Mapping roadside nitrogen dioxide concentrations using non-stationary kriging
Résumé
Atmospheric nitrogen dioxide (N02) concentrations around a major road in Alsace (France) are estimated on a fine grid using measurements given by passive samplers and a geostatistical approach. Data are referenced to a local coordinate system where (x, y) are respectively the distance from and along the road. They show a strong non-stationarity which does not allow ordinary kriging to be used in the estimation. Therefore a trend is modelled by a combination of exponential and polynomial functions. Experimental residuals are then computed as the differences between measurements and the trend. The idea is to interpolate the residuals at the nodes of the grid, applying kriging methods, and to add them to the trend estimate. Since their variance is not stationary either, an intermediary step is required. lt consists in modelling the standard deviation of the residuals as a function of the drift and normalizing the residuals by this model. This defines a new regionalized variable which can be estimated in the framework of stationary geostatistics. Two possible kriging systems are tested, depending on the fitted variogram model: in the first one, a pure nugget effect (white noise) is used, in which case the best linear estimator of N02 concentration is the trend model; in the second one, a structured exponential variogram is adjusted. This case study shows that non-stationarity may not only characterize the raw variable but can also affect the variance of a phenomenon. lt illustrates the interest of modelling it so as to improve the experimental variogram, fit an acceptable variogram model and compute the variance of the estimation error even if the estimator is reduced to a simple regression function.
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