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Duncan Steel: Climate Change And Earth’s Changing Orbit

If you read the right newspapers you will have noticed over the past week numerous reports concerning a paper published in the journal Nature Climate Change, written by Jan Esper of the Johannes Gutenberg University in Mainz, and eleven colleagues from other institutions in Germany, Switzerland, Finland and Scotland. What this team has done is to analyse the growth rings of trees from northern Scandinavia with ages stretching back over the last two millennia, and investigated how these correlate with what is called orbital forcing.

I have a few qualms about the analysis conducted, but will leave those aside and let you, the reader, do an internet search to discover what other people have had to say. Regardless, this is a welcome paper because it re-opened the question of what the variations in Earth’s orbit around the Sun might mean for climate change.

Given the obvious relationship between (i) our annual orbit; (ii) the tilt of our planet’s spin axis; and (iii) the seasons, one might have imagined that this would be a subject well-covered in the various the reports published by the Intergovernmental Panel on Climate Change (IPCC; see, but a perusal of those reports will show you that not to be the case. For balance, let me point out that orbital forcing receives even less attention in the web pages of the independent counter-organisation, the Nongovernmental Panel on Climate Change (NIPCC;

Reading the IPCC’s reports, one finds that there is an apparent consensus that modern human activities dominate the causes of climate change, leading to the philosophy of AGW (anthropogenic global warming). The IPCC Fourth Assessment Report (the FAR, published in 2007), as with earlier reports, identifies several physical agencies altering the climate either through heating or, in a few cases, cooling. These are termed Radiative Forcing (RF) factors.

All except one of the RF factors the IPCC describes are man-made: increasing greenhouse gases (carbon dioxide, methane, nitrous oxide [don’t laugh], and halocarbons), stratospheric and tropospheric ozone levels, stratospheric water vapour, changes in surface reflectivity due to changing land use and soot coating snow and ice, atmospheric aerosols (which promote cooling), and jet aircraft contrails. Some of these have global effects; some are continental-scale; some are local (of limited spatial extent).

The greenhouse gases have the greatest heating effect, estimated at about 2.6 watts per square metre of which about 60 percent is due to carbon dioxide (hence the Carbon Tax recently introduced by the Australian Federal Government); by comparison the flux of sunlight at the Earth is about 1367 W/m2. Because of the cooling influences, of the aerosols in particular, the overall global warming due to human activities since the industrial era began after 1750 is estimated by the IPCC to be around 1.6 W/m2. These figures are mentioned here for comparison with others presented later.

The single natural RF component included by the IPCC in its calculations is solar variability: that is, changes in the intrinsic energy output by the Sun, and therefore alterations in the flux of sunlight reaching our planet. Explosive volcanic events (like Mount Pinatubo’s eruption in 1991) are mentioned but dismissed as they only have short-term (few year) effects. “The only increase in natural forcing of any significance between 1750 and 2005 occurred in solar irradiance” states the FAR, the increase being estimated to lie between 0.06 and 0.30 W/m2, with a best-guess of 0.12. The latter figure is less than ten percent of the AGW estimate described above: hence Australia’s Carbon Tax.

Instant In Time

Australia has a proud record of research in astronomy, and one of the major arguments that professionals trot out when campaigning for continued and expanded funding from the taxpayer (in part through the Carbon Tax, in the future) is that astronomy and astrophysics are subjects which every so often throw up unexpected applications of wide general application and therefore benefit to the taxpayer. For example, the Australian National University’s Mount Stromlo Observatory (which is actually visible from Parliament House in Canberra) was originally founded as the Commonwealth Solar Observatory, because knowing things about how the Sun behaves is obviously useful for climate prediction and the like.

Indeed, it was fortunate that when the Government was considering the climatic (as opposed to economic) need for a Carbon Tax the Chief Scientist of Australia was Professor Penny Sackett, who had formerly been Director of the Research School of Astronomy and Astrophysics at ANU. The Government was doubtless able, therefore, to obtain expert advice from its Chief Scientist, and of course through her the many other astronomers employed by the nation’s universities, the CSIRO Division of Astronomy and Space Science, and the like; for example, the Defence Science and Technology Organisation employs many space experts in the service of the country.

