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.

中文翻译：

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浅水模型分析的天气和气候模型中16位算术的数字格式，错误缓解和范围

有人质疑对天气和气候模型使用64位或32位浮点算法进行高精度计算的需求。精度较低的数字可以加快仿真速度，并且越来越受现代计算硬件的支持。本文研究了在浅水模型中应用16位算术的潜力，该模型可作为中等复杂度的天气或气候应用。有几种可能会使用的16位数字格式（IEEE半精度，BFloat16，正数，整数和定点数）。显然，对于复杂的天气和气候应用，不可能简单地将16位算法更改为，因为它会由于无法忍受的舍入误差而导致模型结果恶化，从而导致模型动力学或模型不稳定性停滞。然而，如果使用正数格式替代标准浮点数，则可以大大减少模型降级。此外，还可以使用缓解方法（例如重新缩放，重新排序和混合精度）来使模型仿真具有抵御精度降低的能力。如果应用缓解方法，则可以在浅水模型中成功使用16位浮点算法。结果表明，至少在复杂的天气和气候模型中，至少有一部分会采用16位格式，而四舍五入的误差将被初始条件，模型或离散误差完全掩盖。可用于使模型仿真具有弹性，可防止精度降低。如果应用缓解方法，则可以在浅水模型中成功使用16位浮点算法。结果表明，至少在复杂的天气和气候模型中，至少有一部分可能会被初始条件，模型或离散化误差掩盖，因此至少有16位格式适用于复杂的天气和气候模型。可用于使模型仿真具有弹性，可防止精度降低。如果应用缓解方法，则可以在浅水模型中成功使用16位浮点算法。结果表明，至少在复杂的天气和气候模型中，至少有一部分可能会被初始条件，模型或离散化误差掩盖，因此至少有16位格式适用于复杂的天气和气候模型。