Milankovitch Insolation study

Summary: The annual insolation of planet earth does not change during Milankovitch cycles. Instead it is the distribution of solar energy with latitude and with season that determines the earth’s climate. The most surprising result of this study is that the latitude gradient of summer insolation seems to determine the onset of glaciations. As a result of this we can predict that the next glaciation would naturally begin in  7000 years time.

I have been looking in detail at how long term orbital changes can affect the distribution of solar energy with latitude and with season. These results are taken from calculations based on Laskar’s  LA2004 orbital solution which covers the last 50 million years and future 10 million years.

  1. Seasonal Variation

First we look at the calculations over 6 million years for  the seasonal monthly changes in daily insolation at 65N.

Daily insolation at 65N for different months over 6 millions.

Figure 1: Daily average insolation calculated at 65N for different months over a 6 million year period. Monthly averages  for all 12 months are plotted.  Jan-June are shown in red, while July-Dec are shown in blue.   The green vertical lines shows the same pattern repetition in the future already occurred  2.8 million years ago.

In general there is a symmetrical 6 monthly seasonal balance about the summer solstice (currently June/July). However, one noticeable additional effect is that the variability in autumn (October) is far greater than that during spring (March). Early polar melt season insolation increases much stronger at high obliquity/eccentricity than it falls at the end of the melt season. Summer months are mostly symmetric about the summer solstice. The future pattern over the next million years has a very similar pattern to that calculated from 2.8 million years ago. Despite large changes in orbital eccentricity and obliquity, the total annually averaged insolation hardly changes at all over 6 million years. This is simply a reflection of Kepler’s 3rd law. High eccentricity brings shorter summers. Orbital effects only change the local distribution of solar energy with latitude and season. The total energy received by earth from the sun each year is essentially constant. It is noticeable that currently the distribution of radiant energy is in a low variability phase caused by a smaller eccentricity modulation than normal. Figure 2 in more detail summer months

65N for April, May, June, July, August,September

Figure 2: 65N for April, May, June, July, August,September

The plot above shows a more detailed look  on how precession works to balance spring insolation against autumn insolation. Note that there  a slight difference in timing depending on the choice of June (May21 – June21) or July (June 21 – July 21). This is due to the precession term changes in summer equinox. For the rest of this study we use the July figures, as do most other authors.

2. Latitude

Next we look at how solar insolation varies with latitude during the peak summer month – July.  The data covering the last 800,000 years of glaciations are shown in Figure 3 below. The insolation values plotted are for 6 different latitudes 90,80,70,60,50 and 40. In addition we show in orange the difference in insolation between the pole (90) and 60N.

Ice Volume is shown in cyan. The top graph shows the latitude dependence for July insolation.

Figure 3: Ice Volume is shown in cyan and the Epica (Antarctic)  temperatures in red. The top graph shows the latitude dependence for July insolation for different latitudes. The greatest spread is between 90 and 60. This 90-60 differential is shown plotted below in orange. The 10k rolling average is shown in red and  follows 41K the obliquity cycle. The blue arrows show coincidences with large and small interglacials whereas the lower blue curves show transient warming events. In general GISP Greenland data show stronger effects correlated with 65N,  but they only cover the last 200k years.

It is well know, and confirmed here,  that major terminations and intermediate ice melt-backs always coincide with maxima insolation. However, when two large maxima occur in quick succession at high eccentricity, the second one has little effect. It would appear that the gap between two peaks must be at least one obliquity cycle of 41,000 years to have a strong effect. This could be related to an albedo like hysteresis effect on growing ice sheets. At the summer equinox the net insolation received each day at the pole is the highest anywhere on earth. This average reduces to a minimum at 60N, but rising into a V-shape increase by 40N. This shape is dependent on  orbital parameters.  Three typical profiles are shown in figure 4.

