This page displays my Forecasts for S-cycles # 24 and # 25.

* The art of solar cycle prediction is unfortunately ambiguous. Our method of forecast is based mainly on SG-model (see pages "Model" and "M**iscellanea**"). SG-model is a tool for the study of solar activity, which is sensitive to factors such as: (**1) a retrospective analysis of existing data; (2) the emergence of new data, both observational and theoretical; (3) at last, the process of matching the forecast with the incoming current data (M-data and others). This last factor implies prediction ( #SGF:GL), which is made before the first M-data of a new S-cycle become available.*

** Introduction. **Elaboration of the

*SG-model*was

*beginning in 2000, when the "Origin" software had appeared in my hands.*

**The first and the only published (see Pesnell, 2008) prediction (**

*24 SG*) has been done in August 2006, which corresponds to the point 3092 in M-data time series (

**F.1***H m,24*=

*70**(± 17.5) at t m,24 = 2012.96).*

**24SGF.1*** {(3121+34.1)-28.7-
(32*×*1.2533*×28.7*) = (3121+57.9)-38.6-(49*×*1.2533*×*38.6) = (3121+87.8)-32.6-(31*×*1.2533*×*32.6)}. *

It fell on the decay period of the cycle #23, when, in principle, many parameters (which being requested for *SG-model*) of that cycle were known, excepting may be of the parameters of D-component (x D, 23 =3081, w D, 23 =39.1 months, H D, 23 = 20.4) and of cycle's length T 0,23 (151 months). Consequently, WO-forecast (*24 SG F: WO*) was not possible yet and also t 0, 24 was unknown. Soon after the forecast

*24 SG*

**F.1**

*has been done, the website on which the*

*SG-model.2006*was described, has become unavailable and I made an unsuccessful attempt to publish

*SG-model.2006*in the "Solar Physics" (2008) journal. Then the new (this one) site has been developed (it has been launched in November 2008 - practically on the eve of S-cycle #24 start), on which in the real time three things are being made:

*the monitoring of S-cycle #24 current data*;

*an analysis of those data on the base of SG-model.2006*; and also

*the SG-model revision, which has been over (mostly, but not completely) as SG-model.C (current) or simply SG-model.*

*The results obtained above in the description of the S-cycle's shape by the SG - model prove that those results are sufficient for constructing a GL-prediction of the next S-cycle.*

** 1. Consider the predictions of cycles # 24 and 25. **Currently (July 2018), the start time of cycle 24 is known (December 2008, or point 3120), and for cycle 25 is not. Starting to build a GL-forecast, we first set the expected parameters of the cycle model, namely, the mean X p = 38.9 months, W = 33 months, X b = 63.5 months, X d = 92.8 months.

** 2.** Then we consider the corresponding sections of the GL- cycle. For cycle 24, they are

*D L*

*-type*cycles # 5 and 14, and for cycle 25 -

*E L*

*-type*cycles # - 4 and 6, as well as an anomalous

*U L*

*- type*cycle # 15. Cycles # 5 and 14 are similar: both long with tail; length, respectively, 151 months and 138 months; both follow the long

*D H*

*-type*cycles # 4 and 13. The cycle # 24 also follows the long # 23 and, according to the "logic of analogues", should have an average length of

**. Then**

*143 months**t 0, 25 =*

**3262**.** 3.** With cycle # 25, the situation is less certain. For lack of other estimates, we start from 3262 and estimate XP = 3262 + 38.9 = 3300.9, and from Fig. 2 (3300.9 + 588) we determine HP = 38 ± 20 and the cycle type as a transitional TS-cycle. In Figure 2, you can see only four TS-cycles (# - 4, # 6, # 15 and # 25). They are clearly different, although all are in the transition region between adjacent GL-cycles. For the cycle # -4, the first S-cycle after the Maunder GM (1645 - 1715), M-data is still missing, but it still looks like a cycle # 6 (low and long). Cycle # 25 could be the same if it were not for cycle # 15, which turned out to be abnormally high and short (i.e, AS-cycle). The transition zone between adjacent GL-cycles seems to be unstable, since at this time the speed of the meridional circulation changes from small to large (and, accordingly, switching from long DS-cycles to short US cycles). Therefore, for the cycle # 25, the following options are possible (see Figure 4): (1) a low and long TS-cycle similar to # 6, (2) a low and short US - cycle similar to # 7 and # 16, or (3) a high and short AS-cycle similar to # 15. As a result, we get:

*Step I:* *This step consists in the GL-forecast of S-cycles in terms of "the logic of the development of GL-cycle". **24SG F:GL* (see fig.3) uses an estimate

*H* P,24*=

*34.1**(± 14). Choosing for # 24 the average parameters of those similar S-cycles, we have got (with*

*H*m,24*=

**at**

*62.9***3180 (2013/12)) :**

* 24SG F:GL =* {((3120

**+ 38.9) - 33 -**

**) = ((3120**

*34.1***+ 63.5) - 33 - 44.6) = ((3120 + 92.8) - 33 - 30.5)} (7.1)**

(see fig.3, navy). *This is the first forecast for K-data*. It is markedly different from *24 SG F: GL 2006*.

