Mariantonietta Ruggieri

An aggregate AQI: Comparing different standardizations and introducing a variability index.

Many studies demonstrate a strong relationship between air pollution and respiratory and cardiovascular diseases. For this reason, assessing air pollution, and conveying information about its possible adverse health effects, may encourage population and policy makers to reduce those activities increasing pollution levels. In this paper a relative index of variability, to be associated with the aggregate Air Quality Index (AQI) among pollutants proposed by Ruggieri and Plaia (2011), is developed in order to better investigate air pollution conditions for the whole area of a city/region. The most widely-used and up to date pollution indices, based mainly on AQI computed by the US Environmental Protection Agency (EPA) and often defined by the value of the pollutant with the highest (opportunely standardized) concentration on a given day, aim at warning the people for short term health impact. An aggregate AQI, taking into account the combined effects of all the considered pollutants, gives emphasis to possible chronic health effects and long term damages on environment caused by air pollution. The proposed index of variability adds precious information to the aggregate AQI, as it allows one to know whether the value assumed by the AQI is influenced by one or more pollutants. The two indices are jointly used on simulated data, considering different possible scenarios. Applications to real air pollution data are also reported. Before applying the two indices, the effects of different standardizations on data are evaluated from a theoretical point of view.

Functional principal component analysis for multivariate multidimensional environmental data

Data with spatio-temporal structure can arise in many contexts, therefore a considerable interest in modelling these data has been generated, but the complexity of spatio-temporal models, together with the size of the dataset, results in a challenging task. The modelization is even more complex in presence of multivariate data. Since some modelling problems are more natural to think through in functional terms, even if only a finite number of observations is available, treating the data as functional can be useful (Berrendero et al. in Comput Stat Data Anal 55:2619–2634, 2011). Although in Ramsay and Silverman (Functional data analysis, 2nd edn. Springer, New York, 2005) the case of multivariate functional data is also contemplated, they do not cope with more than one dimension (only time is considered as covariate) in the domain of the considered functions. In estimating functional data through smoothing methods, a proper framework for incorporating space-time structures can be found in the generalized additive models (GAM), while classical dimension reduction techniques for functional data lead to functional principal component analysis (FPCA). In a previous work Ruggieri et al. (J Appl Stat 40(4):795–807, 2013) extended temporal FPCA, that is FPCA on data modelled as functions of the one-dimensional time, to multivariate (more than one variable, in our case pollutants) context. In this paper the computational aspects of FPCA are extended to more than one dimension: space (long, lat) and/or space-time; moreover, multidimensional (spatial, spatio-temporal) FPCA is extended to multivariate case. In order to provide a generalization of FPCA to multidimensional (spatio-temporal) and simultaneously multivariate data, we link GAM models together with the approach proposed by Ramsay and Silverman (2005). The paper describes all the computational details useful to implement this approach, while its effectiveness will be shown by a multivariate spatio-temporal environmental dataset, whose structure is actually very common in literature.

Functional Principal Component Analysis for the explorative analysis of multisite-multivariate air pollution time series with long gaps

The knowledge of the urban air quality represents the first step to face air pollution issues. For the last decades many cities can rely on a network of monitoring stations recording concentration values for the main pollutants. This paper focuses on functional principal component analysis (FPCA) to investigate multiple pollutant datasets measured over time at multiple sites within a given urban area. Our purpose is to extend what has been proposed in the literature to data that are multisite and multivariate at the same time. The approach results to be effective to highlight some relevant statistical features of the time series, giving the opportunity to identify significant pollutants and to know the evolution of their variability along time. The paper also deals with missing value issue. As it is known, very long gap sequences can often occur in air quality datasets, due to long time failures not easily solvable or to data coming from a mobile monitoring station. In the considered dataset, large and continuous gaps are imputed by empirical orthogonal function procedure, after denoising raw data by functional data analysis and before performing FPCA, in order to further improve the reconstruction.

Comparing Air Quality Indices Aggregated by Pollutant

In this paper a new aggregate Air Quality Index (AQI) useful for describing the global air pollution situation for a given area is proposed. The index, unlike most of currently used AQIs, takes into account the combined effects of all the considered pollutants to human health. Its good performance, tested by means of a simulation plan, is confirmed by a comparison with two other indices proposed in the literature, one of which is based on the Relative Risk of daily mortality, considering an application to real data.

Comparing spatial and spatio-temporal FPCA to impute large continuous gaps in space

Multivariate spatio-temporal data analysis methods usually assume fairly complete data, while a number of gaps often occur along time or in space. In air quality data long gaps may be due to instrument malfunctions; moreover, not all the pollutants of interest are measured in all the monitoring stations of a network. In literature, many statistical methods have been proposed for imputing short sequences of missing values, but most of them are not valid when the fraction of missing values is high. Furthermore, the limitation of the methods commonly used consists in exploiting temporal only, or spatial only, correlation of the data. The objective of this paper is to provide an approach based on spatio-temporal functional principal component analysis (FPCA), exploiting simultaneously the spatial and temporal correlations for multivariate data, in order to provide an accurate imputation of missing values. At this aim, the methodology proposed in a previous proposal is applied, in order to obtain a good reconstruction of temporal/spatial series, especially in presence of long gap sequences, comparing spatial and spatio-temporal FPCA.

Empirical Orthogonal Function and Functional Data Analysis Procedures to Impute Long Gaps in Environmental Data

Air pollution data sets are usually spatio-temporal multivariate data related to time series of different pollutants recorded by a monitoring network. To improve the estimate of functional data when missing values, and mainly long gaps, are present in the original data set, some procedures are here proposed considering jointly Functional Data Analysis and Empirical Orthogonal Function approaches. In order to compare and validate the proposed procedures, a simulation plan is carried out and some performance indicators are computed. The obtained results show that one of the proposed procedures works better than the others, providing a better reconstruction especially in presence of long gaps.