3 typical insolation latitude profiles

Figure 4:  3 typical insolation latitude  profiles for July

Northern Hemisphere weather is driven by the temperature gradients between mid latitudes and the pole. The data show that the largest gradient(DS) in summer insolation is between the pole and 60N and varies with obliquity and precession. This is shown by the orange curve in figure 3. What is very interesting however is to study not the maxima, but the minima in DS. These minima consistently correspond to strong cooling periods throughout the full 800,000 year period,  corresponding to an  increase in (Benthic Fora) ice volume and a decrease in Epica temperatures. This is shown in figure 5.

Arrows show minima in the gradient of solar heating between 90N and 60N.

Figure 5: Arrows now show minima in the gradient of solar heating between 90N and 60N – (brown signal above)

The data show  that there is always a cooling effect on climate whenever the insolation gradient is minimum at high latitudes in mid summer. Furthermore minima in gradient do not correspond to minima in insolation. Presumably this is because a smaller change in energy flux difference with latitude reduces  mixing of warm air masses from lower latitudes towards the poles. This effect is looked at in more detail in the Figure 6, below which also shows the smaller, but more variable, gradient difference between the Pole and 40N

Detail of last 200,000 years. The lower curve is the S(Pole) - s(40). This shows stronger variability of the same cooling effect.

Figure 6: Detail of last 200,000 years. The lower olive curve is the S(Pole) – s(40) difference. This shows stronger variability of the same cooling effect. The next minima occurs in 7000 years time.

There is good agreement. Minima never occur within an interglacial, except the interesting case 190,000 years ago, coincident with a maximum in polar insolation. The large peak in 65N insolation gets cut short, leading to a rapid fall in temperature and increased glaciation. Assuming these observation are correct, then it is a simple matter to ‘predict’ when the current interglacial will end. Sawtooth interglacials like the Eemian 120,000 years ago and especially the Anglian 400,000 years ago always end  at the next DS gradient minimum. The most recent glaciation is also similar to the Anglian since both ended when the 400,000 year eccentricity modulation was at a minimum. The insolation data can be extrapolated forward to successive minima as shown in figure 6.  The next minima will occur in 7000 years time. Under normal circumstances this minimum  would naturally terminate our present Holocene interglacial, and probably also end  human civilisation. Could global warming delay the next ice age?

Anthropogenic Global Warming is real but its long term effects are still uncertain. The best measure of such effects  is climate sensitivity, or the net warming caused by a doubling of CO2. Despite 30 years of research this value has remained unchanged in the range 1.5 to 4.5C. Why is there no progress despite huge investment? I think the basic problem is that there  is a communal agreement that all climate models are valid. However, that can not really be the case as I described here.  Climate sensitivity must  have an exact value, but scientists are reluctant to give any preference on this, lest it damage funding for rival modelling groups. Therefore I will give my best estimate based on those models that best fit the measured temperature data. The answer is ECS=2.3±0.5C. Warming at this level is serious but not disastrous, since we know that such levels have occurred many times in the past.  CO2 levels must eventually begin to fall within a hundred years from now, because by then we will either have developed alternative energy sources,  or else society will have already collapsed. The biggest question 2000 years from now will be whether global warming has been sufficient to delay the next ice age by 50,000 years.  Assuming we are still in control of our destiny then,  we will likely then be trying to keep CO2 levels artificially elevated.

Updates: thanks to Lance Wallace for correcting spring/autumn mistake.

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When is the next Ice Age due?

All of Human civilization fits neatly into the current interglacial period. The development of agriculture, settlements and societies were all enabled by a beneficial climate  for the last  10,000 years. Interglacials usually average ~10,000 years,  so is our luck about to run out? It turns out that the answer is no, because we are very fortunate that human society has developed during an interglacial when the earth’s orbit  has very low eccentricity. Eccentricity is important because it regulates the strength of polar maximum summer insolation caused by precession of the equinoxes every 21,000 years.  Precession determines the distance from the sun during a Polar summer. If summer coincides with the earth’s perihelion then summer insolation can be up to 20% higher than average. However if the earth’s orbit is nearly circular, as it is today,  then precession has little effect at all. That is why we have about 12000 years left before cooling begins.

