When is the next Ice Age due ?

According to Emily Shuckburgh and Prof. Erik Wolf in a letter to the Times , the next Ice Age is not expected for another 50,000 years. Their claim seems to be based on a 2016 paper in Nature by Andrey Ganopolski, R. Winkelmann & H. J. Schellnhuber, Nature 529, 200–203 (14 January 2016).

“Even without man-made climate change we would expect the beginning of a new ice age no earlier than in 50.000 years from now”

The paper also claims that the Earth narrowly avoided the inception of a new ice age just before the Industrial Revolution, because CO2 levels were 40ppm above some hypothetical threshold of 240ppm. Of course humans were responsible for this (luckily this time) due to deforestation and land use change.

The leading hypothesis currently is that Ice Ages initiate when summer insolation reduces sufficiently so that it fails to melt back the previous winter snow. Ice then slowly accumulates leading to an increase in albedo as the northern ice sheets slowly grow. There are two causes for this effect, both of which interplay one with the other. Changes in the obliquity of the earth modulate summer insolation at both poles. Precession of the seasons, due to the precession of the earth’s axis, change the timing of the summer equinox. Combined together they then modulates the distance ‘R’ to the sun during summer months, simply because the earth has an elliptical orbit . The strength of this precession ‘forcing’ is amplified by \frac{1}{R^2} at high eccentricity.

Note how the obliquity cycle reasserts itself if eccentricity is high. The 2 glacial periods 600,000y ago and 300,000y ago are essentially co-joined 41k cycles.

Until 800,000 year ago ice ages followed the 41,000 year obliquity cycle. Low obliquity reduced summer insolation at the poles and glaciers expanded. High obliquity reversed this initiating an interglacial. No-one knows for sure why this change happened, but it is usually assumed that the ice sheets became too large for obliquity alone to melt them back. They then also needed the help of the precession term acting on the expanded northern ice sheets. However, this does not explain why these insolation minima only work once ice sheets have reached some critical size. One attractive explanation to explain this is CO2 starvation . CO2 levels in the atmosphere naturally increase with the onset of an interglacial as a result of the warmer temperatures and an enhanced life cycle. These increases in CO2 act as a small positive feedback on temperatures.

Glaciation begin at high values of CO2, which in general then fall with reducing temperatures and reductions in biosphere activity. However during the Eemian CO2 levels remained above 260ppm for some 35,000 years into the last ice age. If CO2 plays any role in Ice Ages, it is just a supporting role as a feedback.

So when would the next ice age naturally begin had humans not burned any fossil fuels ? The Anglian interglacial some 400,000 years had similar orbital eccentricity to that during the Holocene. The preceding glaciation was also very severe like the that preceeding the Holocene.

Compare the Anglian and Holocene interglacials

The Anglian interglacial lasted about 25,000 years which is roughly twice as long as average. Cooling initiated on a reducing obliquity coinciding with a northern summer minimum. The Holocene interglacial has northern and summer hemispheres inverted but obliquity still follows almost the same pattern. The minimum to which Ganopolski refers to as a close call pre-industrial inception is really nothing of the sort, since obliquity was still too high. I believe cooling would naturally begin another glaciation before 10 thousand years from now as we approach minimum obliquity. At the latest it starts 15,000 years from now. So will anthropogenic global warming delay the onset of the next ice age for 100,000 years as the authors argue ?

Let’s assume that in the worst case we manage to double atmospheric CO2 levels before curbing carbon emissions (perhaps we have magic fusion reactors by then). Then quoting an acknowledged expert in Ocean Climate Chemistry – David Archer

“Dissolution into ocean water sequesters 70–80% of the CO2 release on a time scale of several hundred years. Chemical neutralization of CO2 by reaction with CaCO3 on the sea floor accounts for another 9–15% decrease in the atmospheric concentration on a time scale of 5.5–6.8 kyr. Reaction with CaCO3 on land accounts for another 3–8%, with a time scale of 8.2 kyr. The final equilibrium with CaCO3 leaves 7.5–8% of the CO2 release remaining in the atmosphere. The carbonate chemistry of the oceans in contact with CaCO3 will act to buffer atmospheric CO2 at this higher concentration until the entire fossil fuel CO2 release is consumed by weathering of basic igneous rocks on a time scale of 200 kyr.”

So after 15,000 years we end up with CO2 levels = 280+ (0.08)*280 = 302 ppm. The remaining anthropogenic CO2 forcing works out at only 0.4 W/m2, whereas the drop in summer insolation over the Arctic between now and the next obliquity minimum is 22W/m2 . That is 50 times larger!

Following both the Eemian and the Anglian consequent glaciations all began with CO2 levels well over 280ppm. There is no reason to suppose that the Holocene will be any different, assuming that CO2 levels peak below 600 ppm this century.

Perhaps in 10,000 years time we will have learned to control the earth’s climate to the advantage of all life through managed CO2 emissions.

There again perhaps not.

Posted in Climate Change, Ice Ages | Tagged | 10 Comments

A new measurement of Equilibrium Climate Sensitivity (ECS)

A dynamic analysis of global temperature data  gives a value of ECS = 2.5C ± 0.5C . Values above 3.0C or below 2.0C are ruled out. This analysis is based on two assumptions: 1) That net climate forcing follows that used in CMIP5  (ref 1).  2) That climate equilibrium is reached with an e-folding time of 15 years (derived from GISS Model-II).

Detailed comparison of Hadcrut4.6 with calculated temperatures for different ECS values.

