{"paper_id":"2b362f6d-32f2-40ee-910f-fb18fdf254c5","body_text":"Predicting Maximum Amplitude and Rise Time of Solar Cycle 25 Using Modified Geomagnetic Precursor Technique | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Predicting Maximum Amplitude and Rise Time of Solar Cycle 25 Using Modified Geomagnetic Precursor Technique Anushree Rajwanshi, Sachin Kumar, Rupesh M. Das, Nandita Srivastava, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4570127/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Dec, 2024 Read the published version in Solar Physics → Version 1 posted 7 You are reading this latest preprint version Abstract The sun is rapidly approaching towards the pinnacle of its activity in ongoing cycle 25. Solar activity variations cause changes in interplanetary and near-Earth space environment and may deteriorate the operation of space-borne and ground based technological systems (space flights, navigation, radars, high-frequency radio communications, ground power lines, etc.). Scientists predict the exact duration and intensity of each solar cycle based on a variety of methods ranging from purely statistical models using observations of previous cycles to complex simulations of solar physics. In the present study, we utilized the planetary magnetic activity ‘Ap’ index in relation to sunspot activity and sunspot area for the period 1932–2019, covering Solar Cycles 17 to 24, as geomagnetic precursor pair for predicting the maximum amplitude and its time of occurrence for ongoing Cycle 25. The monthly average sunspot data and disturbed days are processed through regression analysis and the obtained analytical results further validated by the observed sunspots of cycle 17 to 24. Hind casting results show close agreement between predicted and observed maximum amplitudes of cycles 17 to 24 to about 10 percent. A multivariate fit using the two best DI indices in variate block 9 also gives the similar correlation to about 0.94 with standard error of estimation (±14). This study divulges that the maximum sunspot number for Solar Cycle 25 is expected to be ≈ 112 ± 18. The probable peak time of cycle 25, after analysis, is found to be 48 ± 3 months. The peak might appear in between October 2023 – April 2024. The obtained results suggest that ongoing cycle akin to the previous Solar Cycle 24 in terms of predicted maximum sunspot numbers. Solar Cycle Geomagnetic precursors sunspots Geomagnetic index Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction The increasing reliance of society upon space-based technological systems emphasises the need for understanding the underlying mechanism of solar activity and the sunspot prediction. Solar activities are being researched in diverse scientific fields, including solar physics, climate change, and space mission planning (Haigh, 2007 ; Hanslmeier, 2007; Usoskin, 2023 ). Extreme currents in the electric grids, extensive radio blackouts, phone and internet connection outages in space and within the Earth's atmosphere can all result from space weather occurrences. Satellites used for global navigation, communications, and weather forecasting, can also be damaged by severe space weather events. (Fry 2012 ; Berdermann et al., 2018 ; Sato et. al., 2019 ; Nandy 2021 ; John et al., 2021 ; Forte et al., 2024 ; Ishii et. al., 2024; ). Thus, space weather can have a wide range of societal and economic consequences (Pulkkinen, 2007 ). For the safety of contemporary technology and to comprehend the process underlying solar activity, solar activity prediction is crucial (Luo and Tan, 2024 ). Advance prediction of maximum amplitude and timing of the sunspot cycle have gained societal relevance in recent decades, scientificpanels have been created and tasked with producing consensus judgements on the upcoming sunspot cycle, several years before the approaching peak (McIntosh, 2020). The international sunspot number (ISN)is a universal indicator of solar activity based on the ocular observations of the Sun's visible disc (Hathaway 2015 ). ISN is the most extensive record of the evolution of solar activity. World Data Center Sunspot Index and Long-term Solar Observations (WDC-SILSO) maintains and provides records of daily, monthly mean, and yearly mean ISN time-series since year 1700 ( https://www.sidc.be/SILSO/datafiles ). These series play a pivotal role for the accurate predictions of solar cycle (Petrovay 2020 ). Several approaches as depicted in Fig. 1 are being deployed by the researchers to predict the sunspot cycles. Petrovay ( 2020 ) reviewed and elaborated several solaractivity forecast techniques. The precursorbased approach relies on the statistical correlation between an observed variable and the subsequent solar cycle maximum. The statistical association between the two variables might be explained by our understanding of solar physics. Physical modelbased predictions utilize the well-known surface flux-transport models.Though, due to the intricacy of these models, alternative approaches, including simple statistical ones, are being widely explored. The intriguing magnetic personality of Sun is being studied since several decades and now it becomes apparent thatmagnetic field of Sun is created and magnified by continual stretching, twisting, and folding of the field lines caused by the combined actions of differential rotation and convection.Solar dynamo theory suggests that the Sun's magnetic field would increase to a maximum, collapse to zero, and then reverse itself in a relatively cyclical manner (Charbonneau, 2014 ). The change in the quantity of sunspots and their migration to lower latitudes are both results of the field lines intensification and ultimately in fading away. Various researches (Ohl and Ohl, 1979 , Feynman, 1982 , Thompson, 1987 , 1993, Li, 1997 , Shastri, 1998 , Hathaway and Wilson, 2006 , Kane, 2007 a, Du, 2009, Kim Kwee Ng 2016 , Diego 2021 and references enclosed within) have reportedthat geomagnetic activities, during the declining phase of a solar cycle act as the precursor for predicting the peak sunspot number of the subsequent solar cycle. This association can be well explained on the basis of solar dynamo theory. According to this theory, the poloidal solar magnetic field, which is estimated based on geomagnetic activity during the declining phase of the preceding cycle or at the cycle minimum, provides the seed for future toroidal fields within the Sun that in turn cause solar activity (Schatten et al. 1978 ; Schatten & Pesnell 1993 ; Hathaway & Wilson 1999; Choudhuri et al. 2007). Many models have been developed from the Ohl’s Precursor Method and provide varying degrees of success in predicting aforthcoming solar activity. In an earlier study, Dabas et. al. 2008, 2010, predicted the maximum sunspot number of previous cycle 24 using geomagnetic precursor technique to be 124 ± 23 and 131 ± 20, which was very near to the observed one (observed RM = 117 for SC 24) The peak amplitude of solar cycle 25 is predicted by various groups using diversified techniques as shown in Fig. 1 and their results are listed in Table 3 . All of the forecasts for maximum of cycle 25, broadly differs from each other. Also majority of the forecasts point toward a stronger cycle 25 in comparison to cycle 24. However physics based forecasts is not much different from each other as all indicate a climatologically weak cycle (Nandy 2020). This conclusion is based on the Babcock-Leighton mechanism. The mechanism is governing driver of solar cycle variability also the dynamical memory of the solar cycle is short, permitting for forecasts of only the succeeding cycle. The present research relies on modified geomagnetic precursor technique (applied earlier by Dabas et. al., 2008, 2010 for predicting the maximum amplitude and rise time of solar cycle 24) to predict the size and timing of the maximum sunspot amplitude for enduring cycle 25. In this technique, thirteen variable blocks of 6-month duration are constructed by finding the 12-month moving average of the number of disturbed days (( \\({A}_{p} \\ge 25\\) ) during the post-peak segment of 17 to 24 sunspot cycles. The following Section 2 describes the data used and the analysis technique implemented in the present study. Consequent results are described in Section 3.1 for predicting the maximum sunspot number for Solar Cycle 25. The estimated shape and rise time of the current solar cycle are presented in Section 3.2 . The present findings are compared with predictions of others in Section 4 . The key conclusions of this work are discussed in Section 5 , together with a few added remarks and propositions concerning the geomagnetic precursor technique. Analysis Process via Modified Geomagnetic Precursor Technique The precursor technique (Thompson 1993, 1996) aims to establish a link between cycle amplitude and the phenomenon observed on or emanating from the sun during the solar cycle's decreasing phase or at solar minimum. Thompson (1993) suggested that the upcoming solar cycle begins in the decreasing part of the previous cycle, where it manifests itself in the emergence of coronal holes as well as the intensity of the solar polar magnetic field. The constancy of coronal holes causes a series of disruptions which are separated by 27 days, the sun's rotation period. The frequency, severity, and stability of these recurring disruptions in the decreasing phase acts as an excellent indicator of the next cycle's vigor. Figure 2 illustrated the flowchart of geomagnetic precursor technique deployed to anticipate the maximum amplitude/sunspot number of the ongoing solar cycle 25. The current study utilizes 12-month smoothed sunspot number \\({{\\prime }R}_{12}{\\prime }\\) and \\({A}_{P}\\) index as the geomagnetic precursor pair. The number of geomagnetic disturbances (as precursors) arecalculatedas the number of days in a month for which planetary magnetic activity index ‘ \\({A}_{P}\\) ’ is greater than or equal to 25 (Thompson, 1987 )over the decreasing phase (cycle 24 maximum to lowest).After estimating the number of disturbed days of each month, the Disturbance Index (DI) is determined as R12 i.e. by calculating the 12-month running average. The temporal behavior of R12 and the disturbance index ‘DI’ for sunspot cycles 17–24 is shown in the Fig. 3 . The values of DI span from 1 to 8. For cycles 17–22, the descent durations lie in the range of 79 to 91 months. Although for solar cycle 23, the longest descent duration of 108 months is observed. With descent duration of 84 months, solar cycle 24 again lies in the previous window. Data used here for the analysis covers period corresponding to the last eightprecedingsolar cycles 17 to 24. In order to comprehensively understand DI behavior throughout the descending half of each solar cycle, the common descent period (78 months) is divided into thirteen evenly spaced blocks (every six months), beginning after each cycle's R12 peak (RM). Starting with the first month DI after the peak sunspot number, the next twelve DIs are grouped in variate block DI-1 at 6-month intervals. The second month DI after the peak sunspot number, as well as the subsequent twelve DIs, are grouped in variate block DI-2. Same way DI-3, DI-4, DI-5, and DI-6 variate blocks are constructed. In this manner, each variate block comprises thirteen variates. In addition, for each variate block, the minimum (DI-MIN), maximum (DI-MAX), and average (DI-AVG) DI values are also calculated. A linear regression analysis is then performed between thirteen variates of DI-1 to DI-6 with the maximum sunspot number (denoted as RM) of the following cycles. The best regression coefficient yields the best fit equation, which is henceforth utilized for the prediction of the peak sunspot number for ongoing solar cycle 25. Results The first degree regression results or the coefficient of determination ( \\({R}^{2}\\) ) of linear regression analysis between DIs of six variates blocks and the following cycle peak sunspot number are listed in Table 1 . The red colored R 2 values show the highest correlation between DIs and peak sunspot numbers of next cycle for each DI block. It is quite interesting to note from the Table 1 Results of the linear correlation analysis between running average of observed RM and different monthly DI index at each Variate block. Variate block number Coefficient of Determination, R 2 Fixed DI-1 Fixed DI-2 Fixed DI-3 Fixed DI-4 Fixed DI-5 Fixed DI-6 1 − .12 − .19 − .16 − .18 − .18 − .32 2 − .43 − .44 − .58 − .71 − .71 − .73 3 − .66 − .49 − .50 − .55 − .64 − .62 4 − .56 − .51 − .54 − .56 − .56 − .55 5 − .53 − .59 − .55 − .57 − .57 − .58 6 − .52 − .67 − .57 − .41 − .35 − .32 7 − .24 − .21 − .16 − .12 − .03 .04 8 .04 0.22 .33 .48 .66 .79 9 .96 0.89 .69 0.60 .60 .62 10 .61 .57 .42 0.34 .29 .17 11 .14 .31 .50 .64 .46 .28 12 .31 .33 .55 0.51 .57 .61 13 .61 .55 .56 0.52 .52 .45 table 1 that all DI variates exhibit negative correlation with RM until the 7 th DI variate, afterwards it turns positive. In fact show significant correlations in the 9-th variate of DI-1 with values reaching as high as 0.96 and decreasing afterwards. It is known that \\({R}^{2}\\) value is an indicator of closeness of data with the linear regression model. As \\({R}^{2}\\) values approach 1, predictive model becomes a close-fitting model. The DI-1 value in the 9th variate block, correspond to the 49th month after the RM maximum (see Table 2 ), provide the best correlations, with correlation coefficients CC of 0.96 and the least standard error of estimation of 11.5. The second best \\({R}^{2}=0.89\\) value is found in DI-2 (9) variate block corresponds to 50th month after the RM maximum with a least standard error of estimation of19.4. For more eloquence, \\({R}^{2}\\) values are plotted with months after RM maximum and shown in Fig. 4 . Figure 4 visibly demonstrates a negative correlation for the first 36 months after sunspot maximum between DI variates and RM of the following cycle. Subsequent to this, the correlation turns positive and quickly attains a high value ( \\({R}^{2}=0.96\\) ) for the 49th and second high ( \\({R}^{2}=0.89\\) ) for 50th month corresponding to DI-1(9) and DI-2(9) of each cycle. Afterwards it starts decreasing till the 78-th month with the appearance of a small peak ( \\({R}^{2}=0.69\\) ) at 64 monthafter RM. This may be attributed to the geomagnetic disturbances occurrences few years prior to the minimum of a cycle which are well correlated with the maximum of sunspot number (RM) of next cycle, proposition of the precursor method. The corresponding two best correlated regression equations of DI indices with RM values are given below: $$RM=57.68+33.21 \\times DI-1\\left(9\\right)----------\\left[1\\right]$$ $$RM=62.84+28.98 \\times DI-2\\left(9\\right)----------\\left[2\\right]$$ Moreoverthe predictive capability of both the regression equations is tested by applying a hypothesis test on the regression slopes of equations [1] & [2]. The p-value for both the linear fitted curves is found to be around .017 which is quite less than the .05 level. With highlighting the fact that a p-value of less than .05, indicates 95% confidence that slope of regression line is not zero hence rejected the null hypothesis and confirms a strong relationship between the DI indicators with peak RM of following cycle. On the basis of above facts, regression equations[1]and [2] are being applied to backcast/hindcast the observed RM values for previous cycles (18–24)and ongoing cycle (25). Table 2 displays the observed RM with their predicted counterparts. From the results presented in the table, it is illustrious that the difference ( \\(\\) RM) between the predicted and the observed RMsfor cycles 18 to 24lie inside 1–14 range. The results further depict that roughly the predicted values are very close to the observed ones and in general, predicted values are found to concur approximately within ±08%. More often, table 2shows that the predicted RMfor the ongoing solar cycle number 25 to be about 111±12 and 112±20 with the help of equations [1] & [2] respectively. Commonly, predictions are given on 90% prediction intervals (based on the number of degrees of freedom and the sample size). In the present case a sample size of 7 cycles has 5 degrees of freedom and hence each standard error of estimation should be multiplied by 1.796 in order to get the 90% prediction interval. Hence, the above prediction value of maximum amplitude for cycle 25 based on DI-1(9) should be 111 ±21 and the prediction based on DI-2(9) should be 112±34, yielding an overlap of the two predictions of about 112±18, which is adopted henceforth as the final prediction for cycle’s 25 RM. 3.2 Evaluation of Rise time and Profile of Solar Cycle 25 After estimating the peak RM for solar cycle 25, it is likely for practical applications to know how long it takes to be observed and what the cycle's profile, i.e., its rise and fall times, may be.A detailed investigation of the time of rising of solar cycles 10 to 24 revealed a time range of 34 to 64 months for reaching peak RM. It's worth noting that the higher the peak RM, the shorter the time it takes to achieve it. It is observed as well that shorter the ascending period, the longer the descending phase, resulting in an average duration of a solar cycle of around 11 years (Usokin and Mursula 2003). Wilson ( 1987 ) examined the lengths of sunspot cycles using R12 and found them to be distributed symmetrically, with long-period cycle grouping (cycles with periods longer than 134 months) and short-period cycle grouping (cycles with periods shorter than 127 months).Because solar cycle 24 endured strictly in 11 years or 132 months, Wilson criteria place it neither in the long-period cycle group nor in the short-period cycle group. In December 2019, solar cycle 25 began (with a minimum smoothed sunspot number of 1.8). It will most likely continue until around 2030( https://www.swpc.noaa.gov/products/solar-cycle-progression ) The anticipated time to acquire peak RM, i.e. the 'rising time (RT)' for solar cycle 25 is assessed in this work, in line with Dabas et al., (2008, 2010). The RT for solar cycle 25 is estimated by investigating a significant statistical association between the recorded peak RM and the RTs of previous cycles 10 to 24. Figure 6: The link between the rise time (RT) from cycle minimum toits peak amplitude (RM) for solar cycles 10–23. The linear regression is obtained byignoring two extreme data points for cycles 19 and 24. The predicted peak RM = 112 when substituted in the regression equation, yield a roughestimate of rise time to be 48 ± 3 months for solar cycle 25. Figure 6 depicts the plot of RM Vs rising time (in months) for cycles 10–24, revealing an empirically significant inverse relationship (CC = − 0.89). It is worth noting that the rising time (RT) appears to decrease linearly with RM and is represented by a straight-line fit equation of the form; \\(RT=68.8-0.19 \\times RM\\) ----------- (3) When the estimated peak value of RM = 112 for solar cycle 25 is entered into the above computation, the expected RT is 48 ± 3 months. By putting the predicted peak value of RM = 112 for solar cycle 25 into this equation, the expected RT comes out to be 48± 3 months. Once the predicted peak RM and RT for the ongoing cycle 25 are known, the method proposed by Hathaway, Wilson, and Reichmann ( 1994 ) can be utilized for finding the fullshape of the cycle 25. \\({R}_{12}\\left(t\\right)= \\frac{{a(t- {t}_{0})}^{3}}{\\left\\{exp\\left[\\frac{{\\left(t-{t}_{0}\\right)}^{2}}{{b}^{2}}\\right]- c\\right\\}}\\) ----------- (4) where t is the time of a given cycle, t 0 is the time of the start of each cycle, and a, b, and c are fitting parameters. They proposed that the fitting parameter c = 0.71 was found to possess a single value for majority of the cycles. The parameters a and b can easily be evaluated, using the predicted values of RM (= 112 ± 18) and their rise time, RT (= 48 ± 3, in units of months)in line with the analysis given by Hathaway, Wilson, and Reichmann ( 1994 ). For the present study, the calculated values of these parameters are; \\(a=2.59 \\times {10}^{-3}, 2.53 \\times {10}^{-3}\\& 2.45 \\times {10}^{-3}\\) and b=41.6, 44.4 and 47.2, respectively, for the values of RM of 94, 112 & 130. The aforementioned values of a, b, and c have been put in Eq. (4) to obtain the probable shape and length of solar cycle 25. The obtained results can be seen in Fig. 8 . Comparison of Results with Other Predictions for solar cycle 25 The analytical results of the preceding sectionsfor maximum amplitude (RM = 125 ± 22) and its time of occurrence (probably in mid (Jul)–to- late (Dec) 2023), may now be compared with other predictions based on different approaches. Petrovay ( 2010 ) suggested four categories of solar cycle prediction methods: precursor, extrapolation, spectral or model-based methods.The extrapolation methods are based on non-linear approach and displayed inferior performance than precursor methods. Singh & Bhargawa ( 2017 )predicted a weaker cycle25 than cycle 24 based on an extrapolation method in which they utilized the Hurstexponent and a simplex projection algorithm. A similar prediction of weaker cycle 25 is reported by Iijima et al. ( 2017 ) by using a surface flux transportmodel based on temporal variations of axial dipole moment. Moreover, Kakad, Kakad& Ramesh (2017) predicted a very weak solar cycle 25 quite alike to Dalton’s minimum by estimating the Shannonentropy. Petrovay(2020), predicted maximum amplitude of 97.6 (± 10) may occur in 2026.2 (± 1 year) based on (quasi-) physical model linked with the planetsconsequently strengthening the proposal of “Modern minimum”. Macario-Rojas, Smith & E (2018)also applied a similar Table 3 Forecasts for Solar Cycle 25, Abbreviations are SoDa = Solar Dynamo, SFT = Surface Flux Transport, AFT = Advective Flux Transport. NARX = Non-linear Autoregressive Exogenous. Predictions of Solar Cycle 25 Category Peak SSN Rise Time Reference Precursors Internal precursors 175 2023.8 Li, Feng, and Li ( 2015 ) Polar precursor 117 ± 15 Polar precursor 136 ± 48 Pesnell and Schatten ( 2018 ) Helicity 117 Hawkes and Berger ( 2018 ) SoDA 120 ± 39 2025.2 ± 1.5 Based on Pesnell and Schatten ( 2018 ) Rush-to-the-poles 130 2024.8 Petrovay et al. ( 2018 ) Hale-cycle termination 184 McIntosh et al., 2023 Magnetic precursor 134 ± 8 2024 Hathaway & Upton ( 2023 ) Model-based (quasi-) physical model 97.6 2026.2 V. Courtillot et. al. (2021) (quasi-) physical model 97.6 (± 10) 2026.2 Petrovay(2020) SFT 124 ± 31 Jiang and Cao ( 2018 ) SFT 118 109–139 2024 ± 01 Bhowmik and Nandy 2018 SFT Iijima et al. ( 2017 ) AFT 110 Upton and Hathaway ( 2018 ) 2×2D 89 − 14 + 29 2027.2 ± 1.0 Labonville, Charbonneau, and Lemerle ( 2019 ) Shanon entropy 63 ± 11.3 Kakad, Kakad& Ramesh (2017) Truncated 90 ± 15 2024 ± 1 Kitiashvili ( 2016 ) Spectral Wavelet decomposition tree 132 2023.4 Rigozo et al. ( 2011 ) Simplex projection analysis 103 ± 25 2024.0 ± 0.6 Singh and Bhargawa ( 2017 ) Simplex projection/time-delay 154 ± 12 2023.2 ± 1.1 Sarp et al. ( 2018 ) Wavelet transform 146.7 ± 33.40 Luo and Tan ( 2024 ) Neural networks Neuro-fuzzy 90.7 ± 8 2022 Attia, Ismail, and Basurah ( 2013 ) Spatiotemporal 57 ± 17 2022–2023 Covas, Peixinho, and Fernandes ( 2019 ) Singular Spectrum Analysis 97.6 ± 7.8 2026.2 ± 1 Courtillot et al. (2021) NARX 116.6 February 2025 Kalkan et. al., (2023) Time series deep learning method 133.9 ± 7.2 February 2024 Su et. al., ( 2023 ) model-based method and predicted the cycle25 will be 14.4 per cent (± 19.5 per cent) weaker than the cycle 24.Kirov et al. ( 2018 ), utilized precursormethod predicted that peaksmoothed sunspot number of cycle25 may be within 50–55 range. Gopalswamy et al. ( 2018 ) and Hathaway & Upton ( 2023 ) predicted modest amplitudes of cycle 25 based on precursor method though Cameron, Jiang & Sch ̈ussler(2016) reported that cycle 25 may to some extent stronger than the previous cycle 24. Pesnell & Schatten ( 2018 ) reported 135 ± 25 to be as the smoothed peak of sunspot cycle 25 by incorporating the SODA index into precursor method. The SODA index is estimated by polar magnetic fieldsand the spectral index. Also, Jiang & Cao (2017) using a surface flux transport model-basedmethod, reported a stronger cycle 25 than cycle24. Sarp et.al. ( 2018 ) forecasted a peak sunspotnumber of 154 ± 12inyear 2023.2 ± 1.1 for Solar Cycle 25byutilizinga non-linear prediction algorithm based on delay-time and phase space reconstruction.Su et. al. ( 2023 ) using neural basis expansion analysis for the interpretable time series deep learning method, predict a peak amplitude 133.9 ± 7.2 around 2024.2. Some predictions suggest a below average cycle 25 (Nandy, 2021 ; Jiang, Zhang, and Petrovay, 2023) whereas some forecasts have predictedan above-average amplitude for solar cycle 25 (Han and Yin, 2019 ; McIntosh et al., 2020 ). Recently (McIntosh et al., 2023 ) revised their prediction and proposed that the ongoing solar cycle 25 might have maximum amplitude around the average. Indeed, the predictions so far are proposingsolar cycle 25 as a below-average cycle (Carrasco andVaquero, 2022, 2023). According to the NOAA Solar Cycle 25 Prediction Panel, predicted Cycle 25 can reach a maximum of 115 occurring in July, 2025 ( https://www.swpc.noaa.gov/products/solar-cycle-progression#:~:text=The%20Prediction%20Panel%20predicted%20Cycle,November%202024%20and%20March%202026 .). Discussion The eminent sunspot cycles of eleven year are incarnation of solar magnetic activity. solar magnetic cycle influences the rate of occurrence of all geoeffective solar eruptive phenomena. Indeed, prediction of its characteristics is avitalcomponent of space weather forecasting. According to Babcock Leighton dynamo models, the evolution of the surface magnetic field at cycle n, after it is transported inside by meridional flow, acts as a source of toroidal fields for cycle n + 1. It is therefore possible to obtain prediction of the characteristics of cycle n + 1 by observing the magnetic field variations of cycle n. The idea lays the foundation of precursor methods, (Charbonneau 2014 , Petrovay 2010 ). Researchers extensively explored the statistical relationships between solar activity and the number of sunspots, total surface area, and their time of emergence. The two (pertaining) physics-based precursors for forecasting the amplitude of a solar cycle have emerged as the most reliable; geomagnetic activity levels and the Sun's magnetic configuration (polar fields and axial dipole moment) shortly after the sunspot cycle minimum.Nonetheless, there are still some ambiguities linked to these predictors. Among these, the geomagnetic precursors are more resilient as the data set is longer, but their physical mechanisms are less