The main purpose of this study is the determination of solar minimum date of the new sunspot cycle No 24. It is provided by using of four types of mean daily data values for the period Jan 01. 2006 - Dec 31. 2009: (1) the solar radioindex F10.7; (2) the International sunspot number Ri; (3) the total solar irradiance index (TSI), and (4) the daily number of X-ray flares of classes from "B" to "X" from the soft X-ray GOES satellite channel (0.1 - 0.8 nm). It is found that the mean starting moment of the upward solar activity tendency (the mean solar minimum) is Nov. 06th, 2008. So, the solar cycle No 23 length is estimated to ~12.6 years. A conclusion for a relatively weak general magnitude of solar cycle No 24 is made. By using of relationship based on the "Waldmeier's rule" a near maximal mean yearly sunspot number value of 72 \pm 27 has been determined.
Deep Dive into Sunspot minimum between solar cycles No 23 and 24. Prediction of solar cycle No 24 magnitude on the base of "Waldmeiers rule".
The main purpose of this study is the determination of solar minimum date of the new sunspot cycle No 24. It is provided by using of four types of mean daily data values for the period Jan 01. 2006 - Dec 31. 2009: (1) the solar radioindex F10.7; (2) the International sunspot number Ri; (3) the total solar irradiance index (TSI), and (4) the daily number of X-ray flares of classes from “B” to “X” from the soft X-ray GOES satellite channel (0.1 - 0.8 nm). It is found that the mean starting moment of the upward solar activity tendency (the mean solar minimum) is Nov. 06th, 2008. So, the solar cycle No 23 length is estimated to ~12.6 years. A conclusion for a relatively weak general magnitude of solar cycle No 24 is made. By using of relationship based on the “Waldmeier’s rule” a near maximal mean yearly sunspot number value of 72 \pm 27 has been determined.
There are clear evidences that the last solar minimum (AD 2006(AD -2009) )
The The conventional method for detection of the minimal sunspot activity amplitude is based on 13-month smoothed sunspot numbers. The fact that the increasing phase (only 3-4 months up to Feb 2010) is very short suggests that this method could be not sensitive enough on this stage.
A least square procedure for obtaining parabolic full quadratic and qubic polynomial minimized functions of the type ψ ψ= at 2 +bt+c or ψ ψ= at 3 +bt 2 +ct+d are used over each one of the studied data series. There t is the number of days since Jan 1 st , 2006. The both types of trend polynomials for each series has been compared and the better approximation has been chosen by Snedekor-Fisher’s F-parameter. Thus, the general trends are expressed by simple non-linear functions, in which only one extreme (minimum) in the studying interval exists. There could be obtained the starting moments of cycle No 24 for every one of these data series searching for the minima of the corresponding mean least square minimized polynomials.
The calculated minima of the best trend functions are shown in Table 1 where the minima are given in calendar dates. The best-expressed trends are for the sunspot Ri series, as well as for F10.7 where the corresponding coefficient of correlations R are 0.53 and 0.66. Both they belong to cubic type. The trend function for TSI correlates to the original data satisfactorily well (R=0.49), while this R value very close both to the quadratic and cubic polynomial trend type approximations. For the X-flare events it is R=0.38 at cubic approximation. It is important to note that because of the large number of data (1521) all these values of R are statistically significant over 95%. The better cubic trend approximation as the quadratic one for Ri and F10.7 data is caused by asymmetry effect of the faster increasing of these indices during the initial upward phase of solar cycle 24 as the decreasing during the downward phase of the solar cycle No 23 before the minima. This asymmetry is no observable in the TSI dynamics during the same time. As it is afore shown the most reliable solar cycle minima estimations are on the base of F107 and Ri data series, where the half interval error is near or less than two months (54 and 31 days, respectively). The uncertainty of the solar cycle minimum on the base of estimations over X-flares and TSI series is much higher (± ±3-6 months with respect to the corresponding calendar dates). The earliest is the TSI-minimum -in the middle of 2008. The slight increase of TSI in the second half of 2008 could be related to the corresponding increase of the total area of the bright regions (the faculae regions and the so-called “ephemeral regions” (ER)) at this time. Such overtaking of the bright ER minima to the main sunspot one for the last Schwabe-Wolf’s cycles is discussed by Krivova et al. (2007).
The mean minimum moment for the solar cycle No 24, based on the results in Table 1 (Ri andF10 2 should not be considered as strong evidence, but only as a possible scenario. This is related to the fact that the trends in Table 2 are
The next task of our study is the estimation of the near maximum value of the annual sunspot number (W max ) for solar cycle No 24, based on so-called “Waldmeier’s rule” (Waldemeier, 1935). That is expressed by the tendency of the increasing sunspot number rate during the upward phase of the Schwabe-Wolf’s cycles, which is higher for the more powerful cycles than for the weaker ones.
Up to this moment (June 2010) there are only less than 2 years after the start of cycle No 24. By this reason we use information for the sunspot activity rising during the initial 18 months of all solar cycles after AD 1818, i.e. No 7-23. Using the corresponding mean monthly sunspot numbers Ri , we calculate the mean monthly increasing α α = dRi / dt for each solar cycle. The linear correlation relationship between α α and W max has been found (fig. 1). The coefficient of correlation R is +0.69 and the relationship is :
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