Sunspots and Solar Output

I’m glad I started the Climate Data Service, because it makes working with climate data easier. Even for me. I could access and study it before, but now it’s all in one place and one format, and the ease of use is a good motivator for closer study.

Something I’ve just been looking at is the relationship between sunspot counts and solar irradiance. I’ve used TSI (total solar irradiance) to estimate the influence of solar variations on global temperature, but reliable records don’t start until about 1976 when satellite observations began. Before that, we have to rely on proxies, of which the most common is sunspot counts. There are many reconstructions of solar irradiance which use more, but I’m not aware that any of them can be considered particularly better than the others.

But just how good a proxy is sunspot counts? I can directly compare monthly averages of TSI as measured by satellites, to sunspot numbers (re-scaled to estimate TSI):


There’s no doubt that sunspot numbers make a useful proxy for solar irradiance; more sunspots correlates with more solar energy output. But the proxy isn’t perfect (none ever is), and there are some notable shortcomings. In particular, during cycle 23 (the 2nd-to-last on the graph) sunspot counts (in red) weren’t as high as the previous two cycles even though solar irradiance was just as high (a tiny bit higher, even), and when the minimum which followed is estimated by sunspot counts, it doesn’t dip quite as low as solar irradiance actually did.

A natural thing to do is to compare the two variables directly, rather than comparing their time series. It looks like this:


It seems that as sunspot count rises so does TSI, but the rise isn’t linear. TSI increases more slowly when sunspot count gets bigger, a result which is easily confirmed statistically and is visually more clear by computing average TSI over 10-wide sunspot intervals, and smoothing (by modified lowess):


Just for fun, I played around with various power-law relationships (other than linear). The best I’ve found so far is to estimate TSI by the square root of sunspot count. That generates time series which compare thus:


The correlation is slightly improved over an estimate based on bare sunspot counts, although the improvement isn’t large.

If we use the square-root-sunspots proxy to estimate TSI since 1850, it looks like this:


We get a better idea of the longer-term changes, with the solar cycle influence reduced, by simply computing 11-year moving averages:


Now we can see that part of the cause of warming from 1900 to about 1940 may indeed be the increase in solar output. We also see quite a drop after 2000, not just because solar cycle 24 (the most recent) is less than average, also because its preceding minimum was longer-lasting than average.

Even so, the difference between the square-root proxy and the simple sunspot-count proxy is quite small, and probably won’t make much difference when estimating the sun’s influence on global temperature. I’ll keep you posted on that.

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10 responses to “Sunspots and Solar Output

  1. Which sunspot number did you use? You there is a recent revision which is now much flatter than it used to be.

    [Response: From WDC-SILSO, Royal Observatory of Belgium, Brussels, via world data center for the production, preservation and dissemination of the international sunspot number.]

  2. “confirmed statistically and is visually more clear by computing average TSI over 10-wide sunspot intervals”

    I was expecting a different kind of statistical averaging: I thought you were going to do one based on time (e.g., average TSI over a three month period, and total sunspot count for that period, and graph those against each other). There would still be outliers from cycle 23, but I feel ilke there are a lot of noisy TSI spikes which might be better smoothed with temporal averaging than with an average over sunspot numbers.

    But thank you for some neat analysis! (also: I’m wondering how long the “sun-drives-climate” crowd can ignore the fact that the TSI is at a 150 year low while temperatures are hitting record levels) (oh, why do I even ask? They’ll have fifteen different justifications, all inconsistent with each other, and will keep going even if TSi stays low for decades while heat waves blast the world)

  3. There’s no simple way to predict future irradiance from that last graph, but if I were a betting man I’d think it’s going to go up in future decades. Given that we’re already at record high temperatures that doesn’t sound too good.

  4. “Now we can see that part of the cause of warming from 1900 to about 1940 may indeed be the increase in solar output.”

    Let’s see…
    Deniosphere: It’s the SUN! HAHAHAHAHAHAHA we told you so!!!!
    Physics: That was equal to a ~0.08 W/m2 increase in top of atmosphere radiative forcing. We’re already at ~3 W/m2 from anthropogenic GHGs.
    Deniosphere: It’s the SUN! HAHAHAHAHAHAHA we told you so!!!!

  5. I found a useful ready reckoner for the sustained effect of an imbalance.

    -1W/m^2 produces a rate of temperature rise of 1C/century.

  6. Henk Schuring

    The problem with a solar minimum is that the sunspot number may be zero for quite a while. In the most recent minimum in 2009 there was a spotless stretch of 260 days. The TSI seems to diminish during such a spotless period. and there could be a relationship between the length of the spotless period and the dip in the TSI.

  7. Now we can see that part of the cause of warming from 1900 to about 1940 may indeed be the increase in solar output.

    What does the temperature trajectory of the last 150 years look like if this estimate of TSI is factored in as a forcing for the period?

  8. Perhaps it’s obvious, but it may be worth repeating that, despite their similar units (W/m²), changes in solar irradiance and planetary energy balance (‘radiative forcing’) are not equivalent. For Earth they differ by a factor of about 5.7, comprising x 4 for the definitional difference* and another x 1/0.7 for the albedo (reflectivity).

    (* Energy balance W/m² is conventionally averaged over the whole surface of the planet, while solar irradiance W/m² is just across the disc receiving sunlight. Circle area to sphere area is x 4.)

    • No, it’s not obvious, so thanks for clarifying that. I was wondering why Magma said ‘0.08W/m2’ above when reading off the graph looked like around 0.3W/m2. Now it all makes sense, (and fits much better with my general idea of the magnitude of the solar forcing).

  9. The SATIRE models of Krivova et. al has been shown to have an r²=.97, which is about as good as it gets. For that reason, it is in the widest use today.

    It should be noted that the main model (SATIRE-S) uses magnetograms, which are only available from the late 19th century. However Krivova et. al have extended the model using a combination of sunspot counts and cycle lengths to the 17th century (although there is of course no way to determine fits that far back).
    Data can be found at: