Footprint Determination in Stable to Convective Stratification Using an Inverse 3D Lagrangian Particle Model

Common micrometeorological techniques for determing a trace gas flux or concentration give little information about the source location, though any source near the ground could potentially contribute to the measurement at a given receptor. In recent years, several models have been proposed to estimate the size of the upwind surface area of influence (footprint) for a measured flux or concentration and the footprint's dependence on the height of the measurement, the surface roughness, heterogeneous underlying surfaces, atmospheric stability and the turbulent velocity fluctuations has been discussed. However, most of the analytical models to predict footprints are limited to the surface layer, whereas all the footprint models based on a Lagrangian particle model fulfill the well-mixed condition only for one given stability regime.

The present footprint model is of the Lagrangian type and employs a recently established approach using backward trajectories of particles. It is based on a 3-dimensional Lagrangian Stochastic Particle Dispersion model satisfying the well-mixed condition continuously for stable to convective conditions, as well as for receptors above the surface layer (e.g., for use in connection with aircraft measurements). For the first time in a footprint model, a density kernel method is introduced, with locally optimized bandwidths for appropriate smoothing depending on the particle density. This allows for a significant reduction in the number of simulated particles for the same accuracy. Furthermore, the sensitivity of the footprint to modifications regarding the number of touchdowns per particle has been investigated.

As a first step, the model results were evaluated against corresponding estimates using the well-established analytical footprint models FSAM and SAM. Good agreement is found between the two models within the surface layer. As expected, the computed footprints differ under strongly unstable conditions and for receptors above the surface layer. The discrepancy between the two models in the peak location and size of the footprint increases the more unstable the stratification. This is due to the fact that the surface layer model - in contrast to the present Lagrangian approach - does not take into account the skewness of the vertical velocity under convective conditions with the associated consequences on dispersion.