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How can we satisfy the well-mixed criterion in highly inhomogeneous flows? A practical approach


Gerbig,  Christoph
Airborne Trace Gas Measurements and Mesoscale Modelling, Dr. habil. C. Gerbig, Department Biogeochemical Systems, Prof. M. Heimann, Max Planck Institute for Biogeochemistry, Max Planck Society;

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Lin, J., & Gerbig, C. (2013). How can we satisfy the well-mixed criterion in highly inhomogeneous flows? A practical approach. In J. Lin, D. Brunner, C. Gerbig, A. Stohl, A. Luhar, & P. Webley (Eds.), Lagrangian Modeling of the Atmosphere (pp. 59-70). Washington: American Geophysical Union. doi:10.1029/2012GM001232.

Lagrangian particle dispersion models (LPDM) have gained widespread acceptance and usage in different applications. Currently, LPDM simulations over regional to global scales are commonly driven using gridded, 3-D output from numerical weather prediction models or mesoscale models. The turbulence profiles contained in these output fields often differ from profiles assumed in idealized simulations: they are discretized and are complex, often with sharp gradients near interfaces such as the ground surface and the top of the planetary boundary layer. A common problem when running LPDMs using such nonidealized turbulence profiles is deviation from the well-mixed criterion; that is, particle distributions initially distributed according to air density unmix over time.We outline a practical method, based on a reflection/transmission algorithm, for adhering to the wellmixed criterion in Gaussian turbulence. The algorithm represents turbulence properties by way of stepped vertical profiles, such that turbulence statistics are constant within layers and change abruptly at layer boundaries. Tests were carried out to examine possible deviation from well mixedness under different turbulence conditions. We compared runs adopting the reflection/transmission algorithm versus two previous commonly adopted approaches. Unlike the two previous algorithms, the reflection/transmission algorithm was robust under all of the turbulence conditions tested, preserving well mixedness with no need for additional refinement of time steps. These results point to the value of adopting the reflection/transmission algorithm especially for (1) LPDMs simulating regional- to global-scale atmospheric transport, in which Lagrangian particles encounter a wide variety of turbulence, and (2) cases with sharp discontinuities in turbulence strength, such as in the vicinity of obstacles or near the top of the planetary boundary layer.