Energetics of the Climate System
Description
Energetics of the Climate System is derived from a course taught by Hervé Le Treut, who has been delivering this lecture series for decades to students at institutions such as the École Normale Supérieure, École Polytechnique, and Sorbonne University, along with students from other international institutions. This book offers a comprehensive understanding of the intricate energetics driving the Earth's climate system.
The goal was not only to capture the depth and complexity of this subject, but also to preserve the pedagogical brilliance and unique storytelling style of Hervé Le Treut. This work stands as both a tribute to his remarkable contributions and a reflection of his passion for teaching, having mentored generations of climatologists, engineers, and economists, many of whom - including the co-author Mounia Mostefaoui - have greatly benefited from his guidance.
The text retains elements of an oral presentation to evoke the professor's distinctive voice and teaching approach. The book is structured into five chapters, each independent and deeply interconnected, and is complemented by an appendix of exercises to reinforce its material.
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Persons
Hervé Le Treut worked as IPSL Director for IPCC between 2008 and 2019. He built his internationally recognized research career at Polytechnique, Sorbonne University and ENS, France. He co-created AcclimaTerra and received several distinctions. He is a knight of the Legion of Honor.
Mounia Mostefaoui graduated from Polytechnique and completed her PhD in physics of climate change at LMD-IPSL, France. Her advisors were Hervé Le Treut and Philippe Ciais. She was Expert Reviewer for the AR6 IPCC report and participated in several COPs as a speaker in the IPCC Pavilion.
Content
Preface ix
Chapter 1 A Description of the Main Constraints Regulating the Earth Climate 1
1.1 Generalities about the atmosphere and the ocean 1
1.1.1 The atmosphere 4
1.1.2 A brief comparison between some oceans and the atmosphere's main orders of magnitude 9
1.2 A global view of radiative processes 9
1.3 Past climate history 18
1.4 A global evaluation of climate stability 32
1.4.1 Let us consider the first term of equation [1.8] 33
1.4.2 Let us consider the second term of equation [1.8] 37
1.4.3 A global estimate of climate stability considering another source of complexity: the greenhouse effect 43
1.5 Conclusion 47
Chapter 2 The Vertical Dimension of the Energy Processes of the Climate System: Radiative Processes and Radiative-Convective Models 49
2.1 Radiative processes: generalities 50
2.2 Absorption and greenhouse effect 52
2.3 The role of convection 62
2.3.1 Where does the - F ± comes from? 64
2.4 Diffusion of solar radiation 78
Chapter 3 The Horizontal Motion of Atmospheric and Oceanic Transport 93
3.1 Energy budget at the top of the atmosphere 93
3.2 Energy exchanges with the surface 98
3.3 Transport by the atmosphere and the ocean 113
3.4 Vertical and horizontal transports: the links 117
3.4.1 What is stable stratification? 124
3.5 Conclusion 141
Chapter 4 A Transition from Quasi-Equilibrium to Forcing from Anthropogenic Source: A Cartography of Predictable Phenomena, Uncertainties and Feedback Related to the Climate Response to Anthropogenic Disturbance 143
4.1 A transitory evolution 144
4.1.1 Presentation of the Intergovernmental Panel on Climate Change (IPCC) and its missions 147
4.1.2 A focus on IPCC productions 148
4.1.3 Examples of IPCC production impacts 150
4.1.4 Complexity, a main feature of the Earth climate system transitory evolution 151
4.2 Global temperature change and the role of feedbacks 178
4.2.1. About models' uncertainties and radiative forcing associated with CO 2 185
4.2.2 The water vapor feedback 188
4.2.3 The albedo feedback 189
4.2.4 The cloud feedback 190
4.2.5 The lapse-rate feedback 192
4.3 Measured and anticipated impacts: what is predictable? 197
4.3.1 Three generations of model assessments directed toward climate change 198
4.3.2 Socio-economic pathways (SSP) in AR6 205
4.3.3. Articulation between SSP scenarios from AR 6 and RCP scenarios from AR5 207
4.3.4 As for the most probable trajectory currently followed 210
4.3.5 Main novelties for the seventh IPCC Assessment Report 213
4.3.6 Method for the evaluation of a probability in IPCC reports 214
Chapter 5 From Scientific Diagnostic to Decision-Making 235
5.1 The role of uncertainties on assessing global warming, accounting for natural variability and estimating climate impacts 236
