舍入误差对大气环流模式模拟结果的影响

The Influence of Round-off Error on the Atmospheric General Circulation Model

此文旨在研究气候数值模式的长期计算时受舍入误差的影响。通过对大气环流谱模式SAMIL采用不同CPU数计算时获得的长时间积分结果进行分析，发现使用不同CPU数进行单精度计算时，其十年平均月平均500hPa高度场随机误差在正负6～8gpm范围内，而使用双精度计算时相应的误差为正负3～4gpm。对于气候平均场而言，作者的试验表明SAMIL在并行计算时由于计算顺序改变而引起的误差在可接受范围之内。然而，虽然舍入误差的全球平均值不大，但其误差分布的差别范围并不小。数值试验得到的不同模拟结果之间误差大小与模拟结果的自身年际变化大小在同样的量级，因此对于“年际变化”这样的问题来说，其影响是不可忽略的，必须要使用集合预报的办法来减小误差的影响。文中列出了3种研究复杂数值模式舍入误差的实验方法，指出其一定条件下的等效性和不同适用范围，对于其他模式的舍入误差影响研究有一定的参考价值。在舍入误差分析的基础上，介绍了一种新型的专门针对舍入误差的集合预报方法（舍入误差平均集合，RME），指出了其在气候模拟研究中的应用价值。

Round-off error has an influence on the numerical model computations. It is easy to determine the differences between the results of the model SAMIL with different CPUs. After the analysis of the ten-year integration of SAMIL, the error range of global mean height at 500 hPa is determined; it is also found that the global mean height error is decreased at the same level using double precision. The experiment described in the paper proves that the error that arises out of the change in computation sequence is acceptable and that the double-precision computation can help reduce the computing error. Though the global mean error is not very large, the standard error of the difference is not small, and it can be estimated by the experiments in the paper. The estimation shows that it has the same magnitude as the annual change of the simulation results. Therefore, the distribution of mean error cannot be ignored when the model is used to study such cases as annual climate change. In this paper, three different methods adopted to analyze the round-off errors of a complicated numerical model are listed. The equivalence of the three under some conditions is discussed in the paper, as well as their particular applicability conditions. Moreover, the authors introduce a new type of ensemble forecast （RME, Round-off error Mean Ensemble） method to decrease round- off error in climatic study. These methods may be helpful to users who want to analyze the influence of round-off errors of other numerical models.