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New Science 22: Solar TSI leads Earth’s temperature with an 11 year delay

We’re launching headlong back into the New Science series with a major post

Global temperature and 11-year delayed TSI trend together
Lots of things will fall into place — as befits a potential paradigm step forward. For decades, people have been looking to see if the Sun controlled our climate but the message was perplexingly muddy. In the long run, solar activity appears linked to surface temperatures on Earth.  (Solar activity was at a record high during the second half of the 20th century when temperatures were also high.) But when we look closely, firstly the solar peaks don’t exactly coincide with the surface temperature peaks, and secondly, the extra energy supplied during the solar peaks is far too small to do much warming. So how could changes in surface temperature be due to the Sun?

A few researchers noted an esoteric correlation of long solar cycles with lower temperatures in the next solar cycle, but mostly those papers were left on the shelf, ignored. Dr David Evans’ notch-delay solar delay theory can explain this odd pattern.

To unravel the connections David took a new approach which cleared out the dead-end complexity of the current climate research. Instead of trying to predict everything from a bottom up detailed approach, he worked “top-down”, treating the Earth as a black box, as a simple Energy-In-Energy-Out type problem, and used the kind of maths that makes modern electronics work. It was an odd combination of factors that came together: David would have to be the only professional modeller on Earth who has a high level PhD in Fourier transforms, experience in electrical engineering in Silicon Valley, and a science blogger as a wife to focus him on this problem (and raise barely enough funds to pay the bills while he worked — it’s been three years full time work now).

This was an Oooh-look-at-that moment. Eleven Years?!

The light in the darkness was this extraordinary pattern that turned up in the Fourier analysis. It lit up a strange path, and following it uncovered the papers that had been largely ignored. Suddenly the disparate observations which had made no sense in conventional models fitted the new theory.

The light on the new path was finding a “notch” filter (it’s a common garden-thing for an electrical engineer, but probably unknown to climate scientists). That notch filter was published here 18 months ago. With one minor proviso, almost all that work there remains intact, and stronger. The proviso is that at the time we thought the notch guaranteed a delay, but we now know that while notch filters can work with a delay, it’s not obligatory. That difference is mostly immaterial now, because the evidence found for a delay turned out to be so strong.

The notch was “the dog that didn’t bark“, the big clue. Somehow at the peak of solar incoming energy, there was a sudden shift in the way Earth responds to incoming sunlight. The extra energy (which is very small but detectable with Fourier analysis) is reflected or not absorbed by the system. This is a screaming red flag that some important change is going on, through a mysterious unknown mechanism.

If there was a delayed action creating this notch filter pattern, further analysis showed that spookily, the delay was 11 years. Crikey, send up the fireworks — it was unmistakably the exact same length as the average solar cycle. This was an Oooh-look-at-that moment. Eleven Years?! And when I say spooky, I mean spooky. This is not just the usual type of “delay” where some effect takes 11 years to be big enough to notice, or the effect gets smoothed out — it’s like there is an 11 year memory built in to the system, a 11 year gap between two discrete events. A fall 11 year ago correlates better with the present than a rise 5 years ago. It’s just weird. Tantalizing, but odd.

The delay may just be the missing key to understanding the Sun’s effect on Earth.  Earth’s temperature seems to follow the pattern of rises and falls in solar energy, but with an 11 year average delay. Looked at this way, suddenly the correlation improves, the observations fit.  (More specifically, in each cycle the length of the delay seems to wax and wane with the length of the solar cycle).

But there were still mysteries to solve. Make no mistake, it’s not as if the energy from the Sun is arriving on Earth in eight minutes and then taking 11 years to reach thermometers. No way.  Total Solar Irradiance (TSI) is not the cause of global warming, rather it is a leading indicator. What on Earth was the mechanism? David and I (and many others before us) had looked for an accumulation effect, or a smoothing pattern — where the extra energy was stored and took a few years to show in thermometers. It didn’t make much sense. Not many things on Earth would operate on that kind of cycle. Not ocean currents, not jet streams, not ice melting , and not arctic tundra growth. And it certainly wasn’t cicadas. I like the idea of a biological process — it made sense that phytoplankton or plants would be adapted to this cycle that had run for millions of years. But still, that didn’t explain a delay — it explains a smoothing process, but not a gap of a decade.