5.1.1 Process studies and uncertainties 260
5.1.2 From natural variability to climate impacts 279
5.1.3 Zoom about uncertainties and the IPCC 281
5.1.4 Process of uncertainty evaluations by the IPCC as detailed in the Fifth Assessment Report (AR5) 283
5.1.5 Process of uncertainty evaluations by the IPCC as detailed in the Sixth Assessment Report (AR6) 287
5.1.6 Method for the evaluation of a probability in IPCC reports 289
5.2 From global to local climate features: a key shift for the interaction between science and decision-making 290
5.3 From scientific diagnosis to political decision-making 300
5.4 A word of conclusion 301
Appendix 303
References 327
List of Authors 339
Index 341
1
A Description of the Main Constraints Regulating the Earth Climate
1.1. Generalities about the atmosphere and the ocean
The general objective of this introductory material is to provide a description of the main constraints regulating the Earth climate, which come from the laws of energy conservation and from the rotation of the Earth, by moving from the global picture of the Earth to more detailed processes.
The word "climate" comes from the ancient Greek "Klima" which literally means "inclination of the Earth towards the pole". During the third century BCE, the polymath and former library of Alexandria's director, Eratosthenes of Cyrene, calculated with a negligible error the obliquity of the ecliptic, i.e. the tilt of the Earth axis comparing to its axis of rotation around the Sun. Eratosthenes' eclectic work, going from science to philosophy and poetry, is still partially available.
Therefore, the Ancient Greeks already knew that the Earth was a sphere and that it would be warmer near the equator and colder at the poles. From this, they also deduced the existence of another livable "unknown" world at mid-latitudes on the other side of the equator.
Figure 1.1. Eratosthenes teaching in Alexandria
(Source: Bernardo Strozzi (1635))
Figure 1.2. A simplified scheme of the conception of the Earth by Eratosthenes of Cyrene
Later, by 150 CE, Claudius Ptolemy wrote a summary of the state of knowledge in geography in his opus named Geographia.
Figure 1.3. Schematic view of the components of the climate system, their processes and interactions (Le Treut et al. 2007)
Figure 1.3 represents a modern scheme of the ancient idea of a climate system organized in a large number of subcomponents and different "spheres" linked by different processes, among which the energy exchanges play an essential role.
"Atmo-sphere" stands for the sphere of the Earth, "hydro-sphere" stands for the sphere of water, "cryo-sphere" stands for the sphere of ice and "geo-sphere" stands for the sphere of the land beyond the surface that can be compressed. As for the word "biosphere", it was invented in the 20th century by the Ukrainian-Russian scientist Vladimir Vernadsky at Sorbonne University and stands for the sphere of life.
Figure 1.3 also illustrates the Earth complex system characterized by exchanges of energy, which represent the guiding thread of this book. No other types of exchanges such as water or momentum will be discussed in detail in this opus.
Beyond its etymological significance, we can define the word "climate" as the ensemble of statistics that describe the state of the climate system in a given location and over a given period of time (some decades). It is important to note that "statistical" does not only mean average. Moreover, the concept of risk is intimately associated with the climate definition, and it can be defined as an outcome that has a chance to happen, meaning a non-zero probability. Furthermore, we would like to underline that the notion of scale of time is absolutely key for this complex topic, which is highly dependent on a given contingency's context.
Due to the complexity at stake, the science studying climate has no one defined name. It is usually alternatively referred to as "physics of climate change", "climatology", "sciences of the environment", "geosciences", "earth, atmospheric and planetary sciences", etc.
1.1.1. The atmosphere
The Earth's atmosphere is 100 km thick, but 99% of its mass lies in its first 21 kilometers.
Figure 1.4. A side view of the atmosphere from a balloon
(Source: François Danis - LMD 2000)
In this chapter, we will focus on the lower part of the stratosphere, below 20 km, where the atmosphere has a mass. In Figure 1.4, we can also distinguish the ionosphere layer.