The current interglacial period showing how eccentricity is falling to near zero values. Mainly changes in obliquity will regulate future summer melt in the Arctic.

The current interglacial period showing how eccentricity is falling to near zero values. Mainly changes in obliquity will regulate future summer melt in the Arctic (blue curve). This reaches a minimum in 15,000 years time. The arrow marks the cross-over in N-S asymmetry.

The peak of the warmer Eemian interglacial 120,000 years ago lasted less than 10,000 years, because the much larger eccentricity at that time enabled the first minimum precession summer to increase the spread of northern ice sheets.

The last Eemian interglacial was warmer than the current one but lasted much shorter

The last Eemian interglacial was warmer than the current one but ‘lasted’ only about 10,000 years

One needs to go back 420,000 years to find a similar glacial cycle to the current one at low eccentricity. This is known as the Anglian glaciation because the ice sheets spread as far south as Anglia and diverted the Thames southwards from the Wash to its current basin. The Anglian  had very similar orbital parameters to those we experience today.

Compare the Anglian and Palocene interglacials

Comparison of the  Anglian (420K years ago) with our own  interglacial. Note how both seem to have experienced similar Younger Dryas events. However, there are differences in precession evolution with North-South inverted.

This result implies that the the current interglacial would naturally last another 20000 years. However, the alignment of precession is not perfect, and the north-south precession cycle is inverted. Despite this, at very low eccentricity, it is only obliquity that really counts. We conclude that within 12000 years the earth would naturally be returning to a new ice age lasting 100,000 years.  The earth then enters another long period of high eccentricity lasting a further 400,000 years.  Future Interglacials will last only ~10,000 years, before the cycle repeats. One only needs to look at how transient interglacials were 600,000 years ago when eccentricity was high.

Note how the obliquity cycle reasetrts itself eccentricity is high. The glacial periods 600,000y ago and 300,000y ago are essentially co-joined 41k cycles.

Note how the obliquity cycle reasserts itself when eccentricity is high. The glacial periods 600,000y ago and 300,000y ago are essentially co-joined 41k cycles.

Now we look at an even more remarkable correlation. Eccentricity  has an even longer cycle with a time base lasting 2.8 million years. The following plot is the result of calculations  by Laskar and his group covering 50 million years.

LA2010 calclations of the earth's eccentricity over a 4 million year period spanning the present day.

LA2010 calculations of the earth’s eccentricity over a 4 million year period spanning the present day marked by the arrow. Notice how the long term pattern repeats a similar beat to 2.8 million years ago.

The mid-Pliocene was much warmer than today  with CO2 levels similar to those caused by man today (400ppm or above). This is about as warm as most climate models predict the earth will be by  2100  – i.e. about +2C above current temperatures.  The full 5 million year record of Benthic Fora data gives clear evidence of Milankovitch cycles throughout the period, including a 420K eccentricity cycle in earlier times. However by 3 million years ago glacial cycles had  begun to follow a regular 41K obliquity cycle. It was only much later (< 1 million years) that 100k deep glacial cycles began.

5 million years of benthic foram delta&;O16 data. The blue curve is a fit to Milankovitch harmonic data.

5 million years of benthic foram deltaO16 data. The blue curve is a fit to Milankovitch harmonic data.

So can we learn anything by looking at the data 2.8 million years ago in the super-cycle? The plot below shows the Benthic Fora data (Ice volume proxy for temperature) compared to the Milankovitch cycles


Comparison of the Benthic Fora ice volume data (shaded grey) with eccentricity (black), Obliquity (purple) and Polar insolation (blue-north, dashed-south). Average (red) follows obliquity. Cycle follows obliquity except for two shaded areas.

Even 2.8 million years ago it seems that the decrease in polar insolation due to decreasing obliquity needed a helping hand to enter another  glaciation period.

