Modelling spatio-temporal data with multiple seasonalities: TheNO2Portuguese case

Abstract

a b s t r a c tThis study aims at characterizing the spatial and temporal dynamics of spatio-temporal data sets, characterized by high resolution in the temporal dimension which are becoming the norm rather than the exception in many application areas, namely environmental modelling. In particular, air pollution data, such as NO 2 concentration levels, often incorporate also multiple recurring patterns in time imposed by social habits, anthropogenic activities and meteorological conditions. A two-stage modelling approach is proposed which combined with a block bootstrap procedure correctly assesses uncertainty in parameters estimates and produces reliable confidence regions for the space-time phenomenon under study. The methodology provides a model that is satisfactory in terms of goodness of fit, interpretability, parsimony, prediction and forecasting capability and computational costs. The proposed framework is potentially useful for scenario drawing in many areas, including assessment of environmental impact and environmental policies, and in a myriad applications to other research fields.

Modeling Spatiotemporal Rainfall Variability in Paraíba, Brazil

“…The rainfall distribution in the state of Paraíba showed a clear correlation for both space and time, thereby justifying the use of spatiotemporal kriging. When constructing the spatiotemporal variogram of the residues, several researchers found that spatial dependence became weaker with an increase in time, while the temporal dependence became insignificant over vast spatial distances [19,21,27,33]. In the studies mentioned above, the modeled phenomena did not present common characteristics in the spatiotemporal structure during the construction of the variogram.…”

“…Although the covariates exhibit spatial, temporal, and spatiotemporal variations, the regression model alone cannot account for all the variations. Therefore, the residuals of this model may exhibit spatiotemporal dependencies, indicating that a spatiotemporal variogram can be estimated and later used to interpolate the residues with kriging [19].…”

Space–Time Kriging of Precipitation: Modeling the Large-Scale Variation with Model GAMLSS

“…Several studies that deal with spatial-temporal modeling and which have null values in the database have used the regression model with Normal distribution [11,32] or the Gamma regression model [12,13]. However, the Normal regression does not solve the data asymmetry problem, and the Gama regression does not contemplate in its domain the occurrence of zeroes.…”

“…However, recent studies have evaluated non-Gaussian models, including generalized linear models (GLM), with variable response Gamma [12,13]. Once the Gamma model is assumed, the variable domain has to be strictly positive, and it does not include the value zero.…”

“…Once the Gamma model is assumed, the variable domain has to be strictly positive, and it does not include the value zero. For example, Menezes et al (2016) [12] and Monteiro et al (2017) [13] analyzed the concentration of NO 2 , which had asymmetric behavior with excesses of zero. However, when using GLM with Gamma distribution, it is not possible to model the frequency of zeroes in the variable under study.…”