The art of forecasting is exciting and, at the same time, often frustrating, and sometimes dangerous business. In fact, it's hard to predict the future, when really you do not understand either the present or the past. This fully applies to the attempts of the forecast of the solar cycle. Although these attempts began in the early 20th century, special attention to this issue emerged in recent times, namely, in relation to the S-cycles # 21, 22, 23, 24 and 25. Without going into the reasons for this, which are more or less obvious, let's look at the results of solar cycle's forecasting. *Let us take stock of 2009 concerning the solar cycle forecasting.* It is known that the history of the solar cycle's forecasting lasts for about a century [Kimura, 1913], i.e. almost the same time, how long known about its magnetic nature [Hale, 1908]. When forecasting, speaking in general, two aims are persecuted: to understand the physical nature of the solar cycle and anticipate the possible consequences of the expected level of solar activity. When our knowledge of the solar cycle is growing, then both of these goals are being filled with more specific content. In [Kontor, 2008a, fig.11] I tried to illustrate the degree of certainty of modern solar cycle's forecasts . Conclusion was disappointing: for each of the last four cycles ( # 21, 22, 23, and 24), the same situation is approximately repeated - how many forecasters were, there were so many, but various predictions. In other words, there was no convergence of forecasts to one or least several values of the main control variable of the solar cycle, namely R max. This conclusion applies to the period of 2006, when work on the 24 cycle's forecast was not finished yet. Let us consider now the "final" table of Janssens (2009) and let us see what has changed since then. It presents actually 48 forecasts of the solar cycle # 24, which were selected for the period 2000 - 2008; the largest number of forecasts (11) accounts for 2008, at the end of which the cycle # 24, in fact, has begun. Fig.11 from [Kontor, 2008a] is reproduced in Fig.6, taking into account forecasts of 24th cycle, carried out before the end of 2006. Indication for the convergence of forecasts is horizontal (flat) sections of the plot (when several forecasts are close to each other), marked in Fig.6 by arrows. For example, such a section for 24th cycle corresponds to R max = 110. Flat section of the plot (there may be several such sections) does not indicate a correct prediction, but only speak about which forecast is found most often. If, finally, there will be worked out reliable methods of the solar cycle forecasting , they will correspond to the graph with a one broad plateau. The available M-data is shown from January 1986 (dark yellow) as a background. The observed yearly averaged maximums for cycles # 22 (Y m = 157.8) and # 23 (Y m = 119.6), and the predicted maximum for cycle # 24 ( Y m= 74.1, according to the ** Ohl’s method** [ Kozhemyakina and Chernyshova, 2006]) with the anticipated error (± 17.5) [Kontor, 2006] are also shown (black). Forecasts of S-cycle maximum are shown by blue circles, beginning from the lowest one. Values of every following forecast are shifted (for convenience of data representation) on one time interval (month) from the previous one. Blue arrows mark the close values of several forecasts. Two horizontal dotted lines correspond to the maximum and minimum observed levels of the solar activity. The green line shows the envelope of S-cycle’s maximums (

**of forecasting), received in [Kontor, 2006]. The orange asterisk is our estimation of the S-cycle # 24 maximum.**

*GL-method*In fig. 7 a comparison of 24th cycle's forecasts, known up to 2006 ( blue circles) and up to 2008 (gray circles), is presented. Plots are close, because they contain a lot of identical forecasts, but there is an explicit and, in our view, an important difference (marked Z). It consist in appearance of a new flat section in the lower part of the graph (corresponds to low forecasts for solar cycle # 24). Three main kinds of methods of forecast are statistical, physical, and mixed methods. Their quantitative relation is 3:1:1. So, almost all the physical predictions give a low 24th cycle (marked in Fig.7 by magenta circles); at the same time, only a small part of mixed predictions and even smaller part of statistical predictions also give a low 24th cycle. Thus, during 2007 and 2008, there were new indications that the cycle # 24 will be low (see also [ Kozhemyakina and Chernyshova, 2006] and [Kitiashvili and Kosovichev, 2009a], which are not included in table of [Janssens, 2009]).

Because (since May 2009) it became clear (from an analysis of current measurements) that the cycle # 24 started in December 2008, time for predictions in the "zero approximation" (for example, 24SGF) is over, and a period of model parameters adjustment (from the current data of the cycle # 24) starts. For models, which are easy adjusting to the current data (like SG - model), this period is important both for elimination of uncertainties of "Approximation Zero", and for estimation of the chaotic component in the cycle # 24 during its exit out of mGM - period.

