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

O. Kurbanmuradov 1 , A. Levykin 2 , U. Rannik 3 , K. Sabelfeld 2 , 4  and T. Vesala 3
  • 1 Center for Phys. Math. Research, Turkmenian State University, Turkmenbashy av. 31, 744000 Ashgabad, Turkmenistan.
  • 2 Institute of Comput. Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentieva str., 6 630090 Novosibirsk, Russia.
  • 3 Department of Physics, FIN-00014 University of Helsinki, Finland.
  • 4 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D – 10117 Berlin, Germany. E-mail:

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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This quarterly published journal presents original articles on the theory and applications of Monte Carlo and Quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology.