|

June 13, 2021

Millennium analysis: sun shows a long lasting perfect correlation with temperature and transient climate sensitivity CO2 (1.08 °C) is just below the IPCC bandwidth

Martijn van Mensvoort

The sun provides 99.97% of all energy that powers the Earth's climate system. The isotope carbon-14 [¹⁴C] is known as a proxy for Solar magnetic activity. For the period 910-1950, the 378-year average for ¹⁴C shows a particularly high correlation with global temperature: 0.994, with 98.8% of temperature variance explained by ¹⁴C. Taking into account the influence of volcanic activity, the climate sensitivity to a doubling of CO2 shows a value of 1.08 °C. This value is just below the range of 1.2-2.4 °C for the transient climate sensitivity [TCS] described by the IPCC in its most recent comprehensive climate report (AR5, 2013) based on CMIP5 climate models with an estimated range of 5-95%. For the energy transition is the TCS of greater importance than the equilibrium climate sensitivity [ECS]; the IPCC describes a bandwidth of 1.5-4.5 °C for this (which relates to a period of at least a few hundred and possibly even thousands of years). Finally, long-term mean values show that ¹⁴C exhibits a consistent picture with datasets for total solar irradiance. Logically, this means that ¹⁴C serves as a proxy for both the Sun's magnetic activity and total solar irradiance.

The climate system is characterized by natural variability and is accompanied by non-linear relationships and chaos [Rial et al., 2004]. Therefore, making specific reliable predictions is impossible. In 2001, the IPCC described this as follows: "The climate system is a coupled non-linear chaotic system, and therefore the long-term prediction of future exact climate states is not possible." (citation source: IPCC TAR3 2001, p.215). Nonlinear relationships and chaos also play a role in the complex of cycles found at the sun. This explains why the magnitude of fluctuations in solar activity is also hard to predict. The past does show that solar activity plays a role in the development of volcanic activity via non-linear relationships. This relationship is particularly visible within long-term perspectives, whereby the highest volcanic activity is found during prolonged periods of low solar activity (grand solar minima) and vice versa. [Steinhilber & Beer, 2011]. However, the analysis presented in the most recent comprehensive IPCC climate report does not take into account the influence of the sun via non-linear relationships within the climate system [Dudok de Wit et al., 2016]. Nevertheless, the IPCC report does recognize that non-linear relationships and chaos limit the predictive value of climate models for both temperature and precipitation; this applies to both annual average values and decadal values [IPCC AR5 2013].

There is a strong parallel between on the one side prolonged periods of respectively high and low solar activity and on the other side prolonged periods of warming (including the medieval climate anomaly) and cooling (such as the Little Ice Age) [Feuler, 2013]. For studying the sun's influence on climate over the past millennium, we rely largely on proxies; the radioactive isotope ¹⁴C is the main proxy available for this purpose [Usoskin et al., 2021]. However, IPCC AR5 ignores the strong (non-linear) parallels between ¹⁴C and global temperature.

An analysis is presented here which explains the evolution of global temperature (dataset: 2 Degrees Institute; from 1880 onwards this involves NASA's GISTEMP v4) over the past millennium by means of 3 factors: (1) solar activity represented by ¹⁴C (dataset: Damon & Sonnett, 1991), combined with: (2) volcanic activity (datasets: ICI global AOD before 1850 and NASA AOD starting from 1850) and (3) CO2 (dataset: 2 Degrees Institute).
The ¹⁴C dataset describes data for the period 910-1950 because in the period 1955-1960 the concentration in the atmosphere was disturbed due to atomic bomb experiments [Muscheler et al., 2016]. This is also the main reason why the analysis here focuses primarily on the period 910 up to and including 1950. There is a favorable side effect in this approach which involves the logical assumption that for the period up to 1950 the impact of anthropogenic influences on the climate system was relatively small. This combination of factors makes the period up to 1950 ideal for studying the influence of the sun [de Jager et al., 2006].

Long-term perspective shows strong relationship between sun and temperature

Figure 1 shows the result of a regression analysis focused on the values of the 378-year moving average; the residue (red curve) shows the narrowest bandwidth at this time span with a magnitude of slightly less than 0.04 °C, with 99.4% of the variance in temperature being explained by the combination of ¹⁴C, volcanism and CO2. The regression formula for the values of the 378-year moving average is as follows:

Temperature = 0,003874xCO2 - 0,01943x¹⁴C - 11,01xAOD - 1,302

With average values over shorter and longer periods than 378 years, the residual has a larger bandwidth (+ often featured with a trend in the model which does not run parallel to the temperature for the most recent period, but for the 378-year moving average they do run parallel). Figure 1 also shows the values for the 10-year moving average for the purpose of reference (shown with scaling ratios based on the 378-year moving average).

