Number Formats, Error Mitigation, and Scope for 16-Bit Arithmetics in Weather and Climate Modeling Analyzed With a Shallow Water Model.
Number Formats, Error Mitigation, and Scope for 16-Bit Arithmetics in Weather and Climate Modeling Analyzed With a Shallow Water Model.
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DOI：
10.1029/2020ms002246
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发表时间：
2020-10
影响因子：
6.8
通讯作者：
Palmer TN
中科院分区：
文献类型：
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作者：
Klöwer M;Düben PD;Palmer TN
人们质疑天气和气候模型是否需要使用64位或32位浮点运算进行高精度计算。较低精度的数字可以加速模拟，并且越来越多地得到现代计算硬件的支持。本文研究了16位算法在浅水模式中应用的潜力，该模式可用作中等复杂度的天气或气候应用程序。有几种可能使用的16位数字格式（IEEE半精度、BFloat16、posits、整数和定点）。很明显，对于复杂的天气和气候应用来说，简单地改变为16位算法是不可能的，因为它会通过不可容忍的舍入误差降低模型结果，导致模型动力学停滞或模型不稳定。但是，如果使用浮点数格式作为标准浮点数的替代，则可以显著降低模型退化。此外，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。如果采用缓解方法，则可以在浅水模型中成功使用16位浮点运算。结果表明，16位格式至少在部分复杂天气和气候模型中具有潜力，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。与浮点数相比，Posit数减少了舍入误差，实现了可靠的16位算术浅水模拟，减少了由16位算术引起的错误，32位的关键计算可以在当今的硬件上实现16位甚至8位处理器之间的通信引入了可忽略的错误，为减少数据通信提供了一个视角
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. Posit numbers reduce rounding errors compared to floating‐point numbers, enabling reliable shallow water simulations with 16‐bit arithmetic Errors caused by 16‐bit arithmetic are reduced with critical computations in 32 bit, which can be implemented on present‐day hardware 16‐ or even 8‐bit communication between processors introduces negligible errors, providing a perspective for reduced data communication