precise. Polar precursors have a stronger physics foundation;however the functional relationship couldn’t be well defined because of data availability for a shorter time period (Upton & Hathaway 2023 ).Geomagnetic precursor technique was first proposed by Ohl ( 1966 ) to forecast the cycle maxima by using geomagnetic activities near cycle minima. According to Ohl’s precursor method, the lowest in geomagnetic activity seen in the geomagnetic aa index is closely connected to the magnitude of the subsequent cycle. Thompson’s precursor method uses the number of geomagnetically disturbed days (A p ≥ 25) throughout the entire previous cycle to predict cycle amplitudes well before the time of minimum (Thompson 1994, 1996). This paper reports the maximum amplitude and rise time of Solar Cycle 25 underway using modified geomagnetic precursor technique. The solar and geomagnetic data sets utilized here covers solar cycles 17 to 24 i.e. from 1932 to 2019. The declining phase of each cycle is divided into equally spaced time windows (variate blocks) of 06 months duration and disturbance indices are calculated within each time-window. Further, all windows are correlated with peak sunspot numbers of following cycles. The highest correlations are found in DI-1(9) and DI-2(9) variate blocks i.e. 49th month and 50th month after the solar maximum. Ergo, the detailed synthesis of regression equations yields the predicted maximum amplitude of current cycle 25 to be ≈ 112 ± 18. The probable peak time of cycle 25 could be 48 ± 4 months i.e. October 2023 –April 24. The physical mechanism behind geomagnetic precursors is enigmatic. Geomagnetic disturbances which create the precursory signals are typically caused by high-speed solar wind streams from low-latitude coronal holes later in a cycle(Legrand and Simon 1996). According to Schatten. Myers and Sofia (1996), this geomagnetic activity during the time of the sunspot cycle minimum is connected to the intensity of the Sun's polar magnetic field, which is then related to the strength of the subsequent maximum. According to Cameron and Schüssler ( 2007 ), these antecedent correlations with the amplitude of the following cycle result from the overlap of sunspot cycles and the Waldmeier Effect. Wang and Sheeley Jr. (2009) believe that Ohl's technique has closer ties to the Sun's magnetic dipole strength and should thus give better predictions.Each sunspot cycle shows a consistent rise in sunspot numbers to a maximum and a subsequent fall to a low level. In contrast, geomagnetic indices (Ap or aa) exhibit two or more maxima per cycle, with one occurring near or before and other just after the sunspot maximum. The gap between the two maxima is referred as ‘the Gnevyshev gap’ and may lead to quasi-biennial and quasi-triennial periodicities in the geomagnetic indices (Takalo 2021 , Kane 1997).Ahluwalia ( 2000 ) reported the Gnevyshev gap in A p data could be caused by solar polar field reversals.Schatten et al. ( 1978 ) proposed a more cogent physical mechanism to explain Ohl ( 1966 ) hypothesis by reporting thatpolar field strength of the sun close to a solar minimum is strongly related to the solar activity of the subsequent cycle. Dynamo-based prediction techniques of sunspot cycle dwell on its two inherent characteristics: first, solar magnetism swings between poloidal and toroidal components; and second there is a degree of \"magnetic persistence\" in dynamos, which, in the turn causes the dependence of many magnetic-related quantities on the level of magnetism encased beneath the surface of the sun. The geomagnetic indices at the minimum phase of an active cycle exhibit high correlation with the magnitude of the ensuing maximum because geomagnetic indices replicate the magnitude of poloidal field and, as sunspot minimum approaches, it happens to the governing component of solar magnetism (Schatten and Myers, 1996).Thereby, the solar cycle actually begins many years before the sunspot minimum, necessitating the use of geomagnetic indices at various phases in the decaying part of a cycle (e.g., construction of thirteen time windows/variate blocks of 06 month duration in present analysis) for predicting the size of the ensuing cycle. Moreover, this technique can successfully be applicative to predict thesize and timing of following cycle one to two years before itsofficial commencement. Conclusion The geomagnetic precursor technique based prediction of ongoing solar cycle 25 presented in this paper clearly suggest that cycle 25 is going to becomparable with the previous cycle 24 (~ 112 ± 18). The disturbance index, nearly 49 to 50 months after the peak (i.e. variate blocks 9 − 1 and 9 − 2 or few years before cycle minimum) seems to be a righteous precursor to estimate the size of the subsequent cycle 25. Table 1 clearly indicates that this technique displays a fairly good correlation (COD = 0.96) between the predictors and predictions of cycles 17 to 24 are lying within ± 10% window with the observed one (Table 2 ). Moreover, this technique can simply be deployed for advance prediction of maximum amplitude of coming cycle at least 1 to 2 years before its official start. Hathaway, Wilson, and Reichmann ( 1994 ) method is applied for estimating the time to attain the peak amplitude of cycle 25 and the obtained results yield rise time of 47±3 months. Hence from an official start of cycle 25 in December 2019 we expect to observe the maximum amplitude of the cycle to occur in late to early 2024. Declarations Acknowledgements Authors would like to acknowledge Dr. R.S. Dabas, Scientist-G (Retd.), NPL New Delhi, Prof. Sangeeta Shukla, Hon’ble VC, CCS University, Meerut and the University Research Grant Scheme (URGS) [No. DEV/URGS/2022-23/35, dated 22-07-2022] for the all the necessary financial assistance to carried out this research work. References Ahluwalia, H. S. (2000). Ap time variations and interplanetary magnetic field intensity. Journal of Geophysical Research: Space Physics, 105(A12), 27481-27487. Aparicio, A. J. P., Carrasco, V. M. S., & Vaquero, J. M. (2023). Prediction of the maximum amplitude of Solar Cycle 25 using the ascending inflection point. Solar Physics, 298(8), 100. Berdermann, J, Kriegel, M, Banys, D, F. Heymann, M.M. Hoque, V. Wilken, C. Borries, A. Heßelbarth, N. Jakowski. Ionospheric response to the X9.3 flare on 6 September 2017 and its implication for navigation services over Europe, Space Weather, 16 (10) (2018), pp. 1604-1615, 10.1029/2018SW001933 Cameron, R. H., Jiang, J., & Schuessler, M. (2016). Solar cycle 25: another moderate cycle?. The Astrophysical Journal Letters, 823(2), L22. Cameron, R., & Schüssler, M. (2007). Solar cycle prediction using precursors and flux transport models. The Astrophysical Journal, 659(1), 801. Charbonneau, P. (2014). Solar dynamo theory. Annual Review of Astronomy and Astrophysics, 52, 251-290. Dabas, R. S., & Sharma, K. (2010). Prediction of solar cycle 24 using geomagnetic precursors: validation and update. Solar Physics, 266, 391-403. Diego, P., & Laurenza, M. (2021). Geomagnetic activity recurrences for predicting the amplitude and shape of solar cycle n. 25. Journal of Space Weather and Space Climate, 11, 52. Du, Z., Wang, H., & Zhang, L. (2009). Correlation function analysis between sunspot cycle amplitudes and rise times. Solar Physics, 255, 179-185. Feynman, J. (1982). Geomagnetic and solar wind cycles, 1900–1975. Journal of Geophysical Research: Space Physics, 87(A8), 6153-6162. Forte, B., Allbrook, T., Arnold, A., Astin, I., Vani, B.C., Monico, J.F.G., Shimabukuro, M.H., Koulouri, A., John, H.M., (2024), Methodology for the characterisation of the impact of TEC fluctuations and scintillation on ground positioning quality over South America and North Europe, with implications for forecasts. Adv. Space Res. Fry, E. K. (2012). The risks and impacts of space weather: Policy recommendations and initiatives. Space Policy, 28(3), 180-184. Gopalswamy, N., Mӓkelӓ, P., Yashiro, S., & Akiyama, S. (2018). Long-term solar activity studies using microwave imaging observations and prediction for cycle 25. Journal of Atmospheric and Solar-Terrestrial Physics, 176, 26-33. Haigh, J. D. (2007). The Sun and the Earth’s climate. 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Improvement of solar-cycle prediction: plateau of solar axial dipole moment. Astronomy & Astrophysics, 607, L2. Jiang, J., & Cao, J. (2018). Predicting solar surface large-scale magnetic field of cycle 24. Journal of Atmospheric and Solar-Terrestrial Physics, 176, 34-41. John, H.M., Forte, B., Astin, I., Allbrook, T., Arnold, A., Vani, B.C., Häggström, I., Performance of GPS positioning in the presence of irregularities in the auroral and polar ionospheres during EISCAT UHF/ESR measurements, Remote Sens. (Basel), 13 (23) (2021), p. 4798, 10.3390/rs13234798 Kakad, B., Kakad, A., & Ramesh, D. S. (2015). A new method for forecasting the solar cycle descent time. Journal of Space Weather and Space Climate, 5, A29. Kane, R. P. (2007). A preliminary estimate of the size of the coming solar cycle 24, based on Ohl’s precursor method. Solar Physics, 243(2), 205-217. Kirov, B., Asenovski, S., Georgieva, K., Obridko, V. N., & Maris-Muntean, G. (2018). Forecasting the sunspot maximum through an analysis of geomagnetic activity. Journal of Atmospheric and Solar-Terrestrial Physics, 176, 42-50. Legrand, J. P., & Simon, P. A. (1991). A two-component solar cycle. Solar Physics, 131, 187-209. Li, Y. (1997). Predictions of the features for sunspot cycle 23. Solar Physics, 170, 437-445. Luo, P., & Tan, B. (2024). Long-term evolution of solar activity and prediction of the followingsolar cycles. Research in Astronomy and Astrophysics. Macario-Rojas, A., Smith, K. L., & Roberts, P. C. (2018). Solar activity simulation and forecast with a flux-transport dynamo. Monthly Notices of the Royal Astronomical Society, 479(3), 3791-3803 McIntosh, S. W., Chapman, S., Leamon, R. J., Egeland, R., & Watkins, N. W. (2020). Overlapping magnetic activity cycles and the sunspot number: forecasting sunspot cycle 25 amplitude. Solar Physics, 295(12), 1-14. McIntosh, S. W., Leamon, R. J., & Egeland, R. (2023). Deciphering solar magnetic activity: The (solar) hale cycle terminator of 2021. Frontiers in Astronomy and Space Sciences, 10, 16. Nandy, D. (2021). Progress in solar cycle predictions: Sunspot cycles 24–25 in perspective: Invited review. Solar Physics, 296(3), 54. Nandy, D. (2021). Progress in solar cycle predictions: Sunspot cycles 24–25 in perspective: Invited review. Solar Physics, 296(3), 54. Ng, K. K. (2016). Prediction methods in solar sunspots cycles. Scientific Reports, 6(1), 21028. Ohl, A. I. (1966). Wolf’s number prediction for the maximum of the cycle 20. Soln. Dannye, 12, 84. Ohl, A. I., Ohl, G. I.: 1979, In: Donnelly, R.F. (ed.) Solar-Terrestrial Predictions Proceedings, NOAA/Space Environmental Laboratories, Boulder, 258. Pesnell, W. D., & Schatten, K. H. (2018). An early prediction of the amplitude of solar cycle 25. Solar Physics, 293(7), 112. Petrovay, K. (2010). Solar cycle prediction. Living reviews in solar physics, 7(1), 1-59. Petrovay, K. (2020). Solar cycle prediction. Living Reviews in Solar Physics, 17(1), 2. Pulkkinen, T. (2007). Space weather: Terrestrial perspective. Living Reviews in Solar Physics, 4(1), 1. Sarp, V., Kilcik, A., Yurchyshyn, V., Rozelot, J. P., &Ozguc, A. (2018). Prediction of solar cycle 25: a non-linear approach. Monthly Notices of the Royal Astronomical Society, 481(3), 2981-2985. Sato, H., Jakowski, N., Berdermann, J., Jiricka, K., Heßelbarth, A., Banyś, D., Wilken, V., (2019), Solar Radio Burst events on September 6, 2017 and its impact on GNSS signal frequencies, Space Weather., 17 (6) , pp. 816-826, 10.1029/2019SW002198. Schatten, K. H., & Pesnell, W. D. (1993). An early solar dynamo prediction: cycle 23∼ cycle 22. Geophysical research letters, 20(20), 2275-2278. Schatten, K. H., Scherrer, P. H., Svalgaard, L., & Wilcox, J. M. (1978). Using dynamo theory to predict the sunspot number during solar cycle 21. Geophysical Research Letters, 5(5), 411-414. Schatten, K., Myers, D. J., & Sofia, S. (1996). Solar activity forecast for solar cycle 23. Geophysical research letters, 23(6), 605-608. Schatten, K., Myers, D. J., & Sofia, S. (1996). Solar activity forecast for solar cycle 23. Geophysical research letters, 23(6), 605-608. Shastri, S. (1998). An estimate for the size of cycle 23 using multivariate relationships. Solar Physics, 180, 499-504. Singh, A. K., &Bhargawa, A. (2017). An early prediction of 25th solar cycle using Hurst exponent. Astrophysics and Space Science, 362(11), 199. Su, X., Liang, B., Feng, S., Dai, W., & Yang, Y. (2023). Solar Cycle 25 Prediction Using N-BEATS. The Astrophysical Journal, 947(2), 50. Takalo, J. (2021). Separating the aa-index into solar and hale cycle related components using principal component analysis. Solar Physics, 296(5), 80. Thompson, R.:1987, IPS Technical Report IPS-TR-87-03, Sydney, Australia. 2. Thompson, R.:1993, Solar phys. 148, 383. Upton, L. A., & Hathaway, D. H. (2023). Solar cycle precursors and the outlook for cycle 25. Journal of Geophysical Research: Space Physics, 128(10), e2023JA031681. Usoskin, I. G. (2023). A history of solar activity over millennia. Living Reviews in Solar Physics, 20(1), 2. Wang, Y. M., & Sheeley, N. R. (2009). Understanding the geomagnetic precursor of the solar cycle. The Astrophysical Journal, 694(1), L11. Wilson, R. M. (1987). On the distribution of sunspot cycle periods. Journal of Geophysical Research: Space Physics, 92(A9), 10101-10104. