1 Introduction

Solar cycle prediction is an extremely extensive topic, covering a very wide variety of proposed prediction methods and prediction attempts on many different timescales, ranging from short term (month–year) forecasts of the runoff of the ongoing solar cycle to predictions of long term changes in solar activity on centennial or even millennial scales. As early as 1963, Vitinsky published a whole monograph on the subject, later updated and extended (Vitinsky, 19631973Jump To The Next Citation Point). More recent overviews of the field or aspects of it include Hathaway (2009), Kane (2001Jump To The Next Citation Point), and Pesnell (2008Jump To The Next Citation Point). In order to narrow down the scope of the present review, we constrain our field of interest in two important respects.

Firstly, instead of attempting to give a general review of all prediction methods suggested or citing all the papers with forecasts, here we will focus on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. We will thus discuss in more detail empirical methods that, independently of their success rate, have the potential of shedding some light on the physical mechanism underlying the solar cycle, as well as the prediction attempts based on solar dynamo models.

Secondly, we will here only be concerned with 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. This emphasis is also motivated by the present surge of interest in precisely this topic, prompted by the unusually long and deep recent solar minimum and by sharply conflicting forecasts for the maximum of the incipient solar cycle 24.

As we will see, significant doubts arise both from the theoretical and observational side as to what extent such a prediction is possible at all (especially before the time of the minimum has become known). Nevertheless, no matter how shaky their theoretical and empirical backgrounds may be, forecasts must be attempted. Making verifiable or falsifiable predictions is obviously the core of the scientific method in general; but there is also a more imperative urge in the case of solar cycle prediction. Being the prime determinant of space weather, solar activity clearly has enormous technical, scientific, and financial impact on activities ranging from space exploration to civil aviation and everyday communication. Political and economic decision makers expect the solar community to provide them with forecasts on which feasibility and profitability calculations can be based. Acknowledging this need, the Space Weather Prediction Center of the US National Weather Service does present annually or semiannually updated “official” predictions of the upcoming sunspot maximum, emitted by a Solar Cycle Prediction Panel of experts, starting shortly before the (expected) minimum (SWPC). The unusual lack of consensus during the early meetings of this panel during the recent minimum, as well as the concurrent more frequently updated but wildly varying predictions of a NASA MSFC team (MSFC) have put on display the deficiencies of currently applied prediction techniques; on the other hand, they also imply that cycle 24 may provide us with crucial new insight into the physical mechanisms underlying cyclic solar activity.

While a number of indicators of solar activity exist, by far the most commonly employed is still the smoothed relative sunspot number R; the “Holy Grail” of sunspot cycle prediction attempts is to get R right for the next maximum. We, therefore, start by briefly introducing the sunspot number and inspecting its known record. Then, in Sections 2, 3, and 4 we discuss the most widely employed methods of cycle predictions. Section 5 presents a summary evaluation of the past performance of different forecasting methods and collects some forecasts for cycle 24 derived by various approaches. Finally, Section 6 concludes the paper.

 1.1 The sunspot number
  1.1.1 Alternating series and nonlinear transforms
 1.2 Other indicators of solar activity
 1.3 The solar cycle and its variation
  1.3.1 Secular activity variations
  1.3.2 Does the Sun have a long term memory?
  1.3.3 Waldmeier effect and amplitude–frequency correlation

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