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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/gmd-2019-258
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2019-258
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: development and technical paper 24 Oct 2019

Submitted as: development and technical paper | 24 Oct 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).

On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments

Colin Grudzien1,2, Marc Bocquet3, and Alberto Carrassi2,4 Colin Grudzien et al.
  • 1University of Nevada, Reno, Reno, Nevada, USA
  • 2Nansen Environmental and Remote Sensing Center, Bergen, Norway
  • 3CEREA, joint laboratory École des Ponts Paris Tech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
  • 4Mathematical Institute, University of Utrecht, the Netherlands

Abstract. Relatively little attention has been given to the impact of discretization error on twin experiments in the stochastic form of the Lorenz-96 equations when the dynamics are fully resolved but random. We study a simple form of the stochastically forced Lorenz-96 equations that is amenable to higher order time-discretization schemes in order to investigate these effects. We provide numerical benchmarks for the overall discretization error, in the strong and weak sense, for several commonly used integration schemes and compare these methods for biases introduced into ensemble-based statistics and filtering performance. Focus is given to the distinction between strong and weak convergence of the numerical schemes, highlighting which of the two concepts is relevant based on the problem at hand. Using the above analysis, we suggest a mathematically consistent framework for the treatment of these discretization errors in ensemble forecasting and data assimilation twin experiments for unbiased and computationally efficient benchmark studies. Pursuant to this, we provide a novel derivation of the order 2.0 strong Taylor scheme for numerically generating the truth-twin in the stochastically perturbed Lorenz-96 equations.

Colin Grudzien et al.
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Code assets for "On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments" C. Grudzien https://doi.org/10.5281/zenodo.3366375

Colin Grudzien et al.
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Short summary
All scales of a dynamical physical process cannot be resolved accurately in a multiscale, geophysical model. The behavior of unresolved scales of motion are often parametrized by a random process to emulate their effects on the dynamically resolved variables, and this results in a random-dynamical model. We study how the choice of a numerical discretization of such a system affects the model forecast and estimation statistics, when the random-dynamical model is unbiased in its parametrization.
All scales of a dynamical physical process cannot be resolved accurately in a multiscale,...
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