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 16 Dec, 2024 Read the published version in Solar Physics → Version 1 posted Editorial decision: Revision requested 13 Aug, 2024 Reviews received at journal 11 Aug, 2024 Reviewers agreed at journal 24 Jul, 2024 Reviewers invited by journal 05 Jul, 2024 Editor assigned by journal 15 Jun, 2024 Submission checks completed at journal 15 Jun, 2024 First submitted to journal 12 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-4570127\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":323677087,\"identity\":\"3b62b1e1-c22c-4319-bb3b-cfe241d5778f\",\"order_by\":0,\"name\":\"Anushree Rajwanshi\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Chaudhary Charan Singh University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Anushree\",\"middleName\":\"\",\"lastName\":\"Rajwanshi\",\"suffix\":\"\"},{\"id\":323677088,\"identity\":\"1b0d7178-da71-4e49-8442-5fe9124409bf\",\"order_by\":1,\"name\":\"Sachin Kumar\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Chaudhary Charan Singh University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Sachin\",\"middleName\":\"\",\"lastName\":\"Kumar\",\"suffix\":\"\"},{\"id\":323677089,\"identity\":\"f318dcae-4ff3-49b6-a274-d6b86c1bea3a\",\"order_by\":2,\"name\":\"Rupesh M. Das\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"CSIR National Physical Laboratory of India\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Rupesh\",\"middleName\":\"M.\",\"lastName\":\"Das\",\"suffix\":\"\"},{\"id\":323677090,\"identity\":\"29a22ead-b433-4c12-a094-2eb45d3c60fd\",\"order_by\":3,\"name\":\"Nandita Srivastava\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYJACiQQGBjkGBuYGMI+NOC0JDMYMDIykaGFIYEhsgGkhCMzZzx688fCHXfp26YMNzBUVdQx80gS0WvbkJVskJCTn7uxLbGA8c+YwA5vMAfxaDA7kmAH9wpy74QxjA2Nj2wEGNlBo4NVy/g1IS326AVjLvzoitNwA23I4AaKlgZkYLW+MLRLSjhvu7GFsONhw7DAPEQ7LMbz5w6Za3pyH+eDDhpo6OfkZBLQg9ALxASDmIVI9VMsoGAWjYBSMAqwAANtEP3ZPrESzAAAAAElFTkSuQmCC\",\"orcid\":\"\",\"institution\":\"Udaipur Solar Observatory\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Nandita\",\"middleName\":\"\",\"lastName\":\"Srivastava\",\"suffix\":\"\"},{\"id\":323677091,\"identity\":\"b230f7d1-316a-4e6c-ab94-1af60192e91f\",\"order_by\":4,\"name\":\"Kavita Sharma\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Chaudhary Charan Singh University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Kavita\",\"middleName\":\"\",\"lastName\":\"Sharma\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-06-12 12:14:50\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-4570127/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-4570127/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1007/s11207-024-02412-w\",\"type\":\"published\",\"date\":\"2024-12-16T15:57:56+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":60026414,\"identity\":\"ca052a52-8dc0-4af5-8b37-deec5f86e146\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:31:35\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":65044,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eSchematic illustration of various techniques used for sunspot cycle prediction.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/4fef8b3b14b17f458e9cc11d.png\"},{\"id\":60026411,\"identity\":\"91a9aa72-e0d7-4a26-8755-258b7f0ad037\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:31:35\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":1006917,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eFlow chart displaying the functioning of geomagnetic precursor technique.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/b606d32b8ed39da4a46d6cd6.png\"},{\"id\":60026410,\"identity\":\"fe9a0826-f6f0-424b-901b-9df7e69e4225\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:31:35\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":112773,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eVariation of R12 (in upper panel) and of DI indices (in lower panel) for sunspotcycles 17 – 24.Daily values of \\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;indices and 12 - month smoothed sunspot numbers R12, for the above duration was downloaded from the National Geophysical Data Center (NGDC), NOAA ftp site (https://www.ngdc.noaa.gov/ftp.html).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/ea0b7bc7eb5f0815516e0f8a.png\"},{\"id\":60026409,\"identity\":\"ae8fbcef-be1d-4fef-841c-016c9d213da3\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:31:35\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":84791,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eCorrelation between disturbance indices and ensuing cycle maximum. Figure displayed variations of the COD (R2) with months after attaining the solar maximum for solar cycles 17 to 24. R2\\u0026nbsp;is calculated by linear regression analysis between the DI indices (for 78 months)in the declining segment of the previous cycle and the sunspot maximum of the next cycle.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/cb77495afb73c5d912edc213.png\"},{\"id\":60026794,\"identity\":\"c048913b-d74c-4ca9-b68b-37d48a4640ee\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:39:35\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":65592,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003edepicts the scatter plot of RM versus DI-1(9) and DI-2(9) variates where the highest correlation (R2=0.96) and second highest correlation (R2=0.89) are found with SEE of ±11.5 \\u0026amp; ±19.4 respectively for solar cycles 17 to 24.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure5fin.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/320d2b2f6981ef568cae0408.png\"},{\"id\":60026412,\"identity\":\"a0882a5e-967d-42f9-8224-ab8f59f08a20\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:31:35\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":83740,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eThe link between the rise time (RT) from cycle minimum toits peak amplitude (RM) for solar cycles 10 – 23. The linear regression is obtained byignoring two extreme data points for cycles 19 and 24. The predicted peak RM = 112 when substituted in the regression equation, yield a roughestimate of rise time to be 48 ± 3 months for solar cycle 25.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure6.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/ecbd7f44f26c696a9ea85462.png\"},{\"id\":60026795,\"identity\":\"33231085-00c9-414c-aacd-622bc10a6e98\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:39:35\",\"extension\":\"png\",\"order_by\":7,\"title\":\"Figure 7\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":52473,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eObserved R12(thin line) and fitted curve (thick line) projectedby using RM in the function (equation 4), showing close agreement in terms of amplitude and its occurrence time for cycle17 – 24.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure7.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/808112ec50e2ff8860d91531.png\"},{\"id\":60026416,\"identity\":\"c9332f48-a625-470a-8cf0-6d503645861e\",\"added_by\":\"auto\",\"created_at\":\"2024-07-10 17:31:36\",\"extension\":\"png\",\"order_by\":8,\"title\":\"Figure 8\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":57690,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eShape and length ofpredicted solar cycle number 25 having peak amplitude ofRM = 112 ±18 occurring about48 ± 3 months from theminimum of solar cycle number24 (i.e., sometime October 2023 to April 2024).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/82e536bbfe9b8cc1238385ff.png\"},{\"id\":72202558,\"identity\":\"b2a164da-39c9-47fb-9d54-3a254783aad7\",\"added_by\":\"auto\",\"created_at\":\"2024-12-23 16:14:49\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":2157533,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4570127/v1/facd238b-2728-4db2-b0e7-f9c1d9361dd2.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Predicting Maximum Amplitude and Rise Time of Solar Cycle 25 Using Modified Geomagnetic Precursor Technique\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cp\\u003eThe increasing reliance of society upon space-based technological systems emphasises the need for understanding the underlying mechanism of solar activity and the sunspot prediction. Solar activities are being researched in diverse scientific fields, including solar physics, climate change, and space mission planning (Haigh, \\u003cspan class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003e; Hanslmeier, 2007; Usoskin, \\u003cspan class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). Extreme currents in the electric grids, extensive radio blackouts, phone and internet connection outages in space and within the Earth\\u0026apos;s atmosphere can all result from space weather occurrences. Satellites used for global navigation, communications, and weather forecasting, can also be damaged by severe space weather events. (Fry \\u003cspan class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e; Berdermann et al., \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e; Sato et. al., \\u003cspan class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Nandy \\u003cspan class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e; John et al., \\u003cspan class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e; Forte et al., \\u003cspan class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e; Ishii et. al., 2024; ). Thus, space weather can have a wide range of societal and economic consequences (Pulkkinen, \\u003cspan class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003e). For the safety of contemporary technology and to comprehend the process underlying solar activity, solar activity prediction is crucial (Luo and Tan, \\u003cspan class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). Advance prediction of maximum amplitude and timing of the sunspot cycle have gained societal relevance in recent decades, scientificpanels have been created and tasked with producing consensus judgements on the upcoming sunspot cycle, several years before the approaching peak (McIntosh, 2020).\\u003c/p\\u003e\\n\\u003cp\\u003eThe international sunspot number (ISN)is a universal indicator of solar activity based on the ocular observations of the Sun\\u0026apos;s visible disc (Hathaway \\u003cspan class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). ISN is the most extensive record of the evolution of solar activity. World Data Center Sunspot Index and Long-term Solar Observations (WDC-SILSO) maintains and provides records of daily, monthly mean, and yearly mean ISN time-series since year 1700 (\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://www.sidc.be/SILSO/datafiles\\u003c/span\\u003e\\u003c/span\\u003e). These series play a pivotal role for the accurate predictions of solar cycle (Petrovay \\u003cspan class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cp\\u003eSeveral approaches as depicted in Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e are being deployed by the researchers to predict the sunspot cycles. Petrovay (\\u003cspan class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e) reviewed and elaborated several solaractivity forecast techniques. The precursorbased approach relies on the statistical correlation between an observed variable and the subsequent solar cycle maximum. The statistical association between the two variables might be explained by our understanding of solar physics. Physical modelbased predictions utilize the well-known surface flux-transport models.Though, due to the intricacy of these models, alternative approaches, including simple statistical ones, are being widely explored.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cbr\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe intriguing magnetic personality of Sun is being studied since several decades and now it becomes apparent thatmagnetic field of Sun is created and magnified by continual stretching, twisting, and folding of the field lines caused by the combined actions of differential rotation and convection.Solar dynamo theory suggests that the Sun\\u0026apos;s magnetic field would increase to a maximum, collapse to zero, and then reverse itself in a relatively cyclical manner (Charbonneau, \\u003cspan class=\\\"CitationRef\\\"\\u003e2014\\u003c/span\\u003e). The change in the quantity of sunspots and their migration to lower latitudes are both results of the field lines intensification and ultimately in fading away.