Solar Cycle Prediction Research Articles

Toward a Live Homogeneous Database of Solar Active Regions Based on SOHO/MDI and SDO/HMI Synoptic Magnetograms. II. Parameters for Solar Cycle Variability

Solar active regions (ARs) determine solar polar fields and cause solar cycle variability within the framework of the Babcock–Leighton dynamo. The contribution of an AR to the polar field is measured by its dipole field, which results from flux emergence and subsequent flux transport over the solar surface. The dipole fields contributed by an AR before and after the flux transport are referred to as the initial and final dipole fields, respectively. For a better understanding and prediction of solar cycles, in this paper, we provide a database including AR's initial and final dipole fields and the corresponding results of their bipolar magnetic region (BMR) approximation from 1996 onward. We also identify the repeated ARs and provide the optimized transport parameters. Based on our database, we find that although the commonly used BMR approximation performs well for the initial dipole field, it exhibits a significant deviation for the final dipole field. To accurately assess an AR’s contribution to the polar field, the final dipole field with its real configuration should be applied. Despite the notable contributions of a few rogue ARs, approximately the top 500 ARs ordered by their final dipole fields are necessary to derive the polar field at the cycle minimum. While flux transport may increase or decrease the dipole field for an individual AR, its collective impact over all ARs in a cycle is a reduction in their total dipole field.

An Improved Prediction of Solar Cycles 25 and 26 Using the Informer Model: Gnevyshev Peaks and North–South Asymmetry

Forecasting the amplitude and timing of the sunspot cycle is highly important for solar physics and space weather applications, but high-precision prediction of solar magnetic activity has remained an outstanding challenge. The Informer model, as the most advanced deep learning technique, is an ideal approach for predicting solar activity cycle. Using the whole-disk sunspot numbers (SSNs) between 1749 and 2023 and the hemispheric SSNs between 1992 and 2023, the amplitudes and timings of Solar Cycles 25 and 26 are predicted by the Informer model. The main results are the following: (1) the activity levels of Solar Cycles 25 and 26 continue being weak-moderate cycles with their strengths stronger than Solar Cycle 24, implying that the long-term solar variability is significantly modulated in length and magnitude by the Gleissberg century cycle; (2) the Gnevyshev peaks of Solar Cycles 25 and 26 are clearly observed with a higher value in the second peak, suggesting that the numbers of the large sunspot groups are greater compared to the small sunspot groups in these two cycles; and (3) during Solar Cycle 25, the activity level in the southern hemisphere is predicted to be stronger than that in the northern one, revealing significant asymmetry and asynchronization between the two hemispheres. Our analysis results show that solar cycle predictions can be made more accurate if performed separately for each hemisphere. Furthermore, Solar Cycles 25 and 26 are likely to be weak-moderate cycles, in agreement with the precursor-based and model-based prediction methods.

Algebraic quantification of the contribution of active regions to the Sun’s dipole moment: applications to century-scale polar field estimates and solar cycle forecasting

ABSTRACT The solar cycle is generated by a magnetohydrodynamic dynamo mechanism which involves the induction and recycling of the toroidal and poloidal components of the Sun’s magnetic field. Recent observations indicate that the Babcock–Leighton (BL) mechanism – mediated via the emergence and evolution of tilted bipolar active regions – is the primary contributor to the Sun’s large-scale dipolar field. Surface flux transport models and dynamo models have been employed to simulate this mechanism, which also allows for physics-based solar cycle forecasts. Recently, an alternative analytic method has been proposed to quantify the contribution of individual active regions to the Sun’s dipole moment (DM). Utilizing solar cycle observations spanning a century, here, we test the efficacy of this algebraic approach. Our results demonstrate that the algebraic quantification approach is reasonably successful in estimating DMs at solar minima over the past century – providing a verification of the BL mechanism as the primary contributor to the Sun’s dipole field variations. We highlight that this algebraic methodology serves as an independent approach for estimating DMs at the minima of solar cycles, relying on characteristics of bipolar solar active regions. We also show how this method may be utilized for solar cycle predictions; our estimate of the Sun’s dipole field at the end of cycle 24 using this approach indicates that solar cycle 25 would be a moderately weak cycle, ranging between solar cycle 20 and cycle 24.

