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A Bayesian Approach to Forecasting Solar Cycles Using a Fokker-Planck Equation

机译:使用福克-普朗克方程预测太阳周期的贝叶斯方法

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摘要

A Bayesian method for forecasting solar cycles is presented. The approach combines a Fokker-Planck description of short-timescale (daily) fluctuations in sunspot number (Noble and Wheatland, Astrophys. J. 732, 5, 2011) with information from other sources, such as precursor and/or dynamo models. The forecasting is illustrated in application to two historical cycles (cycles 19 and 20), and then to the current solar cycle (cycle 24). The new method allows the prediction of quantiles, i. e. the probability that the sunspot number falls outside large or small bounds at a given future time. It also permits Monte Carlo simulations to identify the expected size and timing of the peak daily sunspot number, as well as the smoothed sunspot number for a cycle. These simulations show how the large variance in daily sunspot number determines the actual reliability of any forecast of the smoothed maximum of a cycle. For cycle 24 we forecast a maximum daily sunspot number of 166±24, to occur in March 2013, and a maximum value of the smoothed sunspot number of 66±5, indicating a very small solar cycle.
机译:提出了一种预测太阳周期的贝叶斯方法。该方法结合了福克-普朗克对太阳黑子数短时间尺度(每日)波动的描述(Noble and Wheatland, Astrophys. J. 732, 5, 2011)与来自其他来源的信息,如前体和/或发电机模型。预测在两个历史周期(周期 19 和 20)和当前太阳周期(周期 24)的应用中得到了说明。新方法可以预测分位数,即太阳黑子数在给定的未来时间落在大或小范围之外的概率。它还允许蒙特卡罗模拟确定每日峰值太阳黑子数量的预期大小和时间,以及一个周期的平滑太阳黑子数量。这些模拟显示了每日太阳黑子数量的巨大方差如何决定任何对周期平滑最大值的预测的实际可靠性。对于第24周期,我们预测2013年3月将出现最大日太阳黑子数166±24,平滑太阳黑子数的最大值为66±5,表明太阳周期非常小。

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