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BIG NEWS Part VII — Hindcasting with the Solar Model

Posted By David Evans On June 24, 2014 @ 8:19 pm In Global Warming | Comments Disabled

The Solar Series: I Background   |  II: The notch filter  |  III: The delay  |  IV: A new solar force?  |  V: Modeling the escaping heat.  |  VI: The solar climate model   |  VII — Hindcasting (You are here)   | VIII — Predictions

All models are wrong, some are useful. That’s how all modelers speak (except perhaps some climate scientists).

The barriers to making a good climate model are many. The data is short, noisy, adjusted, and many factors are simultaneously at work, some not well described yet. Climate modeling is in its infancy, yet billions of dollars rests on the assumption that CO2 will cause catastrophic warming and the evidence that most recent warming was due to CO2 comes entirely out of models. It’s important to focus on the pea:

“No climate model that has used natural forcing only has reproduced the observed global mean warming trend” (IPCC 2007)

It is a crucial plank that modelers say “we can’t explain the current warming without CO2″. Current climate models assume that changes in solar radiation have a small immediate effect and solar magnetic fields have no significant effect on Earth’s temperature. They do not consider the possibility that a solar effect may occur with an 11 year delay (equivalent to one solar cycle), despite the independent studies that suggest this. These GCM models cannot use CO2 to predict modern temperatures without amplifying feedbacks, for which evidence is sparse or even contradictory. They don’t predict the pause, or the upper tropospheric temperatures, or the Medieval Warm Period.

The total climate model described below can reproduce graphs based on a CO2 model, such as one used by GISS, but it can also produce graphs using the solar model developed in these posts, or a mix of both CO2 and solar. (This is the point where the solar assumption is dropped and tested.) The point here is simply to see if there is a viable alternative model to the CO2 model. It appears there is, which is not to say it’s finished, or can’t be improved, or cannot be presented better, or tweaked.  At this stage it’s crude, but it exists.

There are 23 well funded ambitious global climate models that have been developed by international teams over the last 30 years, and a huge effort has been made by PR teams to make those models look good. The model below is one person’s work over 18 months with the aim of asking only, “is this possible” and “what can we learn?” The results are displayed with bare honesty and many caveats about how much (or how little) can be read out of them.

No model, much less one whose predictions have not been tested, is proof of any hypothesis. But they are sometimes good tools to tell us where to look. The notch-delay solar model is a viable alternative to the current CO2 models. It matches most major turning points of temperature (something CO2 models have struggled to do), and is used here back to 1770 — 100 years earlier than most. There’s a definite weak period with the 1950-1980 era where the atmospheric bomb test line resolves to have an improbably large effect. You might think the idea that nuclear tests cooled the planet in the 60′s and 70s is ridiculous. I certainly did. It’s something fans of CO2-theories have used to explain the cooling that Co2 based models can’t explain. Does it have legs? Hard to say, and worthy of a post on its own. But before you write it off, see  John Daly’s site which has an interesting discussion page that compares bombs to Pinatubo eruptions, and points out atomic bomb testing went on in the atmosphere, despite the 1963 test ban treaty, until 1980 (thanks to the Chinese and French).  Nuclear bombs contribute aerosol dust, but moreso, it’s radioactive too (a bit of a cosmic ray effect?). You might think it will rain out quickly, but bombs of 1Megaton reach up to the stratosphere above the clouds that rain. All up, 504 atmospheric nuclear explosions occurred between 1945 and 1980. A total of 440 MT were detonated (Fujii). It hangs around, C14 Radiocarbon levels in the atmosphere peaked in 1963 but the isotope stayed above natural levels for years – into the mid 1980s. (Edwards 2012). Fujii (2011) suggests atmospheric tests caused the “global stagnation“of that era and say it should be included in GCM’s. Maybe it isn’t as mad as it sounds?

The model has no aerosol component, which may or may not offset the cooling theoretically attributed to atmospheric bombs, nor does it have the Pacific Decadal Oscillation or Lunar cycles. The anomaly may be resolved if the model is expanded, or maybe it just means the delayed force from the sun is not the major driver — as we’ll explain in the next post, we’ll probably all have a good idea in a few years.