The Coronal Flattening Index at the 20 April 2023 Total Solar Eclipse and the Prediction of Solar Cycle 25

The Coronal Flattening Index at the 20 April 2023 Total Solar Eclipse and the Prediction of Solar Cycle 25

Hemispheric Prediction of Solar Cycles 25 and 26 From Multivariate Sunspot Time-series Data via Informer Models

Hemispheric Prediction of Solar Cycles 25 and 26 From Multivariate Sunspot Time-series Data via Informer Models

Discovery of a relation between the decay rate of the Sun’s magnetic dipole and the growth rate of the following sunspot cycle: a new precursor for solar cycle prediction

ABSTRACT Sunspots have been observed for over four centuries and the magnetic nature of sunspot cycles has been known for about a century; however, some of its underlying physics still remain elusive. It is known that the solar magnetic cycle involves a recycling of magnetic flux between the poloidal and toroidal components of the magnetic field, that manifests as the solar dipole and sunspots, respectively. Here, we report the discovery of a new relationship between the rise rate of the sunspot cycle and the decay rate of the solar (axial) dipole moment. This provides an extension to the Waldmeier effect in sunspot cycles and points to the existence of a causal connection between the aforementioned physical quantities, which can be succinctly stated as the decay rate of the Sun’s dipole moment is related to the rate of rise of the following sunspot cycle. We demonstrate how one may take advantage of this new relationship to predict the timing of the sunspot cycle. Our analysis indicates solar cycle 25 is expected to be a weak-moderate cycle, peaking in $2024.00_{-0.49}^{+0.68}$.

Hemispheric prediction of solar cycle 25 based on a deep learning technique

In the current work, single-and double-layered Long Short-Term Memory (LSTM) model have been developed and compared to find the most suitable one for hemispheric prediction of solar cycle 25. The smoothed Hemispheric Sunspot Number (HSN) reconstructed by Veronig et al. (2021) has been used to achieve the objective. The deep learning models are evaluated over different pairs of train and test set for both the hemispheres using the 5-fold cross-validation scheme, to determine the best effective model for hemispheric prediction of cycle 25. Our analysis reveals that the single-layered LSTM model achieves lower RMSE when predicting the test dataset. To prove the reliability of our suggested LSTM models, we have predicted the hemispheric profiles of solar cycles 21–24. From our analysis, we found that the single-layered LSTM model performed better in comparison to the double-layered LSTM model in predicting past solar cycles 21–24. Hence, hemispheric prediction of solar cycle 25 is carried out utilizing the single-layered LSTM model due to better performance capability during experimental analysis. This work founds that the northern hemisphere will peak with an amplitude of 56 ± 5 during July 2023 + 3 months while the southern hemisphere will have a maximum amplitude of 54 ± 4 during June 2023 + 2 months. So, it can be said that the southern HSN will peak before the northern HSN and that the peak of northern HSN will be slightly higher than the southern one.

Exploring the reliability of polar field rise rate as a precursor for an early prediction of solar cycle

ABSTRACT The prediction of the strength of an upcoming solar cycle has been a long-standing challenge in the field of solar physics. The inherent stochastic nature of the underlying solar dynamo makes the strength of the solar cycle vary in a wide range. Till now, the polar precursor methods and the dynamo simulations that use the strength of the polar field at the cycle minimum to predict the strength of the following cycle have gained reasonable consensus by providing convergence in the predictions for Solar Cycles 24 and 25. Recently, it has been shown that just by using the observed correlation of the polar field rise rate with the peak of the polar field at the cycle minimum and the amplitude of the following cycle, a reliable prediction can be made much earlier than the cycle minimum. In this work, we perform surface flux transport (SFT) simulations to explore the robustness of this correlation against the stochastic fluctuations of bipolar magnetic region (BMR) tilt properties including anti-Joy and anti-Hale type anomalous BMRs, and against the variation of meridional flow speed. We find that the observed correlation is a robust feature of the solar cycles and thus it can be utilized for a reliable prediction of the solar cycle much earlier than the cycle minimum – the usual landmark of the solar cycle prediction.

Prediction of the Maximum Amplitude of Solar Cycle 25 Using the Ascending Inflection Point

In this work, we predict the maximum amplitude (using the 13-month smoothed Solar Influences Data Analysis Center (SILSO) Sunspot Number, version 2) of Solar Cycle 25 using as a predictor the slope of the inflection point during the ascending part of the cycle. After a description of the data and methodology employed in this work, we obtain a value of 131 ± 32 for the maximum amplitude of Solar Cycle 25. Finally, we discuss this result in the context of the current debate on the prediction of solar activity and compare it with other predictions of Solar Cycle 25 obtained by other methods.

