Fog Droplet Size Distribution and the Interaction between Fog Droplets and Fine Particles during Dense Fog in Tianjin, China

From November 2016 to January 2017, there were large-scale dense fog processes in Tianjin area on the west coast of Bohai Bay, China, even strong dense fog with visibility less than 50 m occurred. Based on the observation data of fog droplet spectrum monitor, visibility sensor, environmental particle monitoring equipment and meteorological automatic station, the characteristics of fog droplet size distribution and the interaction between the fog droplets and fine particles during dense fog events were analyzed. The results show following characteristics: (1) The average concentration of fog droplets (Na), the average liquid water content (La) and the maximum liquid water content (Lmax) in the strong dense fog process are larger than those in the dense fog. The average spectrum of fog droplet size distribution conforms to Junge distribution, and they are all broad-spectrum fog with a spectrum width of about 45 μm. The average spectrum is similar to the dense fog of heavily industrialized inland in the world. (2) The maximum of fog droplet diameter during the formation stage have a good indication for the outbreak of strong dense fog. (3) The mass concentration of PM2.5 (CPM2.5) is ranged from 121–375 μg/m3, and the interaction between fog droplets and fine particles is analyzed. During the formation, development and maturity stages, fog process can scavenge atmospheric fine particles, and the scavenging efficiency of PM2.5 is more remarkable than PM10. When CPM2.5 does not exceed 350 μg/m3, the increase in the concentration of fine particles is conducive to the rapid growth of fog droplets and the sharp drop of visibility. However, when CPM2.5 exceeds the critical value, the increase has a negative feedback effect on the development of the fog process. More investigations and cases are necessary to fully assess the mechanisms related to the dense fog events in Tianjin area and further analysis will be done.


Introduction
The evolution from fog to dense fog is very rapid and difficult to predict, the sudden low visibility phenomenon is very easy to lead to sudden safety accidents [1]. Fog droplet microphysical parameters, such as number concentration (N), liquid water content (L), diameter (D), fog droplet size distribution and atmospheric fine particle concentration directly affect visibility (Vis) in fog [2] and determine the formation and dissipation of fog. Clarifying the distribution characteristics and the rules of microphysical parameter changes at various stages of the fog life cycle can help improve forecasts of dense fog and strong dense fog [3], and provide a theoretical basis for fog modification [4].
In the past 30 years, more and more attention had been paid to the study of the microphysical characteristics of dense fog, and continuous progress had been made in the development and application of observation instruments of fog microphysical parameters. From the early "optical-electrical particle counter" and "three-purpose droplet spectrometer" to the widely used "FM-100" and "FM-120" fog monitor [5,6], the understanding of the microphysical characteristics of fog had been deepened. The formation of dense fog was accompanied by the broadening of the fog droplet size distribution in Alaska, USA [7]. British scholars analyzed the droplet size changes in the process of dense fog in Cardington, Bedfordshire, and found that the average droplet diameter in the early stage of fog outbreak was about 15-20 µm, so the starting signal of dense fog explosion may be clarified from the perspective of microphysics [8]. To some extent, numerical model skill also depends on the adjustment of microphysical parameters scheme. Moroccan scholars improved the skill of coastal fogs by adjusting the microphysics scheme of Casablanca area based on the droplet size distribution analysis [9,10]. If models could predict the N and L at each time step using a detailed microphysics parameterization, visibility could be calculated for warm fog conditions [11]. Early studies on the microphysical parameters of dense fog showed obvious regional differences in China. The N decreased while the L increased in order in urban areas (such as Nanjing and Chongqing), mountainous areas (such as Nanling and Lushan) and coastal areas (such as Zhoushan and Bohe). Many studies proved the D and the L are the main factors leading to low visibility in fog [12]. The N had a negative correlation with Vis. However the L of droplets had a positive correlation with the average diameter (D a ) [13].