For # 25 we'll have three (instead of one) options plus the K-profiles of cycles # 6 and # 15 as they would look in the new M -data.

**25****SGF****:****GL****1 ***{(3262+42.8)-33- (38*×*1.2533*×*33) = (3262+70)-33-(60.64*×*1.2533*×*33) = (3262+102.1)-33-(38*×*1.2533*×*33)} (7.2) ** *

** ****25****SGF****:****GL****2 ***{(3262+38.9)-33- (38*×*1.2533*×*33) = (3262+63.5)-33-(60.64*×*1.2533*×*33) = (3262+83)-33-(38*×*1.2533*×*33)} (7.3)*

**25****SGF****:****GL****3 ***{(3262+38.9)-33- (85.6*×*1.2533*×*33) = (3262+63.5)-33-(74*×*1.2533*×*33) = (3262+83)-33-(38*×*1.2533*×*33)}, (7.4)* where the cycle's length will be 120 or 143 months. Up to now, the possibility of a Grand minimum's start still is not excluded.

*Step II:*** ***This step consists in matching #SGF:GL with #SGF:WO. *Knowledge of the PMF maximum, as it was established after pioneering works of H.W. Babcock (1961), A.I. Ohl (1966) and J.M. Wilcox, allows to predict the height of the next S-cycle prior to observations of its first sustainable high-latitude sunspots (i.e. before the cycle's start t 0, i+1). This type of prediction is considered now as the most reliable and theoretically confirmed (see Pesnell (2008), Petrovay (2010), Cameron and Schüssler (2015)). SG-model uses such an option for WO-forecast: <PMF M > is determined by averaging of current Avgf-data (Wilcox Solar Observatory data for the polar magnetic field strength, PMF) over the interval [x D, i - t 0, i+1 ]; then H m, i+1 = k * <PMF M >** **(see fig.6).** **It was possible during the decay phase of S-cycle #23 to evaluate <PMF M > = 55.5 (± 3) microtesla (cyan in fig.3). *Then **H** m,24 = 1.29 x 55.5 = 71.6; this is 24SGF:WO, which is close to *

*24SG*Correction should take into account the observed t 0, i+1 and combine H m, i+1 in

**F**:GL2006.*#*

*SGF:GL*with H m, i+1 in

*#SGF:WO*. For

*the easiest way to do this is to lift slightly H*m, 24 (multiplying*

**24SGF***24SG*(= 71.6/62.9), see fig.3, K-data, dark cyan). It's

**F**:GL by 1.138*24SG*:

**F***GL/WO*(the maximum at December 2013).

*#SG*is an important correction of

**F**:GL/WO*#SG*using the latest observed data (<PMF M > and t 0, i+1). It allows you to not only specify a maximum of S-cycle (H m, i+1), but also its shape as a whole. PMF-data from Wilcox Solar Observatory (Avgf-data time series) were starting at May 1976. So, for # 22 we have H m,22 = 163.2 = 1.35 x <PMF M > (=121 (± 12)); correspondingly, for # 23 we have H m,23 = 121 = 1.2 x <PMF M > (= 101 (± 3)). Comparison of all currently available (2015) data allows to select the current compromise value of

**F**:GL**k = 1.29**(see fig.6).

Knowing 24SGF:GL/WO, it is possible to build U-data forecast ** SGF:U** and compare it with M-data. It is supposed in

*# SGF:U*that K- data represent the envelope for maximums of U-peaks, while the other parameters are taken from table 1. As data analysis shows there is a noticeable upward trend of H m, U i for U-peaks coinciding (or close) with the moments x P, i , x B, i , x D, i , i.e. moments of maximums of K-peaks shown in fig.3 by the dotted vertical lines. To emphasize this, the correspondent U-peaks will be increased by 30%; it follows that S-cycles are actually should be three-humped (although for high S-cycles this tendency is less pronounced). The real U-data in fig.3 (wine line) show two of three expected peaks.

