Since the beginning of the industrial era, human activities have added new sources of variation to the natural causes which bring about atmospheric change. How, why, and to what extent? How do we build the mathematical modeling of climate change?
The mechanisms that govern climate change have been known for almost two centuries, thanks to the work done by Joseph Fourier in 1824. The intensity of solar radiation (irradiance) reaching the Earth is 1.3 kW per m² on a surface perpendicular to the sun’s rays. Roughly one-third of this radiation is reflected back into space by the atmosphere and the ground, while the remaining two-thirds are mainly absorbed by the Earth’s landmasses and oceans. The Earth’s surface thus absorbs solar energy day after day; it can only stop heating up indefinitely if an amount of energy that is equal to the absorbed energy is released into space. This is achieved by emitting waves of the same nature as the light waves of the sun, but which have a longer wavelength given the much lower temperature of the Earth’s surface. These waves correspond to the color infrared, and are invisible to the human eye. This infrared radiation has to first pass through the atmosphere, where the greater the quantity of absorbing gases, the greater the ratio of energy emitted from the Earth’s surface to energy released into space. The presence of such gases therefore tends to increase the temperature of the Earth. These gases are said to produce a greenhouse effect by analogy with one of the phenomena that occur in gardeners’ greenhouses.
The Earth’s atmosphere contains naturally occurring water vapor and carbon dioxide gas (CO2), both of which are greenhouse gases. Without their presence, the ground temperature would be around 30 degrees less than what it actually is. It is thus the greenhouse effect that has made life possible. Other planets are governed by the same laws of physics. This is why the dense atmosphere of Venus, made up essentially of CO2, results in a very significant greenhouse effect and temperatures of 450°C.
Figure 1: Diagram of the energy balance at the surface of the Earth. The greenhouse effect is as follows: a fraction of the infrared radiation passes through the atmosphere, but most of it is absorbed and reemitted in all directions by greenhouse gas molecules and clouds. This results in the warming of the Earth’s surface and the lower layers of the atmosphere.(Source for this picture and the following ones : Intergovernmental Panel on Climate Change, www.ipcc.ch)
The position of the continents and the composition of the atmosphere have evolved considerably over the geological ages. The Earth’s climate has thus inevitably been greatly affected by these major changes. More recently, over the last million years, the climate has developed in a fairly well-known way. This has occurred under the influence of natural causes that have always existed and that will continue to play a role in the next several millennia.
- Firstly, the orbit of the Earth around the sun undergoes variations because of the attraction of the moon and the other planets. These variations occur slowly over periods of time that are measured in tens of thousands of years. They bring about changes in the angles at which the sun’s rays strike our planet and are at the origin of the large glacial and interglacial cycles with amplitudes of around 6°C for a period of 100,000 years. We are now 10,000 years into an interglacial and hence warm period.
- The sun is itself subject to variability, as revealed by the presence of sunspots that vary over a period of 11 years. However, this 11-year sunspot cycle affects the solar radiation mainly in the ultraviolet range. It thus has an impact on the behavior of the highest layers of the Earth’s atmosphere: the ionosphere (altitudes of 100 km and above) and, to a lesser extent, the stratosphere (altitudes of approximately 30 km, see the ozone page). It has a very slight effect on the total energy radiated and although its influence on climatic phenomena has been detected, it is very small.
- Another factor that affects the surface temperature of the Earth is volcanic activity. During powerful volcanic eruptions, volcanic dust reaches the stratosphere (above 15 km) and may remain there for one or two years before falling back to the ground. These particles, essentially made up of sulfur oxides, act as a screen to the incident solar flux (radiation), which has a cooling effect on the surface for a year or two.
Since the beginning of the industrial era, human activities have added new sources of variation to the above natural causes, which bring about atmospheric change.
Systematic observation of the atmosphere has indisputably shown an increase—for a little over a century—in the level of greenhouse gases such as CO2, methane, and nitrous oxide.
Figure 2: The current concentrations of the main greenhouse gases and their rate of increase are unprecedented. Source: EPA (Updated in 2016)
Looking at the most important of them, CO2, we can see that the number of CO2 molecules found in one million molecules of air has risen from 280 in 1850—before the beginning of the industrial era—to over 380 today. Here, we refer to 280 or 380 parts per million, or ppm. The annual increase in the concentration of CO2 is about half of what it would be if the atmosphere had retained all the CO2 that humanity produced by burning coal, oil, and natural gas. The other half is absorbed by the oceans and the biosphere. Moreover, we can also observe a very small decrease, in relative value, of the concentration of oxygen—oxygen that is necessary to produce additional CO2 that has been removed from the atmosphere. Finally, measurements of isotopic composition of atmospheric carbon complete the body of arguments that enable us to attribute, without any doubt, the changes in atmospheric CO2 concentrations to human activities.
