A Study on Parameterization of the Beijing Winter Heavy Haze Events Associated with Height of Pollution Mixing Layer

North China Plain, Beijing, Tianjin, and Hebei province are the major areas facing the decreasing air quality and frequent pollution events in the recent years. Identifying the effect of meteorological conditions on changes in aerosol concentration and the mechanism for forming such heavy pollution in North China Plain has become the focus of scientific research. The influence of atmospheric boundary layer characteristics on air quality has become the focus of attention and research. However, the boundary layer describes that the influences of air pollution have sometimes been duplicated and confused with each other in some of the studies. It is necessary to pay attention to some extent, raising awareness of related pollution mixing layer. The conclusions of the study include the following: (1)The lowered height of pollution mixing layer (H PML) was favorable for the increase of the PM2.5 density. The lowered height of pollution mixing layer had significant impacts on formation of severe haze. (2) A statistical analysis of large-scale heavy pollution cases in eastern China shows that the H PML parameters have significant contributions. (3) The feedback effect of the high value of the convection inhibition (CIN), which is unfavorable to vertical diffusion of pollution, causes further reduction of H PML, resulting in cumulative pollution again.


Introduction
In December 2016, the North China region witnessed a historically rare pollution event, including the widespread hazy weather across the Yellow River and Huai River basins.Just in 24 hours from 18 to 19 December, the total area under influence of the severe haze was doubled, covering more than a million square kilometers, affecting 12 provinces or municipalities, that is, Jilin, Liaoning, Beijing, Tianjin, Hebei, Shandong, Henan, Shaanxi, Shanxi, Hubei, Anhui, and Jiangsu.Consequently, the red warning signal for heavy air pollution was launched in Beijing.December 2016 ranked top in terms of pollution severity for more than a decade, and the winter haze in North China once again became a focus of public opinion.
Under the global change, the air quality in the Earth's atmosphere tends to be gradually aggravated.The Beijing-Tianjin-Hebei area is the major region that has been frequently affected by air pollution in the recent years [1,2].Emissions and weather conditions are two important factors for air quality.Such questions as how to identify the impacts of weather conditions on local aerosol accumulation and density including impacts of small-and microscale processes are commonly of interest but it is difficult to give a precise answer.Efforts have been made to select some meteorological elements from the common weather parameters to analyze their contributions to possible changes in air quality, and their contributions sometimes are mutually offset and even contradictory [3,4] due to complexity of mechanisms.However, the objective and quantitative assessments on the impacts of changing weather conditions upon aggravation and mitigation of atmospheric aerosol pollution have become a focus of attention in research.
Progress has already been made in studies on numerical air quality modeling [5,6].The difficulty encountered in studies and predictions of chemistry models is that the worldwide emission inventories are not available in a timely manner, usually lagging far behind demand for predictions, hence restricting further improvements of operational predictability in this direction.The studies on identification of density variations of atmospheric particles including PM 2. 5 and their impacts show that the hygrometric characteristics of different emission particles vary significantly under different atmospheric condensation conditions.The duration of maintaining a hygrometric process in adaptation to various atmospheric conditions also has significant impacts on particle density variations [7].
In his series of famous studies on parameterization, Kuo [8] first presented cloud physics, its microphysic processes, and large-scale observations in parameterization schemes, which have been widely used for numerical weather predictions since then.Research findings show that the parameterization allows "incomparably describable" atmospheric microphysics in "different magnitudes" to interact with largescale processes and solving a bunch of relevant equations.Hu et al. present a comprehensive evaluation study to address the importance of PBL parameterization schemes in WRF-Chem predictions of particles with diameters less than 2.5 microns (PM 2.5 ) during February 2014 over the most polluted regions in China, where PM 2.5 concentrations higher than 500 g⋅m −3 were observed [9].In the recent years, encouraging results have been achieved on parameterization methodologies linking air quality and meteorological conditions.Some studies both at home and overseas [10][11][12][13] have presented a new advance in PLAM index methodology to characterize whether the aggravated meteorological conditions are favorable or not for aggravating local air pollution, hence providing an objective basis for identifying the correlation of meteorological conditions with aerosol density variations.This method has been widely recognized and used worldwide.
In this paper, our studies and analyses focus on characteristics of isentropic (iso-) processes based on PLAM index; the height of pollution mixing layer features and the vertical atmospheric structure are analyzed; the correlation of the PLAM sensitive parameter-condensation function () with the height of pollution mixing layer is discussed; correlation and interactions of PLAM index with local aerosol density variations are both explored; and the mechanism for forming the heavy pollution or severe hazy weather event in December 2016 is also addressed.