---

Figure 1: Global temperature development during the past millennium (period 910-1950) is explained almost completely (99.4%) by the variation in the solar activity [¹⁴C] in combination with volcanic activity (AOD = Aerosol Optical Depth) and CO2 based on the 378-year moving average. 98.8% of the variance in temperature is here explained by the sun based on a correlation of 0.994 between ¹⁴C and the temperature. The regression result shows a picture that is representative for the period from the year 1089 to 1761. The evolution of the values of the 10-year moving average is included for the purpose of reference (From a fundamental point of view: it is also important that in 2020, according to the NOAA AGGI, CO2 can be held responsible for approximately 2/3 of the impact of all greenhouse gases together).

---

Figure 1 shows that the temperature between 1089 and 1761 shows a development in which the long-term influence of the sun on the basis of ¹⁴C is followed almost exactly. Between 1100 and 1600 both factors show a gradual decline with the long-term average showing much the same movement; the 10-year average shows a picture showing that in the short-term perspective a non-linear relationship between the two factors is found that lasts until the end of the ¹⁴C dataset in the year 1950 From about the year 1600 the sun shows the beginning of an upward movement which only becomes clearly visible with the temperature later. Both factors show a course that is more or less parallel. The temperature lags (slight) the sun during the period when the two highest levels of volcanic activity of the past millennium are reached; dit heeft betrekking op respectievelijk de beginfase van het Spörer Minimum en de beginfase van het Dalton Minimum.

When the influence of the sun (via ¹⁴C) is not taken into account, the combination of volcanism and CO2 produces a regression result with an explained variance of 79.9% (bandwidth residue: ~0.35 °C), which is considerably lower compared to the explained variance of 99.4% (bandwidth residual: ~0.04 °C) for the combination of the 3 factors. Moreover, the influence of the sun (without volcanism & CO2) shows an explained temperature variance of no less than 98.8% for this perspective.

Climate sensitivity to a doubling of CO2 is low

For CO2, the 378-year moving average reaches its lowest value in 1593 (279.03187 ppm) and its highest value up to that point in 1761 (283.65084 ppm). Based on the scale ratios in Figure 1, this implies a temperature increase of 0.017894 °C between 1593 and 1761, which translates into a climate sensitivity of 1.080 °C [= 0.017894/((283.65084/279.03187)-1)] for a doubling of CO2. This value is indicative of the transient climate sensitivity [TCR], which represents the increase in temperature once the value of CO2 has doubled compared to pre-industrial values.

For example, to check, climate sensitivity can also be calculated using the 10-year moving average - with the caveat that this approach will logically produce a less reliable result compared with the 378-year average approach. For the 10-year moving average of CO2, based on the scale ratios in figure 1, the period between 1750 (277.04 ppm) and the most recent 10-year average in the year 2015 (402.832 ppm) shows a temperature difference of 0.487328 °C, which corresponds to a climate sensitivity of 1.073 °C [= 0.487328/((402.832/277.04)-1)]. And the CO2 annual values for the year 2020 (414.24 ppm) and the year 1750 (277 ppm) show a temperature difference of 0.531679 °C, which indicates a climate sensitivity of 1.073 °C [= 0.531679/((414.24/277)-1)]. Both control calculations produce a result that differs only a few thousandths of a degree Celsius from the result of the calculation based on the 378-year moving average.

¹⁴C vormt proxy voor totale zonnestraling

Cosmic rays are primarily responsible for the production of ¹⁴C in the Earth's atmosphere. The sun also plays a role in this via solar wind: more solar wind ensures that less cosmic radiation can reach the earth and vice versa. This explains why the isotope ¹⁴C is known as a proxy for solar activity. ¹⁴C is also used in reconstructions for total solar radiation [Connolly et al., 2021]. Figure 2 confirms the relationship between ¹⁴C and total solar irradiance based on 280-year moving average values; ¹⁴C shows a strong overlap with the NRLTSI2 dataset for total solar radiation. The overlap between the two factors covers a period of 66 years and is part of an upward dynamic oscillating pattern. For the period 1749-1815, a remarkably strong correlation is found between ¹⁴C and the NRLTSI2 with a value of 0.997. Based on the scale ratios in figure 1, figure 2 results in an associated Lambda (λ) with a value of 0.637 °C per W/m2, which represents a measure of the solar sensitivity of the climate. Other datasets for total solar radiation also show that the long-term average exhibits a dynamic which is in line with ¹⁴C; for example, the 343-year mean in both the SATIRE SandT dataset and the LISIRD dataset shows each a development with a dynamic that harmoniously matches the course of ¹⁴C.

