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April 10, 2021

IPCC dataset for sun explains combined with volcanism more than half of the warming since 1815 during the Dalton minimum

After a phase correction of 30 years, the IPCC AR5 dataset for Total Solar Irradiance [TSI] combined with an index for volcanic activity, shows from 1740 a correlation of 0.95 with the global temperature (according the 2 Degrees Institute) based on the 22-year moving average

Martijn van Mensvoort

The sun provides almost all of the energy that powers the Earth's climate system. With regard to climate change it is therefore important to carefully study the fluctuations in the total solar radiation at the top of the atmosphere. The relationship between the temperature and the main cycle of the sun (the 22-year Hale cycle) is not well understood. That is why an analysis is presented here that focuses on the 22-year moving average of the following 6 factors: global temperature & CO2 [2 Degrees Institute both], three different TSI datasets [NRLTSI2, SATIRE SandT and LISIRD] and an index for volcanism [GISS AOD extended with ICI global AOD index]. For the TSI dataset used in the most recent comprehensive climate report presented by the IPCC (SATIRE SandT provides the basis for the TSI in AR5, 2013) it is shown that after a 30-year phase correction, it explains combined with volcanism more than half of the warming that has occurred since 1815 during the Dalton minimum. The sun and volcanism combined also shows a high correlation (0.952) with temperature for the period from 1740 onwards. For sea surface temperature almost 2/3 (62.8%) of the warming can be explained. Finally, a description follows for the main variations between the latest generation of TSI datasets, which are known under the names CHRONOS (semi-empirical) and EMPIRE (empirical). This shows that since 2011 at least it has been known among expert astronomers that consensus has never emerged about the magnitude of the sun's influence on the Earth; however, it has been known since at least 2012 that the sun might have had a significant impact on the development of global temperature through a delayed effect that potentially lasted into the 21st century.

Recent reports by expert astronomers describe that there is no consensus involving the amplitude of total solar radiation [TSI] since the Maunder minimum around the end of the 17th century [Egorova et al., 2018]. 2016 estimates were still in a bandwidth of 0.6-3.0 W/m2 [Dudok de Wit et al., 2016] but in 2020 this has been reduced to a bandwidth of 1.3-2.7 W/m2 [Yeo et al., 2020]. There is also no consensus about the meantime course of the variations [Yeo et al., 2017]; estimates range here from a decrease of 0.75 W/m2 to an increase of 6.3 W/m2 [Yeo et al., 2020]. Thus, the differences between TSI datasets are large; this explains why the weight attributed to the role of the sun in climate change varies greatly per TSI dataset [Haigh, 2007].

Working towards the next comprehensive climate report from the IPCC (AR6), climate modellers use for the TSI the mean value of NRLTSI2 (this is an empirical model) and SATIRE (this is a semi-empirical model) [Matthes et al., 2017, Kopp & Shapiro, 2021]. The present study also uses the LISIRD dataset, which serves as a TSI time series plot developed at the Laboratory for Atmospheric and Space Physics (LASP) in order to be used by the IPCC [Kopp, 2020].

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In the perspective of the past 4 centuries both sun and temperature show a multi-decade oscillation

Using the 22-year moving average neutralizes the impact of the Hale cycle. Figure 1 describes the 22-year moving average for: three TSI datasets [NRLTSI2, SATIRE SandT and LISIRD] in combination with an AOD volcanic index [GISS AOD verlengt met ICI global AOD] and the datasets for mondial temperature and CO2 datasets that presented by the 2 Degrees Institute. The 2 Degrees Institute temperature dataset uses for the period up to 1880 only data related to the northern hemisphere (using the data set from Mohberg et al., 2005). Figure 1 also describes the TSI dataset used in IPCC AR5 (this dataset is based on SATIRE SandT) plus the GISTEMP v4 dataset (= NASA temperature dataset). The 22-year moving average of the IPCC TSI dataset shows between 1750 and 2000 a bandwidth variation of approximately 1 W/m2.

Figure 1 also shows the core of the most important issue within climate science. On the one hand, temperature shows a (very) strong correlation with CO2. However, on the other hand, both temperature and all datasets for the sun show for the periode since 1700 a multi-decadal oscillation that is missing in the evolution of CO2. Moreover, the three TSI datasets also show a remarkably high correlation with temperature, especially with regard to the period up to 1965 (resulting from the 22-year solar cycle for annual values the correlation value is much lower than for the 22-year moving average values). NASA's GISTEMP v4 dataset - which starts in 1880 - shows correlation values of +0.90 with regard to all three TSI datasets used in this perspective.

