|Fig. 1: Measurement of temperature, CO2 and dust concentrations for the past 420,000 years based on the ice samples obtained at the Vostok station in Antarctica.  (Source: Wikimedia Commons)|
In the last century and a half, rapid industrial development and population growth resulted in significant increase of CO2 emission into the atmosphere. It is well established by now that excessive CO2 concentration leads to the rise of temperature and that a significant increase in temperature has dangerous consequences. [1-3] It is also generally accepted that the excess of CO2 in the atmosphere cannot be eliminated by natural processed sooner than in a hundred years, possibly much longer. 
Consequently, there is a general agreement that the CO2 emission has to be reduced. The real question is what is the best strategy: should we continue the business as usual and wait until the technology development makes the transition to carbon free world easier, should we invest a large amount of money into research now, should we start cutting the carbon emission immediately and how much should we cut? The choice of the best strategy heavily relies on predictions of how the CO2 influences the Earth's temperature.
Modeling the Earth atmosphere is complicated due to several feedback effects. Most of the constraining power on the models come from the study of the past evolution of CO2 concentration and the atmospheric temperature. The evolution of the temperature also tells us what are the natural boundaries for the temperature fluctuations and what can we expect when the temperature rises. It is also a corner stone of the arguments that the recent increase in the temperature is due to human activity.
Provided that the records of temperature exist only in recent history, one has to rely on indirect tracers of past temperature fluctuations such as width of rings in trees, chemical composition of sediments in the ocean, borehole temperature measurements.  This report will be focused on the measurement of the temperature fluctuations and CO2 concentrations using the ice drilling at the Vostok station in Antarctica. 
The basic idea of the measurement is due to an observation made by Dansgaard that the concentration of heavy isotopes of hydrogen and oxigen, i.e. the deuterium and 18O, in the rain or snow depends on the temperature of the atmosphere.  This dependence has a physical explanation based on the fact that the partial vapor pressure for heavy isotopes is smaller than for the light ones.
Consider a parcel of air that contains water evaporated form the ocean. As the parcel travels through the atmosphere, its temperature decreases. When the temperature drops below the local due point, the excess of water is removed from the parcel in the form of rain or snow. Since the partial vapor pressure of the heavy isotopes is smaller, they tend to precipitate first. What is important is the temperature of the parcel when it reaches Antarctica. Assuming that the initial concentration of the heavy isotopes is the same, the final concentration of these isotopes strongly depends on the final temperature over Antarctica. The smaller the final temperature, the more precipitation the parcel has experienced on the way, the lower the final concentration of heavy isotopes. This concentration is reflected in the snow that falls over the observation point.
Together with the concentration of the heavy isotopes, one can also analyze the bubbles of air trapped in the ice to get the chemical composition of the atmosphere at the time the ice was formed.
The results of temperature measurements and the CO2 concentration at the Vostok station are shown in Fig. 1.  Several important features on this plot are:
There are large changes in temperature: the difference between maxima and minima is more than 10°C.
The temperature changes are correlated with the CO2 concentration and anti-correlated with the dust concentration.
The increase in temperature happens very quickly, followed by a more gradual decrease in temperature. The period of the fluctuations is about 100 thousand years.
|Fig. 2:Comparison of global temperature change with the average insolation at 65° North and concentration of CH4 and CO2. The concentration of heavy oxygen in the atmosphere, 18Oatm, is a tracer of global ice volume, it is correlated with all changes of insolation. Temperature, methane, and carbon dioxide are mostly correlated with the 100,000 year cycle.  (Source: Wikimedia Commons)|
The correlation of temperature with the CO2 concentration is an example of a positive feedback: larger concentrations of CO2 lead to larger temperature due to greenhouse effect, while the solubility of CO2 in the ocean decreases with increasing temperature, i.e. more CO2 stays in the atmosphere at higher temperatures.  Dust, on the other hand, reflects light, as a result, less sunlight reaches the surface of the Earth and the temperature decreases.
The period of 100,000 years is one of the Milankovitch cycles corresponding to the change of eccentricity of the Earth orbit around the Sun.  The insolation (average amount of incoming solar radiation) at 65 degrees in the Northern hemisphere is shown at the bottom of Fig. 2.  There are three Milankovitch cycles: precession of the tilt of the Earth axis (40,000 years), time of closest approach of the Earth to the Sun (20,000 years) and the eccentricity of the Earth orbit (100,000 years).  One can notice that the change in the insolation with the 100,000 years period is not significantly different from the other two cycles. Moreover, before approximately 600,000 years ago the most significant cycle was 40,000 years and the change in the Earth temperature expected for a typical change of insolation is much less than 10°C.  Why is then the most significant change in the temperature follows the 100,000 cycle with the total amplitude of about 10°C?
This is an example of the significance of positive feedback loops: a small change in the insolation results in melting of the ice caps, as a result, the ice caps reflect less light, the temperature increases, the oceans get warmer, they absorb less CO2 which concentrates in the atmosphere and creates a greenhouse effect etc. Thus, a small change in insolation triggers a much larger change in the temperature. The system of the feedback loops is highly nonlinear, and it is very hard to predict a priori which effects will lead to a large change and which ones will turn out insignificant. For instance, why the 100,000 cycle is more important now than the other two cycles although the amplitudes in the insolation change are comparable?
The Antarctic ice provides a wealth of information about the temperature evolution and the CO2 concentration for the past 400,000 years.  The temperature fluctuations are highly correlated with the concentration of CO2 in the atmosphere. The large amplitude of the temperature changes (up to 10°C) shows importance of positive feedback loops, so that even small changes in the insolation can trigger much larger changes in the temperature. The consequences of a particular change in the CO2 concentration or insolation are hard to predict a priori due to highly non-linear nature of the feedback loops. Although past fluctuations of the temperature did not end up in a runaway increase of the temperature, most probably due to a moderating effect of some negative feedback mechanisms, the current concentration of CO2 at 380 ppmv is much larger than the CO2 concentrations in the past (the maximum is below 300 ppmv, Fig. 1).  It is not clear whether the mechanisms that prevented the runaway increase of the temperature in the past will be effective for the large concentrations of CO2.
© Dmitry Malyshev. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 S. D. Solomon et al., eds., Climate Change 2007: The Physical Science Basis: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge U. Press, 2007).
 M. Parry et al., eds., Climate Change 2007: Impacts, Adaptation and Vulnerability: contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge U. Press, 2007).
 T. R. Karl et al., eds., Global Climate Change Impacts in the United States (Cambridge U. Press, 2009).
 U.S. National Research Council, Climate Change Science: An Analysis of Some Key Questions (National Academy Press, 2001).
 U.S. National Research Council, Surface Temperature Reconstructions Ror the Last 2,000 Years (National Academy Press, 2006).
 J. R. Petit et al., "Climate and Atmospheric History of the Past 420,000 Years From the Vostok Ice core, Antarctica," Nature 399, 429, (1999).
 W. Dansgaard, "Stable Isotopes in Precipitation," Tellus 16, 436, (1964).
 J. L. Sarmiento et al., "Simulated Response of the Ocean Carbon Cycle to Anthropogenic Climate Warming," Nature 393, 245, (1998).
 A. L. Berger, "Long-Term Variations of Daily Insolation and Quaternary Climatic changes," J. Atmos. Sci. 35, 2362, (1978).
 H. Elderfield et al., "Evolution of Ocean Temperature and Ice Volume Through the Mid-Pleistocene Climate Transition," Science 337, 704, (2012).
 A. Klein, "What Can Ice Tell Us About Climate Change?" PH240, Stanford University, Fall 2011.