In addition, atmospheric fine particles have a complex interaction with the growth of dense fog droplets in recent studies. The increase in the concentration of hygroscopic atmospheric particles can promote the formation of fog droplets even in unsaturated conditions, and the thickness of the fog layer will also increase with the increase of the concentration of atmospheric particles [14]. The intensity of fog will decrease with the decrease of aerosol concentration [15]. The hygroscopicity of atmospheric particles has a high dependence on particle size distribution and chemical composition, which changes with different conditions of relative humidity. So the growth process of fog droplets could be changed by the atmospheric hygroscopic aerosol [16]. For inland cities, the fine particles number concentration ranged from 5000 to 15,000 cm −3 during Paris fog event, and the number concentration exerted a higher influence on the fog microphysical characteristics than chemistry (solubility) did [17,18]. A large amount of aerosol particles could act as condensation nuclei to enhance the formation of fog droplets in North China Plain [19]. For coastal cities, most aerosols (include PM 2.5 ) were effectively scavenged by fog water, while sulfur species could not be easily and effectively scavenged near the industrialized coastal area in Japan [20,21]. Deposition of fog droplets was the most important process for the evolution of the size distribution of aerosols in San Joaquin Valley fog in California [22].
In view of the frequent dense fog weather in North China in recent years [23][24][25], which has seriously affected aviation takeoff and landing. In order to improve the ability of fog modification, Tianjin Weather Modification Office introduced fog monitor equipment and environmental particle monitoring equipment to carry out microphysical observation experiments in the winter dense fog process in Tianjin, China, for the first time. It is hoped that this experiment can clarify the characteristics of fog droplet generation and the interaction between fine particles and droplet growth during the dense fog in Tianjin in winter, and provide a basis for future fog modification.

Measurement and Data Processing
The observation site is located at the Tianjin atmospheric boundary layer observation station [26] (39 • 04 N, 117 • 12 E) from November 2016-January 2017, which is located in the central part of the North China Plain, with the Taihang Mountains to the west, the Yanshan Mountains to the north, and the Bohai Sea to the east, at a distance of 50 km from its west coast. The geographical location of the observation station, designated Tianjin (TJ), is shown in Figure 1. The characteristics of the fog droplet size spectrum from this observation station were compared with those from the observation stations in other areas of China, also shown in Figure 1. Specifically, these stations comprised: NJBJ where n is the number of observations, k is a coefficient determined by people from 0 to 0.5 (0 ≤ k < 0.5), [ ] means to get integer, X represents sequential microphysical statistics. Because the amount of data is very large (time resolution is 1s) and the scientific value of the data must be guaranteed, we set k as 0.25 in this research. The visibility data were obtained from the MODEL 6000 forward scattering visibility meter, using minute-scale measurement data. The mass concentration of PM2.5/PM10 (CPM2.5/CPM10) were obtained from a TEOM (RP1405D) device, using hourly average mass concentration data. The wind speed data captured with the DZZ5 automatic weather station. The instrument specifications are listed in Table 1.  During the intensive measurement period, Tianjin experienced several fog events. Jointed to the weather phenomena and visibility data from the Meteorological Information Service System database of the China Meteorological Administration (CIMISS), every fog process was accompanied by largescale haze conditions, we called the weather phenomena as fog-haze processes. For all the fog-haze The data of fog droplet size distribution were obtained from an FM-120 fog monitor. The droplet diameter (D), liquid water content (L), number concentration (N) data were obtained with the trimmed-mean method [33]. This method follows this equation: where n is the number of observations, k is a coefficient determined by people from 0 to 0.5 (0 ≤ k < 0.5), [ ] means to get integer, X represents sequential microphysical statistics. Because the amount of data is very large (time resolution is 1s) and the scientific value of the data must be guaranteed, we set k as 0.25 in this research. The visibility data were obtained from the MODEL 6000 forward scattering visibility meter, using minute-scale measurement data. The mass concentration of PM 2.5 /PM 10 (C PM2.5 /C PM10 ) were obtained from a TEOM (RP1405D) device, using hourly average mass concentration data. The wind speed data captured with the DZZ5 automatic weather station. The instrument specifications are listed in Table 1. by large-scale haze conditions, we called the weather phenomena as fog-haze processes. For all the fog-haze processes, individual (strong) dense fog event screening was performed based on the following three visibility levels: (1) Vis is not greater than 1500 m; (2) Vis first drops below 1000 m, then rises above 1000 m; (3) Vis stays less than 1000 m for more than 30 min. Six fog events were screened that met the above conditions.