Data and Methodology
2.1.Data.In this section, NCEP 2.5 × 2.5 reanalysis and automatic weather station (AWS) data, both conventional surface and upper air observations from the climate stations of the National Climate Center, are used for calculations to investigate any meaningful implication of PLAM index for aerosol pollution; the atmospheric vertical wind, temperature, and humidity fields in the process of the rarely heavy pollution in December 2016 are explored; the role of atmospheric environment to inhibit pollution dispersion is investigated; and the mechanism for forming heavy pollution in Beijing is also discussed.[9] that although the planetary boundary layer (PBL) parameterizations are critical to air quality modeling, but it is not well quantified that constraining the air quality simulations by PBL parameterization schemes under the heavy haze polluted boundary layer conditions.In recent years, many progresses of studies on the atmospheric boundary layer characteristics and their impact on the air pollution were made (see Table 1) [4,9,[14][15][16][17][18][19][20].However, the way with which boundary layer describes the influences of air pollution is easily duplicated and confused.For example, the planetary boundary layer (PBL) usually refers to the large-scale Ekman dynamic boundary layer [14][15][16].So it is unreasonable to some extent, if the characteristic of the air pollution related to near-surface boundary layer is evaluated by using the concept of PBL.

Height of Pollution Mixing Layer. Hu et al. point out
For the heavy haze pollution measurement, one of selected functionalities of parameterization scheme is to judge whether an air mass over a specific locality satisfies the "static and stable" attribute or not.
It is known that   is an important parameter that reflects such attribute of air masses (Yang et al., 1980) [21], and, with this attribute, the constant "homogeneity" of   , that is,   / ≈ 0, can be used to express the basic physics for diagnosing meteorological conditions.The iso-  process is also called an isentropic atmospheric process.According to the thermodynamic equation, such stable nature of largescale circulation, the attribute with constant "homogeneity" of air masses, may be expressed as follows [13,22]: Expression (1) gives the basic equations to parameterize the "homogeneous" attribute (  ) of the air masses.,   ,   ,   , and   represent air temperature, equivalent wet potential temperature, condensation function, saturation mixing ratio, and specific heat at constant pressure, respectively.In expression (1) defining PLAM index, another important sensitive parameter is the condensation function   , which is the threshold for controlling growth of aerosol density.The reason for introducing this function is to judge whether the aerosol density "grows" or "dilutes," as   describes water vapor condensation, concentration of minute particles, and hygrometric process in the atmosphere.This paper gives an in-depth analysis of descriptive functionality of PLAM index, explores contributions of relevant PLAM sensitive parameters in the relatively "static and stable" isentropic processes, and investigates impacts of the height of pollution mixing layer and vertical atmospheric structure upon the local aerosol density variations.
In expression (1), according to the definition of the wet potential temperature   , any layer in which the saturated mixing ratio is satisfied ( =   ) can be considered as the saturated atmospheric stratification.As   /  = 0.288 in expression ( 1) is a constant value, in the isentropic (iso-  ) process, the air pressure is used to express the lifting condensation level (LCL), which provides favorable weather conditions to allow new aerosol particles to grow continuously in the hygrometric process of pollution emissions in combination with pollution mixing.Thus, when rain droplets have not yet reached the threshold of   , it is favorable for pollution mixing process to be sustained at this level, which is called the height of pollution mixing layer (H PML).Using an iterative algorithm, H PML can be derived in the following expression [23]: Expression (2) presents the air pressure coordinates () as the height of pollution mixing layer.

Analysis on Atmospheric Thermodynamic Structure and Pollution Dispersion Inhibition.
Studies show that when a "dirty" air parcel is warmer than its ambient air in the lower atmosphere, it will be lifted from its initial location or directly enter an ascending process of the wet adiabatic, and this "buoyancy" of the air parcel is contributed by the Convective Available Potential Energy (CAPE): In expression (3),  is the air pressure,   V −  V gives the difference between the virtual temperature of the ascending parcel and virtual temperature of the environment.According to expression (3), CAPE can be calculated by integrating the "buoyancy" of the parcel from the level of free convection (LFC) to the equilibrium level (EL).On the temperature-entropy or T LOGP chart, the total area covered by both atmospheric sounding curve of the environment (red solid line) and the ascending curve of adiabatic parcel of air pollutants (green line) indicates abundance or absence of the "instable energy" CAPE.When CAPE is negative, which is expressed in convective inhibition (CIN), both dispersion and ascending motion of pollutants will be inhibited.Some studies show that when the absolute CIN value is greater than 100 J⋅kg −1 , the dispersion will be inhibited substantially [17,24].

