The effects of the Sun on the Earth and other planets are caused by a combination of:
1) the solar activity itself governed by solar dynamo mechanism acting in the solar interior;
2) the orbital motion of the Earth (or planets) and Sun leading to
- long-term variations (Milankovich cycles https://en.wikipedia.org/wiki/Milankovitch_cycles, 15-100K years durations), caused by the planet tilts, orbit change and various types of axis precession;
- medium-term variations (Hallstatt’s cycle, 2.0-2.2K) caused by the solar inertial motion imposed by gravitation of large planets of the solar system.
Most current studies considered the only effect of the Sun via solar activity variations (item 1. Eddy (1976) established that the solar irradiance in the past 300 years followed by the terrestrial temperature (see Fig.1). On this basis, the solar forcing in all the terrestrial models including the IPCC ones was linked to the solar activity process (item 1 above). And this was a good approach until the time from 1970-80s when solar activity started to decrease when the terrestrial temperature continues increasing while the solar activity started decreasing as shown in Fig. 1.
Fig. 1. Variations of the terrestrial temperature (red lines) and total solar irradiance (blue lines) (measured in W/m2) during each solar cycle (thin lines) and averaged over cycle (thick lines).
This prompted some researchers to look for some alternative heating mechanisms. As result they came up with the ‘Hockey stick’ model and suggested that the terrestrial atmosphere is heated because it creates the greenhouse effect by the infra-red emission of carbon dioxide molecules populated by anthropogenic activity. This extra-heating of the atmosphere was suggested despite of the CO2 molecule emission, by being infra-red, having a rather low energy and very high opacity (a large number of the molecules on the line of sight).
The high opacity of CO2 molecules means that CO2 emission would not be as strong as suggested by IPCC because it is locked by the radiative transfer scattering process of internal diffusion. The rule states that only emission from the optical thickness of unity can be emitted out of the media with large optical sickness, or opacity. This means that the atmospheric layer with CO2 molecules will emit to the Earth and to the space rather limited emission because the emitted CO2 intensity is proportional to the exponent with a negative power of the optical depth of the layer, from which it is emitted. The higher the negative power the smaller the layer contribution to the emitted intensity. Practically, only the layers with optical thickness lower than unity can provide noticeable contribution. Thus, this limited CO2 emission will fail to provide any measurable heating.
However, the IPCC reports stubbornly considered only the greenhouse effects of CO2 molecules as the source of heating. They repeat again and again the radiative transfer mistake by damping on Earth the full CO2 emission stored in the media layers with the optical thickness (opacity) of a few hundred, instead of the real emitted emission, which can only leave the media from the optical depth of unity. This mistaken interpretation of the emitted CO2 intensities was the basis why the IPCC reports refused to look at any other reasons of the recorded Earth atmosphere and ocean heating.
Solar inertial motion and its effect on the Sun-Earth distance and solar irradiance
Although, many researchers though found that solar irradiance effects measured from the biomass radioisotopes reveals medium-term variations of solar irradiance with a period of 2000-2200 years (so called Hallstatt’s cycle) (Steinhibler et al, 2009, 2012; Vieira et al, 2011).
Recently, Zharkova et al, 2019, Sci. Rep., 9, 9197 https://www.nature.com/articles/s41598-019-45584-3 reported that the baseline solar magnetic field shows the oscillations with the similar period of about 2100 years shifting the zero magnetic field either towards northern or southern polarities depending on the phase of the Hallstatt’s cycle. The authors found 60 very clear such periods in the 120 thousand years of the solar magnetic field variations predicted from the WSO magnetic synoptic maps (Zharkova et al, 2015).
The current phase of the Hallstatt’s cycle is shown in Fig.2, which demonstrates the current cycle had a minimum at the start of Maunder minimum and is currently in the ascending phase until 2600 year. The variations of TSI (magenta line) follow closely the baseline magnetic field variations (navy blue line) and the terrestrial temperature variations (the black line).
Zharkova et al, 2019 https://www.nature.com/articles/s41598-019-45584-3 suggested that this increase of solar irradiance since Maunder minimum occurred because the Sun was moving from the focus of the ellipse of the orbit closer to the spring equinox of the Earth orbit because the gravitation from large planets: Jupiter, Saturn, Neptune and Uranus. Thus, the Sun moves
Fig. 2. The close-up view of the current Hallstatt’s cycle of the baseline magnetic field variations (dark blue curve, arbitrary units) with the minimum occurring during Maunder Minimum. The scale of the baseline variations is shown on the left hand side Y axis, the scale of the summary curve variations (cyan line) – on the right hand side Y-axis. The irradiance curve (magenta line, reduced by factor 5) taken from Vieira et al, 2011 .
around the barycentre of the solar system fulfilling the solar inertial motion (SIM). Hence, all planets and the Sun move about the barycentre of the solar system, that leads to the wobbling star effect used as the basis for searching for exoplanets. The SIM motion has a period of about 2100 years.
