Abstract

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number ( \(S\) ) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

中文翻译：

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太阳黑子周期的峰值斜率和峰值之间有趣的相关性

摘要

太阳黑子周期的上升阶段的太阳黑子数的最大斜率与该周期的太阳黑子数的最大值具有良好的相关性。这通过使用 Savitzky-Golay 滤波器来平滑和计算太阳黑子数数据的导数来演示。国际太阳黑子数 ( \(S\) ) 的版本 2 用于表示太阳活动。每个周期上升阶段的斜率最大值与太阳活动的峰值相关。使用三种不同的相关性拟合，太阳周期 25 的平均预测幅度为 130.7 ± 0.5，属于太阳预测中最好的相关性之一。这种相关性的一个可能的解释是由表示太阳黑子数随时间变化的形状函数的类似行为给出的。该通用函数还提供了太阳活动极大期的时间，即 2023 年末或 2024 年初函数中从斜率最大值到峰值的时间。希尔伯特变换给出了类似的结果，这是由 11 年太阳黑子的主导地位引起的-太阳黑子数的傅里叶拟合的周期周期。