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Figure 1 (1610-2020): 22-year moving average of 4 datasets for the total solar irradiance (TSI at top of atmosphere), 2 datasets for the global temperature and a volcanism index + the mutual correlations. The IPCC TSI dataset shows between 1750 and 2000 a variation of 1 W/m2. The relatively high TSI values for the LISIRD in the period before 1885 are the result of using SILSO data, which is known since 2015 to represent the successor to the 'sunspot group numbers', which were introduced in 1998 [Kopp et al., 2016]. By the way, SILSO data will not used in the next IPCC climate report (AR6) [Matthes et al., 2017]. For more details (including annual values of original datasets), see: Excel data file.

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Important as well, the 2013 IPCC climate model (see figure 2) shows that since 1970 total anthropogenic radiative forcing (RF) has grown by about half (~50%) more than the RF due to CO2. This implies that the strong upward movement of temperature and CO2 can by no means be directly related 1-to-1. For, the impact of the total anthropogenic RF is considerably larger than the RF due to CO2. The IPCC RF model also shows that anthropogenic influence was nihil until 1860, while the temperature between the Maunder minimum and 1860 shows an increase of about 0.4 °C. Additionally, both total RF and total anthropogenic RF from 1750 show an upward trend without an oscillation. The IPCC model implies that the temperature in the period 1883-1893 should have been well belower the period 1750-1780; however, figure 3 exhibits that the empirical temperature data shows the opposite development. In short, the IPCC RF model can not explain the evolution of the temperature up till the end of the 19th century.

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Figure 2: IPCC model for the radiative forcing [IPCC, 2013]. Te estimate for the solar forcing is a.o. based on a comparison between the solar minimum years 1745 and 2008 (including the average values over 7-year periods); the magnitude of the solar forcing is approximately 2% of the total anthropogenic forcing. However, IPCC reports up till 2020 do not take into account the existence of non-linear relationships, such as phase differences [Dudok de Wit et al., 2016].

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Curiously, the IPCC RF framework for solar forcing assumes that it's influence is rather small, with fluctuations over a period of a decade in the order of 0.2 W/m2. However, climate modellers have recognized that the Earth's atmosphere may be responsible for the creation of an amplification factor for solar activity [Dudok de Wit et al., 2016]. The solar signal in the upper part of the stratosphere is known to cause a temperature effect of ~3 °C; in the upper part of the mesosphere the effect is in the order of 3°C to 50 °C [Dudok de Wit et al., 2016]. Experts also recognize that the amplification factor is significant in the troposphere as well (in which we live) and it is likely to be in the range of the range 2 to 4 (though a value up to 6 is being considered realistic as well). Also, the amplification factor for natural influences is likely to be significantly larger than the amplification factor for anthropogenic influences, see figure 3 [Haigh, 2007].

Because there is no consensus about the size of the amplification factor the IPCC climate models assume that this amplification does not exist. However, the uncertainty with regard to the anthropogenic influences does has been factored into the climate models. This explains why a large bandwidth has been assigned to the climate sensitivity of CO2. Logically, this implicates that in the IPCC framework solar influence is structurally being underestimated (in addition to the amplification factor and non-linear relationships, the most crucial solar cycle is also overlooked, for, the 22-year Hale cycle has never been mentioned in the IPCC reports up to and including 2020) and the influence of CO2 is therefore probably overestimated. The 22-year Hale cycle forms the basis of a double 11-year Schwabe cycle, which is much better known as the sunspot cycle.

