Borodog
11-13-2006, 09:56 PM
This afternoon I attended the Physics Department weekly colloquium, give by J. A. Rial on his work with M. Yang (both of UNC Chapel Hill) on modelling and predicting abrupt climate change.
A little background. Extremely accurate temperature data is available from both arctic and antarctic ice cores that go back hundreds of thousands (and in some cases millions) of years:
http://i27.photobucket.com/albums/c153/Borodog/Ice_Core_Data.gif
The bottom trace is sea surface temperature (SST).
The question that needs to be answered is what causes the apparently chaotic-seeming switches between warm climate states and hot climate states, often characterized by sea surface temperature changes of up to 15 degrees C (almost 30 degrees F for us backward Imperial Americans) over extremely short time scales, sometimes as brief as 2 years (yes, the data is that well resolved).
The first thing you need to understand is that the Earth's climate is being forced, specifically by the sun, which is an energy input into the climate. The second thing that you need to know is that solar energy input is not constant, it varies over time due to purely celestial mechanical effects. The Earth's orbital eccentricity varies over time (since the Earth-sun system is not a true 2-body system), with a period of about 100,000 years. The Earth's axial tilt oscillates between about 21.5 degrees and 24.5 degrees, with a period of about 41,000 years. The direction of the axis of the Earth's rotation precesses with a period of 19,000 to 23,000 years.
All of these effects combine to make the amount of solar radiation received by the Earth ("insolation") vary in a very particular fashion:
http://i27.photobucket.com/albums/c153/Borodog/insolation.gif
If you have the calibrated eye, like I fancy I do, you can convince yourself that you can already see a corelation between the ice core data and the insolation function. This is called Milankovich forcing.
In general, however, if you look at the power spectra of the data, most of the power is a a frequency that coresponds to a period of about 4,000 years. In other words, most of the climate variation seems to occur over periods of a few thousand years, which is much less than even the most rapid of the solar forcing terms (the precession term). Hence it has historically been the case that solar forcing has been dismissed as a cause for the climate variation, particularly the rapid shifts.
So, an internal climate model was developed to explain these short time scale oscillations (so-called Dansgaard-Oeschger, or DO oscillations), based on 3 things: sea ice coverage, thermo-haline circulation, and greenhouse gases (GHGs).
Sea ice plays an important roll in the Earth's climate. Ice is almost pure white; it is very reflective. When there is a lot of ice on the sea's surface, the Earth's relectivity goes (it's albedo) up, meaning more energy is reflected instead of absorbed into the climate system. Obviously there is the possibility of positive feedback: If the amount of sea ice increases, less energy is absorbed, the climate is cooler, and more ice can form. Vice versa, if the amount of sea ice decreases, more energy is absorbed, the climate is warmer, and ice can melt at a higher rate.
Thermo-haline circulation describes the the global "conveyor belt" of currents that runs throughout the world's oceans, sometimes running high in the ocean, sometimes deep, sometimes warm, sometimes cold, sometimes more dense, sometimes less. The details of the THC are beyond the scope of this post (or my understanding, for that matter), but suffice it to say that energy can be stored in the THC system until it becomes unstable, for example if cold, more dense water is above warm, less dense water. When this occurs the system can rapidly change state to a new equilibrium.
Greenhouse gases like carbon dioxide, methane, and water vapor can act to trap solar radiation in the atmosphere. Higher concentrations of these gases in the atmosphere may lead to a warmer climate. I emphasize may precisely because today's speaker did; which CO2 and methane concentrations are highly corelated with sea surface temperature in the data, nobody is sure which drives which; i.e. the direction of causality (and it may well go both ways, the perfect setup for an instability) is unknown.
So what Rial and Yang did was to model the climate as a set of coupled non-linear thermal oscillators, basically the sea ice, the THC, and GHG. They are coupled by the fact that the THC can have an effect on sea ice; for example if warm deep waters suddenly change state to become warm, shallow waters, the melt rate of sea ice can increase, and vice versa. Similarly, GHGs are coupled to sea water temperature, because when the water gets cold enough, CO2 uptake into the ocean accelerates, and vice versa.
The classic system of coupled oscillators is a system of masses connected with springs of differing stiffness. In this case, the oscillators are thermal, and model the behavior of the sea ice, the THC and GHGs with non-linear coupling between them. The model thus created is the so-called Saltzman-van der Pol Oscillator (SVO) model. It's a set of two non-linear coupled first order differential equations that represent the interaction between sea ice coverage, mean ocean temperature, and GHG concentrations. These can be transformed into a single second order non-linear differential equation that can be set equal to a term given by the Milankovich forcing (insolation).