At some point David realized, from the electrical analogy, that the timing was suspiciously precise. Because the delay was the length of a solar cycle, and the notches were synchronized to the Sun, the cause of the delay wasn’t on Earth — but inside the Sun. The delay was not a smeared out thing, but a literal delay — the effect due to a change in TSI only begins to act one sunspot cycle later, and quickly affects the surface temperature here on Earth.  The flickering signals from total sunlight are a clue that precedes some other change in the solar dynamo.  We’ll talk about the possible mechanisms in future posts, because there are a lot of fields, fluxes and particles coming off the Sun that could potentially affect our climate.

In this post David goes through paper after paper that we found along the path, once we knew we were looking for a delay of one solar cycle. Don’t miss this part. It’s the reason we are now sure that some other factor on the Sun is key to understanding Earth’s climate, and it occurs one solar cycle after TSI changes. Below that, he updates the notch filter which proved so useful (get into that beautiful graph in Figure 2, all you maths-heads and engineers). In future posts we’ll use the delay to predict what seems to be coming for us climate wise. This new theory can be tested soon. It’s falsifiable — unlike the carbon religion. More on that soon too.

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PS: The first part of the New Science series (on the flaws in the architecture of conventional climate models) are summarized on the project home page. The conventional models are stuck in a rut, they don’t even include the possibility that feedbacks might allow the energy to reroute to space via water vapor. And they overestimate the sensitivity to CO2 by a factor of five to ten.  The synopsis was updated this week with several new diagrams of the atmosphere, illustrating the rerouting feedback and movements in the water vapor emissions layer.

— Jo



22. The Delay

Dr David Evans, 12 February 2015, Project home, Intro, Previous.

This post makes the case for a delay of ~11 years or one sunspot cycle between a change in smoothed TSI and the corresponding change in surface temperature. And we mean an actual delay between two discrete events, not just a corresponding gradual surface warming smeared out through time as the effect of the change in TSI builds up.

(By the way, what motivated us to look for a delay, which is a novel thing to do? Well we had initially thought that the notch filter found in post 21 implied that there must be a delay, but this was based on an incomplete analysis that indicated that a notch filter is necessarily non-causal (see the old blog posts). Such a non-causal transfer function requires an accompanying delay to make it physically realistic. But a notch filter can also be causal, as insisted upon by blog reader Bernie Hutchins, and as a complete analysis later showed.** In retrospect this was a lucky mistake to have made, because once we started looking for evidence of a delay we found rather a lot of it.)

Observational Evidence for a Delay

A delay of ~11 years from changes in smoothed TSI to corresponding changes in surface temperature has been found independently several times, though apparently mostly interpreted as delays in the propagation of heat around the Earth. Few, if any, appear to have considered the delay might be in the Sun itself.

– 10 Year Delay to Tropical Atlantic Sea Surface Temperatures

Willie Soon (2009, pp. 156-157, [1]) found a good correlation between changes in 10-year-delayed TSI to changes in the tropical Atlantic sea surface temperature from 1870 (see his Figure 4), and ascribed it to delays in heat propagation in the oceans: “The chosen delay time of 10 years is only a rough estimate for the thermal-cryospheric-salinity and mechanical wind stress effects occurring within the Arctic and northern North Atlantic basins to propagate southward. But it is clear from both empirical evidence … and careful ocean modeling … that a physical delay of some 5 to 20 years is reasonable.”

– 12.42 Year Delay to Sea Surface Temperatures Near Iceland

Moffa-Sanchez, Born, Hall, Thornalley, and Barker  (2014, [2], Supplementary, p. 5, Fig. S3) found a lag of ~12.42 years from changes in TSI to correlated changes in North Atlantic surface temperatures derived from a marine sediment core in the Iceland Basin, from 900 AD.

– 12 Year Delay to Northern Hemispheric Ground Temperatures

Usoskin, Schuessler, Solanki, and Mursula (2004, [3], p. 21) found that the correlation coefficient between the northern hemisphere ground temperature from Mann and Jones (2003) and sunspot numbers reconstructed from Be-10, from 850 AD, was greatest when the temperature lagged the sunspot numbers by ~12 years (see their Fig. 3).

– Delay of One Sunspot Cycle to Northern Hemispheric Ground Temperatures

The correlation between temperature and the length of the previous sunspot cycle (“solar cycle”) is one of the strongest correlations in climate science, unexplained to date and largely disregarded, but the notch-delay hypothesis offers support and explanation.

