Majorant filtering in dispersion modeling: theory and applications to development of Russian regulatory models

All atmospheric characteristics, those of air pollution included, are highly contaminated with turbulent fluctuations and, therefore, cannot be directly predicted with deterministic models without preliminary filtering the noise. It is assumed usually that such a filtering is performed when the procedure of the Reynolds averaging (formally over the ensemble but actually over either time or space) is applied to the governing equations and, therefore, to atmospheric processes. In fact, however, this procedure cannot completely filter out the noise because the spectrum of the atmospheric turbulence is extremely broad. The noise level cannot be sufficiently reduced also with more sophisticated techniques corresponding to the LES and DNS models. This level is especially high when considering the fields of concentrations of anthropogenic atmospheric pollutants on the scales from local to urban- and mesoscale because of high level of the spatial inhomogeneity of these fields. It was noticed first in 1959 by F. Gifford who derived an analytical approximation for the PDF of fluctuations of axial concentrations in the plume from a single point source corresponding to the given meteorological conditions and resulting just from meandering of the plume axis. Evidently, the influence of the noise in so called "short-term averaged concentrations" can be reduced by applying the standard techniques of filtering of stochastic processes. It results, however, in estimating the "mathematical expectations" of these concentrations, which poorly represent the whole sample because of the high energy of noise. More efficient approach is based on calculation of certain statistics of concentrations, first of all, their PDFs. It could be done either directly, e.g., when running ensemble simulations, or indirectly, when one simulates several first moments (to be used to reconstruct PDFs) or directly estimates upper percentiles of the PDFs. The last approach, which could be referred to as majorant (or upper-limit) filtering, was introduced at the Main Geophysical Observatory, Russia. General principles of constructing the majorant concentration fields are discussed in this paper. In particular, a general expression for the majorant concentrations from the ground-level point source is derived here. As an example of application of the abovementioned technique, a Russian regulatory dispersion model OND-86 is discussed, which is applied to industrial and car emissions. It is based on the analytical approximation of the numerical solution of the advection-diffusion equation (ADE) and could be used to calculate the 98th percentile of the annual PDF ("the global majorants"). Similar approach was also used in development of the Russian national guideline on accidental releases, which was based on the dose approach and conditional majorants. This model allows determining the scale of contamination resulting from the accidental release of harmful chemical pollutants. Both models were extensively validated upon sets of data of field and laboratory tracer experiments. When applying this approach to the neighborhood scale, additional efforts should be taken to account properly for the spatial inhomogeneity of the governing meteorological fields that are not of stochastic nature. The procedures of downscaling, which are usually used in this connection, suffer, however, from certain deficiencies due to incompatibility of the interpolated boundary conditions with governing equations. An original approach to this problem is now under development at MGO, which employs the formulation based on the perturbation techniques. The same majorant filtering was used in development of a statistical model for predicting daily maxima of concentrations of urban air pollutants. The methodology for development of the statistical prognostic model for daily maxima of short-term concentration includes the following steps: (i) selection of predictors; (ii) censoring of the sample; (iii) transformation of the predictant to the normal distribution; (iv) transformation of nonlinear dependencies in linear ones; and (v) stepwise regression. Corresponding statistical models were developed for the cities of Krasnoyarsk, Siberia (for carbon disulfide and hydrogen fluoride) and Ufa, the European part of Russia (for ethylbenzene and benzene). The results of validation of these models upon independent data sets showed a reasonably good performance with correlation coefficients around 0.7 and predictability around 80%. A slightly modified version of this approach was used in development of the model for prediction of daily maxima of ozone concentrations. The resulting prognostic schemes including those organized as two-step ("predictor-corrector") procedures were developed and tested for the city of St. Petersburg. The results obtained indicate that statistical forecasting schemes can perform well when predicting daily maxima of ozone concentrations. In particular, the coefficients of correlation of predicted and measured maxima can be higher than 0.9 or 0.8 when using "dependent" or independent data sets, correspondingly, with predictability around 90%. The Russian national regulatory guideline on prediction of daily maxima of ozone concentrations, which is based on the proposed methodology, is now under development.