelatin-slide impactor systems witha low sampling rate(Niu et al., 2010b). A dropletspectrometer(FM-100; Droplet Measurement Technologies, Colorado, USA)with a sampling rate of 1 Hzwas deployed at Pancheng in 2007. The data collectionfrom this spectrometer provides a great opportunity toexamine fog microphysics and the corresponding physical processes. Furthermore, Nanjing is a megacity inthe Yangtze River Delta of China with high population density and a well-developed economy; urbanization has brought great stress to the local environment and emissions of pollutants(SO2, NOx, and NH3)areone or two orders of magnitude higher than in Europe and South America(Lu et al., 2010b). Fog occurringin such a polluted environment is expected to showunique microphysical characteristics, compared withfogs in clean areas.

The rest of the paper is organized as follows. Section 2 briefly describes the observation site, the keyinstruments, and the data. Section 3 presents themain results, including the general features of key microphysical properties and their mutual relationshipsunder different conditions, and the discussion on themain and minor microphysical processes. Concludingremarks are presented in Section 4. 2. Observation site and data

The sampling site is located at Pancheng(32°12'N, 118°42'E; 22 m above sea level)in Nanjing. This area is unique from several perspectives(Fig. 1). It is located to the north of the Yangtze River and adjacent to the Jiajiang River, which is a tributary of theYangtze River. Furthermore, it is close to heavy pollution sources such as petrochemical factories, a steelplant, a thermal power station, a nitrogenous fertilizerplant, and highways. Further details can be foundin Lu et al.(2010b). The data used in this studywere collected from 15 November through 29 December 2007.

Fig. 1. Map of the observation site Pancheng and its vicinity.

Similar to the observations at the same site in2006(Liu et al., 2010; Niu et al., 2010c), visibilitywas automatically measured and recorded every 15s by a visibility meter(ZQZ-DN; the Radio Scientific Research Institute, Wuxi, Jiangsu, China); surface meteorological quantities(surface air temperature, relative humidity, wind speed, and wind direction)were observed with an automatic weather station(EnviroStationTM, ICT International Pty Ltd, Armidale, New South Wales, Australia); the size distributions of fog droplets were measured with a dropletspectrometer(FM-100)(Eugster et al., 2006; Gultepe et al., 2009). It measures fog droplets of 0. 5-25 μm inradius at a sampling rate of 1 Hz, but the data fromthe bin 0. 5-1. 0 μm are thought to be noisy, which arenot included in the calculations of microphysical properties such as N, volume-mean radius(rv), st and arddeviation(σ), and LWC. The dataset is averaged to 1min for this study. 3. Results3. 1 General microphysical characteristics

A total of 8 typical dense fog episodes were observed during the campaign in 2007. The eight casesshared some common features of synoptic weatherbackground. At 500 hPa, Nanjing was often located atthe front of an aerological weak trough or in straightnorthwest wind. At mid and low levels, Nanjing wasoften controlled by local vortex shear and southwesterly wind. On the surface maps, Nanjing was basicallyin a uniform-pressure region in front of a high pressuresystem or influenced by a high pressure system movinginto the sea. Table 1 shows the duration, the surfaceair temperature, and the microphysical properties inthese cases. The durations of these cases are in therange of 4. 3-25. 3 h, and all the cases except case 7have severe fog periods which are defined in light ofvisibility(vis)< 50 m(China Meteorological Administration, 2007). According to the review of fog researchby Gultepe et al.(2007), Petterssen(1956)suggestedthat fog can be divided into three subsections: liquid fog(temperature ≥ -10℃), mixed phase fog(-30℃≤ temperature < -10℃), and ice fog(temperature< -30℃); it follows that the events observed in ourexperiments are all liquid fogs with average temperature above 0℃.