Solar TSI appears to be a leading indicator for some other (probably solar) effect, that we are calling “force X” for now. If that factor, quantified by TSI, was fed into current climate models, then those models would work with less forcing from CO2. Perhaps they would have produced better long term graphs, as well as fitting the recent pause and not requiring such a pronounced tropospheric hotspot. It might solve a lot of problems at once. Presumably projections of catastrophe would be subdued.

Lastly, compounding the many hindcast inaccuracies is the problem of inexplicable adjustments to temperatures (every skeptic will be wondering). It’s possible a model trained on raw temperatures curves (or older published datasets) may produce quite a different fit (which might be better or worse). For instance, if the land thermometer data from 1850 to 1978 exaggerates the general temperature rise then the solar model will be too sensitive — because it trained (or computed its parameters) on this data and “thinks” the TSI changes caused that amount of temperature change. Ultimately we won’t know for a few years whether it is right. (Bring on those independent audits please!)

The theory of the “delay” will be tested soon. It is falsifiable. We’re putting it out there for discussion. We have issued no press release, we aren’t selling a product (we’ll give it all away soon), nor do we demand your tax money. Judge it accordingly.

The bottom line is that modern climate models do not include any delayed force from the Sun.  Saying that models don’t work without CO2, and no natural factors can explain the modern warming, is and always was, a fallacy known as argument from ignorance.  — Jo


Dr David Evans, 24 June 2014, David Evans’ Notch-Delay Solar Theory and Model Home

In the previous posts we built the notch-delay solar model. Now we are going to test it.

The solar model is given the TSI record from 1749 (the start of monthly sunspot records), and it computes the corresponding temperature in each month from 1770 from just the TSI data for the current and previous months. Then we compare this “hindcast” with the measured temperatures. We also test the CO2 model to compare how it performs, and we test a mix of the CO2 and solar models to show that they play together well.

Finally, we look at the significance (or not) of the solar model so far.

1 Our total climate model

The total climate model* includes the notch-delay solar model, a standard CO2 model (two-compartments, with transient and equilibrium responses, computing temperature changes from the observed CO2 levels), a CFCs model (based on Lu 2013), and an atmospheric nuclear bomb tests model (based on the megatons exploded in the atmosphere, from UN reports). It can also apply all the forcings from the GISS model E, a mainstream climate model that released its forcings publicly in 2011—notably volcanoes, black carbon, snow albedo, and land use.

All these models can be switched on or off in any pattern within our total climate model. The total climate model has an optimizer to fit the model’s temperature output to measured temperatures, thus finding a set of optimal parameters. 

We use composite TSI and temperature records for the measured TSI and temperature, as in the previous post. The composite temperature was put together from the main temperature datasets, instrumental back to 1880 then increasingly reliant on proxies, mainly the huge proxy study by Christiansen and Ljungqvist in 2012. Similarly the composite TSI record was constructed out of the main TSI datasets, using measured data where possible.

2 What if CO2 was the main driver?

To show how our “total climate model” works, let’s first fit a CO2 model to the observed temperatures, assuming there is no delayed link between TSI and temperatures (that is, the mainstream assumption).

Let’s run the CO2 model with solar input as per the GISS model (that is, the immediate, direct effect of changes in TSI), with the volcanoes, black carbon, snow albedo and land use also from GISS, and the CFCs. The CO2 model was fitted to the measured temperatures and found to have an equilibrium climate sensitivity (ECS) of 3.4°C, agreeing with the IPCC’s central estimate of 3.3°C. The carbon dioxide theory fits the measured temperatures since 1800 fairly well in a very smoothed sense:


Figure 1: Total climate model without the solar model. It includes immediate warming due to changes in TSI as per the mainstream “GISS Model E” climate model. Thus, most of the warming must come from carbon dioxide. The estimated equilibrium climate sensitivity is 3.4°C, close to the central estimate of 3.3°C by the IPCC

The CO2 model produces a smooth increase in temperature, echoing the smoothly increasing CO2 concentration. Carbon dioxide by itself cannot begin to explain the jiggles in temperature on time scales from one to 10 years, so the carbon dioxide theory calls these jiggles “natural variability”—essentially meaning the bits they cannot explain.

3 What if solar effects were the main driver?

Now let’s run the notch-delay solar model, without any contribution from CO2 or CFCs. In other words, we are running the solar model under the solar assumption, that the recent global warming was associated almost entirely with solar radiation and had no dependence on CO2. As explained at the start of these posts, we set out to build a solar model that could account for the recent global warming under that assumption.

So, we are now testing the proposition that the recent global warming could have been mainly associated with TSI rather than CO2.

There is monthly TSI data from 1749, when the SIDC monthly sunspot records start—they are a decent proxy for TSI, and along with Lean’s yearly reconstruction of TSI from sunspots are the only components of the composite TSI from 1749 to 1882. The step response of the notch-delay solar model takes about 15+ years to fully respond, so the model takes 20 years or so to spin up, and we begin the simulation in 1770. (During the Maunder minimum, from about 1660 to 1705, there were almost no sunspots, so the solar model has no way of estimating force X. Thus it cannot really be expected to work before about 1720 at about the earliest.)

Each monthly temperature computed by the solar model is computed only from the TSI data for previous months and the current month. This is the only data input to the solar model. We then add temperature changes due to volcanoes and so on from the other models, to form the temperature record computed by the total climate model.

The solar model computes the temperature for a given month by adding together all the step responses of the TSI steps of the previous months (that is, by convolution). The change in TSI from one month to the next is a “step” in TSI, and the temperature response to that step is as shown in the step response of the solar model in Figure 4 of Post VI, appropriately scaled by the size of the monthly TSI step. Yes this method is a little slow and there are faster methods, but this way makes it clear that we are using the step response and previous TSI data only—and anyway computers are faster these days, and the data series here have only a few thousand points.

We previously found the parameters of the solar model by fitting the model’s computed temperatures to the observed temperatures (and simultaneously fitting the model’s transfer function to the empirical transfer function). Therefore, so long as the temperature record computed by the solar model basically has the right shape, then of course it is going to fit the measured temperatures reasonably well. The question of how well it does is mainly going to depend on whether the model predicts the right shape of temperature curve, such as getting the turning points about right, because the fitting is going to ensure that the computed temperatures match the measured temperatures in a general sense.

The notch-delay solar model fits the measured temperatures reasonably well:

Figure 2a: 1770 – 2013 Total climate model when driven only by solar radiation, with no warming due to carbon dioxide. The solar model output is not explicitly shown here because having three lines close together (solar model, climate model, and observed temperatures) is too confusing, but it can be inferred by subtracting the other constituent models from the total climate model.


Figure 2b: 1900 – 2013:  As for fig 2a, but for the last century.


The major temperature trends are all reconstructed, with major turning points about right, and the sizes of the reconstructed changes are roughly as observed. Therefore the notch-delay solar model could provide an entirely solar explanation for recent global warming, without any significant warming due to rising CO2 or CFC levels.

The solar model reproduces a lot of jiggles, but gets the timing of them wrong as often as not, especially further back in time. This might simply be due to the fairly uncertain nature of the TSI data, which is reconstructed from sunspot numbers. Sunspot numbers themselves are uncertain because standards of what counted as a sunspot have varied over the years. And, as indicated by the physical interpretation of the delay in Post IV, the delay presumably is not constant but instead it is probably the length of the prevailing sunspot cycle, which averages 11 years but varies from 8 to 14 years. The solar model here is using a constant delay of 11 years. It doesn’t take much timing error to put an up-jiggle where there should be a down-jiggle. So there is some hope that, with better solar radiation data in future from satellites and a more complicated model with variable delay (the subject of future research perhaps, if there is sufficient interest), the solar model could explain some portion of “natural variability”.

