Rounding errors may be beneficial for simulations of atmospheric flow: results from the forced 1D Burgers equation

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• 作者：Peter D. Düben ; Stamen I. Dolaptchiev
• 关键词：Inexact hardware ; Stochastic parametrisation ; Numerical precision ; Turbulent closure ; Ensemble methods
• 刊名：Theoretical and Computational Fluid Dynamics
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：29
• 期：4
• 页码：311-328
• 全文大小：4,589 KB
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• 作者单位：Peter D. Düben (1)
  Stamen I. Dolaptchiev (2)
  
  1. Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, UK
  2. Institut für Atmosph?re und Umwelt, Johann Wolfgang Goethe-Universit?t Frankfurt/Main, Frankfurt, Germany
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Fluids
  Mathematical and Computational Physics
  Engineering Fluid Dynamics
  Computational Science and Engineering
  Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2250

文摘

Inexact hardware can reduce computational cost, due to a reduced energy demand and an increase in performance, and can therefore allow higher-resolution simulations of the atmosphere within the same budget for computation. We investigate the use of emulated inexact hardware for a model of the randomly forced 1D Burgers equation with stochastic sub-grid-scale parametrisation. Results show that numerical precision can be reduced to only 12 bits in the significand of floating-point numbers—instead of 52 bits for double precision—with no serious degradation in results for all diagnostics considered. Simulations that use inexact hardware on a grid with higher spatial resolution show results that are significantly better compared to simulations in double precision on a coarser grid at similar estimated computing cost. In the second half of the paper, we compare the forcing due to rounding errors to the stochastic forcing of the stochastic parametrisation scheme that is used to represent sub-grid-scale variability in the standard model setup. We argue that stochastic forcings of stochastic parametrisation schemes can provide a first guess for the upper limit of the magnitude of rounding errors of inexact hardware that can be tolerated by model simulations and suggest that rounding errors can be hidden in the distribution of the stochastic forcing. We present an idealised model setup that replaces the expensive stochastic forcing of the stochastic parametrisation scheme with an engineered rounding error forcing and provides results of similar quality. The engineered rounding error forcing can be used to create a forecast ensemble of similar spread compared to an ensemble based on the stochastic forcing. We conclude that rounding errors are not necessarily degrading the quality of model simulations. Instead, they can be beneficial for the representation of sub-grid-scale variability.