Analysis Method

Equilibrium Climate Change or ECS is defined as the increase in global temperatures following a doubling of CO2, once the climate system has stabilised. Models can calculate ECS by running a step function for CO2 concentrations from say 280ppm to 560ppm and then plotting how the temperature responds with time. Each  model gives a different value for ECS, and the spread in values represents in AR5 as an estimate of the uncertainty. I am going to use one of the simplest models, GISS Model II to investigate this lag effect of climate stabilisation which is mainly caused by the heat inertia response of the oceans to increased forcing.

Fig 1: Response temperature curve from a pulse doubling of CO2 in 1958 and fit described i the text

Fig 1: Response temperature curve for GISS Model 2 following a sudden doubling of CO2 in 1958. and fit described in the text. The e-folding time is 15 years.

After roughly 100 years the climate reaches a new stable state, and shows that GISS Model II gives a value for ECS of 4.4 C. The red curve is a fit to the temperature response curve which can be written in terms of temperature anomalies in the general form

\Delta{T} = ECS \times (1-e^\frac{-t}{15})

In reality CO2 levels in the atmosphere have been slowly growing over the last 200 years by annual increments as recorded since 1950 by the Mauna Loa data. The direct radiative forcing from increased CO2 has been calculated by radiative transfer codes. My derivation of this formula is described here.  A more precise parameterisation of that forcing is the well known formula

DS = 5.34 \times \ln{C/C_0}

where C_0 is the initial CO2 concentration and C is the incremental value. A doubling of CO2 alone give a forcing of ~3.7 W/m2 which at equilibrium is balanced by a surface temperature rise of 1.1C by applying Stefan Boltzmann’s law.

S = \sigma \epsilon \times T^4 \Longrightarrow DS = 4 \times \sigma \epsilon T^3 DT

Ignoring feedbacks and using \epsilon = 0.6 results in ECS being ~ 1.1C. Higher values of ECS are due to net positive climate feedbacks, mainly from increased H2O. CMIP5 models give a large spread in predicted ECS values due to the different ways H2O and cloud feedbacks are handled. Can we measure ECS directly from the data ?

The problem with measuring  ECS from the temperature data is that net forcing is increasing every year so we can never wait long enough for the climate to reach an equilibrium state. Given these constraints I adopt a different approach.

We treat the temperature record at any time as the response to the sum of previous discrete annual pulses of forcing. Each pulse causes a time dependent temperature response as shown in Figure 1. The resultant annual temperature for year n is then the integral of all previous responses up to that year.

Each pulse response is tracked through time and integrated to yield the overall instantaneous temperature at year N:

\Delta{T}(N) = \sum_{k=1}^N (\Delta{T_0}(1 - e^\frac{(N-k)}{15}))    – Equation 1.

This procedure can then be repeated for various possible values of ECS and compared directly to the temperature data. Rather than using the CO2 forcing directly we use the ‘Total Anthropogenic’ AR5 forcing data as shown below, which turn out to be almost the same thing.



The actual forcing data used in this analysis which is almost identical to CMIP5 net Anthropogenic.

The equilibrium temperature response \Delta{T}_{0} to an incremental forcing DS is  \frac{DS}{3.5-f} , where f is calculated from each possible value of ECS by using:

ECS = \frac{3.7}{3.5-f}

where 3.7 is the direct forcing due to a doubling of CO2 (calculated from 5.34 \ln{2} ) and f is the feedback parameter. This then allows  to calculate the feedback parameter f corresponding to a particular value of ECS, and then use f to to calculate the impulse forcing response. The resultant values of f are as follows.

1.5 1.03
2.0 1.65
2.5 2.02
3.0 2.26
3.5 2.44
4.0 2.57

A perl script was written to integrate forward past temperature responses  into a predicted annual temperature for various values of ECS by applying equation 1. The results are compared to the annual Hadcrut4.6 values.

Comparison of Hadcrut4.6 annual temperature anomalies with predicted temperatures for different values of ECS.

It is instructive to look in more detail at the recent data as it then becomes obvious that high values and very low values of ECS are ruled out.

Detailed comparison of Hadcrut4.6 from 1940 to 2017 with predicted temperatures assuming different values for ECS. Error bars are ±0.05C

The best fit to the observed temperature distribution using this method is ECS = 2.5C. High values above 3.oC  and very low values below 2.0C are ruled out. So my best estimate is

ECS = 2.5 ± 0.5C    (95% probability)

The error is based on post 2000 temperature values. ECS=2.0 falls within just 12% of data point errors (0.05C) while ECS = 3.0 falls within 24%.  This is to be compared with ECS=2.5C which falls within 84%. Both ECS=2.0 and ECS=3.0 are about 2 sigma from the mean average shown in black.  By 2017 ECS=2.0 lies 0.15C below the mean and ECS=3.0 lies 0.26C above the mean. Therefore I estimate a 95% probability that ECS lies within this range.

If climate sensitivity is 2.5C then  global temperatures can never rise more that 2.5C above pre-industrial levels so long as CO2 levels are kept below 560 ppm. This is a far more achievable goal than many activists are calling for since it requires only gradual reductions in CO2 emissions by 2100. This then gives us time to develop realistic alternatives, which I am convinced must have a strong nuclear base.


Forster et al. Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models, J. Geophys. Res.,118 1139-1150, 2013

Posted in AGW, Climate Change | Tagged , | 36 Comments

November temperature down 0.04C

My value for the November global average temperature is 0.65C, down 0.04C since October. The yearly average for 2017 ( 11 months) is now 0.73C making it equal to 2015 and 0.1C cooler than 2016. These are based on Spherical Triangulation of GHCN V3C and HADSST3.

A noticeable La Nina type signal is evident in November.

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