Data Interpolating Variational Analysis for the Generation of Atmospheric Pollution Maps at Various Scales

Abstract

Ordinary kriging is a widely used method to estimate the spatial distribution of atmospheric pollutants at all scales. However, more sophisticated strategies exist. For local mapping, where one often focuses on pollutants with a high spatio-temporal variability, such as nitrogen dioxide or black carbon, land use regression models are commonly used. In epidemiological research, several model reviews have already been published on this topic Hoek et al. (A review of land-use regression models to assess spatial variation of outdoor air pollution. Atmos Environ 42:7561–7578, 2008); Gaines et al. (A review of intraurban variations in particulate air pollution: Implications for epidemiological research. Atmos Environ 39:6444–6462, 2005). For regional mapping, de- and retreading procedures also make use of ancillary variables, such as the population density or the land use, to take into account the local characteristics of the sampling sites before and after the actual interpolation. Due to their low computational cost, these techniques can be implemented operationally Janssen et al. (Spatial interpolation of air pollution measurements using CORINE land cover data. Atmos Environ 42:4884–4903, 2008). In this study we introduce DIVA, a variational inverse method, originally designed for oceanographic applications, that allows one to take into account some new constraints. As it is based on a finite-element approach, physical boundaries such as buildings are naturally taken into account since they actually define the domain of interest. Another useful feature is the possibility to consider an advection field and hence propagate the information in the preferred direction. Finally, this technique also allows one to attribute a different weight to each available measurement, according to the quality of the data, so that heterogeneous data sources, consisting for example of monitoring network, passive sampler and mobile device values, can be used simultaneously and consistently. The model will be tested for two situations: the mapping of NO₂ in the Walloon Region and the air pollution assessment of year 2012 in Antwerp. Results will be qualitatively compared with those of operational models: an ordinary kriging method run at AwAC by Bonvalet et al. (Validation of a geostatistical interpolation model using measurement of particulate matter concentration, Matinée des chercheurs à l’Université de Mons 2013) and a detrended kriging run at ISSeP and originally implemented by Merbitz (Untersuchung und Modellierung der raumzeitlichen Variabilität urbaner und regionaler Feinstaubkonzentrationen. Ph.D. thesis 2013) for the first case, and the RIO-IFDM-OSPM modelling system for the second case as implemented by Maiheu et al. (Luchtkwaliteitsmodellering Ringland, Studie uitgevoerd in opdracht van Stramien cvba en Ring genootschap vzw 2015/RMA/R/13 2015).

Question and Answer

Question: Have you considered introducing anisotropic variogram/covariance in order to facilitate preferential propagation of concentrations e.g. along the direction of streets?

Answer: In DIVA, the covariance function is not explicitly defined, but is the result of the minimization of the cost function. In particular case (infinite domain, specific values for the coefficients), it is possible to compute an analytical solution to the problem, which is an isotropic function (modified Bessel function). When the advection constraint is activated, the covariance is indeed increased in the direction of the flow, even though the covariance function doesn’t have to be explicitly defined.