---

Figure 2: The 280-year moving average shows a strong overlap between ¹⁴C and the NRLTSI2 total solar irradiance dataset; the correlation is particularly high with a value of 0.997. Based on the scale ratios in figure 1, a Lambda (λ) is found with a value of 0.637 °C per W/m2; this concerns a measure of the solar sensitivity of the climate. The temperature and ¹⁴C show a correlation with a value of 0.982 for the 66-year period 1749-1815; for the same period, the temperature and the NRLTSI2 show a correlation with a value of 0.979.

---

The Earth's magnetic field also influences the production of ¹⁴C

Since 1700, the activity of the sun has been directly monitored through observation of sunspots, which represents one of the components for determining the total solar irradiance [=TSI]. For the period up to 1700 we depend on proxies such as ¹⁴C when studying the activity of the sun. However, the changing magnetic field of the earth creates a complication because it inhibits the production of ¹⁴C.
Only very recently a first reconstruction was presented based on ¹⁴C for solar activity during the past millennium, the corresponding data reaches back to the year 971 [Usoskin et al., 2021]. The researchers also took into account the inhibiting influence of the Earth's magnetic field on ¹⁴C production. The impact of geomagnetism has increased steadily, especially in the second half of the past millennium. Logically, this means that it must be taken into account that the influence of geomagnetism causes an underestimation of the more recent activity of the sun (based on ¹⁴C values) compared to the 1st half of the past millennium. At the solar maxima, this effect increases to an impact at the order of a few percent at most; however, at the solar minima this effect is considerably larger because the impact is at the order of 20%. On a net basis, the influence of geomagnetism thus creates an effect in which the underestimation of the impact of the sun around the beginning of the 19th century (based on 10-year average values) has increased to approximately 10% compared to the values at the beginning of the millennium.
Figure 1 does not take into account the influence of geomagnetism. Since geomagnetism has a very limited influence on the dynamics observed with the production of ¹⁴C over the last millennium, this effect logically also has a limited impact on the particularly strong relationship described for ¹⁴C and the temperature based on the values of the 378-year moving average. When this effect is taken into account, the solar activity in the course of the second half of the millennium will show a slightly stronger upward trend than is described in figure 1. From the perspective of the temperature, this difference will have an impact of at most a few hundredths of a degree Celsius.
However, a correction for geomagnetism will have an impact with the bottom of solar activity shifting towards the Spörer Minimum; for the perspective of figure 1, this specific point therefore creates a clear reinforcement for the parallel with the temperature in the perspective of the 10-year moving average. The impact of a correction for the influence of geomagnetism on the ¹⁴C production could therefore potentially have a small net impact on the proportions of the climate model described in figure 1.

In the past millennium until the end of the 1970s, the sun was the dominant factor for temperature

IPCC AR5 FAQ 10.1, figure 1 shows an image that suggests that at the earliest only starting from the 1960s onwards, a temperature development became manifest that cannot be explained on the basis of natural variability (sun + volcanism). This image is more explicitly described in the work of a group of 60 solar experts published in 2016; the book 'Earth's climate response to a changing sun' describes this as follows: "Fig 1 in Box 4.1 demonstrates that natural forcing only (solar + volcanic) cannot explain the warming trend in global temperature over the last 50 years." [Dudok de Wit et al., 2016]

Figure 1 shows the 10-year moving average which confirms that the temperature development up to 1950 was clearly more or less parallel with the activity of the sun via a non-linear relationship. Nonlinear relationships can manifest through phase differences with a length several decades [de Jager et al., 2021]. Within the perspective of the 10-year moving average, the influence of the sun in 1950 reaches a value that is clearly still relatively high in relation to the development of the temperature; moreover, one can notice that around 1950 the temperature was still well over 0.1 °C lower than various peak levels reached during the medieval climate anomaly.

