We are back in the hunt for the main mystery drivers of our climate. The IPCC says it can’t be the Sun because the total amount of sunlight barely changes. Which is the usual half-truth that pretends the Sun is simple a ball of fire with no magnetic field, no solar wind, and has no changes in the “color” of the spectrum it emits. But the Sun has a massive fluxing magnetic field that turns itself inside out and upside down regularly, it churns off a stream of charged particles that rain on Earth, and if human eyes could see infra red and UV, we’d see the color of the Sun change through the cycle. We are only just beginning to figure out how these aspects affect the climate. But we know these factors influence ozone, probably cloud seeding, and possibly jet streams.
The only good long data we have on the Sun are the sunspots, which give us a reasonable idea of total sunlight since 1610. David uses Fourier maths to find the way that total solar irradiance (TSI) might relate to temperatures on Earth. TSI itself barely changes, so it could only have caused about 10% of the variation of Earth’s temperature since 1900 (if the official temperature records are to be believed). But it’s the main clue we’ve got to figure out how other parts of the solar dynamo may be changing the weather here on Earth.
The most likely mechanism is through cloud cover, which covers 60% of the Earth and reflects 30% of the incoming energy. And small change will make a big difference. David‘s model looks for externally driven changes to albedo, which means forces other than surface warming that influence our clouds. The IPCC assumes this doesn’t happen. What can I say? Their models don’t work.
The notch delay solar model is a physical model, based on physical principles, not curve fitting. It uses standard analytical tools employed throughout the electronics industry. Few climate scientists were trained in them — they have probably never heard of most of them. But engineers have to get the maths and the feedbacks right, or the phone and the electricity don’t work… these tools have been tested.
When the signals from the Sun are pulled apart this way, the patterns show a classic notch filter. At the frequency of a half solar cycle (about 11 years), some mechanism operates which temporarily reduces the effect of incoming solar radiation. Because it is so in tune with solar cycles it must originate on the Sun itself. Further, here seems to be a delay between changes in TSI and its effect on Earth’s temperature, also of about 11 years. The maths of notch filters shows this delay might be part of the notching mechanism, or might be separate. Obviously sunlight itself is not having a delayed effect on Earth 11 years later, instead a change in total sunlight is a leading indicator of some other solar factor that changes a half cycle after TSI changes. The delay is synched to the Sun. The exact mechanism is still to be figured out (there are several candidates).
David updates the progress on this from last year. While we said then that a notch filter dictated that there had to be a delay, Bernie Hutchins pointed out that it didn’t guarantee it. But by then we’d found other independent empirical evidence — published in a few papers over the last 20 years, that indicate a delay must be occurring.
20. So What Is the Main Cause of Global Warming?
Background of the last 19 posts: our understanding of carbon dioxide is framed by the top-down conventional basic climate model. But that model has major architectural errors. When the errors are fixed, the model estimates the Earth is not very sensitive to carbon dioxide. Indeed, it’s an order of magnitude less important than the UN’s Intergovernmental Panel on Climate Change (IPCC) calculated. All that extra atmospheric carbon dioxide very likely caused less than 20% of the global warming of recent decades*. (Kindly note that those findings are logically distinct from the notch-delay hypothesis coming up, so even if that hypothesis proves to be wrong then the critique of the architecture of the conventional basic climate stands.)
So if carbon dioxide is not the cause of 80% of global warming, what is? Let’s start by ruling out what it is not.
It’s Not Variations in Direct Heating by the Sun
The dog-obvious suspect is the Sun. But the IPCC is adamant that it’s is not that important. You have to read the fine print – they only consider the direct heating effect of the total solar irradiation (TSI), not all the other potential solar factors.
Figure 1: The energy from the Sun is almost constant. (Source)
As far as giant light bulbs go, the Sun shines a remarkably steady light. The TSI is so steady that it was called “the solar constant” until satellites began to measure it in late 1978, from which time it has varied by less than 0.1%. Before 1978, we can estimate the TSI from the number of sunspots, which remarkably have been recorded right back to 1610. As best as we can tell, in the last 400 years the TSI has varied by less than 0.2%.
The variation in direct heating by TSI is simply too small to explain global warming. It is easily calculated (next post) that fluctuations in TSI caused less than 10% of the 0.8 °C of global warming observed since 1900.