Index Diagnosis of Pollution Transport at the Isentropic Surface.
As it is known, both updraft and subsidence of dry or wet air are usually the most common and frequent air motions in the atmosphere.However,   remains basically unchanged in either ascending or descending motion of air particles under a dry or wet condition [21].In other words, the true trajectory of air particles can be obtained by analyzing and calculating airflows on the isentropic surface relative to their motions on the isentropic surface if the motion of an air parcel is observed from perspective of iso-  .A relative airflow on the isentropic surface is expressed in the following equation [25][26][27]: where  →  obs and  →    and are the observed wind vector and the movement vector of the isentropic surface (i.e., weather system), respectively.Usually, when rainfall and snowfall systems are discussed, some meaningful results can be achieved by analyzing air pressure (), temperature (), specific humidity (), and relative airflow  →  on isentropic surface to track airflow trajectories on the iso-  surface [27,28].Using expression (1), the weather elements , , and  are calculated to give the distribution of PLAM index and its variations on iso-  surface are tracked to find out its transport trajectory.If the wind vector  →  of any arbitrary station around Beijing, which can be derived from expression (4), is projected onto the municipality as  →   →BJ , then the product of PLAM multiplied by  →   →BJ on the isentropic surface can be used to express the pollution transport to Beijing from its surrounding areas [23]: where a positive value of PLAM →BJ represents the meteorological conditions that are favorable for pollution transport to Beijing from its surrounding areas, or vice versa, and the PLAM →BJ value shows the intensity of the transport impact.data in Beijing in the period of 1-31 December 2016.Totally, there are 542 sets of synchronous observation layouts, as it is seen in Figure 1.The PM 2.5 measurements and distribution of the heights of pollution mixing layer (H PML) show that PM 2.5 and H PML oscillate synchronously in the opposite phase.In whole December, there were 6 episodes in which significant PM 2.5 peaks were detected, occurring on 2∼4, 7∼8, 11∼13, 16∼21, 24∼26, and 30∼31 December, respectively.These high PM 2.5 values were 450, 250, 210, 500, 200, and 500 g/m 3 , respectively.Synchronously, 6 low H PML values also appeared, and totally there were 6 fluctuations in the month, showing a 5-day oscillation cycle, a very interesting characteristic (Figure 1).The Explosive Growth Period of PM 2.5 concentration (EGP) seen in Figure 1 represents the episode of 16∼21 December, in which the synchronous oscillation of PM 2.5 and H PML in the opposite phase is the most typical.

Contribution of the Height of Pollution Mixing Layer.
Figure 2 gives an analysis of day-by-day (hourly) PM 2.5 measurements relative to H PML in the period of 1-31 December 2016.Figure 2 shows the following: (1) In the frequent heavy pollution events that occurred in December 2016, H PML was inversely correlated with PM 2.5 measurements.As stated in the above section, the episode of 16-21 December shown in the Explosive Growth Period of PM 2.5 concentration (EGP) in Figure 1 was most typical.At 08:00-14:00 on 15 December, H PML reached its peak value, that is, 3000 m, but a low PM 2.5 value was measured in the same episode, which was less than 50.At 20:00 on 20 December, H PML was less than 200 m, but PM 2.5 value peaked at 500 g/m 3 (see Explosive Growth Period of PM 2.5 concentration (EGP) in Figure 1).Therefore, the height of pollution mixing layer has a universal impact on formation of severe haze.
(2) An inverse correlation exists between PM 2.5 and H PML, and the confirmation coefficient of the negative correlation is  2 = 0.566, with its significance level exceeding 0.001 (Figure 2).This shows that H PML gives a good performance for diagnosing PM 2.5 density.The lower the H PML is, the higher the accumulated PM 2.5 density will be.