Table 1. The duration, surface air temperature, and key microphysical properties in the eight fog cases

In each case, N, LWC, rv, and σ have large st and ard deviations due to both the spatial inhomogeneousstructure(García-García et al., 2002)of the fog and the temporal evolution at different stages in each fogevent. Peak radius(rp)is unique, always at 1. 4 μm;this peak is not a real peak because it is at the firstbin, but we still call it "peak" for convenience; similarspectral shape(peak at 1. 4 μm)was also observedby García-García and Montañez(1991) and Gonser etal.(2012); more discussion about the formation ofthe peak will be given later. Because of the peak atthe first bin, the average values of rv are smaller thanthe results observed in Sierra Madre Oriental, Mexico(García-García and Montañez, 1991) and in Picodel Este, Puerto Rico(Eugster et al., 2006). Althoughthe average N is generally comparable with the resultsreported by Gultepe et al.(2009), the maximum N(around 800 cm-3)is much higher, caused by the highpollution level at this site(Lu et al., 2010b; Yang et al., 2012). Generally, the average LWC is comparable withthat in the fogs in Pico del Este, Puerto Rico(Eugster et al., 2006) and Fichtelgebirge, Germany(Thalmann et al., 2002). Compared with the fog at the samesite in 2006(Niu et al., 2010c), the cases in this studyhave the same rp, smaller N, LWC, rv, and σ. It isnoteworthy that the same droplet spectrometer(FM100)was used in the above observations, except the observation in Sierra Madre Oriental, Mexico, where Forward Scattering Spectrometer Probe(FSSP)(GarcíaGarcía and Montañez, 1991)was used; however, FSSPis similar to FM-100. The similar or same instrumentsassure more reliable comparisons. 3. 2 The dominant microphysical processes

As mentioned above, fog/cloud droplet size distributions and hence the key microphysical properties(N, LWC, rv, and σ)are determined by different physical mechanisms; different relationships among thesemicrophysical properties are expected in response todifferent physical mechanisms(Liu et al., 2008; Liu et al., 2011). Therefore, to examine the physical mechanisms, microphysical relationships among N, LWC, rv, and σ are analyzed. Table 2 shows that these rela-tionships are all positive in the 8 cases. Figure 2 showscase 6 as an example. The reason for choosing case 6is that generally speaking, the values of microphysicalproperties(Table 1) and correlation coeficients(Table 2)for this case are in the middle of the 8 cases. The positive correlation between rv and N is oppositeto some previous fog observations(e. g., Huang et al., 2000; Niu et al., 2010b; Li et al., 2011)or cloud observations(e. g., Wang et al., 2009). Collision-coalescenceis not likely to be responsible for such a phenomenon, because if dominantly affected by collision-coalescence, droplet size(e. g., rv)would be expected to be negatively correlated with N. The dominant processesseem to be droplet activation with subsequent condensational growth and /or droplet deactivation via somecomplete droplet evaporation. Similar conclusion wasalso drawn in the fog case in 2006(Niu et al., 2010c). In addition, the fog in situ observation at Wuqing(39°24'N, 117°03'E)between Beijing and Tianjin inChina, also shows positive correlations between liquid water content, droplet number concentration, and droplet size in three polluted fog cases(Quan et al., 2011).

Table 2. Correlation coe±cients of the relationships among the key microphysical properties of the eight fog cases