With the above in mind, what I describe below will not be a surprise to anyone in the Australian Government, nor indeed the myriad astronomers beavering away at their important research. Nor will it be a surprise to anyone reading the IPCC reports, which highlight the facts that I present below so that no-one could possibly be misled.

One of the major arguments for AGW is the apparent advance to earlier dates of the onset of the spring season as indicated by phenological studies: for example, the dates when certain plants begin to flower. One human-imposed reason for this is our calendar, which copies the leap-year cycle of the Gregorian Calendar (GC). On the GC the date of the vernal/March equinox (and also the equinox in September, the relevant juncture for austral spring) is coming progressively earlier until the year 2100, resulting in spring as defined by the equinox varying over a range of 53 hours (see the note by Raphael Sagarin, Nature, volume 414, page 600, 2001). The point is that the GC was instigated to regulate the date of Easter, not to regularise the seasons, as I described in my book Marking Time (Wiley, 2000).

Astronomically-speaking, the equinox is an instant in time, delineated by when the Sun crosses the celestial equator. The Catholic Church, however, defined with the GC the whole of March 21st to be the ecclesiastical equinox for computing Easter. In terms of its astronomical definition, the equinox will not occur again on that date until the year 2102 (and then only just: by about 35 seconds, in Coordinated Universal Time or UTC). The reason the equinox moves (temporarily) back onto its ‘proper’ date then is the fact that 2100 is not a leap year on the GC.

But let use leave that triviality aside. The argument in the IPCC reports is all about the Radiative Forcing factors, and how these have changed since 1750. With that in mind I made the calculations resulting in the information in the graph that follows. Click on image to enlarge.


Click on the image to enlarge

Here I considered the Earth’s orbit around the Sun, and how it gradually changes. One of the leading scientific explanations for the occurrence of Ice Ages is commonly-termed Milankovitch Theory, for the Serbian who developed the idea in the first half of the 20th century. This is based on slow changes in the shape of the terrestrial orbit (its eccentricity) and the tilt of our planet’s spin axis (its obliquity).

Whilst admitting that slow changes in these parameters (over millennia and tens of millennia) may be responsible for longer-term palaeoclimatic variations, the IPCC dismisses orbital changes as being of no significance over the past 2,000 years (“its impact on climate can be neglected compared to the other forcings” it says in the FAR).

Longitude of Perihelion

There is, however, an orbital parameter that changes rather swiftly. This is called the longitude of perihelion: it is the solar longitude (the angle measured around the plane of the Earth’s orbit from the vernal equinox) at which perihelion (our closest approach to the Sun) occurs. The longitude of perihelion takes about 21,000 years to do a complete revolution around the Sun, due mainly to gravitational tugs from the other planets.

That sounds like a long time, of no significance here. But let me express it in a different way. The time of perihelion moves forward by about one day every 57 or 58 years. Since 1750 it has progressed by more than four days. Around 1750 perihelion was occurring about eight hours before the end of the year. Now it is taking place, typically, late on January 4th (but beware of the perils of calendar vagaries and misleading osculating orbits, which can cause erratic back-and-forth jumps of no climatic significance). Aphelion – our furthest point from the Sun – occurs generally on July 4th, and is the prompter of fireworks, in the United States at least.

Back in the year 1246 Earth’s longitude of perihelion was aligned with the December solstice, meaning that it occurred about nine days before the end of the year, whilst aphelion was aligned with the June solstice. In consequence autumn and winter were of equal length (in the northern hemisphere), with spring and summer also being of equal duration but longer than the other pair.

Currently winter is the shortest season (88.8 days from the December solstice to the March equinox), autumn is next (89.9 days between the September equinox and the December solstice), then spring (92.8 days from the March equinox to the June solstice), and the longest season is summer (93.7 days from June solstice to September equinox). All for the northern hemisphere, again; reverse the seasons for Down Under.

