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.

Seasonal Variation

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

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

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.

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.

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.

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

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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