Predictions of solar activity are an essential part of our Space Weather forecast capability. Users are requiring usable predictions of an upcoming solar cycle to be delivered several years before solar minimum. A set of predictions of the amplitude of Solar Cycle 24 accumulated in 2008 ranged from zero to unprecedented levels of solar activity. The predictions formed an almost normal distribution, centered on the average amplitude of all preceding solar cycles. The average of the current compilation of 105 predictions of the annual-average sunspot number is 106 +/- 31, slightly lower than earlier compilations but still with a wide distribution. Solar Cycle 24 is on track to have a below-average amplitude, peaking at an annual sunspot number of about 80. Our need for solar activity predictions and our desire for those predictions to be made ever earlier in the preceding solar cycle will be discussed. Solar Cycle 24 has been a below-average sunspot cycle. There were peaks in the daily and monthly averaged sunspot number in the Northern Hemisphere in 2011 and in the Southern Hemisphere in 2014. With the rapid increase in solar data and capability of numerical models of the solar convection zone we are developing the ability to forecast the level of the next sunspot cycle. But predictions based only on the statistics of the sunspot number are not adequate for predicting the next solar maximum. I will describe how we did in predicting the amplitude of Solar Cycle 24 and describe how solar polar field predictions could be made more accurate in the future.

Predictions of Solar Cycle 24: How are We Doing?

The dynamic activity of the Sun—sustained by a magnetohydrodynamic dynamo mechanism working in its interior—modulates the electromagnetic, particulate, and radiative environment in space. While solar activity variations on short timescale create space weather, slow long-term modulation forms the basis of space climate. Space weather impacts diverse space-reliant technologies while space climate influences planetary atmospheres and climate. Having prior knowledge of the Sun’s activity is important in these contexts. However, forecasting solar-stellar magnetic activity has remained an outstanding challenge. In this review, predictions for Sunspot Cycle 24 and the upcoming Solar Cycle 25 are summarized, and critically assessed. The analysis demonstrates that while predictions based on diverse techniques disagree across Solar Cycles 24–25, physics-based predictions for Solar Cycle 25 have converged and indicates a weak to moderate–weak sunspot cycle. I argue that this convergence in physics-based predictions is indicative of progress in the fundamental understanding of solar cycle predictability. Based on this understanding, resolutions to several outstanding questions related to solar cycle predictions are discussed; these questions include: is it possible to predict the solar cycle, what is the best proxy for predictions, how early can we predict the solar cycle and how many cycles into the future can we predict relying on our current understanding? Based on our analysis, we also suggest a rigorous pathway towards generating and disseminating a “consensus forecast” by any solar cycle prediction panels tasked with such a challenge.

Progress in Solar Cycle Predictions: Sunspot Cycles 24–25 in Perspective

The long sunspot cycle 23 predicts a significant temperature decrease in cycle 24

Predicting the maximum amplitude of solar cycle 25 and its timing

Study of variations in solar activity parameters has its importance in understanding the underlying mechanisms of space weather phenomena and space climate variability. We have used the already observed data of solar parameters viz. sunspot numbers, F10.7 cm index and Lyman alpha index recorded for last seventy years (1947–2017). We have applied the Hodrick Prescott filtering method to bifurcate each time series into cyclic and trend parts. The cyclic part of each time series was used to analyse the persistence while the trend part was used to obtain the input data for the study of future predictions. Further, the cyclic component of each parameter was analysed by using the rescaled range analysis and the value of Hurst exponent was obtained for sunspot numbers, F10.7 cm index and Lyman alpha index as 0.90, 0.93 and 0.96 respectively. By using the simplex projection analysis on the values of amplitude and phase of the trend component of each time series, we have reconstructed the future time series representing solar cycles 25 and 26. When extrapolated further in time, the reconstructed series provided the maximum values of sunspot numbers as $89 \pm 9$
 and $78 \pm 7$
 ; maximum values of F10.7 cm index were $124 \pm 11$
 and $118 \pm 9$
 and Lyman alpha index were $4.61 \pm 0.08$
 and $4.41 \pm 0.08$
 respectively for solar cycles 25 and 26. In our analysis we have found that the solar cycle 25 will start in the year 2021 (January) and will last till 2031 (February) with its maxima in year 2024 (February) while the solar cycle 26 will start in the year 2031 (March) with its maxima in 2036 (June) and will last till the year 2041 (February). We have also compared the activities of solar cycles 5 and 6 (Dalton minima periods) to solar cycles 25 and 26 and have observed that the other solar minimum is underway.