In the absence of the Milankovich forcing from the insolation function described before, this model produces very periodic "shark fin" shaped climate oscillations. Note that these already resemble the general shape of the warm periods, cold periods, and sharp transitions in the ice core data:
http://i27.photobucket.com/albums/c153/Borodog/unforce.gif
Notice that the main problem is that the climate is not nicely periodic like the model (and of course, the high frequency "noise" is not modeled accurately).
But what happens when you solve the model including the insolation function?
http://i27.photobucket.com/albums/c153/Borodog/forced.gif
This is probably the single most amazing result I have ever seen. A single 2nd order differential equation accurately reproduces the qualitative nature of global climate data for the past hundred thousand years, and to a large extent does a damn good job quantitatively as well. The high frequency behavior is still not modeled well. The model itself is very crude, particularly in its treatment of the carbon cycle (the GHG bit). But the corelation between the model and the data is undeniable.
Have a look at the model compared to the actual data for the last 25,000 years:
http://i27.photobucket.com/albums/c153/Borodog/25k.gif
I can't stress enough that this corespondance between the data and such a simple model is absolutely AMAZING. The corespondance is even better according to Rial, who informed us that newer reconstructions of the most recent temperature data show a much bigger drop in the past 1000-2000 years, which is more in line with the model prediction.
Also, note at the very right hand side that the model predicts that we are currently in a period of abrupt climate change toward warmer climate (before another semi-glacial plunge, to be sure). Hence the model predicts that we would be in a period of rapid global warming even if mankind were still in the stone age.
Rial was quick to point out that any such prediction must be taken with a giant grain of salt. It is easy to dismiss the high frequency "noise" with hindsight in comparing the model to the data, but you can't do any such thing when you make predictions about near term future climate change, which is by definition in the short period/high frequency regime.
He also made it clear that the model does not take into account anthropogenic CO2, which has put atmospheric CO2 concentrations 1/3 higher than they have ever been according to the ice core data.
He finished up his talk by saying that they hope to increase the complexity and the accuracy of the model, particularly the carbon cycle, and they hope to be able to eventually accurately predict abrupt global climate change.
Amazing.
A little background. Extremely accurate temperature data is available from both arctic and antarctic ice cores that go back hundreds of thousands (and in some cases millions) of years:
http://i27.photobucket.com/albums/c153/Borodog/Ice_Core_Data.gif
The bottom trace is sea surface temperature (SST).
The question that needs to be answered is what causes the apparently chaotic-seeming switches between warm climate states and hot climate states, often characterized by sea surface temperature changes of up to 15 degrees C (almost 30 degrees F for us backward Imperial Americans) over extremely short time scales, sometimes as brief as 2 years (yes, the data is that well resolved).
The first thing you need to understand is that the Earth's climate is being forced, specifically by the sun, which is an energy input into the climate. The second thing that you need to know is that solar energy input is not constant, it varies over time due to purely celestial mechanical effects. The Earth's orbital eccentricity varies over time (since the Earth-sun system is not a true 2-body system), with a period of about 100,000 years. The Earth's axial tilt oscillates between about 21.5 degrees and 24.5 degrees, with a period of about 41,000 years. The direction of the axis of the Earth's rotation precesses with a period of 19,000 to 23,000 years.
All of these effects combine to make the amount of solar radiation received by the Earth ("insolation") vary in a very particular fashion:
http://i27.photobucket.com/albums/c153/Borodog/insolation.gif
If you have the calibrated eye, like I fancy I do, you can convince yourself that you can already see a corelation between the ice core data and the insolation function. This is called Milankovich forcing.
In general, however, if you look at the power spectra of the data, most of the power is a a frequency that coresponds to a period of about 4,000 years. In other words, most of the climate variation seems to occur over periods of a few thousand years, which is much less than even the most rapid of the solar forcing terms (the precession term). Hence it has historically been the case that solar forcing has been dismissed as a cause for the climate variation, particularly the rapid shifts.
So, an internal climate model was developed to explain these short time scale oscillations (so-called Dansgaard-Oeschger, or DO oscillations), based on 3 things: sea ice coverage, thermo-haline circulation, and greenhouse gases (GHGs).
