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the ultimate measure of Solar activity

The frequently referenced Relative-Numbering system after Wolf as a measure of solar activity has been known now for a long time. Normally one use the system of Relativenumbers by counting all visible spots, small or big, adding this to the number of sunspotgroups multiplied by the casual factor of 10. A socalled k-factor is additionally used because the aperture of a small or a large telescope in any case will decide how many individual spots you are able to see. The formula for Relativenumbers after Wolf is: 

R = k * ( 10 * g + f )

where 'k' is the k-Factor, 'g' the number of groups, 'f' the number of spots and R the Relativenumber after Wolf. Partly, (f.ex. the BAA in England) use 'g' as number of active areas to be valued as 2 if the group is more than 10 degress long but having the same center.

This system has several disadvantages. You count all the spots you see in the telescope but you do not pay any attention to the size of the spots. A small pore of e.g. 30 mvh (millionths of the visible hemisphere), which is the smallest spot to be seen with a normal sized telescope, is counted as 1. A great spot of, let us say, 300 mvh is also counted as 1! Any keen solar observer, amateur of professional, who has some knowledge of solar physics, know that the potensial of activity in a small spot versus the great spot, has multiple differences!

This is the main reason why I began thinking of some kind of system that would be valuating each sunspotgroup to their potensial for survival on the disk. A pore with a short and quiet life versus a major group with a longer and much more vigourous biography.

"Classification Values" I "invented" as a project in 1978 (25th July) and with several improvements the system went into the trial phase from 15 August 1981. This phase is now hopefully over, since the experience is so good.

In this article I shall explain how this new experiment has proven good existence and also go further into the question of disadvantages of the R-system. This is not meant to critisize the existence of the R-system but point out that other kind of measures, as for instance tracking solar flux-numbers, or perhaps the CV, would hopefully pinpoint the solar activity more accurate. You may judge for yourself!

You may well know that solar sunspotgroups are classified with the Zürich-system with the letters A, B, C, D, E, F, H, and additionally the letters G and J (Waldmeier). The classifications in the modern professional solar astronomy includes classes G and J into the letters E, F and H. In 1973 Patrick S. McIntosh from the NOAA, USA developed a comprehensive system, the Zürich/McIntosh-classifications, building on the 7 modified Zürich-classes and added two more letters (McIntosh) describing the sunspot groups in respect to magnetical complexity, extent and distribution. The result of this extension was 60 defined sunspotgroupclassifications. Each of the three criteria (letters) contribute to the idea of how a certain solar region, for instance, Dkc, may look like appearing on the solar disk.

The following main criteria has to be understood:

(Source: Solar Geophysical Data, 474 Supplement, Feb1984, pp. 21-23),
(US Dept of Commerce, Boulder CO 80303, USA)


A single spot or a single compact cluster of spots with the greatest distance between two spots of the cluster not exceeding three heliographic degrees. In modified Zürich H-class groups, this distance is measured from the outer penumbral border of the largest spot to the center of the most distant spot in the group. Strong new spots which are clearly younger than the nearby h-type spot (see Penumbra: Largest spot) are usually members of a new emerging bipolar group and should be called a separate group.

Two spots or a cluster of many spots extending roughly east-west with the major axis exceeding a length of three heliographic degrees. An h-type major spot can have a diameter of three degrees, so a bipolar group with an h-type spot must exceed five degrees in length.



MODIFIED ZÜRICH CLASS ( 1st upper case letter )


A unipolar group with no penumbra.   *


A bipolar group with no penumbra (no limit to the extent of the group)


A bipolar group with penumbra on spots of one polarity, usually on spots at only one end of an elongated group. Class C groups become compact class D when the penumbra exceeds five degrees in longitudinal extent. There is no upper limit to the length of class C groups.


A bipolar group with penumbra on spots of both polarities, usually on spots at both ends of an elongated group. The length does not exceed 10 degrees of heliographic longitude.


A bipolar group with penumbra on spots of both polarities and with a length between 10 and 15 heliographic degrees.


A bipolar group with penumbra on spots of both polarities and with a length exceeding 15 heliographic degrees.


A unipolar group with penumbra. Attendent spots are less than three heliographic degrees  from the penumbra of the main spot. The principal spots are nearly always the leader spots remaining from an old bipolar group. Class H groups become compact class D when the penumbra exceeds five degrees in longitudinal extent.   *

Note that classes G and J (Waldmeier-1925) are missing in this revision. Class G groups are included in the definition of classes E and F, and class J groups are included in class H.

PENUMBRA: THE LARGEST SPOT (2nd upper case letter)

x No penumbra. The width of the gray area bordering spots must exceed three arc seconds in order to classify as penumbra.
r The penumbra is rudimentary (incomplete/irregular). It is usually incomplete, irregular in outline, as narrow as three arc seconds. brighter intensity than normal penumbra, and has a mottled, or granular, fine structure. Rudimentary penumbra represents the transition between photospheric granulation and filamentary penumbra. Recognition of rudimentary will ordinarily require photographs or direct observation at the telescope. (no projectionary observation!)
s Symmetric, nearly circular penumbra with filamentary fine structure and a spot diameter not exceeding 2 ½ heliographic degrees. The umbrae form a compact cluster near the center of the penumbra. Also, elliptical penumbrae are symmetric about a single umbra. Spots with symmetric penumbra change very slowly.
a Asymmetric, or complex penumbra with filamentary fine structure and a spot diameter along a solar meridian not exceeding 2 ½ heliographic degrees. Asymmetric penumbra is irregular in outline or clearly elongated (not circular) with two or more umbrae scattered within it. The example in the figure is transitional between "s" and "a". Asymmetric spots typically change from from day-to-day.
h A large symmetric penumbra with diameter greater than 2 ½ heliographic degres. Other than size, it has characteristics the same as "s" penumbra.
k A large asymmetric penumbra with diameter greater than 2 ½ heliographic degrees. Other than size, its characteristics are the same as "a" penumbra. When the logitudinal extent of the penumbra exceeds five heliographic degrees, it is almost certain that both magnetic polarities are present within the penumbra and the classification becomes Dkc, Ekc or Fkc.

