Historical Geology/Climate models

In this article we shall look at how climate models are constructed, their strengths and weaknesses, and how they can be applied to the study of plate tectonics.

Climate and climate models

First we should look at what factors should be represented in a model of the climate.

First of all, there is the insolation. This drives the climate, but it doesn't exclusively determine it, otherwise the weather at any point could be expressed as a function of time and latitude.

But in fact there is also the atmospheric circulation to be taken into account. This transports atmospheric heat and moisture from place to place. The atmospheric circulation is partly caused by the Coriolis Effect (fundamentally, because the Earth is rotating). However, the circulation is also caused by variations in the density of the atmosphere, which are caused by variations in the temperature and amount of moisture in the atmosphere; or, to put it another way, one of the main causes of the weather is the weather. It is this fact that makes modeling the weather or the climate particularly difficult; such systems are notoriously hard to model.

One important factor affecting the nature of the circulation is the location and nature of the landmasses. The ocean will absorb more heat than the land; and then the amount of heat absorbed the land will depend on the nature of the ground cover, i.e. whether the land in question is desert, forest, covered by a sheet glacier, etc. Similar remarks can be made about moisture; obviously more water will evaporate from a sea or a lake than from a desert with the same insolation.

By modeling insolation and the circulation of the atmosphere, climatologists can produce what is known as an atmospheric circulation model, or ACM.

Such a model is the simplest that's any use at all, but it still doesn't tell the whole story. The ocean has its own circulation, and this also transports heat in tandem with the atmospheric circulation. A really good model should take this into account.

Surface ocean currents can be driven by the wind. Deeper in the oceans, we have the thermohaline circulation. As the name suggests, or would suggest if we were Greek, this circulation is driven by the temperature and salinity of the oceans, both of which affect the density of seawater. The differences in density drive vast currents, extending thousands of miles and carrying 100 times more water than the Amazon River.

The thermohaline circulation.

The map to the right shows the thermohaline circulation; as you can see, it can be quite complex, with less dense currents actually flowing over denser currents flowing beneath them in a different direction.

The other thing that affects the ocean circulation is, of course, the positions of the continents, which constrain the flow.

By adding the ocean circulation to an ACM, climatologists can produce a General Circulation Model, or GCM.

Even then, there are things which we would like to add to a really good model of the climate. For example, we have noted above that ground cover affects the climate. But it is also the case that the climate will to a large extent determine the ground cover from location to location, causing forests here, and grasslands there; deserts in one place and sheet glaciers in another. Once more we have a case of the climate causing the things that cause the climate, and so we have another complicated set of interactions to model — if we can.

Accuracy of the models

The size and complexity of the climate are a challenge even to modern supercomputers, and limited processing power (in effect, how fast the computer can perform calculations) limits the accuracy and detail attainable in climate models. The most obvious problem is that of scale. No computer can be expected to simulate the behavior of each molecule of air in the atmosphere. Suppose, then, that as a coarser approximation we divided the Earth up into "cells" each one kilometer square, and used a model that assigned to each one at each step of the computer simulation a figure representing the average temperature and the average humidity of the atmosphere inside that "cell". Then our model would be inaccurate by reason of this approximation; it would also be inaccurate by ignoring the oceanic circulation, and it would still involve simulating the interaction of half-a-billion cells; and so even such a degree of approximation might well leave our model intolerably slow. Of course, scientists can always spend more time running slower models, but they rightly suppose that an imperfect model which returns results within the lifetimes of the researchers is, despite its acknowledged flaws, superior to one which delivers more accurate answers to their great-grandchildren.

Any model of the climate must therefore involve some degree of simplification and approximation; and any such model will therefore be wrong to a certain extent. It is for this reason that there are so many climate models: the researchers must choose in what way to simplify their models in order to reduce the degree of error, and it is not yet clear how best this may be achieved. As a consequence of this, the first report of the Paleoclimate Modeling Intercomparison Project (hereafter referred to as PMIP1) lists 22 climate models produced by 19 different research institutions, each in their own way striving after accuracy.

It is possible to find out how good or bad the various models are, and in which respects, by comparing their results to data. We can of course compare the climate now (as measured instrumentally) with the climate as the models say it should be; any model not producing reasonably good agreement has fallen at the first hurdle. But we can also get the models to simulate events in the past and compare them with proxy data. This was done by the PMIP, comparing models with proxies for the mid-Holocene (6,000 years ago) and the last glacial maximum (LGM, 21,000 years ago). At these dates, the climate was markedly different from the present; yet they are recent enough that the full array of proxies can be brought to bear on what the climate was actually like.

The results are such as to be encouraging to an optimist and disappointing to a pessimist. To briefly summarize the results, the models tend to be qualitatively correct: they correctly indicate the nature of the differences between the present climate and the climates of the mid-Holocene and the LGM; on the other hand, they are quantitatively inaccurate, tending to underestimate the magnitude of the differences between then and now.

It should be added that in the first phase of PMIP the research was confined to ACMs which did not take the oceanic circulation into account; most models also omitted the interaction between climate and ground cover. One would expect the results to be more accurate when more factors are taken into account; more complex models which do so will be reported on the in forthcoming second phase of PMIP.

Paleoclimatology in deep time

If we want to look back millions rather than thousands of years, then there is another factor we need to take into account: the fact that the continents have altered their positions. As their location affects both the atmospheric and oceanic circulation, modeling paleoclimates in deep time requires a reconstruction of their positions.

This leads to an interesting line of research. When we reconstruct the position of the continents at some past date, and use climate models to tell us what, in theory, the climate should have been like, does this agree with the sedimentary evidence of what the climate was like at that time?

The answer is "yes". There are a number of results obtained from climate models which are consistent with proxies and sedimentary indicators of climatic conditions. For example:

• Continents at higher latitudes are, other things equal, colder than those nearer the equator. (This is rather obvious, but it is nice to see it confirmed by, for example, evidence of continental glaciers rolling over Africa at a time when paleomagnetic data tell us it was further south.)

• Changes in the average temperature of the Earth have more effect near the poles than the equator.

• Continental glaciation in Antarctica could only begin when the other southern continents were sufficiently separated from Antarctica to allow the existence of the Antarctic Circumpolar Current. (For further details see Katz et al. (2011) Impact of Antarctic Circumpolar Current Development on Late Paleogene Ocean Structure, Science, 332(6033); also Bijl et al (2009) Early Palaeogene temperature evolution of the southwest Pacific Ocean, Nature, 461.) These models are borne out by measurements of Mg/Ca, δ¹⁸O, TEX₈₆ and U^k'₃₇.

• Polar ice-caps will not form unless there are land-masses sufficiently near the poles.

• The interiors of supercontinents should be dry.

• The rise of the Himalayas is implicated in a significant strengthening of the Asian monsoons. See for example Valdiya (1999) Rising Himalaya: Advent and intensification of monsoon, Current Science, 76(4); also Clift et al (2008) Correlation of Himalayan exhumation rates and Asian monsoon intensity, Nature Geoscience, 1.

Now this sort of agreement should increase our confidence in our reconstruction of continental drift, in climate models, and in the use of sediments to reconstruct climates; for if any one of these three techniques was no good, then there would be no reason for the agreement between the models and the evidence.