Although the deviation of our orbit from a circle is small (currently the eccentricity is near 0.0167), it results in a change in the flux of sunlight at the Earth of almost seven percent between perihelion and aphelion. This would not matter in terms of climate change but for the fact that perihelion and aphelion are continually shifting compared to the equinoxes and solstices: the four days since 1750 that I described previously.

At perihelion Earth is moving fastest (30.3 km per second), and at aphelion it is slowest (29.3 km per second). Note that those facts, coupled with the information in the preceding couple of paragraphs, tells you why northern hemisphere summers tend to be longer but cooler compared to the briefer but hotter southern hemisphere summers.

To derive the graph shown above what I did was this. I took the Earth’s eccentricity, obliquity and longitude of perihelion (the latter being the main contributor to solar flux change at different times of year over centurial or millennial timescales) for both 1750 and 2000, and computed the insolation between sunrise and sunset at nine different latitudes (in 20° steps from 80°S to 80°N) for each day of the year.

What does the graph tell us? First let me note this: the total solar energy delivery to Earth (to the top of the atmosphere) in this model is the same for 1750 and 2000 (5.4971 × 1024 joules, in fact). It is the distribution of the impinging solar energy that has changed. Looking at the units on the vertical axis one can see that there are significant changes between 1750 and 2000, when judged against the Radiative Forcing quantities as evaluated by the IPCC and described at the beginning of this article.

All the lines cross at close to the middle of the plot: that is, near the June solstice. To the left (i.e. in the first half of the year) one can see that all latitudes to the north of 20°S now receive more sunlight. On that basis it is hardly surprising that spring is coming earlier. The peak in flux change of above 3 W/m2 for 80°N compared to actual insolation around 180 W/m2 near day 100 indicates an increase of almost two percent: no wonder the polar bears are worried. On the other hand, at about day 240 (the end of August) the minimum at about −4 W/m2 for that polar latitude indicates a cooler summer and autumn.

Truth be told, that two percent (and less elsewhere) is not much, representing a shift of typically one to three days in terms of the time when a certain insolation level is reached in the (shifting and altering) seasonal cycles. But three days is a tenth of a month, making complete nonsense of statements such as “the hottest October on record”, because no two months with the same name can be directly compared any more than October remains the eighth month of the year (which is what its name actually means).

Looking at the right-hand side of the graph, the second half of the year, a change towards cooling is indicated for all latitudes north of the equator. This might be interpreted as indicating an earlier end to summer, or autumn, or winter coming earlier. In terms of phenology, finding suitable indicators may present problems: in the past readers would write to The Times to claim that they had heard the first cuckoo of spring, but no-one wrote to say when they had heard the last cuckoo of autumn.

The curves for the southern hemisphere (20°S, 40°S, 60°S, 80°S) all portray an enhancement in impinging sunlight in the latter half of the year from 1750 to 2000, and therefore spring arriving earlier, although not by the same magnitude as is the case for the northern hemisphere in the first half of the year.

There are various other features of the plot that could be explored, but I’ll leave it to the reader to ponder what all those coloured curves might indicate. One thing I must emphasise is this: the only thing I have calculated and presented herein is the solar flux arriving at the top of the atmosphere (or, more precisely, how that flux has changed at different latitudes between 1750 and the present). I have not considered how that energy is subsequently absorbed or reflected, transported, re-radiated, re-absorbed, stored, conducted, convected, circulated, or otherwise juggled about.

Earlier I mentioned that the Gregorian Calendar was designed to regularise the dates of Easter (and it’s a second-best solution, by the way), rather than to follow the seasons, and it causes many problems to climate scientists because of that in terms of comparing dates. Once Easter is set, so are the other moveable feasts, or fasts. But if you take another look at the graph I have presented here, you’ll see that everything about the climate seems likely to be a moving feast.

Dr Duncan Steel lives in Canberra, Australia. He occasionally checks his email on

© Copyright Duncan Steel