Leif Svalgaard writes: “Several people asked why I said that the SWPC F10.7 graph was ‘just wrong’. And I promised a follow up on that. Here it is.”
Happy to oblige! For reference, here is the original graph from SWPC. – Anthony
The SWPC F10.7 Radio Flux Prediction Graph
Leif Svalgaard, May 2009
Fitting the monthly average the F10.7 flux (reduced to 1 AU) against the International Sunspot number, R, for the entire interval 1951-2009 to a forth order polynomial gives a formula for computing the Flux from the sunspot:
Flux = 67.29 + 0.316 R + 0.01084 R 2 – 0.006813 R 3 + 0.0000001314 R 4 (1)
The correlation is shown in Figure 1 below:
We know that this formula does not accurately portray the most recent relationship between R and F10.7 (see previous essay), but if we make no assumptions or corrections and just take the data as they are we can consider the conversion formula as indicative of the average conditions the last half century.
SWPC gives a table showing the predicted sunspot Number and the predicted F10.7 cm flux for the next decade. Here are the first few rows of that table, with the middle value of the predicted values in bold script, followed by a high and low limit:
Year Month Predicted Sunspot Number Predicted F10.7 cm Flux:
2009 01 2.1 5.1 0.0 67.4 69.4 65.4 2009 02 2.7 7.7 0.0 67.3 70.3 64.3 2009 03 3.3 8.3 0.0 67.2 71.2 63.2 2009 04 3.9 9.9 0.0 67.2 71.2 63.2 2009 05 4.6 11.6 0.0 67.3 72.3 62.3 2009 06 5.5 12.5 0.0 67.5 73.5 61.5 2009 07 6.7 14.7 0.0 67.8 74.8 60.8 2009 08 8.1 17.1 0.0 68.2 76.2 60.2 2009 09 9.7 18.7 0.7 68.8 76.8 60.8 2009 10 11.5 21.5 1.5 69.7 78.7 60.7 2009 11 12.6 22.6 2.6 70.2 79.2 61.2 2009 12 14.6 24.6 4.6 72.1 81.1 63.1
Using this table we can plot the predicted Flux as shown by the smooth red curve for the next solar cycle [or alt least up through 2015, Figure 2]:
I don’t know how SWPC came by their predicted F10.7, but my best guess is that they ran a correlation like the one shown in Figure 1 and applied it to the predicted sunspot number. Doing this using the observed sunspot number up to last month gives the ragged blue curve with the smooth blue curve coming from the predicted sunspot number. There is a good match for the predicted part of the curves [the red and the blue after May 2009]. The graph on SWPC’s website http://www.swpc.noaa.gov/SolarCycle/ seems to match the smooth curves quite well, with the exception of the variation during 2009, which I show as the purple curve. It is simply incorrect to start the curve from a flux of 60 and inexplicable [to my way of thinking – other than plain sloppiness] why the graph should disagree with the published table at http://www.swpc.noaa.gov/ftpdir/weekly/Predict.txt
As discussed in the previous essay and obvious from the discrepancy between the red and blue ragged curves above in Figure 2, the formula (1) for the average correlation between the Flux and the Sunspot Number does not work so well after about 1989, so it is not clear that it should work after May 2009. This means that we have little idea about what the predicted F10.7 flux should be. If the Sunspot Number prediction is correct, then the F10.7 flux is predicted too high, and if the F10.7 flux prediction is correct, then the predicted Sunspot Number is too high. My own feeling is that since the predicted Sunspot Number is really a prediction of the number of active [magnetic] regions which should be reflected in the F10.7 Flux, that the Sunspot Number [based on visible spots] will be much smaller than the predicted values. This will, indeed, be interesting to watch. Either way, we’ll learn a lot.
A possible problem that may surface during SC24 is the way we count sunspots these days compared to the past. Trying to match other solar output records may be skewed because of the sun speck counts not really showing the true picture.
