Computing the Flux Footprint

Abstract

We address the flux footprint for measurement heights in the atmospheric surface layer, comparing eddy diffusion solutions with those furnished by the first-order Lagrangian stochastic (or “generalized Langevin”) paradigm. The footprint given by Langevin models differs distinctly from that given by the random displacement model (i.e. zeroth-order Lagrangian stochastic model) corresponding to its “diffusion limit,” which implies that a well-founded theory of the flux footprint must incorporate the turbulent velocity autocovariance. But irrespective of the choice of the eddy diffusion or Langevin class of model as basis for the footprint, tuning relative to observations is ultimately necessary. Some earlier treatments assume Monin–Obukhov profiles for the mean wind and eddy diffusivity and that the effective Schmidt number (ratio of eddy viscosity to the tracer eddy diffusivity) in the neutral limit \(S_c(0)=1\), while others calibrate the model to the Project Prairie Grass dispersion trials. Because there remains uncertainty as to the optimal specification of \(S_c\) (or a related parameter in alternative theories, e.g. the Kolmogorov coefficient \(C_0\) in Langevin models) it is recommended that footprint models should be explicit in this regard.