The Missing Link In Climate Modeling—The Maunder Minimum Has An Impact

A general view of the U.S. Department of Energy in Washington, DC.

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The recent Department of Energy Report, A Critical Review of Impacts of Greenhouse Gas Emissions on the U.S. Climate, has created quite a stir in pointing out uncertainties in the science of global warming and climate change.

One item of the report is labeled: “Moreover, solar activity’s contribution to the late 20th century warming might be underestimated [Section 8.3.1].” The DOE authors say that the total solar irradiance, TSI, or it’s effects, have been suppressed in climate modeling of earth’s temperature rise, by comparison with greenhouse gases (GHG). Our initial assessment tended to agree, but a deeper analysis was needed. This report provides that.

Why is this important to the oil and gas industry? Because if solar activity is causing some of earth’s global warming, this could mean less is caused by GHG. Since the oil and gas industry is responsible for about 50% of worldwide GHG emissions, the industry would be less culpable for earth’s temperature rise. Let’s look into this.

The Maunder Minimum.

If there’s one single data point that conveys a strong message that the sun is involved in earth’s temperature over decades, it’s the Maunder Minimum. During my PhD studies on solar radiation, I learned that during the Maunder Minimum, about 1700 A.D., the earth was in a deep freeze. Scenes were painted of people skating on the River Thames, for example. The surprise is that there were no sunspots recorded for several decades at this time. Sunspots are a sign of the sun’s magnetic activity. Fewer sunspots means less activity, and lower radiation from the sun, called TSI (total solar irradiance). Hence lower temperature at earth. In climate topics it’s called solar forcing of earth’s temperature and global warming.

A history of glacier retreats has been compiled over the last 3,500 years for the largest glacier in the Alps (the Aletsch glacier). Major retreats (3 km) began at 700, 1400 and 1900 years, and the retreats all corresponded to periods of increasing solar activity and therefore a warming earth. The authors concluded, “The climate has always changed and will continue to do so in the future. As a consequence, the predictions of the impact caused by anthropogenic activities on future climate change must allow for the natural [solar]

variability.… Even though the increase in greenhouse gases is going to be the dominant factor in climate forcing during the coming decades, natural forcing will continue to play a role.”

The authors have also used radioisotope data, from ice cores for instance, as a proxy for the magnetic field in the heliosphere (the extended magnetic field of the sun). The magnetic profile correlates well with the sun’s activity during the years 1600 – 2000, and matches reasonably well earth’s temperature.

Earth Temperature And Proxy By Loehle.

A plot of earth’s temperature, published by Loehle in 2007, was obtained by averaging 18 separate temperature series over 2,000 years. The series were mostly based on lake sediments and ice cores. Essentially, these 18 series have no tree-ring data, which can be affected by precipitation as well as temperature, and are therefore less reliable. The author also criticized a method of averaging results that washed out other temperature features, such as the medieval warming period. This medieval period does not appear in the famous hockey-stick profile that was previously used to justify global warming by man-made GHG emissions. In 2008, some minor corrections were made by Loehle to the data and the corrected plot is shown by Figure 1. This temperature profile will form the basis of correlations we explore with various TSI proxies.

Total Solar Irradiance, TSI, And Its Proxies.

Solar irradiance is the amount of power that falls on the surface of the earth, measured in watts per square meter (W/m²). The simplest proxy for TSI is the sunspot number, which does trend with earth’s temperature. One bookend for this was the Maunder Minimum between 1660 and 1700 when there were no sunspots. This bookend is a recent cornerstone when seeking a correlation between TSI and earth’s temperature.

But there exists a second bookend: the Modern Maximum, when around the years 1950-1970 sunspot counts reached a maximum. Since 1700, over a period of about 300 years, earth’s temperature has increased by 0.75℃ (Figure 1).

Note: the sunspot counts go through an 11-year cycle from minimum to maximum then back to minimum again. This is not of concern here. What is of concern is the trend in the average of the 11-year sunspot cycles, as shown in Figures 1 and 2.

