By obtaining the analytic signal of daily sunspot numbers since 1818 we construct a new solar cycle phase clock that maps each of the last 18 solar cycles onto a single normalized 11 year epoch. This clock orders solar coronal activity and extremes of the aa index, which tracks geomagnetic storms at the Earth's surface over the last 14 solar cycles. We identify geomagnetically quiet intervals that are 40% of the normalized cycle, ±2π /5 in phase or ±2.2 years around solar minimum. Since 1868 only two severe (aa >300 nT) and one extreme (aa >500 nT) geomagnetic storms occurred in quiet intervals; 1–3% of severe (aa >300 nT) geomagnetic storms and 4–6% of C‐, M‐, and X‐class solar flares occurred in quiet intervals. This provides quantitative support to planning resilience against space weather impacts since only a few percent of all severe storms occur in quiet intervals and their start and end times are quantifiable.

中文翻译：

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量化极端空间天气的太阳周期调制

通过获得自 1818 年以来每日太阳黑子数的分析信号，我们构建了一个新的太阳周期相位时钟，将过去 18 个太阳周期中的每一个映射到单个标准化的 11 年历元。该时钟对太阳日冕活动和 aa 指数的极端情况进行排序，该指数跟踪过去 14 个太阳周期中地球表面的地磁风暴。我们确定地磁安静间隔为标准化周期的 40%，相位为 ±2π/5，或太阳极小期附近的 ±2.2 年。自 1868 年以来，只有两次严重 (aa >300 nT) 和一次极端 (aa >500 nT) 地磁暴以安静的间隔发生；1-3% 的严重 (aa >300 nT) 地磁暴和 4-6% 的 C、M 和 X 级太阳耀斑发生在安静的时间间隔内。