Reconstruction and prediction of the total solar irradiance: From the Medieval Warm Period to the 21st century

Total solar irradiance is the primary energy source of the Earth’s climate system and therefore its variations can contribute to natural climate change. This variability is characterized by, among other manifestations, decadal and secular oscillations, which has led to several attempts to estimate future solar activity. Of particular interest now is the fact that the behavior of the solar cycle 23 minimum has shown an activity decline not previously seen in past cycles for which spatial observations exist: this could be signalling the start of a new grand solar minimum. The estimation of solar activity for the next hundred years is one of the current problems in solar physics because the possible occurrence of a future grand solar minimum will probably have an impact on the Earth’s climate. In this study, using the PMOD and ACRIM TSI composites, we have attempted to estimate the TSI index from year 1000 AD to 2100 AD based on the Least Squares Support Vector Machines, which is applied here for the first time to estimate a solar index. Using the wavelet transform, we analyzed the behavior of the total solar irradiance time series before and after the solar grand minima. Depending on the composite used, PMOD (or ACRIM), we found a grand minimum for the 21st century, starting in 2004 (or 2002) and ending in 2075 (or 2063), with an average irradiance of 1365.5 (or 1360.5) Wm 2 1r 1⁄4 0:3 (or 0.9) Wm 2 . Moreover, we calculated an average radiative forcing between the present and the 21st century minima of 0:1 (or 0.2) Wm 2, with an uncertainty range of 0:04 to 0:14 (or 0:12 to 0:33) Wm 2. As an indicator of the TSI level, we calculated its annual power anomalies; in particular, future solar cycles from 24 to 29 have lower power anomalies compared to the present, for both models. We also found that the solar activity grand minima periodicity is of 120 years; this periodicity could possibly be one of the principal periodicities of the magnetic solar activity not so previously well recognized. The negative (positive) 120-year phase coincides with the grand minima (maxima) of the 11-year periodicity.

总太阳辐照度（Total Solar Irradiance, TSI）是地球气候系统的核心能量来源，其变化可驱动自然气候变化。该变化除其他表现形式外，以年代际振荡与长期世纪尺度振荡为主要特征，由此催生了多项预测未来太阳活动的研究尝试。当前尤为值得关注的是，第23太阳活动周的极小期表现出此前已有空间观测记录的所有太阳活动周中均未出现过的活动衰减现象，这或许预示着新一轮特大太阳活动极小期（grand solar minimum）的开启。对未来百年太阳活动的预估是当前太阳物理学领域的核心难题之一，因为未来若出现特大太阳活动极小期，或将对地球气候产生显著影响。

本研究借助PMOD与ACRIM TSI复合数据集，首次将最小二乘支持向量机（Least Squares Support Vector Machines）应用于太阳指数的预估工作，以此推算公元1000年至2100年的TSI指数序列。本研究还通过小波变换（wavelet transform）分析了特大太阳活动极小期前后的总太阳辐照度时间序列特征。

基于所选用的复合数据集（PMOD或ACRIM），本研究预测21世纪将出现一次特大太阳活动极小期：若采用PMOD数据集，该极小期起始于2004年、结束于2075年，平均辐照度为1365.5 W·m⁻²，相对变化幅度为0.3 W·m⁻²；若采用ACRIM数据集，则起始于2002年、结束于2063年，平均辐照度为1360.5 W·m⁻²，相对变化幅度为0.9 W·m⁻²。此外，本研究计算得出，当前时段与21世纪太阳活动极小期之间的平均辐射强迫（radiative forcing）为0.1 W·m⁻²（PMOD数据集）或0.2 W·m⁻²（ACRIM数据集），其不确定度范围分别为0.04~0.14 W·m⁻²与0.12~0.33 W·m⁻²。

作为TSI水平的表征指标，本研究计算了其年度辐照度异常值；具体而言，针对两种模型，未来第24至29太阳活动周的辐照度异常值均低于当前活动周。本研究还发现，太阳活动特大极小期的周期为120年，该周期或许是此前未被充分认知的太阳磁活动主要周期之一。其120年周期的负相位与11年周期的太阳活动极小期相对应，正相位则与11年周期的太阳活动极大期相对应。