Klöwer M, Düben P D, Palmer T N
Atmospheric, Oceanic and Planetary Physics University of Oxford Oxford UK.
European Centre for Medium-Range Weather Forecasts Reading UK.
J Adv Model Earth Syst. 2020 Oct;12(10):e2020MS002246. doi: 10.1029/2020MS002246. Epub 2020 Oct 14.
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 significantly reduced. Furthermore, 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.
天气和气候模型对于使用64位或32位浮点算法进行高精度计算的需求受到质疑。较低精度的数字可以加速模拟，并且越来越受到现代计算硬件的支持。本文研究了16位算法在浅水模型中的应用潜力，该模型可作为中等复杂度的天气或气候应用。有几种16位数字格式可能会被使用（IEEE半精度、BFloat16、posit、整数和定点）。很明显，对于复杂的天气和气候应用，简单地改为16位算法是不可能的，因为这会因不可容忍的舍入误差而使模型结果退化，导致模型动力学停滞或模型不稳定。然而，如果使用posit数字格式替代标准浮点数，则可以显著减少模型退化。此外，还有一些缓解方法，如重新缩放、重新排序和混合精度，可使模型模拟对精度降低具有弹性。如果应用缓解方法，16位浮点算法可以在浅水模型中成功使用。结果表明，对于复杂天气和气候模型的至少部分内容，16位格式具有潜力，其中舍入误差将完全被初始条件、模型或离散化误差所掩盖。