Prediction of declining solar activity trends during solar cycles 25 and 26 and indication of other solar minimum

We propose a new technique for the optimal prediction of the peak of the next 11-year activity cycle prior to the cycle beginning and of the peaks of several succeeding cycles on the basis of long-term variations in the solar radius or solar constant. The method is based on the already established fact that the long-term cyclic variations of the activity, radius, and solar constant are correlated in both phase and amplitude, since they are caused by some common processes in the Sun. The peak of the succeeding cycle 24 is expected to have the height W
 max = 70 ± 10 (in units of relative sunspot number). The subsequent cycles 25 and 26, which will be formed during the descent of the current secular cycle, will have still lower peaks with the heights W
 max = 50 ± 15 and W
 max = 35 ± 20.

Optimal Prediction of the Peak of the Next 11-Year Activity Cycle and of the Peaks of Several Succeeding Cycles on the Basis of Long-Term Variations in the Solar Radius or Solar Constant

Long-wave energy emitted by the Earth-atmosphere into space is characterized by changes in power over time that always lag behind the changes in power of the absorbed solar radiation due to slow variation in enthalpy of the Earth-atmosphere system. Long-term variation of the solar energy radiation absorbed by the Earth remains uncompensated by the energy radiated into space over the interval of time that is determined by the thermal inertia. The basic state of the climate system is when the debit and credit sides in the Earth’s global annual mean energy budget (including the air and water envelopes) are almost always unbalanced. The annual mean balance of the heat budget of the Earth-atmosphere over a long time period will reliably define the behavior and magnitude of the energy excess accumulated by the Earth or energy deficit to allow us to determine adequately and to predict beforehand the trend and amplitude of the forthcoming climate change using the prognosis of variations in the total solar irradiance (solar constant). The decrease in solar constant has been observed since the early 1990s. The Earth as a planet will have a negative balance in the energy budget in the future as well, because the Sun is entering the decline phase of the bicentennial luminosity changes. This will lead to a drop in temperature in approximately 2014. The increase in albedo and decrease in greenhouse gas concentration in the atmosphere will result in the additional decrease in absorbed portion of the solar energy and reduced greenhouse effect. The additional drop in temperature exceeding the effect of decreased solar constant can occur as a result of successive feedback effects. A deep bicentennial minimum in solar constant is to be anticipated in 2042 ± 11 and the 19th Little Ice Age (for the last 7500 years) may occur in 2055 ± 11.

Bicentennial decrease of the solar constant leads to the Earth’s unbalanced heat budget and deep climate cooling

This paper describes a method of monitoring the variations of the earth’s energy balance from Lagrange point L1. The method is based on measurements of the variation of the solar constant in the complete spectral range and of the earth’s radiation flux in the spectral ranges 0.2–100 μm, 8–13 μm, and a number of other ranges. The threshold sensitivity of a telescope with entrance-pupil diameter 400 mm must equal 10−7  W for a dynamic range of four orders. The method makes it possible to record variations of the Bond albedo at the 0.1% level, and this corresponds to a temperature variation of the earth by 0.03 K, taking into account the variation of the solar constant. It is shown how the increments of the Bond albedo, the specific power of solar radiation absorbed by the planet, and the planetary temperature depend on the variation of the albedo of the atmosphere and the earth’s surface and the transmission of solar radiation by the atmosphere.

Monitoring the earth’s energy balance from Lagrange point L1

The thermal aberrations of a telescope-limbograph have been investigated. Calculations have been carried out for the case in which it operates in a cyclic regime: 30 min observation of the sun, 60 min break, number of cycles 12. It is shown that, when high-thermal-conductivity silicon carbide is used as the material for the mirrors, they exhibit virtually no significant temperature gradients or thermal strains. The maximum distortion of the mirror profile does not exceed about 10−5µm, and this is quite satisfactory for the Lambda/50 allowance. The thermomechanical structure of the design of the space complex makes it possible to provide stable, high image quality of the optics and other all-round characteristics of the optical receiver unit of the limbograph as a whole.

Calculating the thermal aberrations of a space-based solar telescope-limbograph

We propose a minimum level of the smoothed values for the solar constant during a period of low sunspot activity as a new additional criterion for determining the time of a minimum between solar cycles. An indicator for the time of a minimum between cycles is the time at which a minimum level in the average monthly values of the integral flux of solar radiation smoothed over thirteen months (when the last four values of the flux are greater than the previous minimum point) is achieved. We successfully tested the new criterion to determine the time of the previous minima between cycles 21 and 22, 22 and 23, and 23 and 24.

Kh. I. Abdusamatov

Papers

Optimal Prediction of the Peak of the Next 11-Year Activity Cycle and of the Peaks of Several Succeeding Cycles on the Basis of Long-Term Variations in the Solar Radius or Solar Constant

Bicentennial decrease of the solar constant leads to the Earth’s unbalanced heat budget and deep climate cooling

Monitoring the earth’s energy balance from Lagrange point L1

Calculating the thermal aberrations of a space-based solar telescope-limbograph

A new criterion for determining the time of a solar minimum