Based on the grade of fog forecast in the national standard of the People's Republic of China (GB/T 27964-2011) [34], fog with Vis ≥ 50 m and < 500 m is classified as dense fog, fog with Vis < 50 m is classified as strong dense fog. Based on this classification, Case 1, 3, 4, 5, and 6 were dense fog events, and Case 2 was a strong dense fog event. Using the visibility as the criterion, the fog process can be divided into the four stages, the formation stage (when the Vis drops from 1500 m to 1000 m), the development stage (between the fog formation and the maturation stages), the maturation stage (after the Vis drops to its lowest level and remains basically constant for more than 30 min), and the dissipation stage (when the Vis increases noticeably from the lowest value to 1000 m).
Because this research mainly focuses on the changes of fog droplets and fine particles during the dense fog processes whose existing background is weak horizontal wind speed ( Figure 2) and vertical wind [8], the changes of advection of fine particles could be ignored. The vertical transport may obviously affect the concentration of fog droplets and fine particles during the fog dissipation stage, while every continuous fog case was considered without any interruption, so the variation of fog spectrum originated from vertical movement is also neglected before fog dissipation. Moreover, being lack of vertical data of fog droplets and fine particles, following discussions about the characteristics and interactions of the droplet spectrum and fine particles at various stages of fog processes, were also based on the assumption that the variation of fog spectrum was only affected by local radiative cooling and the interaction of fine particles.
Atmosphere 2020, 11, x FOR PEER REVIEW 4 of 16 processes, individual (strong) dense fog event screening was performed based on the following three visibility levels: (1) Vis is not greater than 1500 m; (2) Vis first drops below 1000 m, then rises above 1000 m; (3) Vis stays less than 1000 m for more than 30 min. Six fog events were screened that met the above conditions. Based on the grade of fog forecast in the national standard of the People's Republic of China (GB/T 27964-2011) [34], fog with Vis ≥ 50 m and < 500 m is classified as dense fog, fog with Vis < 50 m is classified as strong dense fog. Based on this classification, Case 1, 3, 4, 5, and 6 were dense fog events, and Case 2 was a strong dense fog event. Using the visibility as the criterion, the fog process can be divided into the four stages, the formation stage (when the Vis drops from 1500 m to 1000 m), the development stage (between the fog formation and the maturation stages), the maturation stage (after the Vis drops to its lowest level and remains basically constant for more than 30 min), and the dissipation stage (when the Vis increases noticeably from the lowest value to 1000 m).
Because this research mainly focuses on the changes of fog droplets and fine particles during the dense fog processes whose existing background is weak horizontal wind speed ( Figure 2) and vertical wind [8], the changes of advection of fine particles could be ignored. The vertical transport may obviously affect the concentration of fog droplets and fine particles during the fog dissipation stage, while every continuous fog case was considered without any interruption, so the variation of fog spectrum originated from vertical movement is also neglected before fog dissipation. Moreover, being lack of vertical data of fog droplets and fine particles, following discussions about the characteristics and interactions of the droplet spectrum and fine particles at various stages of fog processes, were also based on the assumption that the variation of fog spectrum was only affected by local radiative cooling and the interaction of fine particles.  Table 2 lists the duration of Vis < 1000 m (Dr), the duration of the maturation stage (Drma), the maximum/average concentration (Nmax/Na), the maximum/average liquid water content (Lmax/La), and the maximum droplet diameter (Dmax), as well as the range of visibility change (Visma) during the maturation stage, and the maximum/minimum mass concentration of PM2.5 (CPM2.5max/CPM2.5min). Figures 2 and 3 shows the change trend of D, L, N, Vis, Wind speed and CPM2.5, we can find the following characteristics.

Evolution Characteristics of the Fog Droplet Size Distribution and Fine Particle
First of all, it can be seen from Figure 2 that the L, N, and D of Tianjin (strong) dense fog display good positive correlation relationships. This is consistent with the research results for Nanjing winter fog [27,28] and Zhanjiang coastal fog [29][30][31]. In terms of the spectral width characteristics of fog droplets, in the six fog processes, the spectral widths are at approximately 45 μm. It can be considered that the winter (strong) dense fog in Tianjin is a broad-spectrum fog based on suggestion of Niu et al. [35].