Friis-Christensen and Lassen (1991, [4]) found that the length of a sunspot cycle correlates well with the northern hemispheric surface temperature on land during the following sunspot cycle — the longer a sunspot cycle, the cooler the Earth during the following sunspot cycle — from 1861. (The correlation is strong to 1970 in their data then there is a dispute. Damon and Laut (2004, [5]) claim they mishandled their data and that the correlation from 1970 instead predicted level temperatures while in fact they went up strongly, thereby breaking the correlation and supporting the CO2 theory. However this is strongly disputed by Friis-Christensen and Svensmark (2004).)

Butler and Johnston (1994, [6]) found the correlation applied to temperatures at the Armagh observatory in Northern Ireland from 1795.

Archibald (2010) showed the correlation applied to the 350 year Central England temperature record, the De Bilt data from Holland, and temperature records at a number of places in the northeastern USA: “in the latter, the relationship is that each 1-year increase in solar cycle length corresponds to a 0.7°C decline of atmospheric temperature during the following cycle”. David Archibald also proposed using the correlation as a predictive tool. He has been championing this correlation in recent years.

The duration of the ascending part of a sunspot cycle (roughly its first half) is anti-correlated with the peak sunspot number of the cycle, which is known as the Waldmeier effect. However the strength of this negative correlation depends strongly on the measure of the rise time and which index of sunspot numbers is used (Dikpati, Gilman, and de Toma, 2008, [7]). Higher sunspot numbers correlate with a higher peak of TSI, so from the Waldmeier effect we deduce that a longer sunspot cycle correlates with lower levels of TSI during the cycle, which correlates with lower surface temperatures during the following sunspot cycle.

Thus lower TSI during one sunspot cycle correlates with lower surface temperatures during the next sunspot cycle. The delay implied by this correlation is roughly one sunspot cycle, or ~11 years.

Note also that the existence of the correlation supports the notion that the Sun has a major influence on temperatures.

– Delay of 10–12 Years to Surface Temperatures in Norway and the North Atlantic

Solheim, Stordahl, and Humlum (2012, [8]) found that a lag of 10–12 years gives the maximum correlation between sunspot cycle length (SCL) and surface temperatures in Norway and the North Atlantic, from 1880: “This points to the Atlantic currents as reinforcing a solar signal.”; “it is reasonable to expect a time lag for the locations investigated, since heat from the Sun, amplified by various mechanisms, is stored in the ocean mainly near the Equator, and transported into the North Atlantic by the Gulf Stream to the coasts of Northern Europe”; “They also found that temperatures shifted 11years back in time, correlated better with SCL measured between minima than between maxima.”

Recent History Suggests a Delay

Lockwood and Froehlich (2007, [9]) found that four measures of solar activity — sunspots, TSI, coronal source flux, and neutron count due to high energy cosmic rays — all peaked around 1986 and 1987 after rising since at least 1970, once the usual fluctuations of the sunspot cycle were removed by a smoothing process. Global surface temperature rose until peaking in 1998 (or maybe 1997 if the effect of the 1998 El Nino is smoothed out), before leveling off.

This suggests a delay of ~11 years from changes in TSI to corresponding changes in surface temperatures. Indeed, without a delay it is difficult to see how TSI could be signaling the major influence on the surface temperature. (The Lockwood and Froehlich paper is often held by the establishment as evidence for the lack of solar influence on global temperature.)

Observations are Suggestive of a Delay

We constructed a composite TSI record and a composite temperature record by splicing together the data mentioned in post 21 on the notch. Fig. 2 below shows global temperature versus 11-year-delayed TSI, back to 1800, where the TSI is 11-year smoothed to remove most of the effect of the sunspot cycle (the smoother simply averages the values in a centered 11-year window; if the sunspot cycle was exactly 11 years such a smoother would remove all cyclic behavior). With the obvious exception of the 1950s through early 1980s, which we discuss in a later post, the temperature and 11-year-delayed TSI trend up and down mainly in unison — which is suggestive of an ~11-year delay. Be aware that the data is from proxies before 1850 for temperatures and before 1979 for TSI.

Global temperature and 11-year delayed TSI trend together

Figure 1: Global temperature and 11-year delayed TSI, both 11-year smoothed, have mainly trended together. (For the the composite TSI from standard sources replaced by Leif Svalgaard’s reconstruction, see here.)


Implications of the Delay for Climate Influences

In the reasoning and observations above, the magnitude of the surface warming is great enough to be easily observed — so something either amplifies the direct heating effect of a change in TSI, or is a climate influence in its own right. In either case, there is a warming influence that lags TSI by ~11 years, and its magnitude is much greater than the direct heating effect of changes in TSI (see post 10).