Over the period of better TSI data from 1610, the TSI was clearly at a maximum from about 1950 to 2000. However the temperature kept increasing during this period, even though TSI plateaued. The delay in the solar model is 11 years, which pushes back that plateau from 1960 to 2010, but that is not enough to explain why the total climate model reconstructs rising temperatures throughout this period when it is based on the solar model and omits the CO2 and CFC models. Here the output of the solar model is explicitly shown:


Figure 3: The solar model from 1900 as in Figure 2, but with the solar model output explicitly shown (in pink). From the 1950s through the 1990s (but mainly the 1960s), the solar model alone computes temperatures significantly warmer than actually occurred. In the total climate model this is counteracted by global cooling due to the atmospheric nuclear bomb tests, which put fine reflective dust into the atmosphere and apparently caused a mini-nuclear winter.


The answer found by curve fitting the total climate model to the observed temperatures is that global cooling caused by the atmospheric nuclear bomb tests may have counteracted the warming associated with the stronger TSI. This initially came as a great surprise to us, because the nuclear data had only been added as a bit of a joke and for completeness, but after a bit of research it started to look kind of plausible. The tests, conducted from 1945 to 1980 but mainly before 1963, put up fine dust that stayed high up in the atmosphere for years, reflecting sunlight back into space and lowering the incoming radiation [Fujii, 2011], and also dropping down radioactive nuclei that might seed clouds. Because the nuclear dust is in the stratosphere, there is no rain to wash it out. The required cooling from the tests is about 0.5°C at its peak in 1963, the year that the USA and the USSR agreed to discontinue atmospheric testing. (If the solar model is too sensitive because the warming of the  land thermometer records is exaggerated, then less cooling is required.)

While this is only an answer found by numerically piecing together the test yield data with the output of the solar model and the observed temperatures, it fits. Maybe the nuclear winter hypothesis is partly correct. We feel it is likely to overestimate the effect.

Alternative causes for a cooling influence during the 1950s to 1990s could be pollutant aerosols and/or whatever caused global dimming, or even the Pacific Decadal Oscillation (PDO). With no data that quantifies their effects, the total climate model only had the nuclear bomb yield data to work with, but it is remarkable that the piece that fits the puzzle quite well is the atmospheric nuclear bomb test data.

4 Mix of CO2 and solar

There are now two solutions to the climate question:

  • If we assume global warming is mainly due to CO2 then we get the CO2 theory, and it fits the measured temperatures from 1800 (though not before).
  • If we assume that global warming is mainly associated with changes in TSI then we get the notch-delay solar model, which also fits the measured temperatures from 1800.

Obviously both assumptions cannot be true, but it may be that the true solution is a mix of both models—such as 40% of one model and 60% of the other. If both solutions fit the measured temperatures on their own, then any linear mix will also fit the data. Here is an example:


Figure 4: Total climate model when driven by a mix of solar radiation and carbon dioxide. The temperature changes computed by the solar model were multiplied by the solar factor of 70%, then the CO2 and other models were fitted. This mix was arbitrarily selected for illustration; do not read any significance into it.


This illustrates that the CO2 and solar models play together nicely. Assuming the climate system is linear for the small perturbations of the last few hundred years, the two solutions can operate almost independently and their temperature changes add (that is, they superpose).

If the optimizer is given both the CO2 and solar models to work with, it finds a solution that is mainly the CO2 solution and only a little of the solar solution. However this is only because the jiggles in the solar solution are wrong as often as not (Figure 2), which the optimizer finds worse than simply ignoring the jiggles and getting them right on average (Figure 1). So there doesn’t appear to be any significance in this, and we will have to find other means of determining the true balance between the CO2 and solar solutions.

5 Significance of the solar model

We have developed a solar model that accounts for the recent global warming, if that warming was almost entirely associated with solar radiation and had no dependence on carbon dioxide.

This is a viable solution to global warming, because:

  • It’s quantifiable, with a model that approximately hindcasts the observed temperatures. It is not just a concept with handwaving, or a rough one-off computation.
  • It’s got physical interpretations for all the parts. This is a physical model, not just curve fitting or an unexplained correlation.

In short, we have demonstrated that the global warming of the last two centuries could have been mainly associated with TSI rather than CO2. This overcomes one of the bedrock beliefs of anthropogenic global warming, namely that the recent global warming could not plausibly be due to anything other than CO2.