Even without human induced increases in CO2 the current interglacial was set to last nearly as long as the Anglian.  The minimum obliquity is due to be reached in 11,000 years time and a minimum Arctic summer in 13,000 years time. A spread in ice sheets and cooling would normally be expected to have started before then. Has global warming delayed this process and if so then by how much ?

If we assume emissions continue to the end of this century and then reduce as we develop other energy sources, then the temperature response might look something like this.

Fig 4: Long term predictions assuming non-carbon energy sources post 2100. The 4 feedback factor curves labeled F use the same calculations as described above based on the red CO2 level curve labelled A1B.

Long term predictions assuming non-carbon energy sources post 2100. The 4 feedback factor curves labeled F are based on the red CO2 level curve labelled A1B. They are equivalent to climate sensitivity.

We can argue about how warm the peak temperature will get and CMIP5 models vary about this roughly  between 2 and 5 degrees. However this manmade climate disturbance should last for not much more than  3000 years so long as our emissions are reduced before 2100. The real question is what level we should then try to keep CO2 to avoid another devastating glaciation in 13,000 years time? If we want to survive long term then probably we should never let CO2 fall below 300ppm ever again!

Posted in AGW, Climate Change, Ice Ages | Tagged | 46 Comments

Ocean Heat Content variability.

Kevin Trenberth once claimed that the hiatus in warming from 1998 to 2014 was simply due to ‘missing’ heat being sequestered in the oceans. The annual global heat content to 700m indeed did show a rise, as estimated by measured temperature profile with depth. I have never looked at this NODC data until now.  Here  is a 3-monthly (JFM,AMJ,JJA,OND) animation of all the available data.


Animation of 3 monthly ocean heat content anomalies

Firstly it is obvious that seasonal changes far outweigh any long term change. There are large regional variations near the equator dominated by El Nino El Nina, while the poles show little net change over time. If we look at the first 3 months of 2016 (below) we see the massive shift of heat by El Nino and that a large cold spot has appeared in the North Atlantic.


Ocean Heat content anomaly for Jan-Mar 2016

This cold spot in the North Atlantic has been highlighted by Ole Humlum through his climate4you reports. Is this perhaps something to do with AMO, and if so what is  driving it? Perhaps one answer lies with the precession cycle of the moon. Commenter ‘charplum’ (see The forgotten Milankovitz effect ) discovered an 18.6y signal in the Ocean Heat content data for the North Atlantic based on Humlum’s data.

Heat Anomaly for the North Atlantic region. Shown in red is charplums fit which includes the 18.6y term with a correlation of 0.95

Heat Anomaly for the North Atlantic region. Shown in red is charplum’s fit to harmonics which includes the 18.6y term with a correlation of 0.95. The red arrows show the dates for Maximum lunar standstills which occur each 18.6 years

Tidal tractional drag is felt at all depths in the ocean and therefore can affect heat mixing. The position of maximum spring tides depends on the declination of the moon. The maximum tidal drag force is centered at around 45 degrees to the lunar declination angle. This varies with the 18.6y precession cycle. Maximum lunar standstill of 28.5 degrees last occurred in June 2006 while the minimum lunar standstill of 18.5 degrees occurred last October. The data suggests that in the North Atlantic enhanced tidal mixing increases the net heat content contained in the top 700m, while reduced mixing at minimum declination leads to central cooling.


The UK sits right within the N. Atlantic study area used by Humlum, and its climate is dominated by westerly winds from the Atlantic. Could such tidal mixing be evident in the Central England temperature data? Again Charplum found evidence of a 18.6 year signal in the annual CET data. I plot below the data since 1750 with a superimposed precession signal.


Central England annual temperature data from 1750 to present. The long term average is ~9.5C. Deviations are shaded blue and the 5 year Fourier average is shown in red. The sine curve represents the lunar precession cycle.

It is always difficult to prove any effect when there are so many variables involved in a temperature series, including of course CO2. However it is tempting to associate just such a lunar signal in CET.

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