The last time we saw the Sun as it is today is probably 200 years ago, so using our counting methods of the past 100 years may not be accurate when trying to compare with the last grand minimum. If we keep getting counts of 18 for specks like we have today, the SC24 tally will be meaningless.
road trip planner (03:17:06) :
May be a dumb question – but how do we have 1000 year record of solar activity?
Naked eye sunspots. Crude, but we do have it.
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/ANCIENT_DATA/Early_Reports
Leif – when you state that ‘observations show otherwise’ with respect to the relation of cosmic rays to clouds, what published papers are you referring to?
Svensmark’s observations covered cycle 22 and showed a clear 3% change in cloud from peak to trough of the cosmic ray flux (which follows the solar cycle pretty closely); he found a similar pattern for cycle 23, though was criticised for using a different cloud data set. That is not to say the criticism nullified the findings – which the Danish Space Center still supports. Usoskin at the University of Oulu in Finland also found a correlation. There were reports in the BBC and New Scientist that a paper by Sloan and Wolfendale failed to find the correlation – but on inspection of that paper, the authors actually confirmed the relationship, but reckoned it could only account for 25% of the cloud changes – their paper was not published in the usual solar-terrestrial journals and hence was not subject to appropriate peer review with regard to their methods. So – as far as I can tell, the jury is still hung on this one.
Geoff Sharp (04:00:55) :
A possible problem that may surface during SC24 is the way we count sunspots these days compared to the past
If L&P continues down it’s path, the current counting methods will quickly become acadmemic. These spots that are mere pinpoints are fine to count a 1 each in a group, but to give a 10 to them is nuts. Saturday’s spot actually had a penumbra, and deserves it’s count.
It’s embarassing to have Leif read my post Sunday morning of a string of pearls observation, then by the time I get to him to project them they are vanished.
Like Leif’s previous article, the SSN and the Flux derived SSN agreed well until it didn’t, and now we know something we didn’t know.
I’d say it’s a safe bet there are yet more surprises in store.
pkatt (00:29:00) :
Hey, if that magnetic region near the equator of the sun spits out a spot… what cycle will it be from?
Cycle 23
steptoe fan (01:07:06) :
what would the coeffs look like for a 4th degree poly if it were generated by data starting in 1990 ? Why stop at a 4th degree ?
Flux = 68.39 + 0.4093 R + 0.01172 R^2 – 0.00007867 R^3 + 0.00000013886 R^4
Stop at four, because further terms do no improve the fit.
Rik Gheysens (02:42:36) :
Can we expect a correction of the SWPC Graph soon? It is indeed incomprehensible why the figure should disagree with their published table.
I don’t think the graph will be corrected in the time while it is still wrong. After the end of the year no correction is needed anymore.
Is this formula the result of fitting the monthly average the F10.7 flux (reduced to 1 AU) against the International Sunspot number, R, for the interval 1989-2009? Or is it for the entire interval 1951-2009?
I’m not quite sure about the time frame used, but it certainly is for the whole time interval for which we had measurements at the time when the formula was derived.
road trip planner (03:17:06) :
May be a dumb question – but how do we have 1000 year record of solar activity?
We don’t, but solar activity modulates cosmic rays that in turn generate radioactive nuclei deposited in tree rings and ice cores. Calibrating those into sunspot numbers is a delicate business and there is great uncertainty in the numbers derived.
Geoff Sharp (04:00:55) :
If we keep getting counts of 18 for specks like we have today, the SC24 tally will be meaningless.
It will, but even more importantly the tally will be too high and the problem identified in the F10.7 data is that the sunspot tally since 1989 is too low.
Peter Taylor (04:43:14) :
when you state that ‘observations show otherwise’ with respect to the relation of cosmic rays to clouds, what published papers are you referring to?
I said that “claim that cosmic rays influence the albedo [although observations show otherwise],” that is the albedo not the clouds. Presumably the albedo is the measure of how much of TSI gets absorbed by the surface. The albedo is measured by observing Earthshine on the Moon. Here is a graph [Palle et al.] of the albedo the past two solar cycles: http://www.leif.org/research/albedo.png It is clear that there is no solar cycle signal in that data.