To further discern the factors affecting microphysical relationships, the dataset is divided into twogroups for each case based on visibility: mature stage(0 m < vis ≤ 500 m) and formation stage(500 m rv vs. N and σ vs. Nare negatively correlated, and σ vs. rv and LWC vs. N are positively correlated in each case; the relation-ships of σ vs. LWC and LWC vs. rv are differentfrom case to case, negatively, positively, or not correlated. As an example, Fig. 2 shows the microphysicalrelationships for these two visibility groups in case 6. Compared with that in the mature stages and in thewhole fog dataset(Table 2), the different behaviorsof microphysical relationships in the formation stagesare likely related to the low and almost constant LWC. The LWC is a measure of available water vapor in air, which can be condensed into liquid water under certainenvironmental conditions, such as appropriate watervapor mixing ratio, air temperature, and air pressure. In the 8 cases, temperature gradually decreases and relative humidity is 100% at the formation stage with500 m < vis < 1000 m; fog forms but LWC increasesslowly, close to 0. The competition for the limitedLWC is expected to be remarkable because fog condensation nuclei are considered as suficient due to thepollutant emission from the nearby industrial park(Lu et al., 2010b) and the high water-soluble fraction ofaerosol in this area(Wang et al., 2002, 2003). As aresult, most droplets are small droplets and concentrated in the first bin(Fig. 3), decreasing rv and σwith an increase in N. The complicated relationshipof LWC to other properties is also probably related tothe nearly constant LWC. In the mature stages, LWCis positively correlated to N, σ, and rv(Fig. 2), indicating that the available water vapor is suficient and the competition for water vapor is weak. Therefore, LWC is an important factor affecting the effect of thedominant processes, such as droplet activation withsubsequent condensational growth and /or droplet deactivation via some complete droplet evaporation, on microphysical relationships. Zhang et al.(2011)alsofound that the value of LWC greatly affects the nucleation of aerosol, cloud number concentration, and droplet size.

Fig. 2. Relationships(a)between the volume-mean radius(rv) and the droplet number concentration(N), (b)betweenthe st and ard deviation(σ) and N, (c)between σ and rv, (d)between σ and LWC, (e)between LWC and N, and (f)between LWC and rv, for two visibility(vis)ranges in case 6.
Fig. 3. Average size distributions for two visibility(vis)ranges in case 6.
3. 3 The combined effect of the dominant processes and collision-coalescence

The dominance of droplet nucleation with subsequent condensational growth and /or droplet deactivation via some complete droplet evaporation cannotrule out the roles of other mechanisms. Fog explosive development is a frequent phenomenon(Pu et al., 2008; Lu et al., 2010a; Niu et al., 2012)with asharp decrease in visibility to below 50 m during ashort period of time(e. g., 30 min). An example during a period in case 5 is shown in Figs. 4 and 5. TheLWC, N, rv, σ, and maximum radius(rmax)remarkably increase during 0140-0150 local st and ard time(LST); correspondingly, the size distributions broadenquickly. It is noteworthy that it takes only 4 minto produce the droplets with rmax around 15 μm(at0144 LST)from the droplets with rmax around 7 μm(at 0140 LST). Similar explosive developments werealso observed in previous fog experiments(Wobrock et al., 1992). Furthermore, some rmax values are evenlarger than 20 μm(Fig. 4f) and Fig. 3 shows thatthe average size distributions in the mature stage havermax in the range of 24-25 μm. It is not likely thatcondensation is the only mechanism responsible forthe formation of big droplets because condensationalgrowth rate of droplet size is negatively correlated withthe droplet size itself(e. g., Rogers and Yau, 1989) and supersaturation in fog is often low(e. g., Hudson, 1980); collision-coalescence is likely to be important, although not dominating. It is often thoughtthat gravitational collision-coalescence could not proceed until the radius of droplets exceeds 20 μm(e. g., Jonas, 1996; Yum, 1998). The appearance of largerdroplets(> 20 μm)shows the possibility of the occurrence of gravitational collision-coalescence.

Fig. 4. Temporal evolutions of(a)visibility(vis), (b)liquid water content(LWC), (c)number concentration(N), (d)volume-mean radius(rv), (e)spectral st and ard deviation(σ), and (f)maximum radius(rmax)during 0120-0330LST in case 5.
Fig. 5. One minute average size distributions during the fog explosive development in case 5.

To further explore the effect of gravitationalcollision-coalescence intensity on the microphysicalrelationships, autoconversion threshold function(T)proposed by Liu et al.(2005, 2006)is calculated for allthe cases(see the Appendix for details). A larger valueof T indicates a stronger collision-coalescence process, ranging from no action(T = 0)to full action(T = 1).