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Figuur 3: [right panel, Haigh, 2007] Empirical data inside the climate system points towards the existence of an amplification factor, which probably has a higher impact for natural influences (such as the sun) than for anthropogenic influences (such as CO2). [left panel, White et al., 1997] White has estimated that the climate sensitivity of seawater surface temperature related to the TSI at the top of the atmosphere is at the order of 0.2-0.4 °C per W/m2 (converted to the earth's surface based on the IPCC calculation method this implies an amplitude value of 0.04-0.07 °C per W/m2). Phase differences between the sun and the temperature are also being considered, which can rise for the inter-decade signal (= based on the Hale cycle) to an upper limit of 7 years maximum for the delayed temperature response resulting from the sun. The TSI data at the bottom of the left panel in figure 3 shows the decade signal (= based on the Schwabe cycle); the trend is very similar to the IPCC TSI data for the period 1955-1995 in figure 1. A comparison focused at the temperature development in figure 1 and figure 3 indicates in the period 1955-1995 that global temperature rose much faster than seawater surface temperature.

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There is no consensus among expert astronomers about both the magnitude and influence of the sun's fluctuations on the climate system of planet Earth's (details are discussed in the final paragraph). In the IPCC RF model the influence of the sun is assumed - based on the spherical shape of the earth and the Albedo factor - about a factor ~6 (= 17.5%) smaller than the TSI at the top of the atmosphere. This calculation is correct in itself but the impact of this calculation should not become separated from the discussion about the magnitude of the amplification factor. Additionally, the final paragraph describes that according to the semi-empirical CHRONOS models, the fluctuations in the solar signal since Maunder minimum (2nd half 17th century) might have been an order of magnitude higher than what the IPCC TSI dataset (based on the SATIRE SandT) describes. The absolute magnitude of the TSI signal converted to the surface of the earth is therefore by no means a solid argument for assuming that the influence of the sun on the development of the global temperature must have been little during the past 4 centuries.

Figure 1 shows that with regard to the period around the Dalton minimum, an RF combination of volcanism and the sun may have been responsible for the development of the temperature dip in the period between 1800 and 1850. However, figure 1 also shows that the other periods with a lot of volcanism have arisen during phases where solar activity shows a prolonged downward trend. It is striking that this temperature dip appears to have arisen parallel with a dip in the solar activity as well as a peak in volcanic activity; nevertheless, at both the Maunder minimum and Modern minimum, the bottom of the temperature dip is not found until a few decades after the dip in solar activity. The following section presents the result of an analysis that takes into account the possibility of the existence of a (stable or unstable) phase difference between the global temperature and the solar activity based on the TSI data set used in the IPCC AR5 report (2013).

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After a phase correction the sun shows combinated with volcanism the same oscillation present in temperature

Using a linear regression analysis (performed with PSPP software), the period between 1741 and 1900 is used in order to investigate to what extent volcanism combined with a delayed impact of the sun can explain the development of global temperature. The choice to start working with data up to and including 1900 serves to avoid the influence of anthropogenic RF. Figure 2 suggests that this choice is justified since before 1914 the IPCC RF model shows a total RF which does not maintain a (clear) positive value during a consecutive period longer than the 11-year sunspot cycle. Therefore, prior to 1914 it is hard to distinguish the influence of anthropogenic factors from natural factors.

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Figure 4a: Figure 4a: After a phase correction of 30 years, the sun explains combined with volcanism more than half (50.5%) of the warming that has occurred since 1815 during the Dalton minimum. For the period before 1740, the SARITE SandT can be extended using the other TSI datasets. When NRLTSI2 is used for the period 1691-1739 and LISIRD for the period 1650-1690, it appears that temperature also follows TSI prior to 1740. The result shows that until 1981 temperature does not show a trend that cannot be explained by the combination of sun and volcanism; in this period in the hole in the ozone layer at the South Pole became manifest (starting from 1979). [The TSI weight of 0.505 applies to the TSI values after deduction of 1360 W/m2, see: Excel data file; the regression analysis produced this formula: Temperature(t) = 0,505xTSI(t) + 3,44xAOD(t) - 0,6345]

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Figure 4a describes the result of the regression analysis. Figure 4a shows that volcanism combined with a 30-year delay in the cumulative effect of the sun (based on the IPCC TSI data set) can largely explain the temperature development in the period 1741-1900. Also,this model follows the direction of temperature development both in the period prior to 1741 and the period after 1900. Up to the year 1929, the temperature trend can be explained by the combination of the delayed sun and volcanism entirely. Only starting from 1981 temperature development does show a continuous warming on top of the steady natural warming due to the delayed sun combined with volcanism; this coincides with the start of the period with ozone layer depletion at the South Pole; this phenomenon became manifest in 1979. The combination of delayed sun and volcanism explains more than half (50.5%) of the warming that occurred since 1815 during the Dalton minimum. Moreover, the combination of the delayed sun combined with a recent decrease in volcanism that started from the mid-1980s, shows that the highest contribution of natural influences to global warming is found in the 21st century. This results in a correlation of 0.952 for the period starting from 1740 with 90.6% of temperature variance explained by this relationship.

