Source-receptor matrix calculation with a Lagrangian particle dispersion model in backward mode

The possibility to calculate linear-source receptor relationships for the transport of atmospheric trace substances with a Lagrangian particle dispersion model (LPDM) running in backward mode is shown and presented with many tests and examples. This mode requires only minor modifications of the forward LPDM. The derivation includes the action of sources and of any first-order processes (transformation with prescribed rates, dry and wet deposition, radioactive decay, etc.). The backward mode is computationally advantageous if the number of receptors is less than the number of sources considered. The combination of an LPDM with the backward (adjoint) methodology is especially attractive for the application to point measurements, which can be handled without artificial numerical diffusion. Practical hints are provided for source-receptor calculations with different settings, both in forward and backward mode. The equivalence of forward and backward calculations is shown in simple tests for release and sampling of particles, pure wet deposition, pure convective redistribution and realistic transport over a short distance. Furthermore, an application example explaining measurements of Cs-137 in Stockholm as transport from areas contaminated heavily in the Chernobyl disaster is included