Furthermore, during the (strong) dense fog processes in Tianjin, CPM2.5max ranges from 188-375 μg/m 3 , CPM2.5min ranges from 121-173 μg/m 3 ( Table 2). Figure 3 and Table 2 reveal that CPM2.5max always appears in the formation stage (Case 1, 2, 3, 4 and 5) or the dissipation stage (Case 6). The trend of the decrease in the concentration of fine particles is basically consistent in each process, but the decline is slightly different, indicating that the fog droplets scavenge the fine particles during the development and maturation stages, and CPM2.5 decreases significantly. Especially an "upturned tail" appears at the end of the temporal variations of hourly averages of CPM2.5 in each process (Figure 3), which means the removal efficiency of fine particles in fog process is significantly reduced during the dissipation stage.
Over and above that, Table 2 reveals that the Na, La, and Lmax of the strong dense fog (Case 2) are larger than those of dense fog. Na, La, and Lmax of Case 2 are 596 particles/cm 3 , 0.041 g/m 3 , and 0.145 g/m 3 , respectively, but they are 184 particles/cm 3 , 0.036 g/m 3 , and 0.122 g/m 3 in the dense fog cases, respectively. The calculation values of Na, La, and Dmax of the (strong) dense fog cases in Tianjin, and the comparison of these values with the respective values of dense fog processes in several coastal and inland cities worldwide are listed Table 3. The La in Tianjin is 0.037 g/m 3 , which is very close to the La in Nanjing [27,28], but it is significantly lower than that in Zhanjiang Coast [29][30][31], Nova Scotia [36,37] and Japan's Yodogawa Basin [20,38]. Moreover, Baoding's La is the smallest [23,39]. Although Tianjin is also a coastal city, the La during the (strong) dense fog process is more similar to the values found in inland areas. Comparing the main chemical composition of fog water and the concentrations of the main aerosols with several coastal and inland cities around the world (Table 3), we found that  Table 2 lists the duration of Vis < 1000 m (Dr), the duration of the maturation stage (Dr ma ), the maximum/average concentration (N max /N a ), the maximum/average liquid water content (L max /L a ), and the maximum droplet diameter (D max ), as well as the range of visibility change (Vis ma ) during the maturation stage, and the maximum/minimum mass concentration of PM 2.5 (C PM2.5max /C PM2.5min ). Figures 2 and 3 shows the change trend of D, L, N, Vis, Wind speed and C PM2.5 , we can find the following characteristics.   First of all, it can be seen from Figure 2 that the L, N, and D of Tianjin (strong) dense fog display good positive correlation relationships. This is consistent with the research results for Nanjing winter fog [27,28] and Zhanjiang coastal fog [29][30][31]. In terms of the spectral width characteristics of fog droplets, in the six fog processes, the spectral widths are at approximately 45 µm. It can be considered that the winter (strong) dense fog in Tianjin is a broad-spectrum fog based on suggestion of Niu et al. [35].

Evolution Characteristics of the Fog Droplet Size Distribution and Fine Particle
Furthermore, during the (strong) dense fog processes in Tianjin, C PM2.5max ranges from 188-375 µg/m 3 , C PM2.5min ranges from 121-173 µg/m 3 ( Table 2). Figure 3 and Table 2 reveal that C PM2.5max always appears in the formation stage (Case 1, 2, 3, 4 and 5) or the dissipation stage (Case 6). The trend of the decrease in the concentration of fine particles is basically consistent in each process, but the decline is slightly different, indicating that the fog droplets scavenge the fine particles during the development and maturation stages, and C PM2.5 decreases significantly. Especially an "upturned tail" appears at the end of the temporal variations of hourly averages of C PM2.5 in each process (Figure 3), which means the removal efficiency of fine particles in fog process is significantly reduced during the dissipation stage.