Compared to figure 4a, figure 4b shows the result after replacing global temperature with sea surface temperature starting from 1899 (the NASA dataset shows for the 5-year moving average of temperature values for land and sea only a small difference in the period between 1900 and 1980; starting from 1980 a gradually increasing difference becomes manifest between the two). The weight of the sun combined with volcanism has increased here considerably, because in this perspective 62.8% of temperature increase is explained (+ the correlation for the periods 1740-2009 and 1650-2009 increases for both to 0.96). The course of the difference between the two curves in figure 4b shows characteristics that match the development of CO2 (see figure 1 & 2) or the total anthropogene signal (see figure 2).

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Figure 4b: Here the global temperature perspective described in figure 4a has been replaced with seawater surface temperature based on GISS temperature data for global seawater surface (the 22-year moving average is calculated using underlying annual values for seawater starting from 1899). 62.8% of the rise in sea surface temperature is explained by volcanism combined with the (delayed) impact of the sun. The course of the difference between the two curves shows a development which is similar to the development of CO2 (see figure 1 & 2) or the total anthropogene signal (see figure 2).

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There is no consensus among expert astronomers about the influence of the sun on climate

Figure 1 shows that the differences between TSI datasets are rather large. Like the LISIRD TSI dataset, the modern CHRONOS models are based on the modern SILSO sunspots data (produced in Belgium), which will be disregarded in the next AR6 IPCC climate report expected in 2022. The CHRONOS models (see figure 5) indicate that the influence of the sun on climate is possibly more than an order of magnitude higher than the assumption used within the present IPCC framework - regarding the datasets shown in figure 5 only the SATIRE & NRL are taken into consideration. Interestingly, CHRONOS variant MU16 (based on the Carbon-14 isotope) is featured by a bandwidth which describes the highest TSI value to be reached halfway the 2nd decade of the 21st century, approximately 1 year prior to the global temperature record year 2016. Also of significant importance, the impact of CHRONOS models compared to more conservative models for the northern hemisphere is accompagnied with a temperature difference of the order of 0,3°C to 0,4°C [Yeo et al., 2020]. In contrast to semi-empirical CHRONOS models, empirical EMPIRE models also use SSI (Solar Spectrum Irradiance) in addition to the TSI [Yeo et al., 2017].

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Figure 5: six datasets for the Total Solar Irradiance. For the period from the Maunder minimum to the 2008 minimum, all CHRONOS models [Egorova et al., 2018] show a significantly larger TSI increase relative to the SATIRE (SATIRE-T) and NRL (NRLSSI2) - the latter two represent the only TSI models which are being used in the preparation for IPCC AR6, which is expected to be presented in 2022.

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Since 2011 astronomers have made an appeal towards climate modellers to include calculation for the uncertainties surrounding the influence of the sun on the climate in their models. At that time this factor of uncertainty was estimated to be in the order of ~50% [Shapiro et al., 2011]. Nevertheless, the most recent comprehensive climate report AR5 [IPCC, 2013] included a calculation for the impact for just 1 TSI model (SATIRE SandT), without taking into account the relatively large uncertainties. In addition, the existence of the main cycle of the sun (22-year Hale cycle) has never been mentioned in the IPCC reports and to date no account has been taken of the influence of phase differences between solar activity and global temperature. Also, the AR5 climate models have not taken into account the influence of non-linear relationships between sun and temperature in any manner [Dudok de Wit et al., 2016]. The difficulties in order to detect the signal of the 11-year sunspot cycle may likely also be explained at least partly by some of these missing matters.

