An autoregressive atmospheric dispersion model for fitting combined source and receptor data sets

A method is developed for recursive prediction of emissions and concentrations at various positions, which obey an atmospheric dispersion model, yet have a least squares deviation from observations at the same points. As a by-product, the technique yields a concentration distribution grid on each time-step. This robust procedure rationalizes data which are in dispute, and makes optimal use of incomplete source or receptor observation records. Thus several unknown source-rates may be estimated on-line as the procedure steps through the remaining observation records. An accurate advection-diffusion solution is formulated as a linear transformation for each time-step, using a sub-grid adaptation of the pseudospectral method. This is extended to the vertical dimension using the zeroth, first and second vertical moments of concentration, allowing only uniform wind profiles, but gradual wind-field and diffusivity variations in the horizontal. A discrete Kaiman filter then provides optimal estimates of all source rates, constituting the state vector, to minimize deviations from any source and receptor observations. The algorithm has been applied in a 90 km × 90 km region of the Eastern Transvaal Highveld, including nine SO₂ sources and eight detectors. Indications are that the method will be a valuable aid in interpreting such data sets.