Over and above that, Table 2 reveals that the N a , L a , and L max of the strong dense fog (Case 2) are larger than those of dense fog. N a , L a , and L max of Case 2 are 596 particles/cm 3 , 0.041 g/m 3 , and 0.145 g/m 3 , respectively, but they are 184 particles/cm 3 , 0.036 g/m 3 , and 0.122 g/m 3 in the dense fog cases, respectively. The calculation values of N a , L a , and D max of the (strong) dense fog cases in Tianjin, and the comparison of these values with the respective values of dense fog processes in several coastal and inland cities worldwide are listed Table 3. The L a in Tianjin is 0.037 g/m 3 , which is very close to the L a in Nanjing [27,28], but it is significantly lower than that in Zhanjiang Coast [29][30][31], Nova Scotia [36,37] and Japan's Yodogawa Basin [20,38]. Moreover, Baoding's L a is the smallest [23,39]. Although Tianjin is also a coastal city, the L a during the (strong) dense fog process is more similar to the values found in inland areas. Comparing the main chemical composition of fog water and the concentrations of the main aerosols with several coastal and inland cities around the world (Table 3), we found that C PM2.5 or C PM1 are about 200 µg/m 3 in heavily industrialized inland area (Nanjing [27,28], Baoding [23,39], Kanpur [40,41]), as well as that in Tianjin. However, the concentrations of the main aerosols in several coastal areas (Nova Scotia [36,37], Yodogawa Basin [20,38], Fairbanks [42,43]) are much lower. The lower L a in Tianjin is due to the fact that under certain water vapor conditions, high C PM2.5 will capture water vapor and form a large number of haze droplets, while high liquid water content is mainly contributed by large fog droplets [44]. Moreover, the main chemical composition of fog water in Tianjin is similar to those of inland cities without obvious sea salt particles [45], which is significant difference from those of other typical coastal areas, maybe because of the observation spot being 50 km far away from Bohai Sea with the addition of its almost inland sea. Large-sized sea salt particles have strong hygroscopic growth capacity to form large fog droplets containing salt ions Na + , and to supplement the liquid water content in the fog process. This may be the reason why C PM2.5 is also large in Zhanjiang, L a is still greater than that in Tianjin. Table 3. Microphysical characteristics of dense fog processes, the main chemical composition of fog water and the concentrations of the main aerosols in several coastal and inland cities around the world.  with the peak appearing in the small-droplet range of 5.4-7.2 µm in diameter. The peak diameter variation range of the droplets in the five dense fog processes is 5.4-6.1 µm, while the peak diameter in the strong dense fog process is 7.2 µm. These results indicate that the peak diameters of the spectrum are negatively correlated with visibility. The larger the peak diameter, the lower the visibility. so its impact on Tianjin is smaller than that of the other open ocean. Therefore, Tianjin is still a continental climate, which is a coastal city greatly affected by industrialization and urbanization. Using Table 3 to continue to analyze the difference of the concentrations and chemical composition of hygroscopic particles in heavily industrialized inland and typical coastal areas. For the dense fog in Tianjin, fine particles have greater impacts on visibility than coarse particles, and his special chemical composition of hygroscopic particles in Tianjin (sulfate > particulate organic matter > elemental carbon > nitrate) [45] is similar to that of heavily polluted inland cities. The main chemical composition of fog water (whether it contains salt particles or not) has influence on the average spectrum. To sum up, due to its specific geographic location and chemical composition of hygroscopic particles, the fog droplet size distribution in Tianjin is similar to the distributions of heavily polluted inland cities but different from those of most coastal areas around the world.   Researchers have demonstrated that the average spectral shape of fog droplet size distributions generally obeys either the Junge distribution [40] or the generalized gamma distribution [9]. The fitting form of Junge distribution follows this equation [46]:

Statistical Characteristics of the Fog Droplet Size Distribution
where a is the shape parameter, and b is the inverse dimension parameter. The goodness-of-fit coefficients R 2 can be determined using the following equation: where SST is the total sum of squares, SSR is the sum of squares of regression, n i represents for the each observation value of N,n i represents for the regression value of N, n represents the average of N. Figure 4a shows the results of fitting spectral shape of each case and Figure 4b for the average spectral shape of the whole six cases in Tianjin using the least squares method [47]. All six cases fit the Junge distribution very well. Only the average spectrum is given as following: With R 2 = 0.985. Chenjiaping of Chongqing, China, winter dense fog average spectrums also fit the Junge distribution [13], the values of a is 2590, b is 3.4. Although the average spectrum of Tianjin and Chongqing all fit the Junge distribution, the droplet spectrums are slightly different, which is determined by the difference of a and b. b determines the shape of the spectrum. When b is closer, a determines the increasing/decreasing range of n(D) with D. So the increasing/decreasing range of n(D) in Tianjin is less than that in Chongqing. The results show that the average spectrum of winter (strong) dense fog in Tianjin presents an exponentially decreasing distribution, which is consistent with the average spectral type of inland fog in some part of China (such as Chongqing).