The ocean system (showing cycles of the order of 2000 years) and glaciers represent natural buffer systems in the climate system; this can likely at least partly explain the delayed impact of solar activity on global temperature. This also provides an explanation for the controversy involving the impact of the 11-year sunspot cycle on global temperature, which hard to assess [van Mensvoort, 2020]. The existence of phase differences between the sun and glaciers of around 20 years was already described in 2010 by an authority in the field of sunspots [Weiss, 2010]. And recently, a Dutch group of astronomers pointed out for the first time to the possibility that the magnitude of the phase difference may show a variability of the order of 16 years [de Jager et al., 2020]. Also, in 2020 Abdussamatov presented a publication describing that the ocean system has a temperature response of 30 ± 10 years [Abdussamatov, 2020] (in time Abdussamatov has broadened this bandwidth in steps, possibly because since 2004 he had already taken into account the possibility of the emergence of a 'new Little Ice Age' comparable to the Maunder minimum [Abdussamatov, 2016] - which does not seem very realistic without the influence of a significant increase in volcanism).

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Figure 6: Four different mathematical models describing the development of a delayed solar forcing (RF) due to the relatively rapid increase of solar radiation (pink curve) during the 1st half of the 20th century [Rypdal, 2012]. These models describe a delayed impact of changes in TSI associated with ocean dynamics (in terms of transfer of heat between different ocean layers). The orange curve shows a theoretical scale-free response model [Rypdal & Rypdal, 2014]. The TSI used shows similarities with the CHRONOS models shown in figure 5.

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Other researchers talk in term of a delayed temperature response (0.1 °C) in the 2nd half of the 20th century, caused by the relatively strong increase in Total Solar Irradiance in the 1st half of the 20th century [Dudok de Wit et al., 2016] - see figure 6. This implies the existence of an unstable phase difference between sun and temperature that can reach a length in the order of half a century; this phenomenon is also incorporated in the right panel in figure 7a which presents an indicative temperature response of the sun for the period 1880-2010. These phase difference example can be putten in perspective with the option where TSI itself can be used to act as a model for solar radiative forcing (RF) [Dudok de Wit et al., 2016].

Figure 7a+b indicates that especially the warming starting from 1965 cannot be explained by the combination of the sun and volcanism. However, the long-term downward temperature development in the periods between 1880-1910 and 1940-1965 cannot be explained by the model either; the model in figure 7a+b therefore does not explain the origins of the oscillatory development of the temperature as described in figure 1. Curiously, in contrast to the model in figure 7a+b, the AR5 RF model [IPCC, 2013] suggests that since 1750 the sun has not played any significant role (~2%) in the intermediate temperature fluctuations associated with climate change.

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Figure 7a: Radiative forcing in the periods 1000-1979 and 1880-2010 for: the sun, volcanism, anthropogenic and the total - based on a scale-free response model [Rypdal & Rypdal, 2014]. This forcing model is based on the dataset of Hansen et al. (2011) which uses the TSI data of the Frölich & Lean - this couple represents the authors of the (controversial) PMOD dataset for the satellite era [Scafetta et al., 2019] - no account is made for the influence of non-linear effects, nor the existence of amplification factors, nor is the model able to reproduce the multi-decade oscillation. In addition, Hansen's dataset works purposefully with a hypothesis regarding the influence of anthropogenic aerosols (aimed at neutralizing the exponential growth of anthropogenic greenhouse gases), even though virtually no empirical data at all is available for this factor up till and including the year 2020. This model is also described in Dudok de Wit et al. (2016). For the period 1700-2010 starting from the Maunder minimum, the forcing due to the sun is associated with a temperature rise of around 0.45 °C. For the period 1750-2010 this is about 0.35 °C; however, in the model of the IPCC the impact of the solar forcing for the period 1750-2012 is no more than ~2% of the total anthropogenic RF and it is ~33x smaller than the RF attributed to CO2 (see figure 2). The temperature graph shown for the period 1000-1980 (showing temperature starting an oscillating upward movement from the end of the Spörer minimum in the 2nd half of the 16th century) refers to the northern hemisphere [Mohberg et al. (2005)].

Figure 7b: The solar radiative forcing with corresponding temperature response for the periods 1000-1980 (left) and 1880-2010 (right). Based on a scale-free response model, for the period 1700-2010 a total temperature response of approximately 0.45 °C is found due to solar forcing (0.35 °C for the period 1750-2010); this model assumes implicit that an amplification factor for the solar signal is missing in the climate system [Rypdal & Rypdal, 2014]. Based on the 22-year moving average in figure 1 between 1700 and 2010 the temperature increased by approximately 1.25 °C (1.15 °C for the period 1750-2010). Elsewhere models are available as well for the radiative forcing based on SSI [Wen et al., 2017].

