Evaluation of backward and forward Lagrangian footprint models in the surface layer

We ran a Lagrangian stochastic (LS) dispersion model in both forward-in-time and backward-in-time ways to derive footprints. Three Eulerian analytical footprint models were compared with this Lagrangian model for a wide atmospheric stability range. Despite some differences among the three analytical footprint models, their results generally agreed. Results from the forward LS simulations agreed well with the analytical solutions for both concentration footprints and flux footprints, if turbulent parameters were properly prescribed. Quantitative equivalence between the forward and backward Lagrangian footprint estimates was demonstrated. However, concentration footprint derived by backward LS simulation can be seriously contaminated by numerical errors. A ‘test-adjustment’ scheme treating the temporal integration, and a ‘buffer’ layer treating the surface reflection of the LS particles eliminate numerical errors. Forward LS simulations or the flux footprint estimates were quite insensitive to these errors.