The result shows that 5 out of 8 cases have T valuessmaller than 0. 2, i. e., gravitational collision-coalescence is weak for most cases; but still, for cases 2, 5, and 6, the maximum values of T are 0. 57, 0. 47, and 0. 80, respectively, showing the importance of gravitationalcollision-coalescence in the three cases. In addition togravitational collision-coalescence, Xue et al.(2008) and Ghosh et al.(2005)pointed out that turbulencecould significantly enhance the collision rate for clouddroplets(> 10 μm in radius). Therefore, in additionto the dominant mechanisms, the collision-coalescence, especially that enhanced by turbulence, may be important in these fog cases as well. To address the combined effects of the dominantprocesses and collision-coalescence in detail, the mature stages(0 m < vis ≤ 500 m)are further divided into three groups based on visibility: 0-50, 50-200, and 200-500 m. Generally, the microphysical relationships are kept positive for the three visibilitygroups in all the cases except cases 2 and 8. As anexample, Fig. 6 shows the relationships for the fourvisibility groups in case 6. Figure 7 further shows thatthe size distributions broaden in case 6 with a decreasein visibility. Thus, we assume collision-coalescence becomes more and more vigorous with decreasing visibility. During collision-coalescence, the formation ofbig droplets consumes small ones, tending to cause increases in rv and σ, and a decrease in N.

Fig. 6. As in Fig. 2, but for four visibility(vis)ranges in case 6.
Fig. 7. Average size distributions for four different visibility(vis)ranges in case 6.

However, therelationships of rv vs. N and σ vs. N are not negative;we argue that this is likely due to the reproduction ofsmall droplets, which can compensate the loss of smalldroplets during collision-coalescence and result in synchronous increases in N, rv, and σ. The reproductioncan be caused by the growth of droplets(< 1 μm inradius). As mentioned above, the droplets(0. 5-1 μmin radius)can be measured by the spectrometer, butnot included in the calculations of microphysical properties because the data in this bin are thought to benoisy. However, they can still give some hints; thenumber concentration in this bin is always larger thanthe value at the current peak at 1. 4 μm in radius, so itis important that the reproduction of small droplets isthrough the growth of droplets(0. 5-1 μm in radius). Furthermore, the high concentration of droplets(0. 5-1μm in radius)always exists, which could be caused bythe nucleation of suficient fog condensation nuclei and subsequent condensation. The positive correlations ofLWC to σ, N, and rv(Figs. 6d, 6e, and 6f)indicatethat there is suficient LWC that could enhance the nucleation of aerosol(Zhang et al., 2011). The reproduction of small droplets confirms the dominant processesidentified above and causes the stable peak radius at1. 4 μm. Therefore, the suficient fog condensation nuclei in the polluted area, along with the higher LWC, is important for the positive correlations of rv vs. N and σ vs. N. Similar phenomena were also presentedby Hudson and Svensson(1995), they analyzed thecloud microphysical properties off the southern California coast and found that in three cases which hadlarger cloud condensation nuclei due to the effect ofship exhaust plumes, rv and N showed positive correlations, whereas for other cases, the correlation wasnegative. Furthermore, Wang et al.(2009)examinedthe marine clouds observed off the coast of Monterey and Point Reyes, northern California with data reflecting ship exhaust plumes deleted, and found a negativecorrelation between rv and N; the average size distributions along different flight horizontal levels showedsmall number concentration of small droplets, indicative of insuficient reproduction of small droplets bynucleation after cloud formation.