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An apparent complication in figure 7a+b seems the lack of temperature rise between the Maunder minimum (~1689) and the Dalton minimum (~1815), while it is clearly visible in the 22-year moving average temperature data set of the 2 Degrees Institute (see figure 1). However, both datasets are based on the same work: Mohberg et al. (2005). So the rise between Maunder minimum and Dalton minimum is also present in the data shown in figure 7a+b.
The significance of this is the following: since the period around the Dalton minimum is known for the highest level of volcanism since the beginning of the Spörer minimum (~1460), it is obvious that the 0.12 °C global temperature rise between the Maunder minimum and the Dalton minimum is very likely mainly caused by the sun (despite the cooling due to the unusually high level of volcanism during the Dalton minimum combined with probably less than 0.02 °C rise due to CO2). Based on the RF model of the IPCC in figure 2, CO2 may have contributed an increase of about 0.125 W/m2 - which corresponds to a temperature rise of approximately 0.05 °C. Therefore, the radiative forcing of CO2 (read: the climate sensitivity to a doubling of CO2) would have to be about 2x larger than the IPCC model in figure 2 in order to be able to explain the temperature rise between 1689 and 1815 (however, the impact of volcanism is then not even taken into account). Since the line of this simple approximation can be extended to the Modern Minimum (~1912) as well, this indicates that the impact of the sun's delayed temperature response may not represent a complication in comparing Grand Solar Minimum periods. The logical reason could be that during these periods changes in RF due to the sun remain always relatively small.

Another complication is the statistical fact that solar minima show particularly strong correlations for TSI and temperature [van Mensvoort, 2020]. In the LISIRD dataset this phenomenon shows remarkable proportions based on the Hale cycle minima: almost half of the warming since 1689 during Maunder minimum can be explained by the sun based on positive Hale cycle minima. Therefore it seems sensible to take into account the possibility that phase differences between sun and temperature can result from dynamics related to spectral differences in how solar radiation gets processed by the atmosphere. For example, UV radiation is known to have a relatively large weight in the production of solar maxima (60% iscaused by solar radiation with a wavelength less than 400 nanometers), this high-frequency radiation is almost completely absorbed in the stratosphere so that it can hardly reach earth's surface. This phenomenon also plays a role in the aforementioned temperature effect of 3 °C in the stratosphere due to the 11-year solar cycle.

Previously was shown for the LISIRD TSI that solar minima based on the Hale cycle show particularly strong correlations with temperature of both ocean water and atmosphere. Here has been shown that an effect with a similar impact is found for the TSI dataset of the AR5 [IPCC, 2013] after taking into account a 30-year phase difference between the solar signal on the one hand and temperature (+ volcanism) on the other. Recently convincing evidence has emerged showing that in recent decades solar minima also play a role in the ENSO cycle, indicating that the strongest El Nino and La Nina phases have emerged in the transition phase from solar minimum to aximum (Leamon et al., 2021).

Finally, this article has has shown why climate modellers should take into account the possibility that the sun has had a delayed impact due to the recent Grand Solar Maximum (which occurred in the 2nd half of the 20th century) which might impact a period with a length of up to possibly around half of a century. The dynamics described in figure 4a are consistent with the dynamics described in figure 7b based on the work of Rypdal & Rypdal (2014). The total temperature response to the sun in figure 4a (~0.50 °C for the period 1750-2010) is probably somewhat larger compared to figure 7b (~0.35 deg;C for the period 1750-2010) because in the perspective of figure 4a there is no restriction used assumping that there is no amplification factor for the solar signal in the climate system (while the researchers involved with figure 7b do have made this assumption implicit). The consequence of figure 4a is that the anthropogenic influence within the framework of the IPCC is likely overestimated by approximately a factor 2 (or up to a factor 3 based on the temperature of the seawater surface + previous analyzes based on the solar minima). This also implies that the gradual rise in temperature that became manifest in recent centuries can probably be attributed for a significant part to the combination of the (delayed) influence of the sun in combined with volcanism. Logically, therefore, within the IPCC RF models attribute too much weight to the influence of CO2 and other greenhousegasses compared to other anthropogenic influences.

Download: Excel data file

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