WIAS Preprint No. 829, (2003)

Stochastic Lagrangian footprint calculations over a surface with an abrupt change of roughness height


  • Kurbanmuradov, Orazgeldi
  • Rannik, Ullar
  • Levykin, Alexander I.
  • Sabelfeld, Karl
  • Vesala, Timo

2010 Mathematics Subject Classification

  • 65C05 76S05


  • Forest canopy, Flux footprint functions, surface roughness change, closure model, backward Lagrangian trajectories


Forward and backward stochastic Lagrangian trajectory simulation methods are developed to calculate the footprint and cumulative footprint functions of concentration and fluxes in the case when the ground surface has an abrupt change of the roughness height. The statistical characteristics to the stochastic model are extracted numerically from a closure model we developed for the atmospheric boundary layer. The flux footprint function is perturbed in comparison with the footprint function for surface without change in properties. The perturbation depends on the observation level as well as roughness change and distance from the observation point. It is concluded that the footprint function for horizontally homogeneous surface, widely used in estimation of sufficient fetch for measurements, can be seriously biased in many cases of practical importance.

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