In Part Three we had a very brief look at the orbital factors that affect solar insolation.
Here we will look at these factors in more detail. We start with the current situation.
Seasonal Distribution of Incoming Solar Radiation
The earth is tilted on its axis (relative to the plane of orbit) so that in July the north pole “faces” the sun, while in January the south pole “faces” the sun.
Here are the TOA graphs for average incident solar radiation at different latitudes by month:
And now the average values first by latitude for the year, then by month for northern hemisphere, southern hemisphere and the globe:
We can see that the southern hemisphere has a higher peak value – this is because the earth is closest to the sun (perihelion) on January 3rd, during the southern hemisphere summer.
This is also reflected in the global value which varies between 330 W/m² at aphelion (furthest away from the sun) to 352 W/m² at perihelion.
There is a good introduction to planetary orbits in Wikipedia. I was saved from the tedium of having to work out how to implement an elliptical orbit vs time by the Matlab code kindly supplied by Jonathan Levine. He also supplied the solution to the much more difficult problem of insolation vs latitude at any day in the Quaternary period, which we will look at later.
Here is the the TOA solar insolation by day of the year, as a function of the eccentricity of the orbit:
Figure 3 – Updated
The earth’s orbit currently has an eccentricity of 0.0167. This means that the maximum variation in solar radiation is 6.9%.
Perihelion is 147.1 million km, while aphelion is 152.1 million km. The amount of solar radiation we receive is “the inverse square law”, which means if you move twice as far away, the solar radiation reduces by a factor of four. So to calculate the difference between the min and max you simply calculate: (152.1/147.1)² = 1.069 or a change of 6.9%.
Over the past million or more years the earth’s orbit has changed its eccentricity, from a low close to zero, to a maximum of about 0.055. The period of each cycle is about 100,000 years.
Here is my calculation of change in total annual TOA solar radiation with eccentricity:
Looking at figure 1 of Imbrie & Imbrie (1980), just to get a rule of thumb, eccentricity changed from 0.05 to 0.02 over a 50,000 year period (about 220k years ago to 170k years ago). This means that the annual solar insolation dropped by 0.1% over 50,000 years or 3 mW/m² per century. (This value is an over-estimate because it is the peak value with sun overhead, if instead we take the summer months at high latitude the change becomes 0.8 mW/m² per century)
It’s a staggering drop, and no wonder the strong 100,000 year cycle in climate history matching the Milankovitch eccentricity cycles is such a difficult theory to put together.
Obliquity & Precession
To understand those basics of these changes take a look at the Milankovitch article. Neither of these two effects, precession and obliquity, changes the total annual TOA incident solar radiation. They just change its distribution.
Here is the last 250,000 years of solar radiation on July 1st – for a few different latitudes:
Figure 5 – Click for a larger image
Notice that the equatorial insolation is of course lower than the mid-summer polar insolation.
Here is the same plot but for October 1st. Now the equatorial value is higher:
Figure 6 – Click for a larger image
Let’s take a look at the values for 65ºN, often implicated in ice age studies, but this time for the beginning of each month of the year (so the legend is now 1 = January 1st, 2 = Feb 1st, etc):
Figure 7 - Click for a larger image
And just for interest I marked one date for the last inter-glacial – the Eemian inter-glacial as it is known.
Come up with a theory:
- peak insolation at 65ºN
- fastest rate of change
- minimum insolation
- average of summer months
- average of winter half year
- average autumn 3 months
Then pick from the graph and let’s start cooking.. Having trouble? Pick a different latitude. Southern Hemisphere – no problem, also welcome.
As we will see, there are a lot of theories, all of which call themselves “Milankovitch” but each one is apparently incompatible with other similarly-named “Milankovitch” theories.
At least we have a tool, kindly supplied by Jonathan Levine, which allows us to compute any value. So if any readers have an output request, just ask.
One word of caution for budding theorists of ice ages (hopefully we have many already) from Kukla et al (2002):
..The marine isotope record is commonly tuned to astronomic chronology, represented by June insolation at the top of the atmosphere at 60′ or 65′ north latitude. This was deemed justified because the frequency of the Pleistocene gross global climate states matches the frequency of orbital variations..
..The mechanism of the climate response to insolation remains unclear and the role of insolation in the high latitudes as opposed to that in the low latitudes is still debated..
..In either case, the link between global climates and orbital variations appears to be complicated and not directly controlled by June insolation at latitude 65’N. We strongly discourage dating local climate proxies by unsubstantiated links to astronomic variations..
I’m a novice with the historical records and how they have been constructed, but I understand that SPECMAP is tuned to a Milankovitch theory, i.e., the dates of peak glacials and peak inter-glacials are set by astronomical values.
Articles in the Series
Part One – An introduction
Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz
Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory
Part Five – Obliquity & Precession Changes – and in a bit more detail
Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name
Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago
Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers
Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover
Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs
Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs
Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age
Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2
Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland
Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II
Last Interglacial Climates, Kukla et al, Quaternary Research (2002)
Modeling the Climatic Response to Orbital Variations, John Imbrie & John Z. Imbrie, Science (1980)