Ice Ages

We have seen that snow cover needs to be taken into account as part of Earth's albedo, but that ice and snow are seasonal phenomena, i.e. they appear in winter and disappear in summer.

If a perturbation alters the albedo - say a volcanic eruption carries copious material into the stratosphere where it increases the formation of high-level clouds, we can expect the planet to cool as more light is reflected into space. This in turn implies that ice and snow will melt more slowly and last well into late spring and eventually into summer. As such covered surfaces usually have a higher albedo than the bare surface, this means even more radiation is reflected back into space and even more cooling. Eventually a point is reached where ice and snow do not melt even during Summer and accumulate year by year - glaciers start to grow.

In reality this can happen in a small, localized spot such as a mountain region from which glaciers can then gradually move into the lowlands. In the simulation, the smallest region in which this can happen is a single surface element, for the Earth model investigated here that's a 10 deg by 10 deg surface, i.e. a rather large area. For that reason the onset of Ice Ages in the simulation can be expected to be much more violent than in reality.


In order to see how the simulation can be driven into an Ice Age, let's alter the weather declaration like this (note the increased upper limit of the high cloud cover):

mid_cloudlevel_min 0.0
mid_cloudlevel_max 0.4
high_cloudlevel_min 0.0
high_cloudlevel_max 1.0
precipitation_factor 1.0

Using a global property record (i.e. averaged across all surface elements) we can get the mean temperature over an evolution time of 20 years.

record_global npoints 100 delay_a 1.0 file test.dat var_x years var_y temperature

If we keep increasing the value for high_cloudlevel_min to simulate more and more of a reflecting layer, we might get to see something like this:

Global average temperatures [K] for different amount of high level clouds

For a while, more clouds just lower the average temperature down from 288 K, but eventually, across a relatively narrow range, the dynamics changes. It seems some 275 K are marginally stable, but a single cold winter (green curve) suffices to drive Earth into glaciation - temperatures drop until they reach a new equilibrium point at about 240 K, and increasing cloud cover much more only serves to drive the climate there faster.

So, the behavior of the system is highly non-linear - for a while the lowering of the temperature is proportional to the amount of albedo increase, but then a completely different pattern is seen.


Using a plot request like

file earth_snow.dat
var_z snow_thickness

we can access the snowcover on the ground after the freezing has occurred. The result shows copious covers on landmasses both on northern and southern hemisphere, with the maximum of the snow in Asia. Also both northern and southern sea ice is snow-covered to some degree, albeit with less thickness, and only an equatorial valley remains free of snow.

Snowcover [cm] at the end of a 20 year freezing period

The reason for this however is not that the tropics would be warm - far from it. Looking at the temperature distribution reveals that even during summer -20 deg C are fairly usual, so in this scenario Earth is frozen over.

Ice Age temperatures [K] during northern hemisphere summer

The issue is rather that the atmosphere's capability to hold and transport humidity depends on temperature - while at high temperatures the air can hold a lot of water, at low temperatures this is no longer true, and this leads to a progressive lessening of precipitation as the planet cools. By the time the tropics freeze over, there is so little moisture left in the atmosphere that precipitation ceases (incidentially that is also the reason more snow ends up in Siberia than on the sea ice). By comparing a fast with a slow transition to Ice Age conditions one can observe the same thing - a fast Ice Age ends up with less snow cover because the water freezes out of the atmosphere quickly, a slow transition to an Ice Age has plenty of time to pick up moisture from the tropics and deposit it as snow on higher latitudes.

Let's note at this point that the simulated scenario is qualitatively plausible, but quantitatively certainly not exact. For instance, the reduced ability of a cold atmosphere to hold moisture will almost certainly have an effect on cloud formation, and with reduced cloudcover, albedo might increase somewhat. Likewise, it is not a given that heat transport remains as strong if the total energy input is reduced by snow reflecting a large portion of light back into space, which might keep the tropics warmer at the expense of the rest of the planet.

But let's defer a discussion of such feedback mechanisms to a later stage and focus now on the opposite of what we've just seen - global warming.

Continue with Global warming.

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