Prediction of solar cycle 25: applications and comparison

Solar activity affects the heliosphere in different ways. Variations in particles and radiation that impact the Earth’s atmosphere, climate, and human activities often in disruptive ways. Consequently, the ability to forecast solar activity across different temporal scales is gaining increasing significance. In this study, we present predictions for solar cycle 25 of three solar activity indicators: the core-to-wing ratio of Mg II at 280 nm, the solar radio flux at 10.7 cm—widely recognized proxies for solar UV emission—and the total solar irradiance, a natural driver of Earth’s climate. Our predictions show a very good agreement with measurements of these activity indicators acquired during the ascending phase of solar cycle 25, representing the most recent data available at the time of writing.

An Improved Prediction of Solar Cycle 25 Using Deep Learning Based Neural Network

An Improved Prediction of Solar Cycle 25 Using Deep Learning Based Neural Network

A Hybrid CNN-LSTM Model for Predicting Solar Cycle 25

The solar cycle is linked to the number of sunspots and follows the fluctuations of the Sun’s magnetic field. It can have powerful global impacts on the Earth. Thus, predicting the timing and amplitude of the peak of the incoming solar cycle 25 is of great importance. This study uses a hybrid deep learning convolutional neural network (CNN) - long short-term memory (LSTM) model and the observed 13-month smoothed sunspot numbers to predict Solar Cycle 25. Here it is shown for the first time that the MinMax normalization method substantially reduces the error of the CNN-LSTM model’s solar cycle predictions compared to the Standard Deviation normalization method. The results also suggest that it is best to use four historical solar cycles to predict the future solar cycle. The predicted Solar Cycle 25 has a 13-month smoothed peak amplitude similar to that of Solar Cycle 24. The predicted Solar Cycle 25 peak spans a relatively long period of time between approximately August 2023 and July 2024.

Comparison of physics-based prediction models of solar cycle 25

Physics-based solar cycle predictions provide an effective way to verify our understanding of the solar cycle. Before the start of cycle 25, several physics-based solar cycle predictions were developed. These predictions use flux transport dynamo (FTD) models, surface flux transport (SFT) models, or a combination of the two kinds of models. The common physics behind these predictions is that the surface poloidal fields around cycle minimum dominate the subsequent cycle strength. In the review, we first give short introductions to SFT and FTD models. Then we compare 7 physics-based prediction models from 4 aspects, which are what the predictor is, how to get the predictor, how to use the predictor, and what to predict. Finally, we demonstrate the large effect of assimilated magnetograms on predictions by two SFT numerical tests. We suggest that uncertainties in both initial magnetograms and sunspot emergence should be included in such physics-based predictions because of their large effects on the results. In addition, in the review we put emphasis on what we can learn from different predictions, rather than an assessment of prediction results.

Prediction of Solar Activity Cycle 25 with NARX Neural Networks

Güneş Aktivite Çevrimlerini (GAC) tahmin etmek; Dünya yörüngesindeki uzay araçlarının güvenliği, iletişim ağları ve genel olarak yaşam üzerindeki olumsuz etkileri nedeniyle önemli hale gelmiştir. Bu çalışmada, 25. GAC tahmini için yaklaşık3246 adet 13 aylık ortalama Güneş Lekesi Sayısı’ndan (GLS) (Temmuz 1749 - Aralık 2019 arasında) oluşan büyük bir veri seti ile Doğrusal Olmayan Otoregresif Eksojen (NARX) sinir ağı tabanlı modeller kullanılmıştır. NARX modelleri veri setini Bayesian Regülasyonu kullanılarak eğitilmiştir. NARX modelinin performansı Ortalama Karekök Sapması (RMSE),Korelasyon Katsayısı (r) ve Nash-Sutcliffe Verimlilik Katsayısı (NSE) kullanılarak hesaplanmıştır ve modelin performansının“çok iyi” (NSE > 0.95) olduğu bulunmuştur. Modellerimiz diğer benzer çalışmalardan elde edilen sonuçlarla karşılaştırılarak doğrulanmıştır ve 25. GAC için maksimum GLS 104,542 ve maksimum ayı Mayıs 2024 olarak tahmin edilmiştir.NARX tabanlı modellerin literatürde bildirilen diğer yöntemlere kıyasla iyi ve uyumlu tahmin sonuçları ortaya çıkardığı görülmüştür.