We have in fact observed an increase in the average temperature of the Earth of an estimated 0.8°C (plus or minus 0.2°C), for a little over a century. The average global temperature is not directly measurable and can only be estimated by compiling all the limited observations of local temperatures available around the world. This estimation is a parameter whose changes reflect, in summarized form, the general trend of temperature variations observed over the whole Earth. Several other indicators, apart from global temperatures, also confirm global warming: the melting of glaciers in all the continents and at all latitudes, the decrease in the snow cover in the Northern Hemisphere; the rise in sea level (3 mm per year), due in part to the thermal expansion of water and the addition of water to the oceans from the melting of continental ice sheets; and changes in the physical and biological systems consistent with local increases in temperature.
This warming is not uniformly distributed. Oceans, by their very nature, heat up less than land because of their well-known regulatory effect on temperatures. Continents are thus warmer than the average earth temperature. Furthermore, it is observed that the rise in temperatures is especially significant in the northernmost regions of America, Europe, and Asia.
Precipitation is also affected by climate change with some regions getting more rain and others less.
We sometimes come across the following statement: “Temperature has stopped rising since the beginning of the century.” In fact, the unpredictable variations from one year to the next do not allow any conclusions to be drawn based on a few years of study alone. Only the averages spread over several decades provide any real insight. The most recent study regarding the evolution of temperature, published in January 2010 by the U.S. National Aeronautics and Space Administration (NASA), concludes that the last decade was the hottest ever recorded; in terms of individual years, last year (2009) came in third place, after 2005 and 1998.
Climatic models numerically simulate well-known physical processes that govern the dynamics and thermodynamics of the oceans and the atmosphere as well as the energy exchanges between infrared radiation and the molecules of certain gases (Laboratory experiments and quantum mechanics have enabled the precise determination of the corresponding absorption spectra.) Computers are indispensable tools for describing these complex phenomena that obey non-linear equations in a non-homogenous milieu that is stratified vertically and is horizontally variable. At the same time, their use is sometimes seen as a potential source of doubt. However, computers are not responsible for the success or failure of a mathematical model. What matters is good knowledge of the phenomena that one proposes to replicate numerically. The results of climate modeling are nevertheless affected by uncertainties, mostly related to the practical impossibility of simulating phenomena spread over small spatial scales (below 100 km), in realistic computing intervals. One has to therefore introduce parameters that describe them empirically. The uncertainty of results is evaluated by comparing the outputs of models for different possible parameterizations. It is in this way that the increase in average global temperatures caused by a doubling of greenhouse gas concentrations has been estimated to be in the range of 1.5°C to 4.5°C. The credibility of climatic models is based on their ability to recreate large geographical structures and past climatic developments.
Models have sometimes been criticized for neglecting the role of water vapor, considered essential. This criticism is totally unfounded. It is true that water vapor is the most effective greenhouse gas present in the atmosphere. However, the introduction of water vapor into the atmosphere has no lasting effect on its concentration in the atmosphere, insofar as its atmospheric lifetime is only one or two weeks. This injection therefore does not modify climate. Yet, the atmospheric lifetime of CO2 is more than one century and its concentration is modified permanently by human waste, which has the capacity to bring about a change in the climate. Even though water vapor might not be directly responsible for climate change, it nevertheless plays a part. The increase in temperature causes an increase in the concentration of water vapor in the atmosphere. This in turn causes a complementary warming and thereby creates a feedback loop with an amplifier effect, which is taken into account by models. This increase in atmospheric water vapor has in fact been observed over the last twenty years.
Thanks to mathematical climate simulation models, it is possible to assess whether or not the warming that is actually observed is quantitatively consistent with the models’ results. When these models take into account the totality of known phenomena—of either natural or human origin—their results match up satisfactorily with observations. This holds true when dealing with average global temperatures, average land temperatures, or average ocean temperatures. Even though the potential for error increases when you focus on more localized regions, the agreement remains significant for individual continents.
However, the discrepancy between the observations and the modeling results is glaring when models deliberately ignore changes in the concentration of greenhouse gases. In other words, natural phenomena do not explain the recent observations.
In particular, variations of total solar radiation, observed by satellite, are insufficient to explain the perceived warming in the absence of an amplification phenomenon that has yet to be specified. Objections to the thesis of a preponderant role for the sun are threefold. Firstly, the greenhouse effect related to the change in atmospheric composition is enough to quantitatively explain the climatic observations; if the sun had a greater impact, it would cause more warming than it actually does. Secondly, the 11-year sun cycle is more important than the variations that occur over a few decades and should therefore translate into a periodicity marked by 11 years in climate variations. Finally, the rise observed in temperature decreases with altitude and actually begins to decrease at the level of the stratosphere. This variation in altitude cannot be explained by a variation in solar radiation. Yet, it is predicted by the models that simulate the modification of the transfer of radiation caused by an increase in gases absorbing infrared radiation.