In this the IPCC’s climate scientists are correct. However this direct heating is the only way they allow the Sun to affect temperatures in their climate models, and their models rely on CO2 to explain most of the warming — which is the basis of their claim that the Sun cannot be the cause of global warming. (Given that they omit all the indirect ways the Sun could cause warming, and overestimate the potency of CO2 by a factor of 5 or 10, that’s a pretty flimsy basis, don’t you think?)
In our search for the cause of global warming, we look for a non-anthropogenic cause.
Why? There was considerable temperature variation during the current inter-glacial before industrialization: globally, the depth of the Little Ice Age around 1640 AD was ~1.5 °C cooler than today, while the Medieval Warm Period around 1000 AD was about as warm as the modern period (Christiansen & Ljungqvist, 2012, ). The last century, which has seen ~94% of human emissions of CO2 in all of history, has warmed only ~0.8 °C.
– Albedo modulation
We seek a non-anthropogenic source of albedo modulation.
Why? Albedo is the fraction of TSI incident on the Earth that is reflected back out to space, mainly by clouds and ice. Reflected radiation head back out to space without warming the planet. Albedo is about 30%. Small changes in albedo make significant changes in the amount of absorbed solar radiation (ASR), enough to account for global warming (a 2% change in albedo increases solar forcing by 2 W/m2, the same forcing as due to the change in CO2 to date since pre-industrial, not that all forcings have the even roughly the same effect on surface temperature). There are many processes that affect clouds and ice, including some potentially affected indirectly by the Sun. Variation in albedo, often called “albedo modulation”, is the most obvious non-anthropogenic mechanism for global warming.
Figure 2: 30% of the sunlight falling on the Earth is reflected back out to space without warming the planet, mainly by clouds and ice. (Plus a bit of nostalgia for something people cannot do anymore. Source)
Yet the conventional models omit any changes in albedo from any source other than feedbacks in response to surface warming. We call this omitted albedo “externally-driven albedo” (EDA). EDA includes albedo due to something external, such as the Sun, as well as due to any feedbacks other than to surface warming. (And to state the obvious: the total change in albedo is the change in EDA plus the change in albedo in response to surface warming).
EDA appears to quite significant, and possibly crucial, as shown in post 10. When we compared the fractional variation in albedo to the fractional variation in TSI, and accounted for albedo feedbacks to surface warming, the effect of changes in EDA on surface warming was shown to be at least twice as great as the direct heating effect of changes in TSI — and possibly many times greater. This is prima facie evidence that EDA is strong enough to be the leading suspect as the cause of global warming.
We search for a natural source of albedo modulation related to the Sun.
The Sun is the most obvious source of EDA, or is at least likely be somehow involved if the cause is something in our solar system, such as the Jovian planets.
Figure 3: Sunspot cycle peak (left) and minimum (right) in UV. (Source)
Figure 4: Eruptive solar prominence, 29 Sep 2008, imaged in extreme UV. (Source)
– TSI vs Surface Temperature
We explore the link between TSI and surface temperature on Earth.
The only thing about the Sun that we’ve measured for long enough to matter is the number of sunspots, which have been recorded since 1610. All the other solar parameters are either inferred from proxies, or were only measured after 1947 — which leaves only three full solar cycles (or Hale cycles, each ~22 years). Notably, this modern period was also a period of an unusually high level of sunspot activity.
The relationship between sunspots and TSI since 1978 has been studied and used to estimate TSI back to 1610; although we use TSI in this search, bear in mind that nearly all of the TSI record is deduced from the sunspot record.
People argue about that exact relationship between sunspots and TSI, and there are competing reconstructions of TSI with significantly different backgrounds (the long slow cycles, or low frequency components). Please note, as the evidence and hypotheses are presented in this series, that the precise reconstruction makes no difference — because the notch-delay hypothesis is mainly about shorter term cycles, nearer the higher 11-year frequency. Only in the predictions post does the background reconstruction make a difference, and there we have made predictions for each of the two main reconstructions.
Roadmap of the Search
Fourier analysis is useful for analyzing the way TSI relates to the surface temperature, because there is a linear invariant system. Carefully analysis using a newly-developed low-noise Fourier technique revealed an apparently new feature: a notch in the transfer function of the system, centered on the frequency corresponding to 11 years. The peaks in TSI every ~11 years as part of the sunspot cycle are not reflected in the surface temperature record.
The notch suggests the possibility of, but does not mandate, a delay of several years between a change in TSI and the corresponding change in surface temperature. Evidence for a delay of ~11 years is found in several disparate sources.