Maximal growth rate of the ascending phase of a sunspot cycle for predicting its amplitude

Context. Forecasting the solar cycle amplitude is important for a better understanding of the solar dynamo as well as for many space weather applications. Different empirical relations of solar cycle parameters with the peak amplitude of the upcoming solar cycle have been established and used for solar cycle forecasts, as, for instance, the Waldmeier rule relating the cycle rise time with its amplitude, the polar fields at previous minimum, and so on. Recently, a separate consideration of the evolution of the two hemispheres revealed even tighter relations. Aims. We aim to introduce the maximal growth rate of sunspot activity in the ascending phase of a cycle as a new and reliable precursor of a subsequent solar cycle amplitude. We also intend to investigate whether the suggested precursor provides benefits for the prediction of the solar cycle amplitude when using the sunspot indices (sunspot numbers, sunspot areas) derived separately for the two hemispheres compared to the total sunspot indices describing the entire solar disc. Methods. We investigated the relationship between the maximal growth rate of sunspot activity in the ascending phase of a cycle and the subsequent cycle amplitude on the basis of four data sets of solar activity indices: total sunspot numbers, hemispheric sunspot numbers from the new catalogue from 1874 onwards, total sunspot areas, and hemispheric sunspot areas. Results. For all the data sets, a linear regression based on the maximal growth rate precursor shows a significant correlation. Validation of predictions for cycles 1–24 shows high correlations between the true and predicted cycle amplitudes reaching r = 0.93 for the total sunspot numbers. The lead time of the predictions varies from 2 to 49 months, with a mean value of 21 months. Furthermore, we demonstrated that the sum of maximal growth rate indicators determined separately for the north and the south hemispheric sunspot numbers provides more accurate predictions than that using total sunspot numbers. The advantages reach 27% and 11% on average in terms of rms and correlation coefficient, respectively. The superior performance is also confirmed with hemispheric sunspot areas with respect to total sunspot areas. Conclusions. The maximal growth rate of sunspot activity in the ascending phase of a solar cycle serves as a reliable precursor of the subsequent cycle amplitude. Furthermore, our findings provide a strong foundation for supporting regular monitoring, recording, and predictions of solar activity with hemispheric sunspot data, which capture the asymmetric behaviour of the solar activity and solar magnetic field and enhance solar cycle prediction methods.

Physical link of the polar field buildup with the Waldmeier effect broadens the scope of early solar cycle prediction: Cycle 25 is likely to be slightly stronger than Cycle 24

ABSTRACT Prediction of the solar cycle is challenging but essential because it drives space weather. Several predictions with varying amplitudes of the ongoing Cycle 25 have been made. We show that an aspect of the Waldmeier effect (WE2), i.e. a strong positive correlation between the rise rate and the amplitude of the cycle, has a physical link with the buildup of the previous cycle’s polar field after its reversal. We find that the rise rate of the polar field is highly correlated with the rise rate and the amplitude of the next solar cycle. Thus, the prediction of the amplitude of the solar cycle can be made just a few years after the reversal of the previous cycle’s polar field, thereby extending the scope of the solar cycle prediction to much earlier than the usual time. Our prediction of Cycle 25 based on the rise rate of the previous polar field is 137 ± 23, which is quite close to the prediction 138 ± 26 based on the WE2 computed from the available 2 yr sunspot data of the ongoing cycle.

Prediction of solar cycle 25 using deep learning based long short-term memory forecasting technique

• Peak & timing of solar cycle 25 has been predicted using sunspot number data. • The concept of Deep Learning algorithm has been used for forecasting. • The proposed model showed good performance on various time intervals with low RMSE value. • Validation of model performance has been done by predicting past solar cycles 20–24. • The model captured non-linearity and cyclic trend within the data with good RMSE. In the current work we have used the deep learning based long short-term memory model to predict the strength and peak time of solar cycle 25 by employing the monthly smoothed sunspot number data obtained from WDC-SILSO, Royal Observatory of Belgium, Brussels. We have used the stacked LSTM forecasting model to predict the upcoming cycle 25. From our analysis it has been shown that our proposed model is capable of capturing long term dependencies as well as trend within the data. For cycle 20 and 21 the error difference between predicted as well as observed peak value is 2.3 and 0.7 respectively while the peak prediction error is 1.47% and 0.30%. The RMSE of the model for cycle 20 and 21 is 3.97 and 4.34 respectively. For cycle 22, the AE and RE is 4.6 and 2.16% while the RMSE of the model for this case is 4.50. The predicted peak amplitude of solar cycle 23 and 24 from our proposed model has a relative error of 1.75% and 1.99% respectively from the observed value while the RMSE is 3.4 for cycle 23 and 4.2 for cycle 24. Our projected prediction of cycle 25 using the proposed LSTM model, says that it will be stronger than cycle 24 and weaker than cycle 23. The solar cycle 25 will peak with an amplitude of sunspot number at 171.9 ± 3.4 and will be 47 % stronger than cycle 24. The solar cycle 25 will reach its peak in August 2023 ± 2 months.