Contribution of Atmospheric Convective Inhibition to
Heavy Pollution.As stated above, studies on vertical thermodynamic structure in the atmosphere show that CAPE is calculated by integrating the buoyancy of the air parcel from the level of free convection (LFC) to the equilibrium level (EL).When positive CAPE energy is obtained, convection develops and it is favorable for air pollution dispersion.On the contrary, when CAPE is negative, the convective dispersion of pollutants will be inhibited.The threshold values of convective dispersion or inhibition energies are given as follows [17]: The convective inhibition (CIN) refers to a negative CAPE value.If CIN is greater than 100 J⋅kg −1 , the aforementioned dispersion will be unlikely to occur without any external forcing.
Figure 3 presents vertical thermodynamic diagrams over Beijing at 08:00 on 20 December, which is prepared based on calculations according to expression (3), using air pressure (), temperature (), and dew point temperature (  ) observations in Beijing.
At 08:00 on 20 December 2016, the air parcel LFC was displaced at 650 hPa; the mean temperature at this level was given in following formula:   V −  V = −6.66∘ C, which was derived from Figure 3.As it is revealed in this typical temperature-entropy diagram for 20 December 2016, just opposite to 16 December, the ascending curve   V along the iso-  line was located on the left side of the stratification curve  V but stayed away from the ambient sounding curve; the temperature of ascending air parcel   V was lower than its ambient temperature by 7 ∘ C (  V −  V = −6.66∘ C).According to expression (3), CAPE can be derived: As above calculation results show, at 08:00 on 16 December, CAPE value was −5200 J⋅kg −1 , whereas the inhibition energy (CIN) peaked at 5200 J⋅kg −1 , which was 50 times higher than the threshold and absolutely stable; the green zone in the thermodynamic diagram was expanding significantly.At this hour, PM 2.5 was soaring from 50 up to 500 g/m 3 (see Explosive Growth Period of PM 2.5 concentration (EGP) in Figure 1), which was a 10-fold increase relative to the initial stage, and absolutely stable [17].Obviously, CIN made a very significant contribution to the heavy pollution event in Beijing.

PLAM-Based Diagnosis on Meteorological Conditions for
Pollution Transport to Beijing from Its Surrounding Areas. Figure 4(a) presents an analysis of the isentropic surface (  = 280 ∘ k) for 08:00 on 20 December 2016 which was calculated using expressions ( 4) and ( 5), and it also shows the distribution of meteorological conditions for orienting pollution transport towards Beijing (PLAM →BJ ) from its surrounding areas.It can be seen from Figure 4 that the Beijing-oriented (note: orientation target is changeable) red zones in the distribution chart indicate that the surrounding meteorological conditions are favorable for pollution transports in positive values towards Beijing.The blue zones show that the weather conditions are unfavorable for Beijing-oriented transports in negative values; in other words, the transports are not oriented to Beijing and even can be in an opposite direction.
Figures 4(b), 4(c), and 4(d) give the predicted PLAM →BJ index distributions for 19 December 2016, which are calculated using expressions ( 4) and ( 5).The starting point of the forecast is: 08:00 on 19 December; the rolling forecast period is for 3 h (Figure 4 From the above analysis, the PLAM →BJ index prognosis charts describing the Beijing-oriented pollution transports On one hand, this shows that the heavy pollution process over Beijing is related to pollution transports from the surrounding Hebei and western Shandong provinces.On the other hand, it also proves that PLAM index can contribute to the predictability of current refined nowcasting.

Contribution of PLAM Index to Heavy Pollution Process.
Figure 5 gives an analysis on correlation of hourly dayto-day PM 2.5 measurements made in the period of 1-31 December 2016 with the PLAM index.As the figure shows, the correlation of actual PM 2.5 density with PLAM index growth is basically an -index correlation, the correlation confirmation coefficient is given in  2 = 0.7324, and its significance level exceeds 0.001 (Figure 5).This shows that PLAM index is a meaningful indicator for aerosol accumulation and formation of heavy pollution in a specific locality, and it has the capability for quantitative diagnosis and prediction.Overall, a composite graphic describing the heavy pollution process known as the severe hazy weather event in Beijing in December 2016 is given in Figure 6.
The meteorological conditions influencing heavy pollution in Beijing are very complicated.Based on analysis of PLAM index, this paper gives a quantitative description of basic physical attributes of the so-called static and stable atmospheric system, which provides some important clues for analyzing and diagnosing the mechanism of meteorological impacts on air pollution.An analysis on isentropic (iso-  ) process described by PLAM index reveals the contribution of the high-value CIN to aerosol accumulation growth in the lower atmosphere.An analysis on tracking PLAM transport index suggested that there was a pollution transport process towards Beijing from its surrounding areas.The displacement of vertical dispersion which was overlapped with the pollution transport from the adjacent areas had a significant impact and made a major contribution to forming the heavy pollution in Beijing, and it was an important factor for the aggravated and persistent hazy weather over Beijing.

