Rounding errors may be beneficial for simulations of atmospheric flow: results from the forced 1D Burgers equation
Rounding errors may be beneficial for simulations of atmospheric flow: results from the forced 1D Burgers equation
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DOI：
10.1007/s00162-015-0355-8
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发表时间：
2015-06
影响因子：
3.4
通讯作者：
P. Düben;S. Dolaptchiev
中科院分区：
文献类型：
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作者：
P. Düben;S. Dolaptchiev
不精确的硬件可以降低计算成本，因为减少了能源需求和提高了性能，因此可以在相同的计算预算内实现更高分辨率的大气模拟。我们调查使用模拟不精确硬件的随机强迫1D Burgers方程的模型与随机次网格尺度参数化。结果表明，数值精度可以减少到只有12位的浮点数的有效位，而不是52位的双精度，没有严重的退化，所有的诊断考虑的结果。在具有更高空间分辨率的网格上使用不精确硬件的模拟显示，与在类似估计计算成本的较粗网格上的双精度模拟相比，结果明显更好。在本文的后半部分，我们比较强迫由于舍入误差的随机强迫的随机参数化方案，用于表示在标准模型设置的次网格尺度的变化。我们认为，随机参数化方案的随机强迫可以提供一个初步猜测的上限的舍入误差的大小的不精确的硬件，可以容忍的模型模拟，并建议舍入误差可以隐藏在随机强迫的分布。我们提出了一个理想化的模型设置，取代昂贵的随机参数化方案的随机强迫与工程舍入误差强迫，并提供类似的质量的结果。工程舍入误差强迫可以用于创建与基于随机强迫的集合相比具有相似扩散的预报集合。我们的结论是，舍入误差不一定会降低模型模拟的质量。相反，他们可以是有益的亚网格规模的变化的代表。
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.