This leads to the force-X hypothesis, that a warming influence called “force X” affects the Earth’s albedo, and that force X is a smoothed version of the TSI delayed by one sunspot cycle. Thus tremors in TSI foretell what force X will be ~11 years later. Force X is at a minimum when the Sun’s magnetic field flips polarity, which causes notching — the flips coincide with the peaks in TSI.
The notch-delay hypothesis is a physical model that describes a solar influence on the Earth’s surface temperatures by its vital properties. It’s a model based on physical principles, as opposed to a mere mathematical curve fit. It is not fully fleshed-out because the mechanics of force X are unknown, but, like x-rays when they were first discovered, enough critical properties are known or hypothesized to be useful.
Fitting the TSI and temperature records to the resulting notch-delay solar model, we find that force X has between 10 and 20 times as much influence on surface temperatures as the direct heating effect of changes in TSI. This is enough to account for global warming, and is compatible with the earlier finding that CO2 caused less than 20% of the recent global warming.
There was a significant fall in TSI around 2004, suggesting a fall in force X and significant surface cooling from ~2017 (the current sunspot cycle is 13 years, 2004 + 13 = 2017). This prediction leads to a falsifiability condition on the notch-delay hypothesis.
We employ some ideas perhaps unfamiliar to many climate scientists, chiefly linear invariant systems and low-noise Fourier analysis. They are mainly relegated, along with nearly all the mathematical details, to supporting files:
- Systems, Sinusoids, the Fourier Transform, and Filters. Frequency-domain knowledge behind this series, explained from scratch, including linear invariant systems, sinusoids, the Fourier transform, simple low pass, delay and notch filters, transfer functions, and step responses. PDF.
- The Optimal Fourier Transform (OFT). The OFT is a low-noise version of the Fourier transform for time series, pioneered for this paper, which is superior to the standard Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) for finding signals in short, noisy datasets. PDF.
- climate.xlsm. Spreadsheet containing all the data and code.
Earlier Blog Series
When last we posted on the notch-delay solar theory (the project home page), we thought that there had been a mistake over the causality of notch filters. This has now been resolved. Some notch filters are causal (Bernie Hutchins was correct), but there are also non-causal notch filters (our methods and calculations were correct, but incomplete). A non-causal filter mandates a delay to make it causal, so when we mistakenly thought all notch filters were non-causal we used this as evidence of a delay. Now we simply rely on empirical evidence for establishing that there is a delay.
In retrospect, this mistake was a bit of a lucky accident. Thinking that there must be a delay caused us to look for supporting evidence, which turned up quite a bit.
Bottom line: A notch does not imply that there must be a delay, but the existence of non-causal notch filters requiring a delay suggest the possibility of a delay. In any case, several disparate observations by others point to a delay, so it seems there really is a delay.
Some technical details: The transfer function for a notch filter is the ratio of two quadratics in a complex frequency variable, each quadratic containing the square root of −1, which could be either +i or –i, where i is the imaginary number. The numerator and denominator of the transfer function could each separately use ±i, for a total of four possibilities. Two of those possibilities lead to a causal notch filter, two to a non-causal notch filter. As it happens I had used + in both cases, which led to a non-causal filter, and, not noticing the other three possibilities, I thought that a notch filter was necessarily non-causal — which would require the notch filter to be accompanied by a delay to make it causal and thus possible, necessitating a delay of at least several years between a change in TSI and the corresponding change in surface temperature on Earth. Now, with the complete picture of causal and non-causal notch filters, the mathematics does not require a delay. So the evidence for the delay now rests solely on several independent observations of the delay. The suspected wrap around problem with the FFT turned out to be insignificant — while imperfect, the approximation was extremely good. See the systems document for the gory details, or play with it in the spreadsheet.
* The Royal Society now talks about carbon dioxide only as causing the warming of the last 50 years, so we take the “recent decades” to mean since about 1970, so it includes the relatively fast warming of the 1970s – 90s. It probably is also applicable back to 1910, the turning point of Mann’s hockey stick, to include the 1910 to 1940 warming (though I imagine there really would have been a hotspot in the 1920s).
[1^] Christiansen, B., & Ljungqvist, F. C. (2012). The extra-tropical Northern Hemisphere temperature in the last two millennia: reconstructions of low-frequency variability. Climate of the Past, doi:10.5194/cp-8-765-2012.