TSI reconstructions have been derived from sunspot numbers in different studies since 1995. A study by Coddington (2024) was based on normalizing sunspot data to the latest CDR model from NOAA which reproduces variations in space-based observations since 1978. But this TSI cannot match both bookends of Figure 2, without upscaling.

In Figure 2, the TSI from Coddington has been upscaled to match both bookends: the Maunder Minimum at about 1700 and the Modern Maximum around 1970. However, the overall scaling stretches the TSI from a range of less than 1 W/m² to almost 3 W/m². And this has always been a problem because spacecraft observations support the smaller number, and no mechanism for amplifying the solar irradiance has been proven.

If the data are normalized to both bookends of Figure 2, the hills and valleys in between do reveal significant correlation. The tracking isn’t perfect but it reinforces substantial solar influence—that solar forcing is the dominant mechanism for global warming of 0.75℃ from 1700 – 1950.

Our position is if the head looks like a duck, and the tail looks like a duck, then the body feathers look like a duck also. The body feathers in Figure 2 are the hills and valleys between Maunder Minimum and Modern Maximum. But if all these features indicate solar forcing of earth’s temperature, the search must continue for a mechanism that amplifies the TSI.

One other study of TSI upscaling has been done by Ammann (2007) who shows how sensitive the earth’s temperature is to solar forcing. The approach is to model three different TSI scalings in a sophisticated climate model to try to match earth’s temperature. The medium scaling applied to TSI predicts earth’s temperature of Figure 2 quite well. It predicts a range of -0.7℃ to +0.2℃ from Maunder Minimum to the Modern Maximum. For this medium scaling, GHG forcing clicks in at 1920. GHG forcing is needed after the period 1920-1950.

The two bookends in Figure 2 represent a global warming of ~0.75℃ between 1700 and 1970, and the major cause is solar forcing. It appears that IPCC 6 focuses on temperature after 1750 using a low-variability TSI model that ignored the Maunder Minimum around 1700. This data exclusion is a huge bias because it neglects the Maunder Minimum which is a cornerstone of solar influence.

To include the missing Maunder Minimum requires an upscaled TSI, as shown in the review by Connelly’s Figure 16, (a), (b) and (d). There, matching of rural and ocean temperatures in the period 1841-2017 showed solar forcing to be the major component (100% in 2/3 cases).

Forcing By GHG Emissions.

Figure 3 shows that global GHG emissions grow slowly until 1950 then accelerate all the way to 2017. The GHG emissions at 1950 are only about a seventh, or 14%, of their peak, which supports that solar forcing, not GHG forcing, is dominant from 1700 to 1950.

By 1950, Coddington’s TSI in Figure 2 seems to have peaked, but this is when GHG emissions rocket upwards, which strengthens the case that GHG forcing of global warming quickly becomes dominant. Other studies support this position. Olilla (2017) models temperature increase by a semi-empirical model that gives the following results. In the period 1700-1800: TSI = 99.5%, GHG = 4.6%. In 1800-1900: TSI = 70.6%, GHG = 21.5%. In 1900-2000: TSI = 72.5%, GHG = 30.4%. In this modeling, TSI is the major forcing of temperature from 1700 to 2000.

Ways To Amplify Solar Irradiance.

This is where it gets complicated. As summarized by the DOE Report, “Scientists have searched… but first a calculation of TSI at the earth has to be found that will cause enough forcing of temperature. Two camps have emerged: one that says TSI is almost negligible in its effect on earth’s temperature, and the other says the opposite.” The argument of the previous section above was that TSI is critical, because between 1700 and 1950 earth’s temperature rose by 0.75℃ (Figure 1) when GHG emissions were non-existent (or very low in the years 1900-1950).

However, in the study by Coddington the TSI range was only 0.7 W/m² over the period 1700-2000. This is about a fourth of what is needed to modulate earth’s temperature in the match of Figure 2. It appears that some additional mechanism is needed to amplify the TSI.

A bigger picture looks at how the sun’s activity affects other variables that impact earth. One is the solar modulation of glacier retreats, described above. These have been discovered hundreds of years ago, before any industrial CO2 appeared.

