Energy from the Sun

Clearly, we might recognise that almost every process on Earth may trace back its energy to the Sun. Therefore, this discussion will attempt to outline some of the keys mechanisms that might affect the amount of energy received on Earth from the Sun prior to a wider discussion of other possible climate change mechanisms. Based on actual measurements, it is known that the Earth receives about 1372 watts/m2 at the top of its atmosphere. However, the actual average amount that arrives at the Earth’s surface is a little more complicated, but not necessarily impossible to outline for the purposes of this discussion. We will start by trying to substantiate the figure above based on the figure of 6.33*109 W/m2 as the average energy output of the Sun itself without reference to any variance associated with an 11-year solar cycles and changes in sunspot activity.

[1]         

The form of the equation in [1] conforms to the inverse square law of radiated energy being distributed on a spherical surface, defined by 4πr2, where [r] is the radius of Earth’s average orbital distance from the Sun. However, the figure of 342W/m2 in the following diagram is a somewhat crude approximation, where half the 1372 watts/m2 of energy is first averaged out over a 24-hour night-day cycle and then halved again to make another approximation of the energy averaged over all latitudes in order to account for the curvature of the Earth towards the Sun. These figures will be discussed further below. As illustrated in the diagram, the energy in W/m2 received at the Earth’s surface is subject to a number of further complications, which will be considered further in the next discussion. However, it might be realised that the figure of 342W/m2 might distort the actual variance of the sun’s energy at any point on Earth, which may range between near-zero at night at the poles through to 1372W/m2 on a sunny cloudless day near the equator. Unfortunately, the complication does not stop there as the Earth is known to have an elliptical path in its yearly orbit around the Sun, i.e. as defined by the aphelion and perihelion . So, while [1] is based on the average orbital radius of 149.6 million kilometres, it extends to 152.1 million kilometres at the aphelion and reduces to 147.1 million kilometres at the perihelion. As such, we might account for this variance in [2].

[2]         

The following table provides a little more detail in terms of both the radial distance and received energy and the variance of both throughout the yearly cycle between aphelion and perihelion.

Earth Radius % delta W/m2 % delta
Average 1.496E+11 100.00% 0.00% 1.371E+03 100.00% 0.00%
aphelion 1.471E+11 98.33% -1.67% 1.418E+03 103.43% 3.43%
perihelion 1.520E+11 101.60% 1.60% 1.328E+03 96.87% -3.13%

In terms of [2] and the table above, we see an ±1.6% variance in the Earth’s orbital radius being converted into an approximate ±3% variance in the energy received from the Sun over one years, due to the inverse square law. However, over the same time, i.e. one year, the Earth's axial tilt of 23.4o, changes the effective angle of latitude of any point on Earth with respect to the Sun, such that the angle presented to the Sun changes by ±23.4o over the year. Again, we might approximate the change in energy intensity as the Earth orbits the Sun.

[3]         

Due to the Earth’s axial tilt, the solstice is the point during the Earth's orbit where the sun is at its greatest distance from the equator, while the equinox is the point of the closest distance from the equator. Based on [3], we might calculate the change in W/m2 at the equator and poles over the yearly orbit.

[4]         

The change in the energy intensity [I] to [I’] is due to the distribution of energy over an increase area as the latitude angle [Φ] is increased towards the pole, although this angle affectively changes with the seasons due to the axial tilt (23.4o), which we might simply tabulate for reference as follows.

I Φ Radians Cos(Φ) I' %
1372 0.0 0.000 1.000 1372 100%
10.0 0.175 0.985 1351 98%
20.0 0.349 0.940 1289 94%
30.0 0.524 0.866 1188 87%
40.0 0.698 0.766 1051 77%
50.0 0.873 0.643 882 64%
60.0 1.047 0.500 686 50%
70.0 1.222 0.342 469 34%
80.0 1.396 0.174 238 17%
90.0 1.571 0.000 0 0%

As such, we appear to have 2 factors that affect the amount of energy being received by the Earth during the year due to the elliptical orbital and axial tilt. However, we might initially summarise this complexity by stating that, over a year, the northern hemisphere varies about 13oC, while the southern hemisphere varies by 5.5oC. This difference is apparently caused by the fact that the southern hemisphere is covered by a much larger percentage of ocean, which is yet another factor in climate change that needs to be considered. However, we might assume that the yearly cycle between the seasons does not in itself trigger wholesale climate change. Of course, the complexity does not necessarily stop there and we might introduce another variability in the energy received by the Earth as described by the Milankovitch Cycles . In 1920, Milutin Milanković forwarded the hypothesis that the Earth’s eccentricity, axial tilt, and precession of the Earth was subject to longer term cycles, i.e.

