Modeling and Regionalization of China’s PM2.5 Using Spatial-Functional Mixture Models

Modeling spatial-temporal variability of PM2.5 concentrations in Belt and Road Initiative (BRI) region via functional adaptive density approach

The rapid development of the Belt and Road Initiative (BRI) has led to severe air pollution dominated by PM2.5 concentrations which can cause a profound negative impact on human health and economic activity. This problem poses a critical environmental challenge to efficiently handling large-scale spatial-temporal PM2.5 data in this extended region. Functional data analysis (FDA) technique offers powerful tools that have the potential to enhance the analysis of spatial distributions and temporal dynamic changes in high-dimensional pollution data. However, modeling the spatial-temporal variability of PM2.5 concentrations by FDA remains unrevealed in the BRI region. To address this research gap, our study aimed to achieve two main objectives: first, to model the spatial-temporal dynamic variability of PM2.5 in 125 BRI nations (1998-2021), and second, to identify the underlying clusters behind the variations. We employed the recently developed functional adaptive density peak (FADP) clustering approach to solve the current problem. The proposed method is based on the joint use of functional principal components (FPCs) and functional cluster analyses. The main results are as follows: (i) The first three FPCs almost captured 99% of the total variations involving all valuable information on PM2.5 concentrations. (ii) PM2.5 pollution was highly concentrated in the developing countries (Pakistan, Bangladesh, and Nigeria) and the developed countries (Arabian Gulf countries: Qatar, United Arab Emirates, Bahrain, Saudi Arabia, Oman), and the least developed countries (Yemen and Chad). (iii) Three optimal clusters were identified and thus classified the PM2.5 into three distinct degrees of pollution: severe, moderate, and light. (iv) Cluster 1 had a severe pollution effect degree with a high rate of change, and it covered the Arabian Peninsula countries, African countries (Cameroon, Egypt, Gambia, Mali, Mauritania, Nigeria, Sudan, Senegal, Chad), Bangladesh, and Pakistan. (v) About 62 BRI countries belonged to cluster 2 showing a light pollution degree with annul average of less than 20 [Formula: see text]; this pointed out that the PM2.5 concentration remains stable in the cluster 2-related countries. The findings of this research would benefit governments and policymakers in preventing and controlling PM2.5 pollution exposure in BRI. Furthermore, this research could pay attention to sustainable development goals and the vision of the Green BRI policy.

Clustering Spatially Correlated Functional Data With Multiple Scalar Covariates

We propose a probabilistic model for clustering spatially correlated functional data with multiple scalar covariates. The motivating application is to partition the 29 provinces of the Chinese mainland into a few groups characterized by the epidemic severity of COVID-19, while the spatial dependence and effects of risk factors are considered. It can be regarded as an extension of mixture models, which allows different subsets of covariates to influence the component weights and the component densities by modeling the parameters of the mixture as functions of the covariates. In this way, provinces with similar spatial factors are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. Further, the identifiability of the proposed model is analyzed, and sufficient conditions to guarantee "generic" identifiability are provided. An L1 -penalized estimator is developed to assist variable selection and robust estimation when the number of explanatory covariates is large. An efficient expectation-minimization algorithm is presented for parameter estimation. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Finally, it is worth noting that the proposed model has a wide range of practical applications, e.g., health management, environmental science, ecological studies, and so on.

Unveiling air pollution patterns in Yemen: a spatial-temporal functional data analysis

The application of spatiotemporal functional analysis techniques in environmental pollution research remains limited. As a result, this paper suggests spatiotemporal functional data clustering and visualization tools for identifying temporal dynamic patterns and spatial dependence of multiple air pollutants. The study uses concentrations of four major pollutants, named particulate matter (PM2.5), ground-level ozone (O3), carbon monoxide (CO), and sulfur oxides (SO2), measured over 37 cities in Yemen from 1980 to 2022. The proposed tools include Fourier transformation, B-spline functions, and generalized-cross validation for data smoothing, as well as static and dynamic visualization methods. Innovatively, a functional mixture model was used to capture/identify the underlying/hidden dynamic patterns of spatiotemporal air pollutants concentration. According to the results, CO levels increased 25% from 1990 to 1996, peaking in the cities of Taiz, Sana'a, and Ibb before decreasing. Also, PM2.5 pollution reached a peak in 2018, increasing 30% with severe concentrations in Hodeidah, Marib, and Mocha. Moreover, O3 pollution fluctuated with peaks in 2014-2015, 2% increase and pollution rate of 265 Dobson. Besides, SO2 pollution rose from 1997 to 2010, reaching a peak before stabilizing. Thus, these findings provide insights into the structure of the spatiotemporal air pollutants cycle and can assist policymakers in identifying sources and suggesting measures to reduce them. As a result, the study's findings are promising and may guide future research on predicting multivariate air pollution statistics over the analyzed area.

Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency

We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially independent functional nugget effect. Observations on each function are made on discrete time points and contaminated with measurement errors. Under the assumption of spatial stationarity and isotropy, we propose a tensor product spline estimator for the spatio-temporal covariance function. When a coregionalization covariance structure is further assumed, we propose a new functional principal component analysis method that borrows information from neighboring functions. The proposed method also generates nonparametric estimators for the spatial covariance functions, which can be used for functional kriging. Under a unified framework for sparse and dense functional data, infill and increasing domain asymptotic paradigms, we develop the asymptotic convergence rates for the proposed estimators. Advantages of the proposed approach are demonstrated through simulation studies and two real data applications representing sparse and dense functional data, respectively.