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Weather and climate models in 16-bit arithmetics: Number formats, error mitigation and scope
  • Milan Klöewer,
  • Peter D Duben,
  • Tim N Palmer
Milan Klöewer
University of Oxford

Corresponding Author:[email protected]

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Peter D Duben
European Centre for Medium-Range Weather Forecasts
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Tim N Palmer
European Centre for Medium-Range Weather Forecasts
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The need for high precision calculations with 64-bit or 32-bit floating-point arithmetic for weather and climate models is questioned. Lower precision numbers can accelerate simulations and are increasingly supported by modern computing hardware. This paper investigates the potential of 16-bit arithmetic when applied within a shallow water model that serves as a medium complexity weather or climate application. There are several 16-bit number formats that can potentially be used (IEEE half precision, BFloat16, posits, integer and fixed-point). It is evident that a simple change to 16-bit arithmetic will not be possible for complex weather and climate applications as it will degrade model results by intolerable rounding errors that cause a stalling of model dynamics or model instabilities. However, if the posit number format is used as an alternative to the standard floating-point numbers the model degradation can be reduced to a tolerable minimum. Furthermore, a number of mitigation methods, such as rescaling, reordering and mixed-precision, are available to make model simulations resilient against a precision reduction. If mitigation methods are applied, 16-bit floating-point arithmetic can be used successfully within the shallow water model. The results show the potential of 16-bit formats for at least parts of complex weather and climate models where rounding errors would be entirely masked by initial condition, model or discretization error.
Oct 2020Published in Journal of Advances in Modeling Earth Systems volume 12 issue 10. 10.1029/2020MS002246