\\u003c/p\\u003e\\n\\u003cp\\u003eVarious researches (Ohl and Ohl, \\u003cspan class=\\\"CitationRef\\\"\\u003e1979\\u003c/span\\u003e, Feynman, \\u003cspan class=\\\"CitationRef\\\"\\u003e1982\\u003c/span\\u003e, Thompson, \\u003cspan class=\\\"CitationRef\\\"\\u003e1987\\u003c/span\\u003e, 1993, Li, \\u003cspan class=\\\"CitationRef\\\"\\u003e1997\\u003c/span\\u003e, Shastri, \\u003cspan class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e, Hathaway and Wilson, \\u003cspan class=\\\"CitationRef\\\"\\u003e2006\\u003c/span\\u003e, Kane, \\u003cspan class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003ea, Du, 2009, Kim Kwee Ng \\u003cspan class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e, Diego \\u003cspan class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003eand references enclosed within) have reportedthat geomagnetic activities, during the declining phase of a solar cycle act as the precursor for predicting the peak sunspot number of the subsequent solar cycle. This association can be well explained on the basis of solar dynamo theory. According to this theory, the poloidal solar magnetic field, which is estimated based on geomagnetic activity during the declining phase of the preceding cycle or at the cycle minimum, provides the seed for future toroidal fields within the Sun that in turn cause solar activity (Schatten et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e1978\\u003c/span\\u003e; Schatten \\u0026amp; Pesnell \\u003cspan class=\\\"CitationRef\\\"\\u003e1993\\u003c/span\\u003e; Hathaway \\u0026amp; Wilson 1999; Choudhuri et al. 2007). Many models have been developed from the Ohl\\u0026rsquo;s Precursor Method and provide varying degrees of success in predicting aforthcoming solar activity.\\u003c/p\\u003e\\n\\u003cp\\u003eIn an earlier study, Dabas et. al. 2008, 2010, predicted the maximum sunspot number of previous cycle 24 using geomagnetic precursor technique to be 124 \\u0026plusmn; 23 and 131 \\u0026plusmn; 20, which was very near to the observed one (observed RM\\u0026thinsp;=\\u0026thinsp;117 for SC 24)\\u003c/p\\u003e\\n\\u003cp\\u003eThe peak amplitude of solar cycle 25 is predicted by various groups using diversified techniques as shown in Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e and their results are listed in Table \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e. All of the forecasts for maximum of cycle 25, broadly differs from each other. Also majority of the forecasts point toward a stronger cycle 25 in comparison to cycle 24. However physics based forecasts is not much different from each other as all indicate a climatologically weak cycle (Nandy 2020). This conclusion is based on the Babcock-Leighton mechanism. The mechanism is governing driver of solar cycle variability also the dynamical memory of the solar cycle is short, permitting for forecasts of only the succeeding cycle.\\u003c/p\\u003e\\n\\u003cp\\u003eThe present research relies on modified geomagnetic precursor technique (applied earlier by Dabas et. al., 2008, 2010 for predicting the maximum amplitude and rise time of solar cycle 24) to predict the size and timing of the maximum sunspot amplitude for enduring cycle 25. In this technique, thirteen variable blocks of 6-month duration are constructed by finding the 12-month moving average of the number of disturbed days ((\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({A}_{p} \\\\ge 25\\\\)\\u003c/span\\u003e\\u003c/span\\u003e) during the post-peak segment of 17 to 24 sunspot cycles. The following Section \\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e describes the data used and the analysis technique implemented in the present study. Consequent results are described in Section \\u003cspan class=\\\"InternalRef\\\"\\u003e3.1\\u003c/span\\u003e for predicting the maximum sunspot number for Solar Cycle 25. The estimated shape and rise time of the current solar cycle are presented in Section \\u003cspan class=\\\"InternalRef\\\"\\u003e3.2\\u003c/span\\u003e. The present findings are compared with predictions of others in Section \\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e. The key conclusions of this work are discussed in Section \\u003cspan class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e, together with a few added remarks and propositions concerning the geomagnetic precursor technique.\\u003c/p\\u003e\\n\\u003ch3\\u003eAnalysis Process via Modified Geomagnetic Precursor Technique\\u003c/h3\\u003e\\n\\u003cp\\u003eThe precursor technique (Thompson 1993, 1996) aims to establish a link between cycle amplitude and the phenomenon observed on or emanating from the sun during the solar cycle\\u0026apos;s decreasing phase or at solar minimum. Thompson (1993) suggested that the upcoming solar cycle begins in the decreasing part of the previous cycle, where it manifests itself in the emergence of coronal holes as well as the intensity of the solar polar magnetic field. The constancy of coronal holes causes a series of disruptions which are separated by 27 days, the sun\\u0026apos;s rotation period. The frequency, severity, and stability of these recurring disruptions in the decreasing phase acts as an excellent indicator of the next cycle\\u0026apos;s vigor. Figure \\u003cspan\\u003e2\\u003c/span\\u003e illustrated the flowchart of geomagnetic precursor technique deployed to anticipate the maximum amplitude/sunspot number of the ongoing solar cycle 25. The current study utilizes 12-month smoothed sunspot number \\u003cspan\\u003e\\u003cspan\\u003e\\\\({{\\\\prime }R}_{12}{\\\\prime }\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan\\u003e\\u003cspan\\u003e\\\\({A}_{P}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e index as the geomagnetic precursor pair. The number of geomagnetic disturbances (as precursors) arecalculatedas the number of days in a month for which planetary magnetic activity index \\u0026lsquo;\\u003cspan\\u003e\\u003cspan\\u003e\\\\({A}_{P}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u0026rsquo; is greater than or equal to 25 (Thompson, \\u003cspan\\u003e1987\\u003c/span\\u003e)over the decreasing phase (cycle 24 maximum to lowest).After estimating the number of disturbed days of each month, the Disturbance Index (DI) is determined as R12 i.e. by calculating the 12-month running average. The temporal behavior of R12 and the disturbance index \\u0026lsquo;DI\\u0026rsquo; for sunspot cycles 17\\u0026ndash;24 is shown in the Fig. \\u003cspan\\u003e3\\u003c/span\\u003e. The values of DI span from 1 to 8. For cycles 17\\u0026ndash;22, the descent durations lie in the range of 79 to 91 months. Although for solar cycle 23, the longest descent duration of 108 months is observed. With descent duration of 84 months, solar cycle 24 again lies in the previous window.\\u003c/p\\u003e\\u003cp\\u003eData used here for the analysis covers period corresponding to the last eightprecedingsolar cycles 17 to 24.\\u003c/p\\u003e\\u003cp\\u003eIn order to comprehensively understand DI behavior throughout the descending half of each solar cycle, the common descent period (78 months) is divided into thirteen evenly spaced blocks (every six months), beginning after each cycle\\u0026apos;s R12 peak (RM). Starting with the first month DI after the peak sunspot number, the next twelve DIs are grouped in variate block DI-1 at 6-month intervals. The second month DI after the peak sunspot number, as well as the subsequent twelve DIs, are grouped in variate block DI-2. Same way DI-3, DI-4, DI-5, and DI-6 variate blocks are constructed. In this manner, each variate block comprises thirteen variates. In addition, for each variate block, the minimum (DI-MIN), maximum (DI-MAX), and average (DI-AVG) DI values are also calculated. A linear regression analysis is then performed between thirteen variates of DI-1 to DI-6 with the maximum sunspot number (denoted as RM) of the following cycles. The best regression coefficient yields the best fit equation, which is henceforth utilized for the prediction of the peak sunspot number for ongoing solar cycle 25.\\u003c/p\\u003e\\u003cdiv id=\\\"Sec4\\\"\\u003e\\u003cbr\\u003e\\u003c/div\\u003e\"},{\"header\":\"Results\",\"content\":\"\\u003cp\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe first degree regression results or the coefficient of determination (\\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e) of linear regression analysis between DIs of six variates blocks and the following cycle peak sunspot number are listed in Table \\u003cspan\\u003e1\\u003c/span\\u003e. The red colored R\\u003csup\\u003e2\\u003c/sup\\u003e values show the highest correlation between DIs and peak sunspot numbers of next cycle for each DI block. It is quite interesting to note from the\\u003c/p\\u003e\\n\\u003cdiv\\u003e\\n \\u003ctable id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv\\u003eTable 1\\u003c/div\\u003e\\n \\u003cdiv\\u003e\\n \\u003cp\\u003eResults of the linear correlation analysis between running average of observed RM and different monthly DI index at each Variate block.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\" rowspan=\\\"2\\\"\\u003e\\n \\u003cp\\u003eVariate block number\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\" colspan=\\\"6\\\"\\u003e\\n \\u003cp\\u003eCoefficient of Determination, R\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eFixed DI-1\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eFixed DI-2\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eFixed DI-3\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eFixed DI-4\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eFixed DI-5\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003eFixed DI-6\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.12\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.19\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.16\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.18\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.18\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.32\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.43\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.44\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.58\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.73\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.66\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.49\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.50\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.55\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.64\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.62\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.56\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.51\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.54\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.56\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.56\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.55\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.53\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.59\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.55\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.57\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.57\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.58\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.52\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.67\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.57\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.41\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.35\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.32\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.24\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.21\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.16\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.12\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e\\u0026minus;\\u0026thinsp;.03\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.04\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.04\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.22\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.33\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.48\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.66\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.79\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.96\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.89\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.69\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.60\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.60\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.62\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e10\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.61\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.57\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.42\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.34\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.29\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.17\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e11\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.14\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.31\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.50\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.64\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.46\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.28\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e12\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.31\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.33\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.55\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.51\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.57\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.61\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e13\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.61\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.55\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.56\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e0.52\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.52\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e.45\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv\\u003e\\n \\u003cp\\u003etable 1 that all DI variates exhibit negative correlation with RM until the 7\\u003csup\\u003eth\\u003c/sup\\u003e DI variate, afterwards it turns positive. In fact show significant correlations in the 9-th variate of DI-1 with values reaching as high as 0.96 and decreasing afterwards.