The Statistical Analysis of H PML Differences in Heavy
Pollution and "Blue Sky".As we know, a large-scale haze weather occurred in the east of China, affecting an area of 1.43 million square kilometers, about 15% of the land area, during the period of 20 to 26 February in 2014.6 consecutive heavypolluted weather warnings were issued by China's Central Meteorological Observatory.An orange alert of heavy haze was being issued continually on 25 February in 2014.The moderate haze events occurred in Beijing, Tianjin, Hebei, Shanxi, Shandong, Henan, Shaanxi, Liaoning, and many other places; in particular, heavy haze was found in Beijing-Tianjin-Hebei and other places.In east, central, and south China, there is also a continuous haze weather.Long-lasting heavily polluted weather swept over half of China, which has a serious impact on people's production and life.In this section, we will try to analyze the significance and contribution of polluted mixed layer height in the quantitative diagnosis of large-scale haze weather system in eastern China.
In order to compare the differences of weather characteristics between the case of heavy pollution and the "blue sky" in winter, which are the two types of weather phenomena in east China, to observe the differences of the H PML and the weather element characteristics, the weather observation reports were analyzed for the large-scale pollution cases mentioned above in eastern China for the area of the east of 100 ∘ E at 08:00 (local time), 26 February 2014.The region of eastern China, the east of 100 ∘ E are selected, from the north of Heilongjiang to the vast area of the Pearl River Delta.
The two types of extreme weather stations, "haze weather" and "Azure Sky", represented 24 and 8 sites, respectively, accounting for 6% and 2% of the total of 400 stations.The two groups of observations are listed in Tables 2 and 3. From Tables 2 and 3, we can see the following: (1) The average situation is that there is little difference in the normal meteorological elements between medium-heavy pollution and "azure" extreme weather.For example, the differences for those two types of extreme weather are not obvious in air pressure (), temperature (), and wind speed; therefore, it is very limited to distinguish between haze and fine weather by using conventional meteorological elements.Only relative humidity (RH) was significantly different, for 87% and 31%, respectively.The difference for those two types of extreme weather in visibility was in 1 km and 22 km, respectively.However, the RH changes are related to various weather processes and can usually be very wide in the nonpolluted weather situation.(2) Comparing Tables 2 and 3, it is shown that the difference of H PML between severe pollution and "azure" extreme weather is very significant, 240 m and 1878 m on average, respectively.The H PML for heavy pollution cases could be 8∼10 times higher than "azure" weather situation.This indicates that the H PML parameters have significant contribution to quantitative identification of the process of heavy pollution and "blue sky."

Conclusions
We conclude the following: (1) As it is revealed in calculations of vertical temperature-entropy chart based on analysis of PLAM

Figure 1 :
Figure 1: Hourly PM 2.5 observations and H PML in Beijing in the period of 1-31 December (542 synchronous observations patterns).

3 )Figure 2 :
Figure 2: Analysis of hourly PM 2.5 measurements relative to H PML in December 2016.

( 1 )( 2 )( 4 )
(b)), 6 h (Figure 4(c)), and 12 h (Figure 4(d)), respectively.Comparing Figure 4(a) with Figure 4(b) and Figure 4(c) with Figure 4(d), we see the following: At 08:00 on 20 December 2016, the PLAM →BJ index in Beijing area exceeded 300 (Figure 4(a)), which was consistent with the fact that PM 2.5 density reached 500 g/m 3 in Beijing at this hour (also refer to Figure 1).It is shown that the meteorological conditions in Beijing fell into a worse category at this time, which were unfavorable for pollution dispersion in the lower atmosphere.As the 3 h prognosis chart (Figure 4(b)) shows, a small zone with high PLAM →BJ index (greater than 100) is oriented to Beijing from the southern Hebei and western Shandong provinces.(3) As it is indicated in the 6 h PLAM →bj index prognosis chart (Figure 4(c)), the small high index value zone near southern Hebei extends in a south-north direction, and Beijing-oriented pollution transport is enhanced.The high index center has grown from 100 to more than 200.Southern Beijing is influenced quite significantly.As shown in 12 h PLAM →BJ index prognosis chart (Figure 4(d)), the unfavorable weather condition in central Hebei has been further maintained and even aggravated.The PLAM →BJ index-based predictions in rolling show that the pollutions with high index values in the southwestern Shandong province move north and they are also oriented towards Beijing.

Figure 5 :
Figure 5: Analysis on correlation of hourly PM 2.5 measurements in Beijing in the period of 1-31 December 2016 with PLAM index under meteorological conditions.

Table 3 :
Observations and H PML of "Azure Sky."

Table 2 :
Observations and H PML of heavy pollution in February 2014.