A second one is the interplanetary magnetic field (IMF) which comes from the sun and stretches way past the outermost planets. A third is galactic cosmic rays (GCR) which stream into interplanetary space from outside the heliosphere. These two variables are clearly modulated by the sun’s activity, meaning sunspots. It seems possible that they could also affect the earth’s temperature.

In the second case, the IMF is carried outwards by the solar wind and bumps into the magnetic field of the earth as the solar wind is diverted around it. One extreme of amplified solar influence is when a coronal mass ejection (CME) starts as a large explosion at the sun then a couple days later collides with earth, causing aurorae and disrupting radio communications and other technology devices.

In the third case, GCR particles that collide with particles in the earth’s atmosphere induce electrical charges which nucleate clouds. When the IMF increases because sunspots increase, GCRs recorded at earth decrease because more of them are reflected backwards by a higher magnetic field. Fewer GCRs penetrating to earth’s atmosphere would mean fewer clouds to reflect heat and thus more global warming.

The third case was explored by Ollila (2017). His theoretical calculation of earth’s temperature increase from 1700 using low TSI values (such as Coddington) would be only 0.12℃, while the inferred increase was 0.75℃ in Figure 1. To get around this, Ollilo proposed the temperature increase was amplified by a decrease in GCRs reaching the atmosphere. He argued that a temperature rise of 0.50°C could be caused by a direct TSI increase of 0.12°C added to a cloudiness decrease of only 2.7% which would boost earth’s temperature by 0.38°C.

The effect of GCRs on temperature is controversial, and we don’t dissect that here. But the solar modulation of glacier retreats, IMF, and GCRs is definitive. Whether a causative link between these and earth’s temperature exists seems to remain an open question.

Conclusion.

In this article, a plot of earth’s temperature, published in 2007, is obtained from averaging 18 different proxy series over 2,000 years. This simplifies the review of Connelly, where a much broader range of temperature proxies dilutes some conclusions. The analysis here honors the Maunder Minimum and Modern Maximum by scaling up the low-variability TSI of Coddington, similar to the approach of Ammann. Between these two bookends, the model replicates peaks and valleys which support the dominant solar influence in 1700 – 1950 that causes a global warming of 0.75℃.

However, the overall upscaling stretches the TSI from a range of less than 1 W/m² to almost 3 W/m². This has always been a problem because spacecraft observations support the smaller number, and no mechanism for amplifying the solar irradiance has been proven. Still, using an upscaled model will add credibility to climate change predictions if solar forcing changes significantly in the century ahead. Meanwhile, the search for a mechanism that amplifies the TSI effect will continue.

It appears that IPCC 6 focuses on temperature after 1750 using a low-variability TSI model that ignores the Maunder Minimum around 1700. This data exclusion is a huge bias because it neglects the Maunder Minimum which is a cornerstone of solar influence.

According to the upscaled TSI model, solar forcing is dominant from 1700 to 1950 when the temperature increases by about 0.7℃. After this, GHG forcing becomes dominant but solar forcing cannot be neglected. This is why the DOE Report claimed that sun’s contribution to global warming might be underestimated. For example, if sunspot numbers stay constant until 2050, an increase in earth temperature will reflect GHG forcing. But if sunspot numbers and TSI fall, GHG effects will be larger than that measured by earth temperature rise.

However, if sunspot numbers and TSI rise, GHG effects will be smaller than measured earth temperature rise. In this case, the oil and gas industry, which is responsible for about 50% of worldwide GHG emissions, would be less culpable in the matter of global warming.

Clearly, these adjustments, minor or large, will be important to know how to deal with climate change in the coming decades. For example, Coddington predicts in the years 2030–2100 that TSI will be about 70% greater than current values (using a basis of zero at the Maunder Minimum). This equates to ~3.3℃ of temp rise that would not be caused by GHG.

The DOE Report on GHG is correct—solar forcing is underestimated in IPCC modeling. An upscaled TSI model needs to be used to honor the Maunder Minimum. But more research is needed to find out what scales up TSI. Glacier retreats are indirect evidence for solar modulation of earth’s temperature. The well-established solar modulation of interplanetary magnetic field and galactic cosmic rays, both of which do affect the earth’s electromagnetic field, keep these open as possible causes of solar modulation of earth’s temperature.