Only mathematical models simulating real phenomena allow an estimation of the potential effect of anthropic emissions on global climate in the decades to come. They therefore need to be based on assumptions about the evolution of these emissions. Greenhouse gas emissions depend on human factors that are by nature unpredictable, such as demography, rate of economic development, the nature of exchanges, behavior, etc. We are therefore led to develop scenarios that are likely to occur within the realm of the possible.
The first family of scenarios that was used is based on the absence of pro-active measures taken to reduce the magnitude of climate change. Present trends show a rapid increase in emissions—especially in terms of CO2—given that 80% of the commercialized energy comes from fossil fuel. We are therefore led to believe that CO2 concentrations will reach 1,000 ppm in 2100, which represents more than 3.5 times the pre-industrial concentrations.
The expected concentrations of CO2 during the 21st century are two to four times those of the pre-industrial era.
The inherent uncertainty associated with models adds to the difficulty of choosing the correct scenario for the evolution of emissions. The result is an increase in global temperatures in 2100 ranging from 1 to 6°C. These numerical values may appear to be small when compared to variations observed on a daily basis. To measure the extent of these changes, we need to remember that these are global averages and that the Earth’s temperature—even in the last glacial period when 3 km of ice covered northern Europe—differed from present day average temperatures by only 6°C.
Average temperature is obviously not enough to characterize climate. That is why important geographical variations are simulated. The increase in continental temperature is double the average and triple the average of northern regions.
Moreover, precipitation is affected. All models simulate an increase in precipitation in northern Europe and a decrease in areas surrounding the Mediterranean, especially in summer for both regions.
Reducing emissions to put a ceiling on greenhouse gases in the atmosphere and restricting the extent of climate change is an objective that is explicitly mentioned in Article 2 of the United Nations Framework Convention on Climate Change, signed at the Earth Summit in Rio de Janeiro, Brazil in 1992. The Convention—prepared by 28 heads of state and taken cognizance of at the Copenhagen summit in December 2009—specified this objective more clearly by giving a value of 2°C as the maximum permissible rise in average global temperature. The declaration does not, however, involve any concrete commitment on limiting emissions that would make this result achievable.
The latest report of the Intergovernmental Panel on Climate Change (IPCC) has provided the range of average global temperatures that the planet could reach for a maximum CO2 equivalent concentration ranging from 450 to 1,000 ppm. This idea of CO2 equivalent concentration involves expressing the average warming potential of all greenhouse gases during the years to come in terms of the change in concentration of CO2 (the main greenhouse gas) alone that would result in the same warming. It is necessary to specify the number of years considered, since all gases do not have the same life. Conventionally, in the absence of any other indication, a time frame of 100 years has been fixed.
For a concentration of 450 ppm equivalent (close to the current values with a CO2 concentration alone of more than 380 ppm), the rise in temperature would be 1.5°C to 3°C and for 1000 ppm 4°C to 8°C. To limit this concentration to around 500 ppm equivalent, it would be necessary to halve the total global emissions from now to 2050. Since French emissions per inhabitant are double the world average, these emissions would have to be divided by a factor of four—if we admit that each inhabitant of the planet has the right to emit the same quantity of CO2 equivalent.
Reducing emissions in such vast proportions is a formidable challenge especially since 80% of commercialized global energy comes from fossil fuels. The various approaches to scale back emissions involve, first of all, a reduction in the quantity of energy required for a given service. This means, for example, better thermal insulation of buildings or an improvement in the efficiency of motors and processes. A second possibility involves the production of energy with little or no greenhouse gas emissions. One way of attaining this objective is through carbon dioxide capture and storage. This involves recovering the gases emitted by the combustion of coal, oil, or natural gas—when the size of the facility allows it—and preventing their release into the atmosphere by storing them in suitable underground structures. Another way is to rely upon the production of energy that does not release greenhouse gases such as hydroelectricity, nuclear energy (fission and fusion), and renewable energies.
It is a fact that underground resources are finite. Estimates relating to oil and natural gas lead to the conclusion that these two fossil fuels should start becoming very scarce in a few decades. Coal, on the other hand, is more abundant and will probably not be exhausted before the next two or three centuries. Since coal produces more CO2 per unit of energy than oil or natural gas, the exploitation of all coal deposits would lead to a variation in atmospheric composition. This would bring about a climate change that is greater than that which separates glacial periods (during the last of which northern Europe was covered with a 3 km-thick ice layer and the sea level was 120 m less than it is today). While it is true that global warming caused by anthropogenic emissions would make us move even further away than the glacial era, this comparison with natural climatic cycles allows us to imagine the extent to which the climate would change. We can specially fear a rise in sea level of several meters, leading to dramatic consequences.
Nonetheless, in a few centuries, when all fossil fuels will be exhausted and will no longer be able to supply us with cheap sources of energy, we will have to learn to do without them in a situation of stress. Learning gradually to live without them from now on will allow us to prevent an energy crisis in a few decades. It will also save us from the disadvantages of a brutal change in the very climate that made our development possible.