Figure 1.5. a) Map of average July GCP precipitation for 1988-1999
(Source: World Climate Research Program);
b) Scheme of Hadley cells
In Figure 1.5, which shows a map of average July GCP precipitation in Bonn for 1988-1999, monthly means show an extremely organized atmospheric circulation, with a moving system from West to East. This is very different from the situation on other planets, with a complex organization. The scheme on the right in Figure 1.5 also shows Hadley cells that are defined below, with warm air climbing at the equator where they lose their water and descending cooler air, as well as a desert belt over continents.
The Hadley cells correspond to a relatively slow movement of the atmosphere in a mean meridian plane: with ascendance near the equator and descending air near the subtropical regions. On an annual mean, this circulation is fed by a convergence of air in the low layers around the equatorial region and a divergence higher in the atmosphere from this same area.
The fuel of this circulation comes from the more intense heating of equatorial regions compared to the other regions, getting more solar energy. This more intense heating creates a dilatation of the atmosphere at low latitudes, whose accumulated effect induces a gradient of pressure which is accentuated in the high layers of the atmosphere.
If we consider the atmosphere in its meridian plane, we can also diagnose this situation as a generator of vorticity because the gradients of pressure and density will not be aligned anymore: the air density varies not only with altitude, but also in latitude.
Despite the weak speed of this meridional flow (the winds are much more violent in the West-East direction), the Hadley cells play an essential role in the climatology of intertropical regions.
Ascending air zones are precipitating zones because of the very rapid decrease of the level of saturation of atmospheric water vapor upper in a troposphere, which gets colder with altitude. The seasonal movements of Hadley cells come together with the interplay between dry seasons or wet monsoons in the equatorial regions.
The Hadley cells play a main role in the climate system, as they transport the surplus of energy from equatorial regions to the Poles. The latitudes which limit the domain of Hadley cells in the North and in the South are therefore main indicators of the climate zones on the Earth surface.
Figure 1.6 is a representation of Hadley cells. On the y-axis on the left, the height is given in decibars; in the center, the lines are a representation of the mass of the troposphere; and the y-axis on the right, the vision is given in latitudes for three different scales of time: annual mean, winter (December/January/February) and summer (June/July/August). The horizontal lines indicate the latitudes.
Figure 1.6. A representation of Hadley cells
(Source: Peixoto and Oort (1992))
The stream function of meridian flow (flow averaged over longitudes and the time) is represented on a diagram of altitude/latitude. The abscissas are expressed in degrees of latitude. The lines of stream "iso-function" are by definition parallel to the flow. In the case of a stationary mean flow, we can consider that the flow is between the isolines. The values of stream functions are expressed in mass flow rate (the unity is 1010 kg/s): between two separated isolines of 1010 kg/s and 1010 kg of air every second. The diagram shows from the top to bottom in three situations: (1) the yearly mean of the flow, characterized by an approximate symmetry relatively to the equator; (2) the mean for boreal winter (December/January/February), where the main ascend is displaced from the equator toward the southern hemisphere; and (3) the mean for the boreal summer (June/July/August), where the main ascent is displaced from the equator toward the north hemisphere.
Figure 1.7 represents the atmospheric circulation viewed by the satellite radar TRMM, providing an instantaneous view of the Earth (synthesis image for demonstration by NASA). The radar echoes provoked by the presence of condensed water show ascending air. We can note, even on this instantaneous image corresponding to the month of July, an opposition between intertropical and extratropical regions. The intertropical zones are characterized by zones of ascending air essentially near the equator, and zones of air ascent more frequent approximately 30°N or 30°S. The extratropical regions are characterized by disturbances where the air ascends progressively all along "spirals" structures of several thousands of kilometers.
Figure 1.7. Atmospheric circulation viewed by the satellite radar TRMM
(Source: NASA Project TRMM)
Figure 1.8. Perhaps the world's first thematic map: Edmund Halley's map of trade winds
(Source: Halley, Philosophical Transactions (1686))
To mention some elements of history, part of this organization was already known by Halley...