The SIM is suggested by Zharkova et al, 2019 to be related to the changes the Sun-Earth distances, which, in turn, leads to the increase of solar irradiance in the past four hundred years because this S-E distance was decreasing. This suggestion made all the AGW people furious, a they twisted the arms to the SR Editors and made them to retract our paper by Zharkova et al, 2019 on the basis that the Sun-Earth distance does not change as stated in the Retraction note.
However, this objection was overturned by the book chapter ‘Millennial Oscillations of Solar Irradiance and Magnetic Field in 600–2600’ by Zharkova, 2021 https://www.intechopen.com/chapters/75534, which explored the real ephemeris of the Sun-Earth distances taken from the JPL and PMO ephemeris websites. Indeed, Zharkova, 2021 has clearly shown that contrary to statements of many AGW people (K.Rice, G. Schmidt and others), in the two millennia 600-1600 (M1) and 1600-2600 (M2) the S-E distances are changing, as suggested by Zharkova et al, 2019. The S-E distances are strongly reduced in February – July and increased in August-January of every year. Furthermore, because the distances between Earth and Sun were strongly reducing every first halves of years during the whole millennium 1600-2600, the deposition of the TSI to the Earth in the millennium M2(1600-2600) is higher by about 20-25 W/m^2 every year than in the millennium M1 (600-1600) (see Fig.3, bottom plot) (see the chapter for the full details).
Obviously, this extra-deposition of TSI is distributed over the Northern and Southern hemispheres, depending on the orbit position of the Earth. This extra-deposition of TSI since Maunder minimum can naturally account for the most increase of the terrestrial temperature in the past four centuries following the item 2 given at the start of this summary. This increase of TSI caused by the SIM is expected to continue for another 400-500 years.
Solar effects: interplay between Solar activity and SIM
Although, this constant increase of solar heating caused by the Sun movements towards the Earth orbit in the current phase of SIM in millennium 1600-2600 will be interrupted by the variations of solar activity on the Sun itself (item 1).
For example, in the next 32 years the Sun is entered the modern grand solar minimum (GSM) (2020-2053) predicted by Zharkova et al, 2015, Sci.Reps. https://www.nature.com/articles/srep15689 (see Fig.4), explained in more details by Zharkova, 2020 https://www.tandfonline.com/doi/full/10.1080/23328940.2020.1796243 and actively supported by the other researchers who unfortunately did not cite our paper and pretended they did the original discovery themselves (Kitiashvili, 2020, ApJ https://iopscience.iop.org/article/10.3847/1538-4357/ab64e7/pdf; Obridko et al, 2021, MNRAS, 504, 4990 https://arxiv.org/pdf/2104.06808.pdf; Herrera et al., 2021, JASR, 68, 1485 https://ui.adsabs.harvard.edu/abs/2021AdSpR..68.1485V/abstract).
The decrease of solar activity is expected to significantly reduce the input of TSI to the Earth causing the reduction by 1.0C of the average temperature on Earth https://www.intechopen.com/chapters/75534. The other GSM2 will happen in 2375-2415 that will again lead to a reduction of terrestrial temperature by the similar amount. Between the two GSMs the TSI will be producing extra-heating of the terrestrial atmosphere and ocean until 2500.
Fig.3. The total annual TSI variations (W=m2) in the millennia M1 and M2 derived by summation of the TSI magnitudes averaged monthly (top) and daily (not averaged per month) magnitudes (bottom).
Fig.4. The summary curve (in arbitrary units) of solar activity calculated for 1200 to 3200 years from the ’historical’ period (cycles 21−23) (Zharkova et al, 2015 https://www.nature.com/articles/srep15689, Zharkova, 2020,https://www.tandfonline.com/doi/full/10.1080/23328940.2020.1796243 ). Positive magnitudes of the summary curve represent northern magnetic polarity while the negative ones – southern one. The grand solar minima (GSMs) (from left to right): Wolf minimum (1280-1350), Maunder minimum (1645-1710), modern GSM1 (2020-2053) and GSM2 (2375-2415).