However, negative correlations of rv vs. N and σ vs. N are found for 0 m < vis ≤ 50 m in case 2(figure omitted) and in case 8(Fig. 8). In the abovediscussion, the negative correlations for 500 m < vis< 1000 m are due to the competition for nearly constant LWC and suficient fog condensation nuclei. Buthere LWC is not close to a constant as indicated by thepositive correlations of σ vs. LWC, LWC vs. N, and LWC vs. rv(Figs. 8d, 8e, and 8f). Thus, collisioncoalescence could be an important reason for the negative correlations. Furthermore, with a decrease invisibility, the relationships of rv vs. N and σ vs. Nchange from positive(200 m < vis ≤ 500 m)to irrelevant(50 m < vis ≤ 200 m), and then to negativecorrelations(0 m < vis ≤ 50 m). Similar conclusioncan be drawn for case 2. In other cases, there is a similar trend. For example, in case 6(Fig. 6), the slopeof rv vs. N decreases from 0. 00740(200 m < vis ≤500 m)to 0. 00237(50 m < vis ≤ 200 m), and then to0. 00159(0 m < vis ≤ 50 m). Therefore, in all the casesanalyzed, the slopes of rv vs. N and σ vs. N decreasewith increasing visibility, consistent with the assumption that collision-coalescence becomes stronger. Weargue that whether rv vs. N and σ vs. N are positively, negatively, or not correlated in all the eightcases depends on the competition between the lossof small droplets due to collision-coalescence and thecompensation of small droplets due to nucleation and condensation; generally, compensation is larger thanthe loss because six cases have positive correlationsfor lower visibility, and only two cases have negativecorrelations. ation after cloud formation.

Fig. 8. As in Fig. 6, but for case 8.

In the above discussion, turbulent and gravitational collision-coalescence processes are assumed tobe stronger for a lower visibility. Based on T, theeffect of gravitational collision-coalescence can be further studied. The data in cases 2, 5, and 6, whichhave T larger than 0. 2, are divided based on the sameTranges in Niu et al.(2010c)(0 ≤ T ≤ 0. 2, 0. 2 ≤ T ≤ 0. 6, and 0. 6 ≤ T ≤ 1. 0). Cases 2 and 5 have the firsttwo T ranges. Case 6 has three T ranges but the datapoints for 0. 6 ≤ T ≤ 1. 0 are rare; so 0. 2 ≤ T ≤ 0. 6 and 0. 6 ≤ T ≤ 1. 0 are combined to be 0. 2 < T ≤1. 0 for case 6. Figure 9 shows case 6 as an example. The negative correlations of rv vs. N and σ vs. N for higher T show that the loss of small dropletsdue to gravitational collision-coalescence is expectedto be higher than the compensation. Similar phenomena are found in cases 2 and 5. Furthermore, it isinteresting to find that rv vs. N and σ vs. N arenegative for 0. 2 < T ≤ 1. 0(Figs. 9a and 9b)butpositive for 0 m < vis ≤ 50 m(Figs. 6a and 6b)incase 6. Comparison of the two figures indicates thatthe data points with 0 m < vis ≤ 50 m are muchmore than those with 0. 2 < T ≤ 1. 0. Therefore, onlya few size distributions are affected by gravitationalcollision-coalescence; most droplet spectral broadeningis likely related to turbulent collision-coalescence. Thereproduction of small droplets can compensate the lossof small droplets due to turbulent collision-coalescencebut not gravitational collision-coalescence.

Fig. 9. As in Fig. 2, but for two autoconversion threshold function(T)ranges in case 6.

It is interesting to find that cases 2, 5, 6, and 8have negative correlations for a large T or a low visibility. These cases have larger mean LWC, mean rv, and maximum rv than the other cases(Table 1). Animportant reason is that there was precipitation before the fog events and evaporation of water in the soilprovided plenty of water vapor. 4. Concluding remarks

Warm fog microphysics is examined using thein situ observations conducted at Pancheng in 2007. Through analysis of the different microphysical relationships in the eight fog cases, the microphysical processes and key factors affecting fog microphysics areexplored.