Atmosphere 2020, 11, 258 9 of 15 In inland areas such as Nanjing, and Kanpur, the droplet spectra obey the Junge distribution (Table 3). Tianjin is a large city with a high population density situated on the west coast of Bohai Bay in North China Plain. Because the Bohai Sea is an inland ocean and its sea area is small, so its impact on Tianjin is smaller than that of the other open ocean. Therefore, Tianjin is still a continental climate, which is a coastal city greatly affected by industrialization and urbanization. Using Table 3 to continue to analyze the difference of the concentrations and chemical composition of hygroscopic particles in heavily industrialized inland and typical coastal areas. For the dense fog in Tianjin, fine particles have greater impacts on visibility than coarse particles, and his special chemical composition of hygroscopic particles in Tianjin (sulfate > particulate organic matter > elemental carbon > nitrate) [45] is similar to that of heavily polluted inland cities. The main chemical composition of fog water (whether it contains salt particles or not) has influence on the average spectrum. To sum up, due to its specific geographic location and chemical composition of hygroscopic particles, the fog droplet size distribution in Tianjin is similar to the distributions of heavily polluted inland cities but different from those of most coastal areas around the world.
It is envisaged that if the similarities and differences of the microphysical characteristics of fog droplets in the formation stage of dense fog and strong dense fog can be clarified, it may be possible to judge the strong dense fog outbreak in advance, thereby improving the ability to predict the strong dense fog. Based on this idea, we had a comparative analysis of the characteristics of the fog droplet spectrum in the four stages of fog, and focused on the formation stage. Figure 5 shows the maximum and average particle diameters of the droplets during the formation stages of dense fog and strong dense fog. The average values of the droplet size in the six fog processes were similar, ranging from 4.02-5.20 µm. However, the maximum droplet size varies widely. Five dense fog processes droplet sizes were 13.45 µm, 14.91 µm, 14.97 µm, 11.48 µm, and 16.98 µm, respectively. In the strong dense fog process (Case 2), larger fog droplets appeared, exhibiting a maximum droplet size of 24.95 µm. Based on the maximum droplet size distribution during the formation stage, it was divided into two ranges ( Figure 5 It is envisaged that if the similarities and differences of the microphysical characteristics of fog droplets in the formation stage of dense fog and strong dense fog can be clarified, it may be possible to judge the strong dense fog outbreak in advance, thereby improving the ability to predict the strong dense fog. Based on this idea, we had a comparative analysis of the characteristics of the fog droplet spectrum in the four stages of fog, and focused on the formation stage. Figure 5 shows the maximum and average particle diameters of the droplets during the formation stages of dense fog and strong dense fog. The average values of the droplet size in the six fog processes were similar, ranging from 4.02-5.20 μm. However, the maximum droplet size varies widely. Five dense fog processes droplet sizes were 13.45 μm, 14.91 μm, 14.97 μm, 11.48 μm, and 16.98 μm, respectively. In the strong dense fog process (Case 2), larger fog droplets appeared, exhibiting a maximum droplet size of 24.95 μm. Based on the maximum droplet size distribution during the formation stage, it was divided into two ranges ( Figure 5 Figure 6 shows the size distribution characteristics of fog droplets at each stage of the six (strong) dense fog processes. For the five dense fog processes, it can be seen that during the formation stage, the droplet size spectrum were narrow and the droplet diameters were small, with an average value of 4.50 μm. Thus, the air contained mostly haze particles or small-scale fog droplets, as well as a few large droplets (indicated by the stars in the Figure 6), with N values ranging from 1-3 per cm 3 . The spectrum of condensation nucleus determines droplet concentration [48][49]. During the development process, the number of large particles that can act as droplet condensation nuclei increases sharply [19], the visibility quickly drops below 500 m, and the spectrum rises and noticeably widens. During the maturation stage, the number of fog droplets of all sizes reached their maximum values for the process. The range of spectrum width was 42.4-48.9 μm, which became significantly wider. The finding that N did not decrease but rather increased during this stage is different from the phenomenon that large droplets increase and small droplets decrease due to collision-coalescence summarized by Liu et al. [27].