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eIt is known that \\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e value is an indicator of closeness of data with the linear regression model. As \\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e values approach 1, predictive model becomes a close-fitting model. The DI-1 value in the 9th variate block, correspond to the 49th month after the RM maximum (see Table \\u003cspan\\u003e2\\u003c/span\\u003e), provide the best correlations, with correlation coefficients CC of 0.96 and the least standard error of estimation of 11.5. The second best \\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}=0.89\\\\)\\u003c/span\\u003e\\u003c/span\\u003e value is found in DI-2 (9) variate block corresponds to 50th month after the RM maximum with a least standard error of estimation of19.4. For more eloquence, \\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e values are plotted with months after RM maximum and shown in Fig. \\u003cspan\\u003e4\\u003c/span\\u003e. Figure \\u003cspan\\u003e4\\u003c/span\\u003e visibly demonstrates a negative correlation for the first 36 months after sunspot maximum between DI variates and RM of the following cycle. Subsequent to this, the correlation turns positive and quickly attains a high value (\\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}=0.96\\\\)\\u003c/span\\u003e\\u003c/span\\u003e) for the 49th and second high (\\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}=0.89\\\\)\\u003c/span\\u003e\\u003c/span\\u003e) for 50th month corresponding to DI-1(9) and DI-2(9) of each cycle. Afterwards it starts decreasing till the 78-th month with the appearance of a small peak (\\u003cspan\\u003e\\u003cspan\\u003e\\\\({R}^{2}=0.69\\\\)\\u003c/span\\u003e\\u003c/span\\u003e) at 64 monthafter RM. This may be attributed to the geomagnetic disturbances occurrences few years prior to the minimum of a cycle which are well correlated with the maximum of sunspot number (RM) of next cycle, proposition of the precursor method.\\u003c/p\\u003e\\n\\u003cp\\u003eThe corresponding two best correlated regression equations of DI indices with RM values are given below:\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equa\\\"\\u003e\\n \\u003cdiv id=\\\"FileID_Equa\\\" name=\\\"EquationSource\\\"\\u003e$$RM=57.68+33.21 \\\\times DI-1\\\\left(9\\\\right)----------\\\\left[1\\\\right]$$\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equb\\\"\\u003e\\n \\u003cdiv id=\\\"FileID_Equb\\\" name=\\\"EquationSource\\\"\\u003e$$RM=62.84+28.98 \\\\times DI-2\\\\left(9\\\\right)----------\\\\left[2\\\\right]$$\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eMoreoverthe predictive capability of both the regression equations is tested by applying a hypothesis test on the regression slopes of equations [1] \\u0026amp; [2]. The p-value for both the linear fitted curves is found to be around .017 which is quite less than the .05 level. With highlighting the fact that a p-value of less than .05, indicates 95% confidence that slope of regression line is not zero hence rejected the null hypothesis and confirms a strong relationship between the DI indicators with peak RM of following cycle.\\u003c/p\\u003e\\n\\u003cp\\u003eOn the basis of above facts, regression equations[1]and [2] are being applied to backcast/hindcast the observed RM values for previous cycles (18\\u0026ndash;24)and ongoing cycle (25). Table \\u003cspan\\u003e2\\u003c/span\\u003e displays the observed RM with their predicted counterparts. From the results presented in the table, it is illustrious that the difference (\\u003cspan\\u003e\\u003cspan\\u003e\\\\(\\\\)\\u003c/span\\u003e\\u003c/span\\u003eRM) between the predicted and the observed RMsfor cycles 18 to 24lie inside 1\\u0026ndash;14 range. The results further depict that roughly the predicted values are very close to the observed ones and in general, predicted values are found to concur approximately within \\u0026plusmn;08%. More often, table 2shows that the predicted RMfor the ongoing solar cycle number 25 to be about 111\\u0026plusmn;12 and 112\\u0026plusmn;20 with the help of equations [1] \\u0026amp; [2] respectively. Commonly, predictions are given on 90% prediction intervals (based on the number of degrees of freedom and the sample size). In the present case a sample size of 7 cycles has 5 degrees of freedom and hence each standard error of estimation should be multiplied by 1.796 in order to get the 90% prediction interval. Hence, the above prediction value of maximum amplitude for cycle 25 based on DI-1(9) should be 111 \\u0026plusmn;21 and the prediction based on DI-2(9) should be 112\\u0026plusmn;34, yielding an overlap of the two predictions of about 112\\u0026plusmn;18, which is adopted henceforth as the final prediction for cycle\\u0026rsquo;s 25 RM.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cimg src=\\\"https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1720598746.png\\\"\\u003e\\u003cbr\\u003e\\u003c/p\\u003e\\n\\u003cdiv\\u003e\\n \\u003ctable id=\\\"Tab4\\\" border=\\\"1\\\"\\u003e\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Sec4\\\"\\u003e\\n \\u003ch2\\u003e3.2 Evaluation of Rise time and Profile of Solar Cycle 25\\u003c/h2\\u003e\\n \\u003cp\\u003eAfter estimating the peak RM for solar cycle 25, it is likely for practical applications to know how long it takes to be observed and what the cycle\\u0026apos;s profile, i.e., its rise and fall times, may be.A detailed investigation of the time of rising of solar cycles 10 to 24 revealed a time range of 34 to 64 months for reaching peak RM. It\\u0026apos;s worth noting that the higher the peak RM, the shorter the time it takes to achieve it. It is observed as well that shorter the ascending period, the longer the descending phase, resulting in an average duration of a solar cycle of around 11 years (Usokin and Mursula 2003). Wilson (\\u003cspan\\u003e1987\\u003c/span\\u003e) examined the lengths of sunspot cycles using R12 and found them to be distributed symmetrically, with long-period cycle grouping (cycles with periods longer than 134 months) and short-period cycle grouping (cycles with periods shorter than 127 months).Because solar cycle 24 endured strictly in 11 years or 132 months, Wilson criteria place it neither in the long-period cycle group nor in the short-period cycle group. In December 2019, solar cycle 25 began (with a minimum smoothed sunspot number of 1.8). It will most likely continue until around 2030( \\u003cspan\\u003e\\u003cspan\\u003ehttps://www.swpc.noaa.gov/products/solar-cycle-progression\\u003c/span\\u003e\\u003c/span\\u003e)\\u003c/p\\u003e\\n \\u003cp\\u003eThe anticipated time to acquire peak RM, i.e. the \\u0026apos;rising time (RT)\\u0026apos; for solar cycle 25 is assessed in this work, in line with Dabas et al., (2008, 2010). The RT for solar cycle 25 is estimated by investigating a significant statistical association between the recorded peak RM and the RTs of previous cycles 10 to 24.\\u003c/p\\u003e\\n \\u003cp\\u003eFigure 6: The link between the rise time (RT) from cycle minimum toits peak amplitude (RM) for solar cycles 10\\u0026ndash;23. The linear regression is obtained byignoring two extreme data points for cycles 19 and 24. The predicted peak RM\\u0026thinsp;=\\u0026thinsp;112 when substituted in the regression equation, yield a roughestimate of rise time to be 48\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;3 months for solar cycle 25.\\u003c/p\\u003e\\n \\u003cp\\u003eFigure 6 depicts the plot of RM Vs rising time (in months) for cycles 10\\u0026ndash;24, revealing an empirically significant inverse relationship (CC\\u0026thinsp;=\\u0026thinsp;\\u0026minus;\\u0026thinsp;0.89). It is worth noting that the rising time (RT) appears to decrease linearly with RM and is represented by a straight-line fit equation of the form;\\u003c/p\\u003e\\n \\u003cp\\u003e\\u003cspan\\u003e\\u0026nbsp;\\u003cspan\\u003e\\\\(RT=68.8-0.19 \\\\times RM\\\\)\\u003c/span\\u003e\\u0026nbsp;\\u003c/span\\u003e----------- (3)\\u003c/p\\u003e\\n \\u003cp\\u003eWhen the estimated peak value of RM\\u0026thinsp;=\\u0026thinsp;112 for solar cycle 25 is entered into the above computation, the expected RT is 48 \\u0026plusmn; 3 months. By putting the predicted peak value of RM\\u0026thinsp;=\\u0026thinsp;112 for solar cycle 25 into this equation, the expected RT comes out to be 48\\u0026plusmn; 3 months.\\u003c/p\\u003e\\n \\u003cp\\u003eOnce the predicted peak RM and RT for the ongoing cycle 25 are known, the method proposed by Hathaway, Wilson, and Reichmann (\\u003cspan\\u003e1994\\u003c/span\\u003e) can be utilized for finding the fullshape of the cycle 25.\\u003c/p\\u003e\\n \\u003cp\\u003e\\u003cspan\\u003e\\u0026nbsp;\\u003cspan\\u003e\\\\({R}_{12}\\\\left(t\\\\right)= \\\\frac{{a(t- {t}_{0})}^{3}}{\\\\left\\\\{exp\\\\left[\\\\frac{{\\\\left(t-{t}_{0}\\\\right)}^{2}}{{b}^{2}}\\\\right]- c\\\\right\\\\}}\\\\)\\u003c/span\\u003e\\u0026nbsp;\\u003c/span\\u003e ----------- (4)\\u003c/p\\u003e\\n \\u003cp\\u003ewhere t is the time of a given cycle, t\\u003csub\\u003e0\\u003c/sub\\u003e is the time of the start of each cycle, and a, b, and c are fitting parameters. They proposed that the fitting parameter c\\u0026thinsp;=\\u0026thinsp;0.71 was found to possess a single value for majority of the cycles. The parameters a and b can easily be evaluated, using the predicted values of RM (=\\u0026thinsp;112 \\u0026plusmn; 18) and their rise time, RT (=\\u0026thinsp;48 \\u0026plusmn; 3, in units of months)in line with the analysis given by Hathaway, Wilson, and Reichmann (\\u003cspan\\u003e1994\\u003c/span\\u003e). For the present study, the calculated values of these parameters are; \\u003cspan\\u003e\\u003cspan\\u003e\\\\(a=2.59 \\\\times {10}^{-3}, 2.53 \\\\times {10}^{-3}\\\\\\u0026amp; 2.45 \\\\times {10}^{-3}\\\\)\\u003c/span\\u003e\\u003c/span\\u003eand b=41.6, 44.4 and 47.2, respectively, for the values of RM of 94, 112 \\u0026amp; 130. The aforementioned values of a, b, and c have been put in Eq. (4) to obtain the probable shape and length of solar cycle 25. The obtained results can be seen in Fig. \\u003cspan\\u003e8\\u003c/span\\u003e.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003ch3\\u003eComparison of Results with Other Predictions for solar cycle 25\\u003c/h3\\u003e\\n\\u003cp\\u003eThe analytical results of the preceding sectionsfor maximum amplitude (RM\\u0026thinsp;=\\u0026thinsp;125\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;22) and its time of occurrence (probably in mid (Jul)\\u0026ndash;to- late (Dec) 2023), may now be compared with other predictions based on different approaches. Petrovay (\\u003cspan citationid=\\\"CR39\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e) suggested four categories of solar cycle prediction methods: precursor, extrapolation, spectral or model-based methods.The extrapolation methods are based on non-linear approach and displayed inferior performance than precursor methods. Singh \\u0026amp; Bhargawa (\\u003cspan citationid=\\\"CR49\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e)predicted a weaker cycle25 than cycle 24 based on an extrapolation method in which they utilized the Hurstexponent and a simplex projection algorithm. A similar prediction of weaker cycle 25 is reported by Iijima et al. (\\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e) by using a surface flux transportmodel based on temporal variations of axial dipole moment. Moreover, Kakad, Kakad\\u0026amp; Ramesh (2017) predicted a very weak solar cycle 25 quite alike to Dalton\\u0026rsquo;s minimum by estimating the Shannonentropy. Petrovay(2020), predicted maximum amplitude of 97.6 (\\u0026plusmn;\\u0026thinsp;10) may occur in 2026.2 (\\u0026plusmn;\\u0026thinsp;1\\u0026nbsp;year) based on (quasi-) physical model linked with the planetsconsequently strengthening the proposal of \\u0026ldquo;Modern minimum\\u0026rdquo;. Macario-Rojas, Smith \\u0026amp; E (2018)also applied a similar\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab5\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eForecasts for Solar Cycle 25, Abbreviations are SoDa\\u0026thinsp;=\\u0026thinsp;Solar Dynamo, SFT\\u0026thinsp;=\\u0026thinsp;Surface Flux Transport, AFT\\u0026thinsp;=\\u0026thinsp;Advective Flux Transport. NARX\\u0026thinsp;=\\u0026thinsp;Non-linear Autoregressive Exogenous.