Footprint model performance under inhomogeneous flow conditions

In this work we assess the performance of Lagrangian stochastic backward footprint model under heterogeneous flow conditions. We determine the respective footprints with a LES embedded Lagrangian simulations to find out the limits of applicability of a conventional backward LS model.

In the stochastic Lagrangian (LS) approach a large number of particles are followed as they traverse between their sources and the observation point either forward or backward in time. The LS models are of different levels of sophistication depending on their intended applications. The backward approach to determine flux and concentration footprints is especially suitable for horizontally inhomogeneous flow conditions because it does not use the inverted plume assumption as does the forward approach. For traditional LS models the description of the flow field is given as an input.

The method of large eddy simulation (LES) has been applied in the field of footprint analysis mainly as a research and development tool. In footprint evaluation an essential difference between the LES method and the standard footprint models is the fact that within an LES model both turbulence statistics and turbulent fluxes are calculated. In this work we use the LES model PALM that has been coupled with a Lagrangian stochastic forward model for the evaluation of particle trajectories in the framework of this study with embedded Lagrangian stochastic dispersion of the trajectories of passive scalar for footprint modelling.

As the heterogeneity is given as a step change of surface properties in the surroundings of the measurement point, in the LES case this will lead to a flow pattern consisting of the component to the direction of the background wind and a component due to small scale circulation driven by the heterogeneity. Thus, the local wind properties at an arbitrary observation point vary according to the distance from heterogeneity and observation height. In conventional stochastic model case the local wind field properties at each position are only determined by the properties of the surface below and the wind direction is constant everywhere. Due to cyclic boundary conditions for LES simulations one steps change within the domain leads into effectively stripelike pattern of surface properties.