“Although my answer was ‘none’, there are some that claim that cosmic rays influence the albedo [although observations show otherwise], and since the cosmic ray flux should go up with decreasing magnetic field, one could surmise that more clouds would form and temperatures therefore drop [although clouds also have a positive greenhouse effect]. Temperatures have generally increased since 1860, so perhaps this effect is not so strong. I think that ‘none’ still is a good answer.”
Svensmark’s theory (right or wrong I don’t know :)) is that the earth’s magnetic field would not have much impact due to it not being strong enough to deflect muons from reaching the lower atmosphere which is where he believes the increase in cloud occurs when GCRs hitting the Earth are high. In other words, the muon count in the lower atmosphere varies only a very small amount as a direct result of changes in the Earth’s magnetic field.
Leif,
Allthough the observed sun spot/speck count will be low in SC24, how will that effect
the F10.7 Flux. I understand it is not the the spot but the plage that does the
emmiting, and we will have plages even if the spot is not visable.
As a recent radio ham (retirement hobby) I need the F2 layer to be ionised to get
some decent DX (long distance and preferably rare or exotic locations) before I
pop my clogs.
How much Flux in SC24 ? and how will that effect Radio Communications ?
Enjoy all your informative essays (especially informative for me as a geologist and mining engineer). I realize that the “fit” decayed only after 1989, but given this departure from the fit, why wouldn’t one use this to predict a lower sunspot number curve for cycle 24? It is afterall only the next cycle and seems fair probability that it may take at least until the next cycle for F10.7cm and sunspot number correlation to snap back together.
Geoff Sharp:If we keep getting counts of 18 for specks like we have today, the SC24 tally will be meaningless.
This affirmation is simply heretic, and the evolution of events and history always confirms the heretics view.
Leif Svalgaard (20:37:38) :
You don’t have me fully convinced yet. The last area of activity produced a dead pixel and we have another active area just come into view. There seems nothing new showing on stereo behind. So my question is this, do active areas such as we are seeing, by their nature elevate TSI and 10.7 flux? If they prove to be transient and no more areas develop for a week or two should we expect to see TSI and flux wane. When the active areas are on the other side of the sun, will TSI and flux remain elevated.
It’s about time I thanked you for perseverance and amusingly droll attempts to educate us. I’m sure many WUWT readers have learned much and in doing so abandoned their first misguided assumptions about our star and are developing new ones. 🙂
I know there is an adjustment to the solar flux as reported, due to the earth’s varying distance from the sun during the year, but what is that adjustment, relative to the time of year please?
KEN (05:23:25) :
How much Flux in SC24 ? and how will that effect Radio Communications ?
The F10.7 flux is a proxy of the Ultraviolet flux [which is what is doing the ionizing, not the radio flux]. I think that the radio flux will be 120 sfu, and the ionosphere will not go away
Gary Pearse (05:45:13) :
why wouldn’t one use this to predict a lower sunspot number curve for cycle 24?
Because the breakdown of the relation has only now been realized and it takes a while to confirm and convince the scientific community about such a thing. Scientists are [rightly] extremely conservative when it comes to such radical ideas.
MartinGAtkins (06:05:47) :
do active areas such as we are seeing, by their nature elevate TSI and 10.7 flux?
Yes, with the added little twist that if a significant spot develops in the middle of the active region that dark spot decreases TSI. You can see the recent increases here:
http://www.leif.org/research/TSI-SORCE-2008-now.png
i>If they prove to be transient and no more areas develop for a week or two should we expect to see TSI and flux wane.
Yes, and perhaps more importantly the areas will rotate out of view, and:
When the active areas are on the other side of the sun, will TSI and flux remain elevated.
no longer elevate TSI and Flux.
