Inverse modelling

Inverse modelling covers several approaches to deduce emissions from observations. At SMHI we are working with local scale emission estimates from traffic and long-range so called adjoint modelling.

On the local scale we are using NO_x as a tracer and measurements of PM10 for estimation of emissions factors for PM10. This method has then been used for calculations of PM10 concentrations in the city of Stockholm with reasonable good result.

By combining dispersion calculations, using a simple box model, with measured concentrations of NO_x or NO₂, daily NO₂ emissions in three cities in Sweden were calculated and compared with calculated emissions from a traffic emission model.

For long-range applications an adjoint version of MATCH has been developed. The adjoint model is integrated backwards in time feed by observations giving a so called weighted influence function from which estimates of the source characteristics (strength, duration etc.) could be drawn. Alternatively a unit response at observation locations could be fed into the adjoint model. This would, however, lead to a more qualitative estimate of the importance of different source regions in relation to the receptor locations.

The figures below shows the weighted influence function for concentrations of Cs¹³⁷ in southern Sweden after the Chernobyl accident.

Figure 1. Weighted influence function from observations in Sweden, 26 April to 1 May 1986, after the Chernobyl accident.

Figure 2. Weighted influence function at the location of Chernobyl for different heights. The source term may be deduced from this type of product.