Solar Cycle Prediction

Abstract

A review of solar cycle prediction methods and their performance is given, including forecasts for cycle 24. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Prediction methods form three main groups. Precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. Their implicit assumption is that each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time and, therefore, it lends itself to analysis and forecasting by time series methods. Finally, instead of an analysis of observational data alone, model based predictions use physically (more or less) consistent dynamo models in their attempts to predict solar activity. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. Nevertheless, most precursor methods overpredicted cycle 23, while some extrapolation methods may still be worth further study. Model based forecasts have not yet had a chance to prove their skills. One method that has yielded predictions consistently in the right range during the past few solar cycles is that of K. Schatten et al., whose approach is mainly based on the polar field precursor. The incipient cycle 24 will probably mark the end of the Modern Maximum, with the Sun switching to a state of less strong activity. It will therefore be an important testbed for cycle prediction methods and, by inference, for our understanding of the solar dynamo.

Figure 1

13-month sliding averages of the monthly average relative sunspot numbers R (green) and group sunspot numbers R_G (black) for the period 1611 – 1998.

Figure 2

Monthly values of the 10.7 cm radio flux in solar flux units for the period 1947 – 2009. The solar flux unit is defined as 10–22 W/m² Hz. The green curve shows R_m + 60, where R_m is the monthly mean relative sunspot number. (The vertical shift is for better comparison.) Data are from the NRC Canada (Ottawa/Penticton).

Figure 3

The variation of the monthly smoothed relative sunspot number R during the period 1749 – 2009, with the conventional numbering of solar cycles.

Figure 4

Amplitudes of the sunspot cycles (dotted) and their Gleissberg filtered values (blue solid), plotted against cycle number.

Figure 5

Monthly smoothed sunspot number R at cycle maximum plotted against the rise time to maximum (left) and against cycle length (right). Cycles are labeled with their numbers. In the plots the red dashed lines are linear regressions to all the data, while the blue solid lines are fits to all data except outliers. Cycle 19 is considered an outlier on both plots, cycle 4 on the right hand plot only. The corresponding correlation coefficients are shown. _

Figure 6:

Monthly smoothed sunspot number R at cycle maximum plotted against the values of R at the previous minimum (left) and 2.5 years before the minimum (right). Cycles are labeled with their numbers. The blue solid line is a linear regression to the data; corresponding correlation coefficients are shown. In the left hand panel, cycle 19 was considered an outlier.

Table 1

A selection of forecasts for cycle 24.

Figure 7

Magnetic field strength in the Sun’s polar regions as a function of time. Blue solid: North; red dashed: (−1) South; thin black solid: average; heavy black solid: smoothed average. Strong annual modulations in the hemispheric data are due to the tilt of the solar equator to the Ecliptic. Data and figure courtesy of Wilcox Solar Observatory (see http://wso.stanford.edu/gifs/Polar.gif for updated version).

Figure 9

Pseudo-Wigner power distribution in the sunspot number record, with time on the abscissa and frequency on the ordinate. The three horizontal bands of high power correspond, from bottom to top, to the Gleissberg cycle, the 11-year cycle and its first harmonic. The sunspot number curve is shown on top for guidance (figure courtesy of Z. Kolláth).

Figure 8

Power spectrum of the smoothed monthly sunspot number series for the period 1749 – 2008. Solid vertical bars mark the 11-year period, its first harmonic and subharmonic; dashed vertical bars are drawn at a fiducial period of 14.5 years, its harmonic and subharmonic.