Solar cycle parameteric curve fit and modeling

[Drax Spacex]

A solar cycle (SC) is typically characterized by a plot of sunspot number as a function of time.  This plot usually has a sharp rising phase, followed by leveling inflection towards the peak (or peaks) of solar maximum, followed by a downward inflection and a trailing declining phase.   The overall shape is not symmetric and is most often characterized by a positiveness skewness.  The exact shape of each SC plot varies, some tall and narrow, others short and wide, faster or slower rise times, higher or lower maxima, longer or shorter declining phases, etc.

Several probability density functions (PDFs) provide adjustable parameters that  can provide a good curve fit and model the characteristics of the SC plot described above.  (Note that in this exercise there is no probability that's being a modeled - it is simply that the formula that describes the PDF happens to provide a good curve fit to observed data with appropriate parameter values.)

The Weibull probability density function is relatively simple, typically defined by 2 parameters:  shape and scale.  
https://statisticsbyjim.com/probability/weibull-distribution/

With some iteration, it is possible to converge on values for these 2 parameters for a Weibull distribution that provide a pretty good match to historical SC plots, shown here for SC20-SC24:

https://ibb.co/7jdhb1f

[hamateur 1953]

I looked at em Drax. Very interesting.  Its somewhat helpful to me, having looked at solar curves at least for the last fifty years as a ham.  I’ve always thought cycle 20 was one of the “ ringers” so to speak. With its “ steps down” For ya younguns cycle 20 had possibly the most energetic cluster we’ve seen since 1940s  Checkitout. allegedly went into Gamma region. Triggered magnetic mines during the vietnam war as well. caused a lot of “ issues”. 

Try Aug 4 1972 horsehead  CME in a search string.  Should yield ya a mess of cool stuff!

Edited February 7, 2023 by hamateur 1953

[Philalethes]

52 minutes ago, hamateur 1953 said:

I looked at em Drax. Very interesting.  Its somewhat helpful to me, having looked at solar curves at least for the last fifty years as a ham.  I’ve always thought cycle 20 was one of the “ ringers” so to speak. With its “ steps down” For ya younguns cycle 20 had possibly the most energetic cluster we’ve seen since 1940s  Checkitout. allegedly went into Gamma region. Triggered magnetic mines during the vietnam war as well. caused a lot of “ issues”. 

Try Aug 4 1972 horsehead  CME in a search string.  Should yield ya a mess of cool stuff!

Very interesting. I'm reading now on Wikipedia that it did indeed have a "historic series of solar flares and coronal mass ejections", and what you just mentioned about mines:

Quote

An extremely active active region, McMath 11976, produced a historic series of solar flares and coronal mass ejections (CMEs) in August 1972. One CME traveled to Earth in a record low of 14.6 hours and produced a strong geomagnetic storm that caused widespread electrical and communications grid disturbances and the accidental detonation of numerous U.S. Navy magnetic sea mines in North Vietnam.

Yikes.

Also very interesting that a cycle you remember to be a bit odd in that regard immediately succeeded SC19, the most active one on record. I've read and heard in many places that the activity around 1957-1959 was particularly extreme.

[hamateur 1953]

I personally “ cut my teeth” piqued my interest during cycle 19!  It caused a huge upsurge in amateur radio! 

[Drax Spacex]

The high rising phase slope of SC 19 may have been a good predictor that it was going to be a doozy!  

https://ibb.co/ZcjSC7vI

3 hours ago, hamateur 1953 said:

I personally “ cut my teeth” piqued my interest during cycle 19!  It caused a huge upsurge in amateur radio! 

I've often heard hams talk about the glory days of amateur radio around that time when you could "work the world" with just a few watts and a wire.

I'm excited that the 10 meter band has opened up with the increased solar activity.  Lots of domestic and DX activity on that band while just a year ago there was nothing on 10m.

3 hours ago, Philalethes Bythos said:

Also very interesting that a cycle you remember to be a bit odd in that regard immediately succeeded SC19, the most active one on record. I've read and heard in many places that the activity around 1957-1959 was particularly extreme.

SC16-SC19 were monotonically increasing; SC21-24 were monotonically decreasing.  The only way is up for SC25.

Edited February 8, 2023 by Drax Spacex
10m

[hamateur 1953]

Gentlemen and ladies, it sure as heck looks pretty doggone good for 25 at this point in time.  I won’t be stupid enough to open the betting table again 🤣🤣. Let’s just enjoy the next five years or so!!! 

[hamateur 1953]

As an aside I have never looked at the potsdam planetary A index.  must’ve been up there pretty good though. 

[hamateur 1953]

Looked it up on our datasets looks to be around Ap 180 or so 

[3gMike]

11 minutes ago, hamateur 1953 said:

Looked it up on our datasets looks to be around Ap 180 or so 

Which datasets are you referring to ?

[hamateur 1953]

the historical data sets ( the ones on solen.info solar cycles 1-20)

I suck at reading german perhaps Min could post a link to the running Potsdam A index? or another kind individual for our direct comparison. Must be available SOMEWHERE over there!  Tnx 3g! 

Heck I’ve a dutch buddy! He already thinks im whacko 🤣 shouldn’t be too hard to get him interested if nobody else is geeky enough. They should be publicly available. 

By the way y’all are lucky we didn’t call the wavelengths 10 yards vs meters!  hahaha 

[3gMike]

1 hour ago, hamateur 1953 said:

the historical data sets ( the ones on solen.info solar cycles 1-20)

I suck at reading german perhaps Min could post a link to the running Potsdam A index? or another kind individual for our direct comparison. Must be available SOMEWHERE over there!  Tnx 3g! 

Heck I’ve a dutch buddy! He already thinks im whacko 🤣 shouldn’t be too hard to get him interested if nobody else is geeky enough. They should be publicly available. 

By the way y’all are lucky we didn’t call the wavelengths 10 yards vs meters!  hahaha 

Yes, Solen is a good source for that. I like it because it compares a number of different indicators.

If you want the Potsdam original data you can get it here...  https://www.gfz-potsdam.de/sektion/geomagnetismus/daten-produkte-dienste/geomagnetischer-kp-index You just need to click the English language button.

In order to download the complete dataset you will need an FTP Client - like FileZilla ... https://filezilla-project.org/

then download the FTP file... 

  ftp://ftp.gfz-potsdam.de/pub/home/obs/kp-ap

 

[hamateur 1953]

Well ima outta likes again. I shouldn’t have laughed at Mins post and PBs meme doggone it!!

Danke!!