Figure 1 and figure 2 combined shows a development in which the temperature only shows a development from the late 1970s that is clearly not explained by the sun, nor by the sun in combination with volcanism. During the final quarter of the 20th century the 10-year moving average shows a strong parallel with CO2; however, figure 1 shows that CO2 cannot fully explain the increase in temperature. This can partly be explained by the fact that the increase in radiative forcing due to CO2 now accounts for approximately 2/3 of the influence of all greenhouse gases together. In addition to the influence of the increase in other greenhouse gases, other anthropogenic factors also started playing a significant role in the climate system over the course of the 20th century, such as: the influence of air pollution (cleaner air has contributed to global warming since the late 1980s, especially in Europe and other Western countries), the use of land (urbanization often causes extra warming locally [Connolly et al., 2021]) and the problem of ozone layer depletion became manifest since the late 1970s.

Logically, this means that a more complex situation arose in the period after 1950; Nuclear weapons have been used in wars since 1945 and it is not clear whether these contributed to the decades in the mid-20th century when a clear pattern of global cooling is seen. This involves the period between the early 1940s and the late 1970s. Solar activity probably peaked in the late 1950s, although several TSI data sets show peak solar activity only around the end of the 20th century [Connolly et al., 2021]. This implicates that the strength of the analysis in figure 1 is partly related to the fact that the analysis is based on data that does not extend beyond the 1950s, when the situation was less complex than during the following decades.

Finally, the Earth's temperature history as shown in figure 1 based on the 378-year moving average is easily recognized in both the perspective for the current Holocene for the past 10,700 years as shown in Figure 3 and the Earth's temperature history over the last 500 million years (a similar graph for CO2 is available HERE). The near-perfect correlation between ¹⁴C and global temperature displayed in figure 1 as well as the period of overlap in figure 2 (where very strong correlations are found between temperature, ¹⁴C and the total solar radiation among themselves) is indicative for both the impact and the relevance of the sun in the temperature development of the earth. The climate sensitivity of CO2 shows a low value (1.08 °C) which points in the direction of a negative amplification of anthropogenic influences in the atmosphere because the theoretical value for the impact of CO2 without amplification is even a fraction higher with a value of 1.1 °C [Schwartz, 2008]. The perspective of the 10-year moving average in figure 1 makes it easy to understand why the relatively large influence of the sun hardly leaves space for the existence of a strong amplification in relation to a doubling of CO2. Assumptions aimed at nihilizing the influence of the sun appear necessary to support speculations aimed at the existence of a strong amplification for the influence of CO2. Indicative for the relevance of the sun within the climate system is the fact that it is responsible for 99.97% of the earth's energy budget [Nurtaev, 2016]; fluctuations in the output of the sun at the order of 0.1% have a relatively large numerical impact compared to the influence of other factors.

CarbonBrief & the IPCC underestimate the impact of the sun and overestimate the impact of CO2

An analysis presented by CarbonBrief (december 2017) shows implicit a transition climate sensitivity of 2.11 °C for a doubling of CO2 (assuming that according to the NOAA AGGI in 2017 the temperature impact of the increase in CO2 amounted to 65.77% of the total impact of all greenhouse gases combined). The CarbonBrief analysis assumes that the influence of the sun has been more or less nil since 1850 with an impact value of +0.0018 °C; however, this does not take into account the existence of non-linear relationships inside the climate system.

CarbonBrief's description is at the high end of the 1.2-2.4 °C bandwidth the IPCC describes in AR5 (2013) for transition climate sensitivity based on an estimated range of 5-95%; the 23 CMIP5 models collectively describe a TCR bandwidth of 1.1-2.5 °C (see: figure9.42, page 817 in AR5).
For the energy transition, the TCR is considerably more important than the equilibrium climate sensitivity [ECS], for which a bandwidth of 1.5-4.5 °C is described, which relates to the climate sensitivity to a doubling of CO2 once it has reached the equilibrium state - this probably takes hundreds or even thousands of years because the ocean system reacts very slowly to changes within the climate system (for example, at the bottom of the ocean system cycles are found with a duration of the order of 2000 years).
The IPCC implicitly assumes that the sun has been responsible for about ~2% of the increase in radiative forcing that has occurred since 1750 [IPCC, 2013].