A Dynamo-Based Prediction of Solar Cycle 25

The solar activity cycle varies in amplitude. The last Solar Cycle 24 is the weakest in the past century. Sun’s activity dominates Earth’s space environment. The frequency and intensity of Sun’s activity follow the solar cycle. Hence there are practical needs to know the amplitude of the upcoming Solar Cycle 25. Dynamo-based solar cycle predictions not only provide forecasts, but also offer an effective way to evaluate our understanding of the solar cycle. In this article we apply the method of the first successful dynamo-based prediction developed for Solar Cycle 24 to predict Solar Cycle 25, so that we can verify whether the previous success is repeatable. The prediction shows that Solar Cycle 25 would be about 10% stronger than Solar Cycle 24 with an amplitude of 126 (international sunspot number Version 2.0). The result suggests that Solar Cycle 25 will not be the beginning of a Maunder-like grand solar minimum as suggested by some publications. The solar behavior in about four to five years will confirm whether the prediction method captures the key mechanism for solar cycle variability, which is the polar field around the cycle minimum in our model.

Hemispheric sunspot numbers 1874–2020

Context. Previous studies show significant north–south asymmetries for various features and indicators of solar activity. These findings suggest some decoupling between the two hemispheres over the solar cycle evolution, which is in agreement with dynamo theories. For the most important solar activity index, the sunspot numbers, so far only limited data are available for the two hemispheres independently. Aims. The aim of this study is to create a continuous series of daily and monthly hemispheric sunspot numbers (HSNs) from 1874 to 2020, which will be continuously expanded in the future with the HSNs provided by SILSO. Methods. Based on the available daily measurements of hemispheric sunspot areas from 1874 to 2016 from Greenwich Royal Observatory and National Oceanic and Atmospheric Administration, we derive the relative fractions of the northern and southern activity. These fractions are applied to the international sunspot number (ISN) to derive the HSNs. This method and obtained data are validated against published HSNs for the period 1945–2004 and those provided by SILSO for 1992 to 2016. Results. We provide a continuous data series and catalogue of daily, monthly mean, and 13-month smoothed monthly mean HSNs for the time range 1874–2020 –fully covering solar cycles 12 to 24– that are consistent with the newly calibrated ISN (Clette et al., 2014). Validation of the reconstructed HSNs against the direct data available since 1945 reveals a high level of consistency, with Pearson correlation coefficients of r = 0.94 (0.97) for the daily (monthly mean) data. The cumulative hemispheric asymmetries for cycles 12–24 give a mean value of 16%, with no obvious pattern in north–south predominance over the cycle evolution. The strongest asymmetry occurs for cycle no. 19, in which the northern hemisphere shows a cumulated predominance of 42%. The phase shift between the peaks of solar activity in the two hemispheres may be up to 28 months, with a mean absolute value over cycles 12–24 of 16.8 months. The phase shifts reveal an overall asymmetry of the northern hemisphere reaching its cycle maximum earlier (in 10 out of 13 cases), with a mean signed phase shift of −7.6 months. Relating the ISN and HSN peak growth rates during the cycle rise phase with the cycle amplitude reveals higher correlations when considering the two hemispheres individually, with r ≈ 0.9. Conclusions. Our findings provide further evidence that to some degree the solar cycle evolves independently in the two hemispheres, and demonstrate that empirical solar cycle prediction methods can be improved by investigating the solar cycle dynamics in terms of the HSN evolution.

Effects of observational data shortage on accuracy of global solar activity forecast

ABSTRACT Building a reliable forecast of solar activity is a long-standing problem that requires an accurate description of past and current global dynamics. Relatively recently, synoptic observations of magnetic fields and subsurface flows have become available. In this paper, we present an investigation of the effects of short observational data series on the accuracy of solar cycle prediction. This analysis is performed using the annual sunspot number time-series applied to the Parker–Kleeorin–Ruzmaikin dynamo model and employing the Ensemble Kalman Filter (EnKF) data assimilation method. The testing of cycle prediction accuracy is performed for the last six cycles (for Solar Cycles 19–24) by sequentially shortening the observational data series to predict a target cycle and evaluate the resulting prediction accuracy according to specified criteria. According to the analysis, reliable activity predictions can be made using relatively short time-series of the sunspot number. The accuracy of the solar activity has a weak dependence on the length of available observations. It is demonstrated that at least three cycles of observations are needed to obtain robust forecasts.