State-Space Modeling for Atmospheric Pollution

Abstract

Two different aspect concerning the state-space modeling for atmospheric pollution are dealt with separately in this paper: (i) the treatment of the advection-diffusion equation and (ii) the use of time series analysis. A method for forecasting the pollutant concentration is proposed. It is based on discretizing the rectified advection-diffusion (RAD) equation by means of a finite-differences scheme and transforming the resultant numerical algorithm into a state-space form. The state-space model uses an optimum estimator algorithm called the Kalman filter to forecast the air pollutant spatial distribution. The state-space modeling defines two basic equations: system state and measurement equations. With regard to the second aspect, state-space methodology is applied to forecast atmospheric aerosol lead (Pb) concentration including wind speed and wind direction as exogenous variables of the models. Data of daily aerosol Pb concentration, wind speed, and wind direction are available for a single site in a semiurban area of Madrid. Previously, wind direction data are scored by applying the direct gradient method related to aerosol Pb concentrations. The lowest scores are those of the west, northwest and north sectors and the score of the calm day is the highest. An adaptive space-state model is selected as the best predictive model of the stochastic models proposed in this paper. One-day-lagged wind speed influences strongly the time variation of aerosol Pb concentration.