Estimation of Anisotropic, Time‐Varying Spatial Spillovers of Fine Particulate Matter Due to Wind Direction

Abstract

This paper investigates the effect of daily wind direction and speed on the spatio-temporal distribution of particulate matter, PM 2.5 . Interdependencies between the PM 2.5 values of different monitoring sites are characterized by incorporating time-varying anisotropic spatial weighting matrices. These weights are parameterized with respect to wind direction, speed and a range that marks the bandwidth of admissible deviations between wind direction and bearing. The empirical analysis is based on daily PM 2.5 values recorded by monitoring sites located across the eastern United States in 2015 as well as several meteorological regressors. More precisely, we propose a space-time dynamic panel data model with different spatial autoregressive, temporal and exogenous dependencies. All model parameters are estimated by the quasi-maximum likelihood approach. The estimation procedure, including the identification of the range and spatial parameters, is verified by Monte Carlo simulations. We show that part of the spatial dependency of PM 2.5 values is explained by wind direction.Estimation of Anisotropic, Time-Varying Spatial Spillovers 255 spillover effects of PM 2.5 (particulate matter with a diameter less than or equal to 2.5 μm). Wind directions induce spatial dependencies that are not uniform in all directions, so the time-varying spatial weights are also considered to be anisotropic. While the influence of meteorological regressors, which contribute considerably to the distribution and even deposition of PM 2.5 , has been extensively investigated (e.g., DeGaetano and Doherty 2004;Fassò 2013;Tai, Mickley, and Jacob 2010), fewer studies have considered the effect of wind direction. Tai, Mickley, and Jacob (2010) investigated which wind directions were strongly associated with high concentrations of major PM 2.5 components. Sanchez-Reyna et al. (2005) also found that particular wind directions were frequently accompanied by PM 10 increases in London. Similarly, Guerra et al. (2006) reported that wind directions from major industrial areas led to higher PM 2.5 and PM 10 concentrations in Kansas. However, in other respects, time-varying anisotropic spatially autoregressive dependencies due to wind direction have been widely ignored when analyzing or interpolating distributions of particulate matter. We therefore investigate the contribution of these dependencies by employing time-varying anisotropic spatial weighting matrices.The specification of a weighting matrix that reflects the spatial structure and interrelations of cross-sectional units of a sample is one of the key issues in spatial regression models. When working with georeferenced data, those weights are typically predetermined by geographical characteristics such as common borders, nearest-neighbour dependencies or distance decays. In these cases, the typical assumption of non-stochastic weights is not violated. In addition, those characteristics are often permanent or at least slowly evolving over time such that it has become conclusive to draw on constant ...

spGARCH: An R-Package for Spatial and Spatiotemporal ARCH and GARCH models

“…For instance, they could incorporate economic disparities, e.g., differences in the gross domestic products, poverty rates, household incomes etc., or other covariates, like the wind direction and speed when modeling spatial dependence of air pollutants (cf. Merk and Otto 2019). For spatiotemporal autoregressive processes, there are also some approaches to estimate the entire spatial dependence structure using machine learning methods (e.g., Lam and Souza 2016;Otto and Steinert 2018).…”

Multivariate state space methods for official statistics and climate modelling

“…Since spatial spillovers of N O 2 are due to its transportation by the wind, the spatial weight matrix should ideally capture this role of the wind, and therefore be built on information about it. We do so by slightly modifying the approach of Merk and Otto (2020) in using data about wind speed and direction in order to construct a deterministic time-varying spatial weight matrix. Namely, we let…”

“…We refer to Merk and Otto (2020) for a visualisation of the above-described method to build a time-varying spatial weight matrix based on data about wind speed and direction.…”

“…In practice we choose φ = 0.85 and r = 150, which are the values that Merk and Otto (2020) observe in their empirical study, even though they analyse a different pollutant (particulate matter) in a different geographical location (eastern United States) 6 . However, this choice for r does not prevent some rows of W (W ) t from having only zero elements; we therefore let those rows of W t be equal just to the corresponding rows of W (D) .…”

“…Merk and Otto (2020) estimate φ by standard maximum likelihood and choose, from a grid of values for r, the one that maximises the log-likelihood function, in order to estimate r. Nonetheless, the theoretical properties of these "estimators" have not been derived and we therefore prefer to fix values for the two parameters a priori.…”