Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 9, 2441-2457, 2016
https://doi.org/10.5194/gmd-9-2441-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Methods for assessment of models
22 Jul 2016
Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models
Huda Mohd. Ramli and J. Gavin Esler Department of Mathematics, University College London, London, UK
Abstract. A rigorous methodology for the evaluation of integration schemes for Lagrangian particle dispersion models (LPDMs) is presented. A series of one-dimensional test problems are introduced, for which the Fokker–Planck equation is solved numerically using a finite-difference discretisation in physical space and a Hermite function expansion in velocity space. Numerical convergence errors in the Fokker–Planck equation solutions are shown to be much less than the statistical error associated with a practical-sized ensemble (N = 106) of LPDM solutions; hence, the former can be used to validate the latter. The test problems are then used to evaluate commonly used LPDM integration schemes. The results allow for optimal time-step selection for each scheme, given a required level of accuracy. The following recommendations are made for use in operational models. First, if computational constraints require the use of moderate to long time steps, it is more accurate to solve the random displacement model approximation to the LPDM rather than use existing schemes designed for long time steps. Second, useful gains in numerical accuracy can be obtained, at moderate additional computational cost, by using the relatively simple “small-noise” scheme of Honeycutt.

Citation: Ramli, Huda Mohd. and Esler, J. G.: Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models, Geosci. Model Dev., 9, 2441-2457, https://doi.org/10.5194/gmd-9-2441-2016, 2016.
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Short summary
A rigorous methodology is presented to assess numerical integration schemes for stochastic models in atmospheric dispersion known as Lagrangian particle dispersion models. A series of one-dimensional test problems modelling dispersion in the atmospheric boundary layer is used to evaluate commonly used stochastic integration schemes. The results allow for optimal time-step selection for each scheme and recommendations to be made for use in operational models.
A rigorous methodology is presented to assess numerical integration schemes for stochastic...
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