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"4\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colspan=\\\"4\\\" nameend=\\\"c4\\\" namest=\\\"c1\\\"\\u003e \\u003cp\\u003ePredictions of Solar Cycle 25\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eCategory\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003ePeak SSN\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eRise Time\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eReference\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"4\\\" nameend=\\\"c4\\\" namest=\\\"c1\\\"\\u003e \\u003cp\\u003ePrecursors\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eInternal precursors\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e175\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2023.8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eLi, Feng, and Li (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2015\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003ePolar precursor\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e117\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;15\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003ePolar precursor\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e136\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;48\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePesnell and Schatten (\\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eHelicity\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e117\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eHawkes and Berger (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSoDA\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e120\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;39\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2025.2\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;1.5\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eBased on Pesnell and Schatten (\\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eRush-to-the-poles\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e130\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2024.8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePetrovay et al. (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eHale-cycle termination\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e184\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eMcIntosh et al., \\u003cspan citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMagnetic precursor\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e134\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2024\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eHathaway \\u0026amp; Upton (\\u003cspan citationid=\\\"CR53\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"4\\\" nameend=\\\"c4\\\" namest=\\\"c1\\\"\\u003e \\u003cp\\u003eModel-based\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e(quasi-) physical model\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e97.6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2026.2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eV. Courtillot et. al. (2021)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e(quasi-) physical model\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e97.6 (\\u0026plusmn;\\u0026thinsp;10)\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2026.2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePetrovay(2020)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSFT\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e124\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;31\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eJiang and Cao (\\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSFT\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e118\\u003c/p\\u003e \\u003cp\\u003e109\\u0026ndash;139\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2024 \\u0026plusmn; 01\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eBhowmik and Nandy 2018\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSFT\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eIijima et al. (\\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eAFT\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e110\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eUpton and Hathaway (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2\\u0026times;2D\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e89\\u0026thinsp;\\u0026minus;\\u0026thinsp;14\\u0026thinsp;+\\u0026thinsp;29\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2027.2\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;1.0\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eLabonville, Charbonneau, and Lemerle (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2019\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eShanon entropy\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e63\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;11.3\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eKakad, Kakad\\u0026amp; Ramesh (2017)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eTruncated\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e90\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;15\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2024\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eKitiashvili (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2016\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"4\\\" nameend=\\\"c4\\\" namest=\\\"c1\\\"\\u003e \\u003cp\\u003eSpectral\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eWavelet decomposition tree\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e132\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2023.4\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eRigozo et al. (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2011\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSimplex projection analysis\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e103\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;25\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2024.0\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eSingh and Bhargawa (\\u003cspan citationid=\\\"CR49\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSimplex projection/time-delay\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e154\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;12\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2023.2\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;1.1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eSarp et al. (\\u003cspan citationid=\\\"CR42\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eWavelet transform\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e146.7\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;33.40\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eLuo and Tan (\\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"4\\\" nameend=\\\"c4\\\" namest=\\\"c1\\\"\\u003e \\u003cp\\u003eNeural networks\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eNeuro-fuzzy\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e90.7\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2022\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eAttia, Ismail, and Basurah (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2013\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSpatiotemporal\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e57\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;17\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2022\\u0026ndash;2023\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eCovas, Peixinho, and Fernandes (\\u003cspan type=\\\"Underline\\\" class=\\\"Underline\\\" name=\\\"Emphasis\\\"\\u003e2019\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSingular Spectrum Analysis\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e97.6\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;7.8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2026.2\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eCourtillot et al. (2021)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eNARX\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e116.6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eFebruary 2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eKalkan et. al., (2023)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eTime series deep learning method\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e133.9\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;7.2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eFebruary 2024\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eSu et. al., (\\u003cspan citationid=\\\"CR50\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e)\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003emodel-based method and predicted the cycle25 will be 14.4 per cent (\\u0026plusmn;\\u0026thinsp;19.5 per cent) weaker than the cycle 24.Kirov et al. (\\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e), utilized precursormethod predicted that peaksmoothed sunspot number of cycle25 may be within 50\\u0026ndash;55 range. Gopalswamy et al. (\\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e) and Hathaway \\u0026amp; Upton (\\u003cspan citationid=\\\"CR53\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) predicted modest amplitudes of cycle 25 based on precursor method though Cameron, Jiang \\u0026amp; Sch ̈ussler(2016) reported that cycle 25 may to some extent stronger than the previous cycle 24. Pesnell \\u0026amp; Schatten (\\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e) reported 135\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;25 to be as the smoothed peak of sunspot cycle 25 by incorporating the SODA index into precursor method. The SODA index is estimated by polar magnetic fieldsand the spectral index. Also, Jiang \\u0026amp; Cao (2017) using a surface flux transport model-basedmethod, reported a stronger cycle 25 than cycle24. Sarp et.al. (\\u003cspan citationid=\\\"CR42\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e) forecasted a peak sunspotnumber of 154\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;12inyear 2023.2\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;1.1 for Solar Cycle 25byutilizinga non-linear prediction algorithm based on delay-time and phase space reconstruction.Su et. al. (\\u003cspan citationid=\\\"CR50\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) using neural basis expansion analysis for the interpretable time series deep learning method, predict a peak amplitude 133.9\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;7.2 around 2024.2.\\u003c/p\\u003e \\u003cp\\u003eSome predictions suggest a below average cycle 25 (Nandy, \\u003cspan citationid=\\\"CR33\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e; Jiang, Zhang, and Petrovay, 2023) whereas some forecasts have predictedan above-average amplitude for solar cycle 25 (Han and Yin, \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; McIntosh et al., \\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). Recently (McIntosh et al., \\u003cspan citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) revised their prediction and proposed that the ongoing solar cycle 25 might have maximum amplitude around the average. Indeed, the predictions so far are proposingsolar cycle 25 as a below-average cycle (Carrasco andVaquero, 2022, 2023).\\u003c/p\\u003e \\u003cp\\u003eAccording to the NOAA Solar Cycle 25 Prediction Panel, predicted Cycle 25 can reach a maximum of 115 occurring in July, 2025 (\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://www.swpc.noaa.gov/products/solar-cycle-progression#:~:text=The%20Prediction%20Panel%20predicted%20Cycle,November%202024%20and%20March%202026\\u003c/span\\u003e\\u003cspan address=\\\"https://www.swpc.noaa.gov/products/solar-cycle-progression#:~:text=The%20Prediction%20Panel%20predicted%20Cycle,November%202024%20and%20March%202026\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e.).\\u003c/p\\u003e\"},{\"header\":\"Discussion\",\"content\":\"\\u003cp\\u003eThe eminent sunspot cycles of eleven year are incarnation of solar magnetic activity. solar magnetic cycle influences the rate of occurrence of all geoeffective solar eruptive phenomena. Indeed, prediction of its characteristics is avitalcomponent of space weather forecasting. According to Babcock Leighton dynamo models, the evolution of the surface magnetic field at cycle n, after it is transported inside by meridional flow, acts as a source of toroidal fields for cycle n\\u0026thinsp;+\\u0026thinsp;1. It is therefore possible to obtain prediction of the characteristics of cycle n\\u0026thinsp;+\\u0026thinsp;1 by observing the magnetic field variations of cycle n. The idea lays the foundation of precursor methods, (Charbonneau \\u003cspan citationid=\\\"CR6\\\" class=\\\"CitationRef\\\"\\u003e2014\\u003c/span\\u003e, Petrovay \\u003cspan citationid=\\\"CR39\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e). Researchers extensively explored the statistical relationships between solar activity and the number of sunspots, total surface area, and their time of emergence. The two (pertaining) physics-based precursors for forecasting the amplitude of a solar cycle have emerged as the most reliable; geomagnetic activity levels and the Sun's magnetic configuration (polar fields and axial dipole moment) shortly after the sunspot cycle minimum.Nonetheless, there are still some ambiguities linked to these predictors. Among these, the geomagnetic precursors are more resilient as the data set is longer, but their physical mechanisms are less precise. Polar precursors have a stronger physics foundation;however the functional relationship couldn\\u0026rsquo;t be well defined because of data availability for a shorter time period (Upton \\u0026amp; Hathaway \\u003cspan citationid=\\\"CR53\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e).Geomagnetic precursor technique was first proposed by Ohl (\\u003cspan citationid=\\\"CR36\\\" class=\\\"CitationRef\\\"\\u003e1966\\u003c/span\\u003e) to forecast the cycle maxima by using geomagnetic activities near cycle minima. According to Ohl\\u0026rsquo;s precursor method, the lowest in geomagnetic activity seen in the geomagnetic aa index is closely connected to the magnitude of the subsequent cycle. Thompson\\u0026rsquo;s precursor method uses the number of geomagnetically disturbed days (A\\u003csub\\u003ep\\u003c/sub\\u003e \\u0026ge; 25) throughout the entire previous cycle to predict cycle amplitudes well before the time of minimum (Thompson 1994, 1996).