Driving mechanism of the solar cycle. Taking into account a tendency of BL - model's development ( a deep dynamo) [Nandy, 2004; Yeates et al., 2008; Munoz - Jaramillo et al., 2008; and references herein], and also the ideas of a shallow dynamo model of the solar cycle [Schatten, 2007, 2009 and references herein], it is possible to describe the driving mechanism of the solar cycle as follows.

1. The Sun's convection zone (CZ) has some features, which concern directly the solar cycle :

the subadiabatic transient layer between radiation zone and CZ [Ossendrijver, 2003], which could be called "the bottom magnetic layer" (BML);

the turbulent subphotospheric layer, pierced through by small scale magnetic fields [Stenflo, 1994; de Wijn et al., 2009], which could be called "the upper magnetic layer" (UML);

the global meridional circulation, or the Sun's great conveyor belt (SGCB) [Nandy, 2004;Phillips, 2006; Lopes and Passos, 2009], which connects UML and BML.

2. Taking into account the results of SG - model, it is possible to assume, that the solar global poloidal magnetic field (PMF) is the key element of the solar cycle. It is created in UML as a result of interaction of the small scale magnetic fields, generated by the shallow dynamo, and/or of decay of toroidal magnetic fields (TMF), i.e. sunspots, coming to the surface from BML and CZ.

3. PMF is transfered by SGCB to the poles, and the maximum value of the polar PMF (PPmax) depends on the speed of SGCB, Vc(t).

4. Elaboration of S - cycle forecasting showed, that PPmax is proportional to the amplitude of the coming S - cycle, Hs (see [Schatten, 2007] and references herein). It can be shown, that

Hs ~ 0.625*DM (A3.1)

Hs ~ 1.212*SODA (A3.2)

Hs ~ 17.94*Io + 69.4 (A3.3) ,

where such indexes of PPmax as Dipole Moment (DM) [ Svalgaard et al., 2005] and index SODA [Schatten, 2007] are measured in microTesla, whereas the geomagnetic index of Ohl ( Io ) [Ohl, 1966; Ohl and Ohl,1980; Kozhemyakina and Chernyshova, 2006] is measured in relative units. It means, that the surface PMF is proportional to PMF in BML, which is also linearly converted into TMF by the omega - effect of Cowling [Cowling, 1953]. SG - model indirectly shows, that both the process of transformation PMF into TMF, and the process of latitudinal TMF drift to the solar equator (the butterfly diagram) are complex enough and consist of three steps (P-, B-, and D-components of S - cycle).

5. In modern BL - models a great attention is given to the meridional circulation (SGCB), because its speed, Vc, determines the length (Ts) of S-cycle [ Nandy, 2004; Yeats et al., 2008 ]. It follows from fig.4 of Yeates et al. (2008) that

Ts ~ 11* ((Vo/Vc)^0.8) years (A3.4),

where Vo is equal 31.4 m/s for the surface SGCB speed, and approximately 1m/s for the SGCB speed inside BML [Phillips, 2006].

6. SG - model allows to receive dependence Hs (Ts ). It is possible because of anticorrelation Hp and XD (see fig.13 in [Kontor, 2008a]), which is a description of Waldmeier's rule in terms of SG - model. As a result one gets:

( Hs - HB )/2.3 = ((16 - Ts )^2) (A3.5) .

7. It follows from (8 - 10), that all main values, concerning S - cycle, i.e. Vc(t), PPmax, Hs, and Ts are connected each other by the simple empirical relations. Excluding Ts from (9) and (10), one receives the relation between Hs and Vc, that could be observed at the time of PPmax :

Vc = VT*CV (A3.6) ,

where VT = 0.625 *V0 is the SGCB speed, corresponding to transition from the period of S - cycle regeneration to the GM - period and vice versa (6). "Coefficient of variability", CV = (1 - 0.0412* (( Hs - HB )^ 0.5))^(-1.25). HB is the amplitude of B - component (see table 1), what corresponds to the smallest S - cycle; for the highest S - cycle # 19 ( Hs = 190) CV = 2.3. Variability of Vc(t) could result in GL - cycle appearance, which can be seen in fig. 8. Mechanism of such a variability is unknown, but it could explain all long term variability of solar activity ( then LCN time series represents rather stretched (in amplitude) variations of Vc(t)). In fig.8 LCN time series is shown by black circles, GM periods - by red circles, WSN time series - by blue circles, and Vc(t) variation - by magenta circles.