The analyzes of both CarbonBrief and the IPCC are based on a relatively short period of time, for which the calculations do not account for the influence of the existence of non-linear relationships within the climate system. Nor is there any awareness of the fact that the sun (whether or not combined with volcanism) has long been the determining factor in the course of the temperature in the period up to 1750 during the past millennium. This largely explains why the estimates of CarbonBrief and the IPCC for the transition climate sensitivity to a doubling of CO2 compared to pre-industrial values is approximately a factor 2 higher compared to the value of 1.080 °C described here on the basis of long-term values for the sun combined with volcanism and CO2. The influence of the sun has been negated in the framework of CarbonBrief and the IPCC, but it is known that CMIP5 climate models, for example, do not take into account the amplification of natural forcings in the atmosphere. As a result, both perspectives describe values for the equilibrium climate sensitivity that are approximately 2x higher than the values for the transient climate sensitivity (however, in theory it is likely that both factors become approximately equal when both values are close to 1 °C). Both CarbonBrief and the IPCC operate on the assumption that anthropogenic influences are amplified with a value close to the top of the most likely band of 0.75-2 possible for the anthropogenic amplification factor. However, it is known that the natural amplification factor is potentially significantly higher with a most likely bandwidth of 1-6 [Haigh, 2007]; this influence is completely overlooked in the analysis of both CarbonBrief and the IPCC because no attempt is even made to numerically describe the possible impact of this for one's own analyses.

Conclusion

Without the amplifying influence of the atmosphere, the ECS will most likely be limited to a value of the order of 1.1 °C. The described TCS value of 1.08 °C; is just below this value. Logically it can be deduced from this that the ECS probably also has the same order of magnitude. An ECS of 1.08 °C implies an anthropogenic amplification factor with a value of 0.98 (which is within the corresponding most likely range of 0.75-2); this would mean that, based on the perspective described, the ECS is almost a factor of 3 lower than the midpoint value of 3.0 °C (based on the bandwidth: 1.5-4.5 °C) that the IPCC in AR5.
The impact of anthropogenic influences (b) appears to be limited because negative feedback mechanisms dominate the climate system based on the Stefan-Boltzman law, which describes that the amount of heat radiated from the earth into space changes with the fourth power of the temperature. of the Earth's surface and atmosphere. This law primarily explains how the sun has made a significant contribution to global warming since the end of the 16th century, especially until the late 1970s.

Download: Excel data file

---

Figure 3: The temperature on Earth during the Holocene with a temperature anomaly based on the average of 1000 proxy time series in the period 4500-550 BC. [Marcott et al., 2012 - Supplementary Materials].

---

REFERENCES:

de Jager et al. (2020) Solar magnetic variability and climate (boek).

Dudok de Wit et al. (2016) Earth's climate response to a changing sun (boek).

de Jager et al. (2006) Climate Change Scientific Assessment and Policy Analysis - Scientific Assessment of Solar Induced Climate Change. Bron: KNMI & NIOZ (rapport)

IPCC (2013) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (rapport).

Connolly et al. (2021) How much has the Sun influenced Northern Hemisphere temperature trends? An ongoing debate. n Research in Astronomy and Astrophysics. Accepted preprint paper: https://arxiv.org/ftp/arxiv/papers/2105/2105.12126.pdf

Feuler (2013) Understanding the influence of solar irradiance changes on Earth's climate during the Holocene. AIP Conference Proceedings 1531, 748. DOI: https://doi.org/10.1063/1.4804878

Haigh (2007) The Sun and the Earth's Climate. Living Rev. Sol. Phys., 46 (2), 26-29. DOI: https://doi.org/10.12942/lrsp-2007-2

Marcott et al. (2013) Supplementary Materials for: A Reconstruction of Regional and Global Temperature for the Past11,300 Years. Science 339, 1189. DOI: 10.1126/science.1228026

Muscheler et al. (2016) The Revised Sunspot Record in Comparison to Cosmogenic Radionuclide-Based Solar Activity Reconstructions. Solar Physics 291, 3025-3043. DOI: https://doi.org/10.1007/s11207-016-0969-z

Nurtaev et al. (2016) Helioclimatology of the Alps and the Tibetan Plateau. Earth Sciences 5, 2, 19-25. DOI: https://doi.org/10.11648/j.earth.20160502.11

Rial et al. (2004) Nonlinearities, feedbacks and critical thresholds within the Earth's climate system. Climatic Change 65, 11-38. DOI: https://doi.org/10.1023/B:CLIM.0000037493.89489.3f

Schwartz (2008) Defining and Quantifying Feedbacks in Earth's Climate System. American Geophysical Union, Fall Meeting 2008, abstract id.A21D-0195. Publication: https://ui.adsabs.harvard.edu/abs/2008AGUFM.A21D0195S/abstract

Steinhilber & Beer (2011) Solar activity - the past 1200 years. PAGES Magazine articles, vol. 19(1), 5-6. DOI: https://doi.org/10.22498/pages.19.1.5

Usoskin et al. (2021) Solar cyclic activity over the last millennium reconstructed from annual ¹⁴C data. A&A Volume 649, A141. DOI: https://doi.org/10.1051/0004-6361/202140711