Type Description Duration
in years
per 100
 years
Eccentricity Change is orbital radius 100,000 0.100%
Axial tilt Change is axial tilt 41,000 0.244%
Precession Change in tilt orientation 26,000 0.385%

At this stage, we are just trying to make some quantification of the potential change in the energy received by the Earth, which might have contributed to earlier climate change, i.e. the various ice-ages, as previously outlined. While the table highlights the much longer periodicity within the various Milanovitch cycle, it also highlights that the percentage change over the next 100 years might be relatively small. Therefore, ‘eccentricity ’ is a long-term change to Earth’s elliptical orbit of the sun, which today varies between 147.1 and 152.1 million kilometres, while over the 100,000 year cycle the variation extends to 129 and 187 million kilometres, which may then have an appreciable effect of the W/m2 figure original calculated in [1].

[5]         

The orbital variance in the Milanovitch eccentricity cycle might initially be quantified against the current orbital radius, i.e. 149.6 million kilometres, which gives the following results:

Earth Radius % delta W/m2 % delta
Today 1.496E+11 100.00% 0.00% 1.371E+03 100.00% 0.00%
min 1.290E+11 86.23% -13.77% 1.843E+03 134.49% 34.49%
max 1.870E+11 125.00% 25.00% 8.773E+02 64.00% -36.00%

The table above reflects a variation in orbital distance between -13% and +25%, which converts to a +34% and -36% swing in the W/m2 figures. One can only assume that such a percentage swing in the energy reaching Earth could have a profound effect on any climate change over the 100,000-year eccentricity cycle.

What about any change in the axial tilt?

Apparently, the Earth's axial tilt varies between 22.1° and 24.5° over a cycle of about 41,000 years, such that the current tilt 23.44° is near mid-point. We might quantify the effect of the swing in the axial tilt, where the highlighted rows correspond to the maximum change at the equator and poles today.

I Φ Radians Cos(Φ) I' %
1372 21.1 0.368 0.933 1280 93%
23.4 0.408 0.918 1259 92%
24.5 0.428 0.910 1248 91%
90-24.5 1.143 0.415 569 41%
90-23.5 1.162 0.397 545 40%
90-21.1 1.203 0.360 494 36%

Examining the figures in the table above, we see that the net effect of increasing axial tilt is that the total annual solar radiation received increases at higher latitudes, but decreases closer to the equator. While the net effect appears small in terms of eccentricity, even a small increase in the average energy received in the northern latitudes might be significant, although it is highlighted this might only amount to a 0.25% change over the next 100 years within the overall 41,000-year cycle. Finally, we might simply describe the idea of precession as a ‘rotational wobble’ of the axial tilt over a period of 26,000 years, which would effectively switch the current orientation of the summer-winter seasons.

So might we conclude that there will be no major change in the energy received over the next 100-years?

While it seems reasonable to assume that the energy received by the Earth from the Sun will not be unduly affected over the next 100-years due to the much longer cycle times associated with the Milankovitch cycles, there are other potential factors at work. In essence, all the factors in the Milankovitch cycle relate to positional changes of the Earth with respect to the Sun without any reference to the energy output of the Sun itself, which is often discussed in terms of an 11-year ‘solar cycle’ . We might start by simply showing the number of sunspots recorded over the last 400 years, where the period of minimum sunspot activity appears to align to historic periods of colder weather, e.g. the Maunder Minimum appears to coincide with the Little Ice Age that severely affected average temperatures in Europe and North America in the 17th century.

In the previous chart, we see a cycle of minimum and maximum periods of sunspot activity, which while averaging to an approximate 11-year cycle can fluctuate between 9-14 years. The solar cycles shown in blue are numbered between 1-24, such that the transition into cycle-25 is expected by 2019, which on average would last to 2030. However, the details of how sunspots are actually produced appears to be yet another matter of ongoing theoretical debate, such that it is unclear whether there is any definitive causal mechanism that correlates the number of sunspots with the Sun’s overall energy output (W/m2).

Note: Best estimates to-date suggest that the total sun irradiance (TSI) of 1372 W/m2 may only change by as little as 0.3 W/m2 over an average sunspot cycle. See Solar Irradiance and Solar Constant for more details.

This said, many speculate that sunspot activity also reflects the strength of the Sun’s magnetic fields, and solar winds, which depend on various circulations and rotations within the Sun’s internal structure, while others have proposed more radical models that this discussion will not expand on. However, we might use the following chart as a broad outline of climate change over the last 4000-years or so.

While the chart shows a clear pattern of warm and cold periods, the severity of the change is not necessarily easy to predict. However, we might crudely highlight that the last 4000 years has seen 4 warm-cold cycles that might be averaged to every 1000 years or so, which would correspond to 500 years of warm followed by 500 years of cold. So, irrespective of whether we really understand all the causal mechanisms at work, we might reasonably conclude that there is a process of climate change that appears to be operating on a much faster periodicity than can be attributed to the Milankovitch cycles and pre-dates man-made CO2 emissions. Based on the chart above, there is a suggestion that the next transition will be towards a colder period, the severity of which can only be speculative at this time. However, any suggestion that the Earth might be entering a period of colder climate has also to be discussed in the context of the current IPCC prediction of a global warming. As such, we possibly need to consider the potential for a wider scope of causal mechanisms that might affect future climate change.