Nic (07:03:33) :
but what is that adjustment, relative to the time of year
When we are closest to the Sun in January, the flux is 3.5% higher, and when we are farthest from the Sun in July, the flux is 3.5% lower. So, if we have a ‘real’ flux at 1 AU in July of 70, then we’ll only observe 70*(1-0.035) = 67.5 sfu.
Looking backwards. does this “adjustment” fix the 1989 difference between SSN and f10.7 radio flux?
“The progressive drift is much larger than the 3% correction and is therefore not due to the correction. It seems inescapable that the relation between the sunspot number and the microwave flux has changed significantly in recent years. Another way of showing this is Figure 12:”
http://wattsupwiththat.com/2009/05/14/the-solar-radio-microwave-flux/#comments
Adolfo Giurfa (08:28:38) :
Looking backwards. does this “adjustment” fix the 1989 difference between SSN and f10.7 radio flux?
“The progressive drift is much larger than the 3% correction and is therefore not due to the correction.
And, in fact, the correction is only half that, as it is made on only one half of the data [on one of the two series].
Leif: The answer you gave in SolarCycle24.com made the best sense of any….
that the rise in activity does not have to be tied to sunspots. Faculae are active regions, and they have increased. So I do believe you are correct that SC24 has begun in earnest. It is somewhat spotless, however. Earlier, you had attested to there being a normally active Sun during the Maunder, again mostly spotless, but active nonetheless.
I do try not to sound stupid, but I have to ask. If the active regions on the sun go straight from an area that could produce a sunspot to a degraded magnetic area or coronal hole, would they not still emit f10.7 radio flux?
Interesting graphs, Leif. One can see the increase in 10.7m and TSI corresponding to the two large ex-CME Sun splats moving across the Sun over the past few days, but the MF is still moribund; Probably why major sunspots didn’t form from the regions from the CMEs ??
@ur momisugly Leif Svalgaard (07:55:27)
When we are closest to the Sun in January, the flux is 3.5% higher, and when we are farthest from the Sun in July, the flux is 3.5% lower. So, if we have a ‘real’ flux at 1 AU in July of 70, then we’ll only observe 70*(1-0.035) = 67.5 sfu.
So, we have the ‘real’ flux value and the observed flux value which are the same only when the Earth is at 1 AU in April & October. The rest of the time the observed flux value has to be adjusted by varying amounts up to ±3.5% (reached at apogee (July) and perigee(January)). This adjusted flus value then gives us a standardized frame of reference with which to study the sun.
My question(s) – what gives us the 3.5% adjustment at apogee & perigee? Upon what is the figure based? Is there a chart or a formula to determine each date’s adjustments for when we’re not at apogee or perigee?
Leon Brozyna:what gives us the 3.5% adjustment at apogee & perigee? Upon what is the figure based? Is there a chart or a formula to determine each date’s adjustments for when we’re not at apogee or perigee?
Why is it so that now 2+2=4.14? 🙂
rbateman (04:34:39) :
Naked eye sunspots. Crude, but we do have it.
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/ANCIENT_DATA/Early_Reports
Interesting that there seem to be plenty of naked eye sunspot reports from around 100 years ago, when the solar activity was relatively low. None after 1918 in that catalog however.
Another thanks to Leif for the follow up article. Fascinating indeed.
Leif, if you will, 😉
can you give us an approximation based on the F10.7 flux prediction, what then the max Sunspot Number prediction would be?
No one will hold you to it lol.
Tx
If not in public then E-mail it to me 😉
Could we have a nice piece on solar cycles of various sorts and earth temps, covering what we know, what we don’t know, and what we hypothesize–in layman’s terms, please.
Leon Brozyna (10:25:01) :
My question(s) – what gives us the 3.5% adjustment at apogee & perigee?
The correct terms for an orbit around the Sun is Aphelion (farthest) and Perihelion (closest). The adjustments come from the varying Sun-Earth distance of a near elliptic Earth orbit. Such adjustments to 1AU apply for every point in the orbit, not just at Aphelion and Perihelion.
No wrinkles after botox….:-)