The most important element of the solar model is the delay, which is most likely 11 years (but definitely between 10 and 20 years). The delay was found here as a necessary consequence of the observed notch, but it has been independently corroborated to varying degrees several times over the last decade, apparently without its significance being noticed.

A major objection to substantial solar influence is the finding of Lockwood & Froehlich in 2007, who showed that four solar indicators including TSI peaked in about 1986 then declined slightly. However temperature continued rising for several years after 1986. This has been widely interpreted to mean the recent warming cannot have been due to the Sun. However, the delay can explain this: 1986 + 11 = 1997, about when global warming ended. Thus the delay overcomes another of the bedrock beliefs of anthropogenic global warming.

Conversely, without the delay, the objection of Lockwood and Froehlich appears solid and it is hard to see how a substantial solar influence is possible.

The weakest points of the notch-delay solar theory are:

  • The assumption of sufficient linearity of the climate system,
  • The need for the nuclear winter hypothesis to counteract the early part of the TSI plateau from 1950 to 2000, especially the 1960s.
  • The inability to precisely identify force X (see Post IV).

Some may challenge the discovery of the notch, but the notch implies a delay and the delay receives support from several independent findings.

What we have not shown so far in these posts is that the notch-delay solar model is true, or to what extent it is true. There is nothing in the posts so far to support the assumption that the recent global warming was almost entirely or even partly associated with solar radiation. On the material presented so far, the CO2 and solar solutions are both viable and no reasons have been given to suppose that either one is more influential.

The notch-delay theory provides a second, alternative solution to the climate problem, with a physical model and a plausible interpretation. No longer is climate a “one horse race”, where you are limited to either supporting the CO2 theory or focusing on its deficiencies. We are now in a “two horse race” (though one horse is very new to the world and not fully introduced or fleshed out yet).

Regular readers of this blog are well aware that the CO2 solution has a lot of problems. Soon we will be turning to the second part of this series, where we will look at reasons for believing that the solar model is dominant and the CO2 solution is only a small part of the overall solution.

In the next post on this topic, we will use the notch-delay solar model for forecasting. This is where it gets interesting.

Notch-delay solar project home page, including links to all the articles on this blog, with summaries.


* Our climate model is in a spreadsheet that we will be releasing shortly. We chose to do all the work for this project, right from the beginning, in a single Microsoft Excel spreadsheet for pc. It’s not the fanciest or the fastest, but an Excel spreadsheet is the most ubiquitous and one of the friendlier programming environments. It runs on most computers (any pc with Excel 2007 or later, maybe on Macs with Excel 2011 or later), can hold all the data, makes nice graphs, and all in a single file. The models use VBA code, a form of the basic programming language that is part of Microsoft Office. The spreadsheet is professionally presented, and you press buttons on the sheets to make models run and so on. You can inspect and run or step through the code; it will be all totally open. Thank you for your patience, but giving away the spreadsheet early would preempt the blog posts and disrupt a focused discussion.



IPCC, Assessment Report 4, 2007, Working Group 1 Understanding and Attributing Climate Change, Chapter 9. Executive Summary. [IPCC site] Page 665

Edwards (2012)  Entangled histories: Climate science and nuclear weapons research, The Bulletin of Atomic Scientists,

Fujii, Y. (2011). The role of atmospheric nuclear explosions on the stagnation of global warming in the mid 20th century. Journal of Atmospheric and Solar-Terrestrial Physics, Volume 73, Issues 5-6, April 2011, Pages 643-652. [PDF]

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.

Lockwood, M., & Froehlich, C. (2008). Different reconstructions of the total solar irradiance variation and dependence on response time scale. Proceedings of the Royal Society, 464, 1367-1385.

Lu, Q. (2013). Cosmic-Ray-Driven Reaction and Greenhouse Effect of Halogenated Molecules: Culprits for Atmospheric Ozone Depletion and Global Climate Change. International Journal of Modern Physics B, 27.

Pinker, R. T., Zhang, B., & Dutton, E. G. (2005). Do Satellites Detect Trends in Surface Solar Radiation? Science, Vol. 38, 6 May 2005, 850 – 854.

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