Performance of geostatistical interpolation methods for modeling sampled data with non-stationary mean

The measured ozone pollution peak in the atmosphere of Mexico City region was considered in order to study the effect of a non-stationary mean of the sampled data in geostatistics interpolation methods. With this objective the local mean value of the sampled data was estimated through a linear regression analysis of their values on the monitoring station's coordinates. The residuals obtained by removing the data trend are considered as a set of stationary random variables. Several interpolation methods used in geostatistics, such as inverse distance weighted, kriging, and artificial neural networks techniques were considered. In an effort to optimize and evaluate its performance, we fit interpolated values to sampled data, obtaining optimal values for the parameters defining the used model, that means, the values of the parameters that give the lowest mean RMSE between the interpolated value and measured data at 20 stations at 1500 hours for a set of 21 days of December 2001, which was chosen as the training set. The training set is conformed by all the days in December 2001 excepting the days (3,6,9,12,...,27,30) which were considered as the testing set. Once the optimal model is obtained, it is used to interpolate the values at the stations at 1500 hours for the testing days. The RMSE between interpolated and measured values at monitoring stations was also evaluated for these testing values and is shown as a percentage in Table 2. These values and the defined generalization parameter G, can be used to evaluate the performance and the ability of the models to predict and reproduce the peak of ozone concentrations. Scatter plots for testing data are presented for each interpolation method. An interpretation of the ozone pollution levels obtained at 1500 hours at December 21 was given using the wind field that prevailed in the region 1 h before the same day.