Rosaria Ignaccolo

Functional zoning for air quality

Environmental local agencies have to enforce European directives that impose a land classification, according to air quality status, to distinguish zones needing further actions from those needing only maintenance. This paper presents a land classification in zones featured by different criticality levels of atmospheric pollution, considering pollutant time series as functional data: we call this proposal “Functional Zoning”. Our proposal is articulated in order to also meet two specific requirements: upscaling pollutant concentration data to the municipality scale, since municipalities are the reference territorial administrative units for undertaking actions; aggregating different pollutants in order to provide a multi-pollutant zoning outcome reflecting the air quality status. Specifically, we present three different alternatives to upscale data from a regular grid to the municipality scale. Then, to aggregate by pollutant, we evaluate two strategies summarizing time series: the assessment of an air quality index and the use of the Multivariate Functional Principal Component Analysis (MFPCA). The partition of municipalities is obtained by clustering air quality time series and MFPCA scores. In particular, the proposed functional zoning is carried out for Piemonte (Northern Italy), considering the hourly concentration fields of the main pollutants. We obtain six classifications of the same land and we propose a comparison study of the different strategies’ results, by mapping and analyzing the differences between clusters’ labels. By taking into account the comparison study’s findings, we finally suggest an analysis strategy to environmental agencies and policy makers to obtain an easily interpretable outcome at a very reasonable computational cost.

Modeling threshold exceedance probabilities of spatially correlated time series

The Commission of the European Union, as well the United States Environmental Protection Agency, have set limit values for some pollutants in the ambient air that have been shown to have adverse effects on human and environmental health. It is therefore important to identify regions where the probability of exceeding those limits is high. We propose a two-step procedure for estimating the probability of exceeding the legal limits that combines smoothing in the time domain with spatial interpo- lation. For illustration, we show an application to particulate matter with diameter less than 10 microns (PM10) in the North-Italian region Piemonte.

Modelling collocation uncertainty of 3D atmospheric profiles

Atmospheric thermodynamic data are gathered by high technology remote instruments such as radiosondes, giving rise to profiles that are usually modelled as functions depending only on height. The radiosonde balloons, however, drift away in the atmosphere resulting in not necessarily vertical but three-dimensional trajectories. To model this kind of functional data, we introduce a “point based” formulation of an heteroskedastic functional regression model that includes a trivariate smooth function and results to be an extension of a previously introduced unidimensional model. Functional coefficients of both the conditional mean and variance are estimated by reformulating the model as a standard generalized additive model and subsequently as a mixed model. This reformulation leads to a double mixed model whose parameters are fitted by using an iterative algorithm that allows to adjust for heteroskedasticity. The proposed modelling approach is applied to describe collocation mismatch when we deal with couples of balloons launched at two different locations. In particular, we model collocation error of atmospheric pressure in terms of meteorological covariates and space and time mismatch. Results show that model fitting is improved once heteroskedasticity is taken into account.

Modeling the Short-Term Effect of Traffic and Meteorology on Air Pollution in Turin with Generalized Additive Models

Vehicular traffic plays an important role in atmospheric pollution and can be used as one of the key predictors in air-quality forecasting models. The models that can account for the role of traffic are especially valuable in urban areas, where high pollutant concentrations are often observed during particular times of day (rush hour) and year (winter). In this paper, we develop a generalized additive models approach to analyze the behavior of concentrations of nitrogen dioxide (NO2), and particulate matter (PM10), collected at the environmental monitoring stations distributed throughout the city of Turin, Italy, from December 2003 to April 2005. We describe nonlinear relationships between predictors and pollutants, that are adjusted for unobserved time-varying confounders. We examine several functional forms for the traffic variable and find that a simple form can often provide adequate modeling power. Our analysis shows that there is a saturation effect of traffic on NO2, while such saturation is less evident in models linking traffic to PM10 behavior, having adjusted for meteorological covariates. Moreover, we consider the proposed models separately by seasons and highlight similarities and differences in the predictors’ partial effects. Finally, we show how forecasting can help in evaluating traffic regulation policies.

Goodness-of-fit tests for dependent data

We establish some properties for a class of functional tests of goodness-of-fit for correlated observations generated by α-mixing discrete time stochastic processes. These tests are associated with projection density estimators. This class of functional tests contains in particular Pearsons χ2 test and the ‘smooth test’ of Neyman, J. (1937). Smooth test for goodness of fit. Scand. Aktuar. 20, 119–128. Results in the case of independent observations, in a general framework, can be found in Bosq, D. (2002). Functional tests of fit. Goodness-of-Fit Tests and Model Validity, Statistics for Industry and Technology, Birkhäuser, Boston, pp. 341–356. We analyze the asymptotic behavior of the test statistics, both under the null hypothesis and under the alternative, establishing the rate of convergence to their limit distributions. We determine the necessary and sufficient conditions for consistency of the test. Indications for implementing the test are provided.