The Complex Nonlinear Causal Coupling Patterns between PM2.5 and Meteorological Factors in Tibetan Plateau: A Case Study in Xining

10 PM2.5 pollution influences the population health and people’s daily life. Because 11 meteorological factors are main factor affecting the formation of PM2.5, the interaction between 12 PM2.5 and meteorological factors needs to be better understood, both for air quality management 13 and for PM2.5 projection. Here, we use a nonlinear state space method called the convergent cross 14 mapping method to identify the complex coupling patterns between PM2.5 and meteorological 15 factors in a plateau city: Xining. The results prove that PM2.5-meteorological coupling patterns 16 change with seasons and PM2.5-meteorological coupling patterns are fixed in spring, autumn and 17 winter. In spring, there is a negative unidirectional effect from precipitation to PM2.5 and a negative 18 bidirectional effect between relative humidity and PM2.5. In autumn, there are some negative 19 bidirectional effects between PM2.5 and relative humidity, precipitation, and air pressure, while 20 solar radiation has a positive bidirectional effect on PM2.5. In winter, there are negative 21 bidirectional couplings between PM2.5 and wind speed and temperature and a positive bidirectional 22 coupling between relative humidity and PM2.5. Furthermore, relative humidity is a consistent 23 driving factor affecting PM2.5. Air quality managers may alleviate PM2.5 by increasing relative humidity. Thus, the results provide a meteorological means for improving air quality in plateau cities. 25


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PM2.5 pollution pose a serious threat to the health of the population. Long-term or short-term 28 exposure to PM2.5 concentrations can increase the mortality rate caused by cardiovascular diseases 29 (especially ischemic heart disease and stroke), the number of respiratory diseases, and the risk of 30 disability in daily activities among the elderly 1-3 . In addition, PM2.5 pollution also influence 31 people's life, because PM2.5 concentrations cause serious visibility problems 4 . The poor visibility 32 may lead to more traffic accidents. Therefore, to solve the PM2.5 pollution is essential for the 33 prevention of medical accidents due to air pollution. 34 Because atmospheric conditions are one of the main factors affecting the formation of PM2.5 35 concentrations, Air quality managers may attempt to alleviate PM2.5 through meteorological means. 36 Meanwhile, some scholars have noted that physical-chemical models such as chemical transport 37 models were effective for predicting PM2.5 concentrations by PM2.5-meteorological interactions. 38 However, it is difficult to adjust their parameters for different regions or select proper parameters 39 for different meteorological factors from first principles 5-6 . In this way, they need more information 40 to guide parameter adjustment. Therefore, clarifying the complex nonlinear coupling between 41 multiple meteorological factors and PM2.5 concentrations is of great theoretical significance and 42 practical value for the PM2.5 prediction and for the decision-making of government for the 43 environmental management 7-8 . 44 Most studies have emphasized the direct effect of meteorological factors (e.g., temperature, 45 humidity, wind, precipitation and water vapor pressure) on PM2.5 concentrations. For example, 46 Tran and Mölder 9 noted that wind, temperature and moisture (water vapor pressure and relative 47

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As Table 1 shows, meteorological data were acquired from the China Meteorological Data 127 Sharing Service System (http://data.cma.cn/). We studied eight kinds of meteorological factors: 128 precipitation (PRE), wind speed (WS), wind direction (WD), pressure (PRS), temperature (TEM), 129 water vapor pressure (e), sunshine duration (SSD), and relative humidity (RH). These factors were 130 further categorized into subfactors. Precipitation is the total precipitation from 20 pm-20 pm. Wind 131 speed includes the extreme wind speed (WSex), maximum wind speed (WSmax), wind speed and 132 an average maximum wind speed of 2 minutes (WSmean2mins). The wind direction includes the 133 maximum wind speed of the wind direction (WDex) and the maximum wind speed direction 134 (WDmax). Pressure includes the daily mean pressure (PRSmean), daily maximum pressure 135 (PRSmax), and daily minimum pressure (PRSmin). Temperature includes the daily mean 136 temperature (TEMmean), daily maximum temperature (TEMmax) and daily minimum temperature 137 (TEMmin). Water vapor pressure is the mean water vapor pressure. Solar radiation is represented 138 by the daily sunshine duration (SSD). Relative humidity includes the daily mean relative humidity 139 (RHmean) and daily minimum relative humidity (RHmin).  and identify what direction the coupling was (unidirectional causality/bidirectional causality). Take 174 cross-mapping from X to Y as an example. First, we formed the lagged-coordinate vectors ( ) = 175 〈 ( ), ( − ), ( − 2 ), … , ( − ( − 1) )〉 for t=1+(E-1) to t=L. This set of vectors was 176 defined as the "reconstructed manifold" or "shadow manifold"