For the strong dense fog, the spectral width during the formation phase is significantly wider Figure 5. The maximum and average diameter during the formation stages of dense fog and strong dense fog. Figure 6 shows the size distribution characteristics of fog droplets at each stage of the six (strong) dense fog processes. For the five dense fog processes, it can be seen that during the formation stage, the droplet size spectrum were narrow and the droplet diameters were small, with an average value of 4.50 µm. Thus, the air contained mostly haze particles or small-scale fog droplets, as well as a few large droplets (indicated by the stars in the Figure 6), with N values ranging from 1-3 per cm 3 . The spectrum of condensation nucleus determines droplet concentration [48,49]. During the development process, the number of large particles that can act as droplet condensation nuclei increases sharply [19], the visibility quickly drops below 500 m, and the spectrum rises and noticeably widens. During the maturation stage, the number of fog droplets of all sizes reached their maximum values for the process. The range of spectrum width was 42.4-48.9 µm, which became significantly wider. The finding that N did not decrease but rather increased during this stage is different from the phenomenon that large droplets increase and small droplets decrease due to collision-coalescence summarized by Liu et al. [27].
Atmosphere 2020, 11, x FOR PEER REVIEW 10 of 16 Figure 6. Fog droplet size distributions of (strong) dense fog in four stages and the Dmax during the formation stage. (The four phases are formation, development, maturation and dissipation. Case1, 3, 4, 5, 6 are dense fog. Case 2 is strong dense fog. The star in each plot denotes the size of the largest droplet and the corresponding N during the formation stage for the respective fog process).

Interaction between Fog Droplets and Atmospheric Fine Particles
Select the strong dense fog process to further study the interaction between fog droplets and atmospheric fine particles. Case 2 was accompanied by severe haze, and the CPM2.5max and CPM10max were 375 μg/m 3 and 419 μg/m 3 , respectively. The absolute changes of CPM10 and CPM2.5 in the four stages of fog are shown in Figure 7a For the strong dense fog, the spectral width during the formation phase is significantly wider than that during the dissipation phase (that is different from the five dense fog processes). A small number of fog droplet with value of 24.95 µm appear in short time (indicated by the stars in the Figure 6), which is a good indication for the eruption of strong dense fog. During the development stage, the change trend of each microphysical parameter is consistent with the dense fog processes. During the maturation stage, the maximum particle size increased to 45 µm, the spectral width increased to 38 µm, the droplet concentration increased by two orders of magnitude, and L max suddenly increased to 0.105 g/m 3 .

Interaction between Fog Droplets and Atmospheric Fine Particles
Select the strong dense fog process to further study the interaction between fog droplets and atmospheric fine particles. Case 2 was accompanied by severe haze, and the C PM2.5max and C PM10max were 375 µg/m 3 and 419 µg/m 3 , respectively. The absolute changes of C PM10 and C PM2.5 in the four stages of fog are shown in Figure 7a,b. The maximum mass concentration of fine particles all appeared in formation stage of fog. During the stage of development and maturation, the mass concentration of fine particles show a rapid downward trend, which do not increase until the dissipation stage. Thus, the strong dense fog process in Tianjin has a strong effect on the removal of PM 10 and PM 2.5 , which is consistent with previous studies in Tianjin [24]. The upward trend of the PM 10 /PM 2.5 , as shown in Figure 7c, obviously, after the formation stage, regardless of the median, 25% sample average, or 75% sample average, the ratio shows a steady upward trend, which fully indicates that the fog droplets are more significant clearance effect to PM 2.5 than PM 10 . This conclusion is confirmed by the scavenging effect of water soluble aerosols by fog droplets during the dense fog in Indo Gangetic Plain [50].   Figure 8 shows the distributions of L a and N/C PM2.5 in different fine particle mass concentration intervals. For Case 2, Tian et al. [25] found that before fog appearance, the supply of exogenous water vapor was sufficient, and specific humidity rised slowly. However, after fog appearance, there was no longer the transport of exogenous water vapor, and the local water vapor content decreases slightly compared with the early stage (figure is slightly). The data selected in this paper is after fog appearance, the water vapor content no longer changes significantly. Therefore, it can be approximated that the water vapor content is nearly constant. In the course of strong dense fog, with the increase of C PM2.5 , the value of N/C PM2.5 and L a rapidly increased first. Especially when C PM2.5 is in the range of 190-230 µg/m 3 , the maximum value of N/C PM2.5 appears. It is consistent with the conclusion of Yue et al. [29] that as the L increases, the ratio of the concentration of fog droplets to fine particles will increase. N increases with the rise of C PM2.5 , which indicates that when water vapor is sufficient, a large amount of PM 2.5 is activated as fog droplet condensation nucleus and PM 2.5 promotes the formation of fog. With the further increase of C PM2.5 to 310 µg/m 3 , N/C PM2.5 remain stable, but L a value decrease rapidly. In other words, when C PM2.5 is in the range of 230-310 µg/m 3 , more PM 2.5 are simultaneously activated into fog droplets. However, with the increase of N, due to the limited amount of water vapor, a large number of fog droplets rob the water vapor, so that the water vapour content decreases rapidly. When C PM2.5 is in the range of 310-350 µg/m 3 , the value of N/C PM2.5 rises again slightly, while the decrease trend of L a is unchanged. This shows that the competition of fine particles for water vapor is up to the peak period, and more PM 2.5 is activated as fog droplet condensation nucleus. As C PM2.5 continues to increase in the range of 350-390 µg/m 3 , the value of N/C PM2.5 decreases instead, at the same time L a appears the minimum value. It is shown that excessive PM 2.5 no longer promote the increase of fog droplets, but instead consumes more water vapor. When the water vapor is not enough to support the activation of a large number of fine particles to form fog droplets, the condensed liquid water content will be lower (L a in the Figure 8).

