A New Spatio-Temporal Clustering Method And Its Application In Pollution Modeling In The Beijing-Tianjin-Hebei Region

In recent years,China has faced problems such as increased air pollution(for instance,PM_2.5)and frequent haze weather.The situation of air pollution control remains severe.Faced with the long-standing phenomenon of"regional heavy pollution in autumn and winter"in air quality,the country’s requirements for precise and scientific governance in the process of air pollution control are more important and urgent.In order to accurately formulate scientific,effective and differentiated policies and measures to deal with air pollution in different regions,the article established a mixture linear spatiotemporal clustering model suitable for spatio-temporal data,as well as used PM_2.5 concentration and other data to carry out spatio-temporal clustering analysis of cities in the Beijing-Tianjin-Hebei region.Liang et al.（2020）proposed a spatio-temporal clustering method based on the reduced-rank spatial-functional mixture model.This method is based on PM_2.5concentration data for clustering,but the model does not consider the meteorological factors that affect the PM_2.5 concentration.Since meteorological factors have a significant impact on the concentration of pollutants,the current paper proposes a new mixture linear spatiotemporal clustering model based on meteorological covariates based on the model of Liang et al.（2020）.Firstly,the article uses Markov random field to model the categories,and establishes a mixture linear spatiotemporal model of PM_2.5 concentration under each category.The model consists of a mean function,a spatiotemporal random process and a random disturbance term.The article models the mean function as a linear combination of meteorological covariates,and performs Karhunen-Loève expansion on the spatiotemporal random process that obeys the normal distribution based on functional principal component analysis,and finally obtains the conditional distribution of PM_2.5 concentration.Secondly,because the objective function contains latent variables,the article uses Monte Carlo EM algorithm to estimate the unknown parameters involved in the log-likelihood function formed by the observable variable and the two latent variables.The parameters that need to be estimated include the parameters that determine the category in the Gibbs distribution that models the Markov random field.While obtaining the estimated value of the parameter,the spatio-temporal clustering result is also obtained.The article conducts numerical simulation experiments on the above-mentioned mixture linear spatio-temporal model from both homoscedastic spatial structure and heteroscedastic spatial structure.It is found that in the case of homoscedasticity and heteroscedasticity,the model proposed in the current paper fits the PM_2.5 concentration distribution that is more in line with the actual situation than the functional mixture model established by Liang et al.（2020）,and the clustering effect of the former is better.Through the analysis of the actual data in the Beijing-Tianjin-Hebei region from 2013 to 2016,it is found that the model can make good use of the spatio-temporal variables PM_2.5 and meteorological covariates to perform spatio-temporal clustering of thirteen cities in the Beijing-Tianjin-Hebei region.In addition,the fact that the estimated three types of PM_2.5 distribution curves all have different degrees of downward trends and can be separated from each other indicates that the mean functions estimated by the Monte Carlo EM algorithm accurately describe the different distributions of PM_2.5under the three categories,which also reflects the necessity of spatio-temporal clustering.Based on the clustering results given by the model,a leave-one-city-out spatial prediction for thirteen cities in the Beijing-Tianjin-Hebei region is made,and it is found that the effect of spatial prediction based on clustering results is better than that of direct prediction,which also reflects clustering has an important impact on air pollution control and air quality forecasting.