Introduction Study Area and data set Variography

Variography Moving Windows Correlation Matrix

Introduction

In order to investigate the temporal correlation between the different stations in the area under study, we used the method of "Moving Windows Correlation Matrix." The latter proposes a gliding box (window) which scans the time series. The only hyper parameters to define by the user is the lag h between consecutive windows and their size. Within this window, the correlation between the stations taken in pairs is calculated. It is important to specify that this approach does not take into account the spatial distances Source : Lional Rajappa

NO2 air pollution in the city is an important problem influencing environment, health of society, economy, management of urban zones, etc. The problem is extremely difficult due to a very complex distribution of the pollution sources, morphology of the city and dispersion processes leading to multivariate nature of the phenomena and high local spatial-temporal variability. The task of understanding, modelling and prediction of spatial-temporal patterns of air pollution in urban zones is an interesting, challenging and crucial topic having many research axes from science-based modelling to geostatistics and data mining. Moving Windows Correlation Matrix (MWCM) and Spatial-Temporal (ST) Geostatistical analyses were performed in order to understand the ST distribution of carbon dioxide. The spatial and time correlation have been calculating trough the variograms, which were also used as the structural analysis for the kriging models in order to predict ST patterns. We are wondering wether or not Time brings a significant information to the prediction.

Our study area (fig.1) is located in the Canton of Geneva.This canton shares more than 90% of its borders with France. This is among the smallest in Switzerland with 282 square kilometers, but is one of the most densely populated with 1,650 inhabitants per km2. Canton Geneva

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This exploratory tool allows us to understand the temporal continuity of the phenomena. For example (fig.2), we might ask why two stations C1 (deposit TPG) and C2 (Rte de la synagogue) spatially close and generally having two time series with excellent correlation, occasionally experience strong differences. Will the space-time modelling take such behavior into account?

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The assessment of space-time isotropy was made in order to reduce the complexity of the model. The semi-variogram for NO2 (fig. 3) shows that there are only small variabilities between the different time lag t. The calculation of the variogram and the fitting of this one was realised in R-free software programming language. In order to realize the fitting, the software provide different models, such as metric, sumMetric, Product, product Sum,...

Modelling a space-time process can be done in several ways. The easiest way is to treat space and time separately, which means that time is seen as another dimension. We used a separable model: a variogram for space and time each and a joint spatio-temporal sill (variograms may have a separate nugget effect, but their joint sill will be 1).Partial results are shown in fig.4. Figure 2. MWCM plot

Spatial Prediction NO2model