Spatial interpolation techniques for stimating levels of pollutant concentrations in the atmosphere

Abstract

The inverse distance-weighting method (IDW) and kriging techniques are the most commonly used spatial interpolation techniques for estimating levels of pollutant concentrations in regions that contain a number of monitoring stations. The measured ozone pollution peaks in a period, in the atmosphere of the Mexico City region, are considered to be a sampled data set with a non-stationary mean. In order to study the effect of a non-stationary mean in the performance of interpolation methods IDW and kriging, the data set is transformed by removing the data trend of the sampled data set. The residuals obtained are considered to be a set of stationary random variables. This work initially considers the residuals obtained from measured ozone concentration data at 20 stations at 15:00 hours for a set of 21 days in December, 2001. This set of 420 data is considered to be the training set. To determine the parameter values that define the statistical weights for each of the IDW and kriging methods that are analyzed in this work, a cross-validation method is considered. This method assumes initial parameter values, which are fitted by minimizing the root mean squared error, RMSE, between the observed and estimated values in each of the stations. This process takes the training set in consideration for calculation. Once the parameter values that define the statistical weights for each IDW and kriging methods are obtained, by the process described above, these methods are used to interpolate its corresponding values at the stations at 15:00 hours for the days (3$^{rd}$, 6$^{th}$, 9$^{th}$, \ldots 27$^{th}$, 30$^{th})$ of December, 2001, which are considered to be the testing sets. The RMSE between interpolated and measured values at monitoring stations is also evaluated for these testing values and is shown as a percentage in Table I. 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 when the residuals or the sampled data are considered. Scatter plots for testing data are presented for each interpolation method. An interpretation of the ozone pollution levels obtained at 15:00 hours on December 21$^{st}$ was given using the wind field that prevailed in the region at 14:00 hours on the same day.