It is shown that the key microphysical propertiessuch as droplet number concentration(N), volumemean radius(rv), spectral st and ard deviation(σ), and liquid water content(LWC)in the eight cases all exhibit positive correlations with one another, indicatingthat the dominant microphysical process is likely tobe droplet activation with subsequent condensationalgrowth and /or droplet deactivation via some completedroplet evaporation. The LWC is a key factor affectingthe effect of the dominant processes on microphysicalrelationships. In the formation stages(500 m < vis <1000 m), σ vs. N and rv vs. N are negatively correlated due to the competition of suficient fog condensation nuclei for nearly constant LWC; in the maturestages(0 m < vis ≤ 500 m), the LWC is not close to a constant, but positively correlated to N, σ, and rv, asa result, the competition for LWC is not remarkable and σ vs. N and rv vs. N are positively correlated.

Besides the dominant mechanism, the explosivedevelopment along with abrupt broadening of fogdroplet size distributions indicates that turbulent and gravitational collision-coalescence processes are alsoimportant. The mature stages(0 m < vis ≤ 500 m)are further divided into three groups(0 m < vis ≤ 50m, 50 m < vis ≤ 200 m, and 200 m < vis ≤ 500 m). Positive correlations among LWC, N, rv, and σ holdin the three visibility ranges for six cases; in the othertwo cases(cases 2 and 8), LWC vs. N, LWC vs. rv, σvs. LWC, and σ vs. rv are positive, but the correlations of rv vs. N and σ vs. N are found from positiveto irrelevant, and to negative correlations with thedecreasing visibility, indicating increasingly strongercollision-coalescence. We argue that the complicatedrelationships of rv vs. N and σ vs. N are closely related to the competition between the loss of smalldroplets due to collision-coalescence and the compensation of small droplets due to nucleation and condensation. Generally, the compensation is larger than theloss because of the large concentration of fog condensation nuclei in this polluted area.

To further explore the effect of gravitationalcollision-coalescence, autoconversion threshold function(T)is calculated. Among the 8 cases, cases 2, 5, and 6 have T larger than 0. 2 and the dataset is divided based on T values. Negative correlations of rvvs. N and σ vs. N are found for a large T. Furthermore, with the increasing T, correlation coeflcients ofσ vs. rv, σ vs. LWC, LWC vs. N, and LWC vs. rv become less positive or even negative. The gravitationalcollision-coalescence tends to weaken the positive correlations among key microphysical properties causedby the dominant processes.

Two points are noteworthy. First, numericalmodels are also useful to study fog lifecycle and relatedmicrophysical processes, but main-stream fog modelsdo not consider the effect of turbulence well, suchas turbulent collision-coalescence(e. g., Bergot and Guedalia, 1994; Shi et al., 1996; Hu et al., 2006). Direct numerical simulation is another tool for studyingmicrophysical processes in fogs, especially quantitativedescription of the influence of turbulence on condensational growth and turbulent collision-coalescence. Second, this study focuses on the fog microphysics; it isknown that macro conditions for the fog formation, duration, and dissipation are also important to underst and ing of the microphysical processes(e. g., Huang et al., 2011). For example, as mentioned above, theLWC is greatly affected by some environmental conditions(such as water vapor mixing ratio, air temperature, and air pressure), which are further related toradiation, turbulence, etc.(Zhou and Ferrier, 2008;Yuan and Huang, 2011). Therefore, detailed analysison the macro mechanisms responsible for fog formation is necessary in future studies. Appendix Autoconversion Threshold Function

According to Liu et al.(2005, 2006), all the autoconversion parameterizations that have been developed so far can be generically written as:

where P is the autoconversion rate, P0 is the ratefunction describing the conversion rate after the onset of the autoconversion process, and T is the threshold function describing the threshold behavior of theautoconversion process. The size truncation function employed to quantify the effect of truncating the clouddroplet size distribution on the autoconversion ratecan be used as a threshold function to represent thethreshold behavior associated with the autoconversionprocess, providing a physical basis for the thresholdfunction. The expression of T can be generally described by: where r is the droplet radius, n(r) is the cloud/fogdroplet size distribution, and rc is the critical radiusfor autoconversion. Liu et al.(2004)derived an analytical expression for predicting rc in the autoconversion parameterization: where βcon= 1. 15×1023 is an empirical coeflcient.
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