\\u003c/p\\u003e \\u003cp\\u003eThis paper reports the maximum amplitude and rise time of Solar Cycle 25 underway using modified geomagnetic precursor technique. The solar and geomagnetic data sets utilized here covers solar cycles 17 to 24 i.e. from 1932 to 2019. The declining phase of each cycle is divided into equally spaced time windows (variate blocks) of 06 months duration and disturbance indices are calculated within each time-window. Further, all windows are correlated with peak sunspot numbers of following cycles. The highest correlations are found in DI-1(9) and DI-2(9) variate blocks i.e. 49th month and 50th month after the solar maximum. Ergo, the detailed synthesis of regression equations yields the predicted maximum amplitude of current cycle 25 to be \\u0026asymp;\\u0026thinsp;112\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;18. The probable peak time of cycle 25 could be 48\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;4 months i.e. October 2023 \\u0026ndash;April 24.\\u003c/p\\u003e \\u003cp\\u003eThe physical mechanism behind geomagnetic precursors is enigmatic. Geomagnetic disturbances which create the precursory signals are typically caused by high-speed solar wind streams from low-latitude coronal holes later in a cycle(Legrand and Simon 1996). According to Schatten. Myers and Sofia (1996), this geomagnetic activity during the time of the sunspot cycle minimum is connected to the intensity of the Sun's polar magnetic field, which is then related to the strength of the subsequent maximum. According to Cameron and Sch\\u0026uuml;ssler (\\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003e), these antecedent correlations with the amplitude of the following cycle result from the overlap of sunspot cycles and the Waldmeier Effect. Wang and Sheeley Jr. (2009) believe that Ohl's technique has closer ties to the Sun's magnetic dipole strength and should thus give better predictions.Each sunspot cycle shows a consistent rise in sunspot numbers to a maximum and a subsequent fall to a low level. In contrast, geomagnetic indices (Ap or aa) exhibit two or more maxima per cycle, with one occurring near or before and other just after the sunspot maximum. The gap between the two maxima is referred as \\u0026lsquo;the Gnevyshev gap\\u0026rsquo; and may lead to quasi-biennial and quasi-triennial periodicities in the geomagnetic indices (Takalo \\u003cspan citationid=\\\"CR51\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e, Kane 1997).Ahluwalia (\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e2000\\u003c/span\\u003e) reported the Gnevyshev gap in A\\u003csub\\u003ep\\u003c/sub\\u003e data could be caused by solar polar field reversals.Schatten et al. (\\u003cspan citationid=\\\"CR45\\\" class=\\\"CitationRef\\\"\\u003e1978\\u003c/span\\u003e) proposed a more cogent physical mechanism to explain Ohl (\\u003cspan citationid=\\\"CR36\\\" class=\\\"CitationRef\\\"\\u003e1966\\u003c/span\\u003e) hypothesis by reporting thatpolar field strength of the sun close to a solar minimum is strongly related to the solar activity of the subsequent cycle. Dynamo-based prediction techniques of sunspot cycle dwell on its two inherent characteristics: first, solar magnetism swings between poloidal and toroidal components; and second there is a degree of \\\"magnetic persistence\\\" in dynamos, which, in the turn causes the dependence of many magnetic-related quantities on the level of magnetism encased beneath the surface of the sun. The geomagnetic indices at the minimum phase of an active cycle exhibit high correlation with the magnitude of the ensuing maximum because geomagnetic indices replicate the magnitude of poloidal field and, as sunspot minimum approaches, it happens to the governing component of solar magnetism (Schatten and Myers, 1996).Thereby, the solar cycle actually begins many years before the sunspot minimum, necessitating the use of geomagnetic indices at various phases in the decaying part of a cycle (e.g., construction of thirteen time windows/variate blocks of 06 month duration in present analysis) for predicting the size of the ensuing cycle. Moreover, this technique can successfully be applicative to predict thesize and timing of following cycle one to two years before itsofficial commencement.\\u003c/p\\u003e\"},{\"header\":\"Conclusion\",\"content\":\"\\u003cp\\u003eThe geomagnetic precursor technique based prediction of ongoing solar cycle 25 presented in this paper clearly suggest that cycle 25 is going to becomparable with the previous cycle 24 (~\\u0026thinsp;112 \\u0026plusmn; 18). The disturbance index, nearly 49 to 50 months after the peak (i.e. variate blocks 9\\u0026thinsp;\\u0026minus;\\u0026thinsp;1 and 9\\u0026thinsp;\\u0026minus;\\u0026thinsp;2 or few years before cycle minimum) seems to be a righteous precursor to estimate the size of the subsequent cycle 25. Table\\u0026nbsp;\\u003cspan refid=\\\"Tab3\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e clearly indicates that this technique displays a fairly good correlation (COD\\u0026thinsp;=\\u0026thinsp;0.96) between the predictors and predictions of cycles 17 to 24 are lying within \\u0026plusmn; 10% window with the observed one (Table \\u003cspan refid=\\\"Tab4\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e). Moreover, this technique can simply be deployed for advance prediction of maximum amplitude of coming cycle at least 1 to 2 years before its official start. Hathaway, Wilson, and Reichmann (\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1994\\u003c/span\\u003e) method is applied for estimating the time to attain the peak amplitude of cycle 25 and the obtained results yield rise time of 47\\u0026plusmn;3 months. Hence from an official start of cycle 25 in December 2019 we expect to observe the maximum amplitude of the cycle to occur in late to early 2024.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eAcknowledgements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eAuthors would like to acknowledge Dr. R.S. Dabas, Scientist-G (Retd.), NPL New Delhi, Prof. Sangeeta Shukla, Hon\\u0026rsquo;ble VC, CCS University, Meerut and the University Research Grant Scheme (URGS) [No. DEV/URGS/2022-23/35, dated 22-07-2022] for the all the necessary financial assistance to carried out this research work.\\u003c/p\\u003e\"},{\"header\":\"References \",\"content\":\"\\u003col\\u003e\\n\\u003cli\\u003eAhluwalia, H. S. (2000). Ap time variations and interplanetary magnetic field intensity. Journal of Geophysical Research: Space Physics, 105(A12), 27481-27487.\\u003c/li\\u003e\\n\\u003cli\\u003eAparicio, A. J. P., Carrasco, V. M. S., \\u0026amp; Vaquero, J. 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(Basel), 13 (23) (2021), p. 4798, 10.3390/rs13234798\\u003c/li\\u003e\\n\\u003cli\\u003eKakad, B., Kakad, A., \\u0026amp; Ramesh, D. S. (2015). A new method for forecasting the solar cycle descent time. Journal of Space Weather and Space Climate, 5, A29.\\u003c/li\\u003e\\n\\u003cli\\u003eKane, R. P. (2007). A preliminary estimate of the size of the coming solar cycle 24, based on Ohl\\u0026rsquo;s precursor method. Solar Physics, 243(2), 205-217.\\u003c/li\\u003e\\n\\u003cli\\u003eKirov, B., Asenovski, S., Georgieva, K., Obridko, V. N., \\u0026amp; Maris-Muntean, G. (2018). Forecasting the sunspot maximum through an analysis of geomagnetic activity. Journal of Atmospheric and Solar-Terrestrial Physics, 176, 42-50.\\u003c/li\\u003e\\n\\u003cli\\u003eLegrand, J. P., \\u0026amp; Simon, P. A. (1991). A two-component solar cycle. Solar Physics, 131, 187-209.\\u003c/li\\u003e\\n\\u003cli\\u003eLi, Y. (1997). Predictions of the features for sunspot cycle 23. 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Living Reviews in Solar Physics, 20(1), 2.\\u003c/li\\u003e\\n\\u003cli\\u003eWang, Y. M., \\u0026amp; Sheeley, N. R. (2009). Understanding the geomagnetic precursor of the solar cycle. The Astrophysical Journal, 694(1), L11.\\u003c/li\\u003e\\n\\u003cli\\u003eWilson, R. M. (1987). On the distribution of sunspot cycle periods. Journal of Geophysical Research: Space Physics, 92(A9), 10101-10104.\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"solar-physics\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"sola\",\"sideBox\":\"Learn more about [Solar Physics](http://link.springer.com/journal/11207)\",\"snPcode\":\"11207\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11207/3\",\"title\":\"Solar Physics\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"Solar Cycle, Geomagnetic precursors, sunspots, Geomagnetic index\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-4570127/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-4570127/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe sun is rapidly approaching towards the pinnacle of its activity in ongoing cycle 25. Solar activity variations cause changes in interplanetary and near-Earth space environment and may deteriorate the operation of space-borne and ground based technological systems (space flights, navigation, radars, high-frequency radio communications, ground power lines, etc.). Scientists predict the exact duration and intensity of each solar cycle based on a variety of methods ranging from purely statistical models using observations of previous cycles to complex simulations of solar physics. In the present study, we utilized the planetary magnetic activity ‘Ap’ index in relation to sunspot activity and sunspot area for the period 1932–2019, covering Solar Cycles 17 to 24, as geomagnetic precursor pair for predicting the maximum amplitude and its time of occurrence for ongoing Cycle 25. The monthly average sunspot data and disturbed days are processed through regression analysis and the obtained analytical results further validated by the observed sunspots of cycle 17 to 24. Hind casting results show close agreement between predicted and observed maximum amplitudes of cycles 17 to 24 to about 10 percent. A multivariate fit using the two best DI indices in variate block 9 also gives the similar correlation to about 0.94 with standard error of estimation (±14). This study divulges that the maximum sunspot number for Solar Cycle 25 is expected to be ≈ 112 ± 18. The probable peak time of cycle 25, after analysis, is found to be 48 ± 3 months. The peak might appear in between October 2023 – April 2024. The obtained results suggest that ongoing cycle akin to the previous Solar Cycle 24 in terms of predicted maximum sunspot numbers.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Predicting Maximum Amplitude and Rise Time of Solar Cycle 25 Using Modified Geomagnetic Precursor Technique\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-07-10 17:31:30\",\"doi\":\"10.21203/rs.3.rs-4570127/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2024-08-13T09:43:49+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2024-08-11T18:00:17+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"14114846858212462899083018806060069802\",\"date\":\"2024-07-24T18:59:53+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2024-07-05T09:36:27+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2024-06-15T09:23:51+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2024-06-15T09:23:35+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Solar Physics\",\"date\":\"2024-06-12T12:13:33+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"solar-physics\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"sola\",\"sideBox\":\"Learn more about [Solar Physics](http://link.springer.com/journal/11207)\",\"snPcode\":\"11207\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11207/3\",\"title\":\"Solar Physics\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"f097bb34-0db0-4154-9ba9-bc26362e0759\",\"owner\":[],\"postedDate\":\"July 10th, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2024-12-23T16:08:07+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-4570127\",\"link\":\"https://doi.org/10.1007/s11207-024-02412-w\",\"journal\":{\"identity\":\"solar-physics\",\"isVorOnly\":false,\"title\":\"Solar Physics\"},\"publishedOn\":\"2024-12-16 15:57:56\",\"publishedOnDateReadable\":\"December 16th, 2024\"},\"versionCreatedAt\":\"2024-07-10 17:31:30\",\"video\":\"\",\"vorDoi\":\"10.1007/s11207-024-02412-w\",\"vorDoiUrl\":\"https://doi.org/10.1007/s11207-024-02412-w\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-4570127\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-4570127\",\"identity\":\"rs-4570127\",\"version\":[\"v1\"]},\"buildId\":\"qtupq5eGEP_6zYnWcrvyt\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}