N.N. Kontor, e-mail: sgnnk@Live.com

Updated: 10/14/2009

The cycle's start. It is time now (February 2009) to begin a discussion about the results of my SG - forecast. It concerns, first of all, the date of t 0,24. t 0 is an important parameter of SG - model. However, up to now its prediction can be considered only as the rough estimate (~ +/- 1 year). The table of Janssens (2006) shows, that only 17 from 45 forecasts give t 0,24. The most probable date for t 0,24 is somewhere in the second half of 2007. On the other hand, t 0,24 can be waited somewhere on the boundary of 2008 and 2009, if the tendency, mentioned by Hathaway (2008), will be confirmed. However, neither K-data, nor U-data do not show the local minimum yet. The closest to the second t 0,24 position forecast is the DB-forecast of Choudhuri et al. (2007) and Choudhuri (2008). It was postulated by Dikpati and Gilman (2008), that DB-forecast has a possibility to predict t 0, i , but I doubt it (an appropriate estimate should be about +/- 1 month). After May 2009 it can be said that the question of t 0, 24 resolved by observations. K- and U-data are not suitable for this purpose because of their large delay.

The Gleissberg cycle. GL-cycle does exist. It has a double humped shape and a considerable variability [Ogurtsov et al., 2002; Kontor, 2006, 2008a, 2008b; Ma, 2009; and references herein]. From the viewpoint of SG - model it means, that GL - peak is the main component of GL - cycle and its ultimate shape depends on the amplitude of GL - peak and the temporal distances between the neighboring GL - peaks. However, till now there is no an appropriate GL - cycle model, which could be compatible with a DB - forecast model.

Nevertheless, there are already indications, both observational (see [Hathaway, 2010]) and theoretical [Solov'ev, 2009; Nandy et al., 2011], that the GL - cycle can be explained by long - term ( order solar cycle time and more) velocity variations of the meridional circulation in the solar convection zone (compare with fig. 8). I also hope that will be found short-term (order several years) velocity variations of the meridional circulation in the lower part (BML) of the solar convection zone that can explain the G K - peaks (see (4) and table 1) in solar cycles, first introduced in SG - model.

Fig.2 shows the long - range variation of P - component's amplitude, which follows from SG - model. That variation is the foundation of the long - range SG - model based forecast ("GL-method").

Applying SG - model to the S-cycle # 24 forecast before its real beginning, one just takes notice of the end of the active part of the S-cycle # 23. It means that mGM period starts and SSN level is < 20. The observable start of mGM t_{mGM,s }= March 2006 (3087). There are two possibilities for the future solar activity: mGM will pass into GM period, or (approximately in 30 months) a new S-cycle will follow. The occurence of Grand Minima appears chaotic [Moss et al., 2008], so, the transition from mGM to GM period as a characteristic feature of current state of solar activity is not excluded (24SGF_GM). Nevertheless, there are sufficient reasons to believe, that the next S-cycle # 24 is coming. But, trying to predict it, one meets another two uncertainties: the position of the next GL - peak (** ΔX**, see table 1) and the date of t 0, 24. Taking into account the supposed weakly chaotic origin of solar activity system, one can anticipate that the next GL-peak can be "distant" (

*ΔX**= 63.5 years*

**or "close" (**

*)*

**ΔX**= 46 years**)***It has an influence upon the forecast level: for close GL-peak one gets a high forecast level, and for distant GL-peak one gets a low forecast level . And the last two meaningful uncertainties are the date of t 0, 24 and the height*

**.****H**

**B**.

4. SG - model allows, in principle, to develop *the long range prediction of solar activity**.* It is based on extrapolation of long range variation of **H ****P, i** (see fig.2). So, one can get regular forecasts for S-cycles # 25, 26, and 27. To get forecasts for next cycles, it must be proposed the position of the next GL - peak...

