Kriging with external drift for functional data for air quality monitoring

Abstract

Functional data featured by a spatial dependence structure occur in many environmental sciences when curves are observed, for example, along time or along depth. Recently, some methods allowing for the prediction of a curve at an unmonitored site have been developed. However, the existing methods do not allow to include in a model exogenous variables that, for example, bring meteorology information in modeling air pollutant concentrations. In order to introduce exogenous variables, potentially observed as curves as well, we propose to extend the so-called kriging with external drift-or regression kriging-to the case of functional data by means of a three-step procedure involving functional modeling for the trend and spatial interpolation of functional residuals. A cross-validation analysis allows to choose smoothing parameters and a preferable kriging predictor for the functional residuals. Our case study considers daily PM 10 concentrations measured from October 2005 to March 2006 by the monitoring network of Piemonte region (Italy), with the trend defined by meteorological time-varying covariates and orographical constant-in-time variables. The performance of the proposed methodology is evaluated by predicting PM 10 concentration curves on 10 validation sites, even with simulated realistic datasets on a larger number of spatial sites. In this application the proposed methodology represents an alternative to spatio-temporal modeling but it can be applied more generally to spatially dependent functional data whose domain is not a time interval.

Modelling collocation uncertainty of 3D atmospheric profiles

“…Applications of functional data analysis can be found in various scientific areas, including climatological and environmental ones (see e.g. [24], [6], [2], [13]). However, to our knowledge, little reference is made to heteroskedasticity in the functional data literature.…”

Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles

“…Functional spatial statistics has been recently developed, see e.g. Delicado et al (2010) and Ignaccolo et al (2014), and could be used to handle such data in the framework of a spatial HFR model.…”

Advances in spatial functional statistics

“…However, in many applied cases, the assumption of a constant mean function is clearly not realistic. To address this problem, there have been a number of contributions dealing with this situation (see Caballero et al 2013;Menafoglio et al 2013;Ignaccolo et al 2014;Reyes et al 2015). In all these cases, the stationarity assumption is relaxed.…”

“…Reyes et al (2015) generalise the classical residual kriging method used in univariate geostatistics proposing a three step procedure. Finally, by considering more complex forms of non-stationarity when the mean function depends on exogenous variables (either scalar or functional), the work of Ignaccolo et al (2014) develops the so-called kriging with external drift or regression kriging in a functional data setting.…”