SUNSPOT DISTRIBUTION (3rd upper case letter)

x Single spot.
o An open spot distribution. The area between leading and following ends of the group is free of spots so that the group appears to divide clearly into two areas of opposite magnetic polarity. An open distribution implies a relatively low magnetic field gradient across the line of polarity reversal.
i An intermediate spot distribution. Some spots lie between the leading and following ends of the group, but none of them possesses penumbra.
c A compact spot distrution. The area between the leading and following ends of the spot group is populated with many strong spots, with at least one interior spot possessing penumbra. The extreme case of compact distribution has the entire spot group enveloped in one continuous penumbral area. A compact spot distribution implies a relatively steep magnetic field gradient across the line of polarity reversal.

The first letter of the McIntosh classification is essentially the Brunner classification with the following exceptions:

Ero, Fro, Eso, Fso, Eao, Fao, Eho, Fho, Eko, Fko = Brunner class G

Hrx, Hsx, Hax = Brunner class J


THE CV after Malde system

The Classification Values System aims to improve the Zürich/McIntosh-classifications system with its 60 classes by weighting these by calculative numbers. These numbers are built solely on my own experience and statistics from solar terrestial data sources. A class like the smallest spot "Axx", can only be counted as 1, while the most complex/best surviving group "Fhc" must have 60 points' value. All classes are placed in logical series. From time to time, there have been thoughts of placing classes, not in series from 1 to 60, but in a more progressive series; good illustrations are number of flares erupting from these groups. On the other hand, we have had many scenarios of small groups being rather active, so I have left the question, and continue using the series from 1 to 60. A comparison with averaged Relative numbers, Solar Flux, has proved that the correlation is good anyway. The CV actually reflects times where we have had many strong groups, times when we have had many, but small groups.

The basis for ranging groups have been these, strongest to weakest across each line:



First letter:









Second letter:









Third letter:






By using the description above, you may judge your own CV-combination class and by the tables you can give the classes their values. All groups/regions are totalled by values every day, and by the end of the month you derive your monthly averaged CV-value.

The table here converts Zürich/McIntosh-classifications to CV, and is supported by the explanation to each classification.

Below are some examples to "what-happens-if", situations that may be experienced many times during a solar cycle. They are worthwhile thinking over, when you are using Relative numbering system after Wolf:


1) False North/South correlation:

Simple A-,B-, or C-groups in the North, major D-,E- or F-groups in the South. Perhaps the spotcount would be of 50/50 distribution using R-nos., using CV will give quite another impression, many times a great difference.

2) Activity high, simple, major, spot-poor groups, Relativenumbers are low:

Activity high, few spots in major groups, Relative numbers "relatively" low. The Relative numbers does not take any notice of sizing and thereon possible high activity in poor-spotted groups. Result: Realtime activity is high: CV high, R low. The opposite example is below:

3) Activity low, many pores, Relativenumbers high:

Activity is low, rich-spotted groups, perhaps many. Realtime activity is low: CV-total is low, R can be very high (but the real activity is not!)


These three correlations happen quite a few times during a cycle, especially during the lower phase before and immediately after minimum, or during more "quiet" maximumtimes.

The impression you get when you study this by telescopic experience at least one cycle, is that you may feel more and more that the Relative numbering system is rather casual.


I hope, that many of you will find the CV-system as an interesting alternative solar observation system.

An amateur astronomer is limited to use his telescope of relatively small aperture and with no major measuring equipment. The better way of measuring the real solar activity would perhaps be the Solar Flux emission, the second best perhaps measuring the total covered area of spots per day (mvh, explained above).

The method using CV described above implies a system that most amateurs can use without having access to expensive and professional equipment, so why not have a try on the CV after Malde?


Some problems have occurred determining Regions within the classes Axx and H-x due to the understanding of Unipolarity and/or Bipolarity problems.  CV-Helios Network does well know, and has also been notified (Schröder, Wydra, Lachowicz) during 1998 of this, and has decided that the terms outlined in the Classifications above will prevail, though it is the fact that:
The sunspotregions are bipolar once they have accompanying spots due to the weak magnetic fields just below the photosphere make the form of  'pipes', so that Regions due to be named e.g.:
Axo, Axi, Hso, Hsi is possible, though chosen not to be valid in the Zürich/McIntosh or CV after Malde systems.

                                                                                                                                K.I.Malde, August 1998

p.s. For further instructions related to this problem,
Letter from Patrick S. McIntosh  (K.I.Malde, Jan. 2001)


Your comments, references, questions, experience, etc.
are most welcome, please to:
c v h e l i o s @ g m a i l . c o m
or to "snailmail" below:

Kjell Inge Malde, CV-Helios Network,
Private: Böreholen 20, N-4085 Hundvaag, Norway
phone: 47 98 69 28 56
c v h e l i o s @ g m a i l . c o m
(with spaces here to avoid spam)

CV after Malde: Observing Values
Explanation to the Classifications
Explanation II to the Classifications

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This page last edited:    02.11.17 12:38