Note also the observed delay of ~11 years cannot be simply due to propagation of heat around the Earth because:


**Why We Considered the Possibility of a Delay: The Notch

We are interested in all possible systems that both fit our formal description (Fig. 1 of post 21) and are compatible with the empirical transfer function (Fig. 2 of post 21): a notch in the amplitude transfer function, centered on a period of ~11 years, with no constraints on phases.

We assume the system is describable by a linear differential equation, like a typical physical system of continuous variables. The simplest filter that could produce a notch is 2nd order, corresponding to a 2nd order linear differential equation (an equation containing only the input and output functions, their derivatives, and their second derivatives). Higher order notch filters are merely cascades of 2nd order notch filters, corresponding to higher derivatives — for example, a cascade of two 2nd order filters is described by a 4th order linear differential equation. A 2nd order filter is sufficient to produce a notch, so, invoking Occam’s razor, we assume the system contains just a single 2nd order filter.

The “step response” of a system is the output of the system when the input is a unit step function — which is zero until time zero and one thereafter (it “steps up” from 0 to 1 at time zero). A causal step response is zero before time zero — it obeys the “law of cause and effect”, the response comes after the cause or stimulus. But a non-causal step response is non-zero before time zero, which is impossible physically, though mathematically plausible.

It turns out 2nd order notch filters come in four “classes” — filters within a class may have different values of the real-valued parameters but are qualitatively similar, while the classes differ only by the values of two binary parameters (k and l below). Two of the four classes of 2nd order notch filters have causal step responses, while the other two have non-causal step responses. See Fig. 1. (See here for the complete analysis.)

Step responses of notch filters.

Figure 2: The step responses of the four classes of 2nd order notch filter, for realistic parameter values for the Sun-Earth relationship (values determined in an ensuing post). We characterize each class by the values of two binary parameters k and l: when l is 1 the step response is casual, but when l is 0 the step response is non-causal.

While the causal step responses are possibilities for the Sun-Earth relationship, what about the non-causal ones? Well their non-causality dies out exponentially with decreasing time, so simply delaying the step response by a few years (by combining the notch filter with a delay filter) makes the step response of the combined filter causal, to a good approximation. Note that a delay filter only affects the phases of the transfer function, not its amplitudes, so adding a delay does not affect notchiness.

If the Sun-Earth relationship involves only the causal step responses then a delay is compatible with the observed empirical transfer function, but if it involves the non-causal step responses then a delay of several years is mandatory. This suggests that there might be a delay of several years, which motivated us to look for evidence of a delay.


[1^] Soon, W. W.-H. (2009). Solar Arctic-mediated Climate Variation on Multidecadel to Centennial Timescales: Empirical Evidence, Mechanistic Explanation, and Testable Consequences. Physical Geography, 30, 2, pp. 144-184.

[2^] Moffa-Sanchez, P., Born, A., Hall, I. R., Thornalley, D. J., & Barker, S. (2014). Solar forcing of North Atlantic surface temperature and salinity over the past millennium. Nature Geoscience, Supplementary Information.

[3^] Usoskin, I. G., Schuessler, M., Solanki, S. K., & Mursula, K. (2004). Solar activity over the last 1150 years: does it correlate with climate? Proc. The 13th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun (pp. 19 – 22). Hamburg: ESA SP-560, Jan. 2005, F. Favata, G. Hussain & B. Battrick eds.

[4^] Friis-Christensen, E., & Lassen, K. (1991). Length of the Solar Cycle; An Indicator of Solar Activity Closely Associated with Climate. Science, Vol.254, No.2032, pp. 698-700.

[5^] Damon, P. E., & Laut, P. (2004). Pattern of strange errors plagues solar activity and terrestrial climate data. Eos, Transactions American Geophysical Union, Volume 85, Issue 39, pages 370–374.

[6^] Butler, C. J., & Johnston, D. J. (1994). The Link between the Solar Dynamo and Climate – the Evidence from a long Mean Air Temperature Series from Northern Ireland. Irish Astronomical Journal, J.21, 251 – 254.

[7^] Dikpati, M., Gilman, P., & de Toma, G. (2008). The Waldmeier Effect: An Artifact of the Definition of Wolf Sunspot Number? Astrophysical Journal, 673: L99–L101.

[8^] Solheim, J.-E., Stordahl, K., & Humlum, O. (2012). The long sunspot cycle 23 predicts a significant temperature decrease in cycle 24. Journal of Atmospheric and Solar-Terrestrial Physics.

[9^] Lockwood, M., & Froehlich, C. (2007). Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature. Proceedings of the Royal Society, 10.1098/rspa2007.1880.

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