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arXiv 2104.15076physics.ao-ph
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低精度气候模拟:确定性和随机舍入的影响

Climate Modelling in Low-Precision: Effects of both Deterministic & Stochastic Rounding

E. Adam Paxton, Matthew Chantry, Milan Klöwer, Leo Saffin, Tim Palmer

摘要:

受业务天气预报的最新进展的启发,我们研究了低精度算法对气候模拟的有效性。我们开发了一个框架来测量舍入误差的气候模式,它提供了一个压力测试的低精度版本的模型,我们将我们的方法应用到各种模型,包括洛伦兹系统;浅水近似的流量超过山脊;和一个粗分辨率的全球大气模式简化参数化(SPEEDY)。虽然双精度(52有效位)是标准的业务气候模式,在我们的实验中,我们发现,单精度(23 sbits)是绰绰有余,低至一半精度(10 sbits)往往是足够的。例如,SPEEDY可以在整个代码中以12 sbits运行,舍入误差可以忽略不计,如果可以接受非常小的误差,例如平均网格点降水量小于0.1 mm/6 hr,则可以将其降低到10 sbits。我们的测试是基于Wasserstein度量,这提供了严格的非参数范围的舍入误差占年度平均值以及极端天气事件。此外,通过测试模型,同时使用舍入到最近(RN)和随机舍入(SR),我们发现,SR可以减轻舍入误差在一系列的应用。因此,我们的研究结果也提供了证据,SR可能是相关的下一代气候模式。虽然许多研究表明,低精度算法可以适用于短期天气预报时间尺度,但我们的研究结果首次证明,类似的低精度水平可以适用于气候。

英文摘要:

Motivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model which provides a stress-test for a low-precision version of the model, and we apply our method to a variety of models including the Lorenz system; a shallow water approximation for flow over a ridge; and a coarse resolution global atmospheric model with simplified parameterisations (SPEEDY). Although double precision (52 significant bits) is standard across operational climate models, in our experiments we find that single precision (23 sbits) is more than enough and that as low as half precision (10 sbits) is often sufficient. For example, SPEEDY can be run with 12 sbits across the entire code with negligible rounding error and this can be lowered to 10 sbits if very minor errors are accepted, amounting to less than 0.1 mm/6hr for the average grid-point precipitation, for example. Our test is based on the Wasserstein metric and this provides stringent non-parametric bounds on rounding error accounting for annual means as well as extreme weather events. In addition, by testing models using both round-to-nearest (RN) and stochastic rounding (SR) we find that SR can mitigate rounding error across a range of applications. Thus our results also provide evidence that SR could be relevant to next-generation climate models. While many studies have shown that low-precision arithmetic can be suitable on short-term weather forecasting timescales, our results give the first evidence that a similar low precision level can be suitable for climate.

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