Methods
. Next, we needed to generate a 177 cross-mapped estimate of Y(t), denoted by ̂( )| , by locating the contemporaneous lagged-178 coordinate vector on and finding its E+1 nearest neighbors. E+1 is the minimum number of 179 points needed for a bounding simplex in an E-dimensional space. We used the distance , 180 generated by the E+1 nearest neighbors on , to weight ( ) and obtain the estimate ̂( )| . 181 Finally, the skill of the cross-map estimate (indicated by the correlation coefficient ρ value between 182 observed and predicted), which ranged from 0 to 1, revealed the quantitative causality of X on Y. 183 After obtaining the ρ value among multiple factors, we drew the coupling network among them. In 184 this way, we acquired the coupling pattern between PM2.5 and meteorological factors. 185 represents the Euclidean distance between two vectors. 188 The convergent cross-mapping algorithm is a backward-looking pattern. It examines the 189 relationship between the current states and predicts the current Y rather than predicting the future 190 value of Y based on the current X. To summarize, if variable Y from variable X by using the 191 historical data is more reliable, the quantitative causality of variable X on the variable Y will be the 192 stronger result. were the lowest in spring, summer, and autumn. 208

Correlation between meteorological factors and PM2.5 209
air quality in Xining 41 . In addition, previous studies 31, 42-44 have shown some influences of radiation, 211 air pressure, wind speed, wind direction and water vapor pressure on PM2.5. To more 212 comprehensively analyze the impact of meteorological factors on PM2.5, we examined precipitation, 213 relative humidity, temperature, radiation, air pressure, wind speed, wind direction and water vapor 214 pressure. In the last chapter, these factors were further categorized into subfactors: precipitation, 215 wind speed (extreme wind speed, maximum wind speed wind speed, an average of 2 minutes 216 maximum wind speed), wind direction (maximum wind speed of the wind direction, the maximum 217 wind speed direction), pressure (average pressure, low pressure, high pressure), temperature (mean 218 temperature, maximum temperature and minimum temperature), water vapor pressure, solar 219 radiation (daily sunshine duration) and relative humidity (average relative humidity, minimum 220 relative humidity). 221

Causality between meteorological factors and PM 2.5 233
For the significant variables in Fig. 4, we adopted the CCM method to obtain the individual 234 influence of meteorological factors on PM2.5 concentrations. According to different seasons, we 235 could calculate the seasonal causality for each station. Despite multiple subfactors affecting PM2.5, 236 the most significant p-value of subfactors represented the meteorological factors for each station. 237 The ρ values between meteorological factors and PM2.5 are shown in Table 2. The value of 238 prediction skill (p-value) ranged from 0 to 1, indicating the influence of one variable on another 239 variable. 240    In spring, precipitation and humidity were the most influential meteorological factors affecting 273 the PM2.5 concentrations. Both relative humidity and precipitation had a negative effect on PM2.5. 274 Higher precipitation led to lower PM2.5 concentrations because of wet deposition. When 275 precipitation increased, relative humidity increased. Similarly, when relative humidity increased, 276 precipitation increased. In a wet environment, there was bidirectional coupling between PM2.5 and 277 humidity. This result means that high humidity led to low PM2.5 concentrations and that feedback 278 from low PM2.5 concentrations could increase the humidity. In this way, strong negative 279 bidirectional PM2.5-humidity coupling would strengthen the effects of humidity on PM2.5 280 concentrations. At the same time, the increased precipitation caused increased relative humidity, 281 which would also indirectly influence the PM2.5 concentrations (Fig. 7(a)).

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In autumn, relative humidity, precipitation and air pressure all had negative effects on PM2.5, 285 while sunshine duration had a positive effect on PM2.5. The influence of air pressure on PM2.5 was 286 relatively independent. That is, it did not affect the PM2.5 concentrations indirectly through the 287 influence of meteorological factors. Precipitation had a strong positive influence on relative 288 humidity, which increased the negative influence on PM2.5. Precipitation had a negative effect on 289 sunshine hours, which also strengthened the negative effect on PM2.5 concentrations. There was a 290 negative bidirectional coupling between relative humidity and sunshine hours (Fig. 7(b)). 291 In winter, in a dry state, there was a positive coupling between PM2.5 and relative humidity. 292 Temperature had a negative effect on relative humidity. Wind speed and temperature had a negative 293 bidirectional coupling on PM2.5. As the temperature increased, the saturated water vapor pressure 294 increased, and the relative humidity decreased. This result means that temperature not only directly 295 affected PM2.5 but also indirectly influenced PM2.5 by affecting relative humidity. Temperature 296 positively impacted wind speed, so it strengthened the negative impact on PM2.5 (Fig. 7(c)). 297