For S-cycle #25 this step has not yet come.

*Step III* *consists in analysis of deviations between forecasts and the current observations in the process of S-cycle evolution. *It concerns both K-data and U-data. As new M-data (grey points in fig.3) are coming they can be first partially and then completely compared with forecasts, and after that "the quality of forecasts" is analyzed. Technically it includes fitting of reliable data in some time interval by SG- model. Unlike the observed M-data, a smoothed (filtered) data is unreliable both at the beginning of S-cycle (because during mGM period the Sun is still not active) and at the end of the available interval (because the future M-data are unknown). By definition the Sun is becoming active (only from that moment S-cycle is described by SG-model), when K-data begin to exceed 20 (for S-cycle # 24 that moment corresponds to the point 3138). To minimize the existing uncertainty, it is possible to consider as the future M-data 24SGF:GL/WO or *24SGF:U*. In fig.4 an expected future M-data are shown as *25SGF:GL (see (7.2-7.4)).* As a result, it was obtained the following current description of the whole cycle #24 (blue K-data, compare with (7.1)):

*24SG D:3227 = * {((3120

**+38.9) - 33.7 - 42.2) = ((3120 + 63.9) - 32.8 - 51) = ((3120 + 84.9) - 30.8 - 16.6)}; Χ**

^{2}= 0.029 (7.5)

For June 2016 we have: *H m,24 K = 73 **at September 2013; and **H m,24 U 1 = 70.3 at Nov.2011 & *H m,24 U 2 *= 88 at Feb. 2014 (at the same time M-data also reach their maximum, 102.8). *As for description of U-data, we get:

*24SG D:Ut.3204* = U 1, 24 (3120.45 - 3.3 - 4) + U 2, 24 (3131.6 - 4.93 - 8) + U 3, 24 (3141.3 - 9.3 - 19) +

U 4, 24 (3152.7 - 8.7 - *56.4*) + U 5, 24 (3160.9 - 9.9 - 43) + U 6, 24 (3169.6 - 9.4 - 42) +

U 7, 24 (3181.3 - 10.35 - *78.3*) + U 8, 24 (3191.9 - 10.35 - 55) + U 9, 24 (3202.5 - 7.9 - 36) + ... Χ^{2}= 0.037

It can be seen from Fig. 3 that the phase of the decline of cycle # 24 deviates significantly from the 24SGF: GL / WO forecast, namely, the D component in 24SGD: 3227 (7.5) reaches a maximum of 7.9 months earlier and is almost half as low (but that's all even within the limits of 2Ϭ).

**Nevertheless,** as it said in "a Guide book" on the page *"M**iscellanea**"**, the final comparison can be made only after the current S-cycle's end.*

## The SG-model current expectations for the cycle 25 are shown in Fig. 4. Four 25SGF:GL variants are shown, plus S-cycles # 6 (green) and # 15. All 25SGF:GL-new will be compared with M new – data (see note A.5 in page "Miscellanea"). So, up to the current time we have accomplished for S-cycle # 25 only Step I. Nevertheless, already now (in October 2017 and later) you can make a preliminary 25SGF: WO forecast (<PMFmax> (for the period 3205 – 3234) = 58.9; so

H** m,25should be 58.9×1.84 = 108 (see fig. 4)). The current elaboration of the description for S-cycles 24 and 25 (both 24SGF and 25SGF), shown in Fig. 3 and 4, is given in page "Conclusion". It should also be noted that the extrapolated K - and U - data so far correspond to the GM - forecast.

Figure 4 shows that today (the first half of 2018) the situation with the forecast of the 25th cycle is quite contradictory. This is due to the assumed position of the cycle 25 within the Gleissberg cycle (see Fig.2). The fact is that it is in the region of the extremum (specifically, at the minimum) of the GL - cycle. Observations show that in the region of the extrema of the GL - cycle, the probability of development of anomalous S - cycles is markedly increased (see S - cycles # - 4, 4, 6, 12, 15, 19, 25). Therefore, in Fig. 4, there were all four possible types of forecasts: (1) the absence of a S - cycle due to the onset of a Grand minimum (see Ref.2018/1 and current extrapolated behavior of K-data and U-data); (2) emergence of a critically low S - cycle (see 25SGF:GL1and 6K - data); (3) emergence of an intermediate S - cycle (see 25SGF.2) and (4) emergence of a high S - cycle (see 25SGF:GL3 and 15 K-data). My regular forecast refers to type 3, and the inability to clarify it in one direction or another indicates a too crude understanding of the physics of the S - cycle.