Sea ice plays an important roll in the Earth's climate. Ice is almost pure white; it is very reflective. When there is a lot of ice on the sea's surface, the Earth's relectivity goes (it's albedo) up, meaning more energy is reflected instead of absorbed into the climate system. Obviously there is the possibility of positive feedback: If the amount of sea ice increases, less energy is absorbed, the climate is cooler, and more ice can form. Vice versa, if the amount of sea ice decreases, more energy is absorbed, the climate is warmer, and ice can melt at a higher rate.
Thermo-haline circulation describes the the global "conveyor belt" of currents that runs throughout the world's oceans, sometimes running high in the ocean, sometimes deep, sometimes warm, sometimes cold, sometimes more dense, sometimes less. The details of the THC are beyond the scope of this post (or my understanding, for that matter), but suffice it to say that energy can be stored in the THC system until it becomes unstable, for example if cold, more dense water is above warm, less dense water. When this occurs the system can rapidly change state to a new equilibrium.
Greenhouse gases like carbon dioxide, methane, and water vapor can act to trap solar radiation in the atmosphere. Higher concentrations of these gases in the atmosphere may lead to a warmer climate. I emphasize may precisely because today's speaker did; which CO2 and methane concentrations are highly corelated with sea surface temperature in the data, nobody is sure which drives which; i.e. the direction of causality (and it may well go both ways, the perfect setup for an instability) is unknown.
So what Rial and Yang did was to model the climate as a set of coupled non-linear thermal oscillators, basically the sea ice, the THC, and GHG. They are coupled by the fact that the THC can have an effect on sea ice; for example if warm deep waters suddenly change state to become warm, shallow waters, the melt rate of sea ice can increase, and vice versa. Similarly, GHGs are coupled to sea water temperature, because when the water gets cold enough, CO2 uptake into the ocean accelerates, and vice versa.
The classic system of coupled oscillators is a system of masses connected with springs of differing stiffness. In this case, the oscillators are thermal, and model the behavior of the sea ice, the THC and GHGs with non-linear coupling between them. The model thus created is the so-called Saltzman-van der Pol Oscillator (SVO) model. It's a set of two non-linear coupled first order differential equations that represent the interaction between sea ice coverage, mean ocean temperature, and GHG concentrations. These can be transformed into a single second order non-linear differential equation that can be set equal to a term given by the Milankovich forcing (insolation).
In the absence of the Milankovich forcing from the insolation function described before, this model produces very periodic "shark fin" shaped climate oscillations. Note that these already resemble the general shape of the warm periods, cold periods, and sharp transitions in the ice core data:
http://i27.photobucket.com/albums/c153/Borodog/unforce.gif
Notice that the main problem is that the climate is not nicely periodic like the model (and of course, the high frequency "noise" is not modeled accurately).
But what happens when you solve the model including the insolation function?
http://i27.photobucket.com/albums/c153/Borodog/forced.gif
This is probably the single most amazing result I have ever seen. A single 2nd order differential equation accurately reproduces the qualitative nature of global climate data for the past hundred thousand years, and to a large extent does a damn good job quantitatively as well. The high frequency behavior is still not modeled well. The model itself is very crude, particularly in its treatment of the carbon cycle (the GHG bit). But the corelation between the model and the data is undeniable.
Have a look at the model compared to the actual data for the last 25,000 years:
http://i27.photobucket.com/albums/c153/Borodog/25k.gif
I can't stress enough that this corespondance between the data and such a simple model is absolutely AMAZING. The corespondance is even better according to Rial, who informed us that newer reconstructions of the most recent temperature data show a much bigger drop in the past 1000-2000 years, which is more in line with the model prediction.
Also, note at the very right hand side that the model predicts that we are currently in a period of abrupt climate change toward warmer climate (before another semi-glacial plunge, to be sure). Hence the model predicts that we would be in a period of rapid global warming even if mankind were still in the stone age.
Rial was quick to point out that any such prediction must be taken with a giant grain of salt. It is easy to dismiss the high frequency "noise" with hindsight in comparing the model to the data, but you can't do any such thing when you make predictions about near term future climate change, which is by definition in the short period/high frequency regime.
He also made it clear that the model does not take into account anthropogenic CO2, which has put atmospheric CO2 concentrations 1/3 higher than they have ever been according to the ice core data.
He finished up his talk by saying that they hope to increase the complexity and the accuracy of the model, particularly the carbon cycle, and they hope to be able to eventually accurately predict abrupt global climate change.
Amazing.