Any way it is necessary to choose between two versions of long term forecast ( i.e. positions of the next GL - peak). I am choosing a * d- version* (the next GL - peak will be distant ); at the same time, Kane's forecast [Kane, 2007] corresponds to

**c**- ver*sion*(the next GL - peak will be close ).

*Eventually, the regular SGF, just as winter's naked tree is decorated by the summer's crown, will be transformed by chaotic variations of the real mechanism of the solar cycle...*

N.N. Kontor, e-mail: sgnnk@Live.com : Updated 11/10/2009

** 2011,** **a**** review of the year:*** **the SG - model against SSN - data. *During 2007 - 2009 the mGM - period between solar cycle # 23 and solar cycle #24 has been observed . In 2010 there was observed a relatively slow growth of the sunspot numbers. By the end of 2010, the sunspot numbers reached a conditional border size (SSN ~ 20) between the inactive and active phases of the solar cycle. At the same time, all year the data were slightly higher than forecast. In 2011, a rapid growth in the sunspot numbers (from ~20 to ~100) took place. The general impression is that the forecast lags of data and is below them , but quantitative score of differences and qualitative conclusions about the extent, to which data and forecast correspond each other, should be postponed at least until 2012.

**2012**

**. A new 11-year solar cycle (S-cycle) begins just after the polar reversal of PMF (t PR,0) at the maximum of the previous S-cycle . For the current S-cycle #24 it happened at February 2000. It is easy to see that when analyzing the behavior of the solar cycle with the help of SG-model, we use two types of smoothed M-data, namely, U-data and K-data. In addition we monitor changes in PMF. Before appearance of the first sunspots of a new cycle (it happened 8 years after t PR,0), it was little known about it (except for the predictions).When the new sunspots began to appear (and in fact the possibility that the new S-cycle will not appear at all and the sun will enter into a "new Maunder minimum» (GM-period) was considered as an equal variant), the sun was in the inactive phase (SSN <20), which I call "mGM-period" . The main event of mGM-period is, of course, the beginning of a new cycle ( t 0,24 = December 2008) and also the fact that PMF at this time is maximal.**

*RESULTS***K-data**allow us to estimate the parameters of P-component (2).

**July 2011 comment.** Solar cycle is formed as a result of a sequence of many interrelated processes that develop in the convection zone and partially are observed in the photosphere. SG - model deals with the sunspot number, SSN, which are associated with the strong local toroidal magnetic fields (TMF); in addition, there are sufficiently long measurements of the weak poloidal polar magnetic fields, PMF, which, are believed, are directly related to the origin of the solar cycle.

SG - model allows to highlight several significant stages in the development of the solar cycle. It is **mGM - periods** in the beginning and at the end of each cycle. mGM begins at the end of the solar cycle decay, when SSN is getting less 20 and ends in the beginning of the rising period of the next cycle, when SSN is getting more 20. So, the average duration of the mGM is 30 (+/- 12) months.

During mGM, PMF is close to the maximum. It is convenient to associate the beginning of PMF decay with t 0, 24 (December 2008), which occurs somewhere in the middle of the mGM .

At the end of mGM **an active phase **of 24th cycle begins. It corresponds to the development of the **P-component**. For high cycles a time of P-component's maximum (X P) is convenient to associate with **the moment of Polar reversal (PR)**. For low cycles, to which, in particular, belongs 24th cycle, the cycle maximum is defined by the B -component. Therefore, in such cycles the moment of PR likely corresponds to X B . Once you could determine the parameters of the P-component, it becomes possible to build the regular forecast for the next cycle (currently, it is 25SGF). To determine the parameters of P 24, we are fitting K-data by three G-peaks (see table 1), namely, by D 23, with parameters that are already known (X D = Dec. 2004, W = 33 months, and H D = 31.5); by P 24, the parameters of which need to be fitted, because we know only its mean values (see table 1); by B 24 , the average parameters of which (except for X B ) we fix , and by D 24 in order to assess how fitting will change the forecast .

The next step is determination of the **B - component parameters and the maximum of 24th cycle. **Near that point **PR** should be observed . After that the decay stage of the 24th cycle ( and, correspondingly, an increase of PMF) begins. This is followed by determination of the D 24 parameters and the start of the new mGM. At the time of X D the PMF reaches a maximum and it is close to it up to t 0, 25.

At that time there is an opportunity to compare predictions for the 25th cycle made with using of SSN time series and PMF time series.