This page displays my Forecast for S-cycle # 24.
Approximation Zero (a mixed SGF( t 0, 24 , ΔX)).
Step 1: Forecast for t 0,24 (the date of the SC24 (t) predicted beginning, see (3)) is January 2008 (+7/- 4 months); it corresponds to the point (month) 3109 in fig.1 (dotted vertical line). See also the page "Discussion".
Step 2: Evaluation of the G P -peak maximum date. It is t 0 + x C = 3109 + 42.6 = 3151.6 ~ August 2011 (see table 1). It is necessary now to estimate H P . For that we can extrapolate two adjacent G GL -peaks, i.e. the last, current one ( x C = 1987.5, w = 27.7 years, H = 142) and the next, predicted one ( ΔX = 63.5 years and,consequently, x C = 2051, w = 28.3 years, H = 122). Then (for August 2011) H P = ~ 32 [Kontor, 2006; Kontor, 2008a]; it is 24SGF_L1 (see fig.5 and 6); for the forecast shown in fig.1, the value H P = 57.5 (corresponding to ΔX = 46 years ) was used; it is 24SGF_H1. Origin of such an ambiguity (see [Pesnell, 2008], and [Janssens, 2006] herein) is connected, in the long run, with my misunderstanding of the mixed nature of solar cycle forecasts in Approximation Zero. It is explained in Discussion and shown for SG - model in fig.6.
Step 3: It allows to get parameters for all three G K -peaks and so to build the K-curve (blue) for S-cycle # 24 :
G P -peak : x C = 3151, i.e. August 2011; w = 33 months; H P = 57.5;
G B -peak : x C = 3176, i.e. August 2013; w = 33 months; H B = 49.5;
G D -peak : x C = 3214, i.e. October 2016; w = 33 months; H D = 35;
Step 4: Fitting the decay of S-cycle # 23 by G U -peaks, one receives the last G UA -peak at x C = 3090 (June 2006). It is followed by a sequence of two G U1 -peaks (x C = 3102, i.e. June 2007; and x C = 3114, i.e. June 2008), forming the mGM between cycles # 23 and # 24 (from March 2007 to September 2008,see figure 1, green vertical lines). The first
G UA -peak for S-cycle # 24 has x C = 3125 (May 2009) and H ~ 20. It is followed by ten G UA -peaks, which form the U-shape of S-cycle # 24 (cyan). In accordance with our forecast, S-cycle # 24 has the maximum 87 (+/- 11.83) at February 2012.
updated: 08/16/2009
Thus, the SGF algorithm, described above (SGF is a forecast of a solar cycle based on SG - model, see the page "Model"), allows to get a shape of the forthcoming S - cycle on the basis of averaged statistical parameters of the S - cycle.
Because not all, even the average parameters, are unambiguous (this applies, first of all, to t 0, 24, which in zero approximation is known only to within +/-1 year, and , to ΔX , which can be either close ( ΔX = 46 years) or distant (ΔX =
63.5 years)), SGF (in a zero-order approximation) is ambiguous (see fig.6), and the forecast, shown in fig.1, is actually one of the several possible SGFs.
updated: 04/16/2010
Approximation 1 (an ambivalent SGF(ΔX)).
On the some step of SSN monitoring and data analysis a possibility for transition from Approximation 0 to Approximation 1 appears. It means, that someone can now choose the single SGF, which corresponds ( and probably will correspond henceforward) to the SSN course in the new S - cycle # 24 ( see fig. 6). Now (October - November 2009) such a possibility takes place. It is conditioned by discovery of t 0,24 = December 2008 (May 8, 2009) and also by a circumstance, that during almost a year (December 2008 - November 2009, excepting August 2009) the SSN course is close to 24SGF_L2 (see fig.2c). Correctness of my Approximation 1 will be seen in the future, but if it is correct, it has long lasting consequences:
1. Primary Approximation 0, representing six equivalent 24SGFs (see fig.6), is defined more accurately; 24SGF_H1 is rejected as not corresponding to the observations, and replaced (due to new observations) by the single
24SGF_L2 with Hm = 63 and tm = April 2014 (see figs. 1a and 6a).
2. The choice of a single 24SGF, i.e. 24SGF_L2, exerts influence not only upon the parameters of the expected S - cycle # 24, but upon the long term forecast of the several following S - cycles. It means that the next GL - peak will be distant (see fig.7), and 25SGF , 26SGF, 27SGF, and so on, will be corresponding (they are shown in fig.7 by wine color).
updated: 11/10/2009
But soon (as early as December 2009 - January 2010) eligibility of these findings has been questioned by further progress in the the SSN course. During the past four months ( December 2009 - March 2010) SSN increased dramatically, no longer correspond to 24SGF_L2, and was consistent with 24SGF_H2 (!), see fig. 6a. This compels us to rethink the submission of the Approximation 1 as the transition from the mixed Approximation 0 to the single-valued Approximation 1.
In fact, in the approximation 1 the only one reason (associated with t 0,24) for the forecast's ambiguity is eliminated; another reason, related to ΔX, remains. The question of when will be charged this last "large-scale chaotic uncertainty" is currently open ...
updated: 04/16/2010