Conclusions
Considering the fog-haze harmful effect to the important port city and the largest open coastal city in North China, field observations of fog droplet size distribution and fine particles are set to improve the ability of fog modification at Tianjin atmospheric boundary layer observation station. Based on the analysis of microphysical parameters of fog droplet and fine particles from limited six (strong) dense fog cases, which were observed during November 2016 to January 2017. Some results Studies in Beijing, China have found that when C PM2.5 > 200 µg/m 3 , the aerosol concentration has a strong effect on the rapid growth of dense fog droplets and the decrease in visibility [32]. The positive feedback effect on the growth of fog droplets becomes prominent when the C PM2.5 > 230 µg/m 3 in Tianjin (the C PM2.5 value is higher than that in Beijing, China). Moreover, as described above, the interaction between C PM2.5 and fog droplet growth in Tianjin is more complicated, because with the increase of C PM2.5 , its positive feedback effect on droplet growth will weaken, and even inhibit the growth of fog droplets. It is found by combining Figures 7b and 8, that during the development stage, the range of the C PM2.5 value is the largest (215-371 µg/m 3 ), and only in the development stage, C PM2.5 was found to be in the range of 310-350 µg/m 3 . In other words, in the early stage of the development, the presence of a large number of fine particles is conducive to activation into more fog droplets, and also accelerates the condensation of liquid water content, and promotes the formation and development of strong dense fog. However, at the later stage of the development, when the C PM2.5 exceeds 350 µg/m 3 , the growth of fog droplets is inhibited.

Conclusions
Considering the fog-haze harmful effect to the important port city and the largest open coastal city in North China, field observations of fog droplet size distribution and fine particles are set to improve the ability of fog modification at Tianjin atmospheric boundary layer observation station. Based on the analysis of microphysical parameters of fog droplet and fine particles from limited six (strong) dense fog cases, which were observed during November 2016 to January 2017. Some results about the chemical composition of fog water and aerosols in coastal and inland cities were cited to explain the observation phenomena, the summary is as following.
Due to its specific geographic location and background pollution, the fog droplet size distribution in haze days in Tianjin are fitted with Junge spectrum models, which is similar to the heavily industrialized inland areas. The spectral width of (strong) dense fog are approximately 45 µm and peak diameters ranges from 5.4-7.2 µm. The D max up to 16.98 µm during the formation stage have a good indication to the outbreak of strong dense fog. The interaction between fog droplets and fine particles during dense Fog in Tianjin is distinctive and bidirectional. On the one hand, the strong dense fog process have a strong effect on the removal of PM 10 and PM 2.5 , and scavenging efficiency to PM 2.5 is more significant than PM 10 . On the other hand, fine particles have different function to fog. Fine particles are benefit to enhance the fog process when C PM2.5 is below the threshold, while showing contrary feedback effect and suppressing fog process when C PM2.5 is larger than the threshold.
It should be noted, that the effect of dynamical parameters change (such as wind, humidity or turbulence) have not been neglected in fog processes, and the conclusions of this study are only drawn from the analysis of atmospheric microphysical characteristics. In addition, the threshold quantitative analysis of large droplets size during the fog formation stage and the spectral characteristic of fog droplets from only six (strong) dense fog events, more fog cases investigation need to enhance its credibility.