Why does the atmosphere move?
This seemingly naive question is not as simple to answer as one may think. First, it is not obvious that it should move at all. Most physical systems left on their own device reach a state of rest after a while. Take a glass of water. After you stir it, the water may move for some time, but it will settle later on. The physical principle at hand here is the Second Law of Thermodynamics (sorry for caps, but that’s one of the Big One in physics…). The full formulation of the second law is a bit complex, but one of its implications is than an isolated physical system – meaning here a system that does not exchange mass or energy with its environment – an isolated system will reach a state of thermodynamic equilibrium, where, in effect, nothing interesting happens.
The Earth’s atmosphere however it is not isolated but continuously receives energy in the form of short wave radiation from the Sun and looses energy through the emission of infrared radiation to space. Importantly, the energy from the Sun is primarily absorbed near the surface and in the tropics – at fairly warm temperature. In contrast, the emission of infrared radiation takes place in the upper troposphere, at fairly low temperature. This sets up a situation where the atmosphere acts a heat engine that can generate kinetic energy by transporting the energy from a warm source to a cold sink. In effect, warm air rises, cold air sinks, and wind is generated.
The Carnot cycle is probably the best known heat engine. It was introduced by the brilliant French engineer and scientist Sadi Carnot in his seminal Reflexions sur la puissance motrice du feu (which started the whole second law business). It is a theoretical engine – no one as far as I know as ever constructed a Carnot cycle. The work done by a Carnot cycle is given by $$ W = Q \frac{T_{in}-T_{out}}{T_{in}},$$ where $Q$ is the heating and $T_{in}$ and $T_{out}$ are the temperature of the energy source and the energy sink. The Carnot cycle is also an optimal case: not heat engine can produce more work than a Carnot cycle for a given heating rate and temperature of the energy sources and sinks.
The atmosphere crucially does not act as a Carnot cycle. For instance, the average surface heating is about 100 Watts per meter square. With an average surface temperature of 288K and an emission temperature of 255K, the work done by a Carnot cycle would be about 11 Watts per meter square. By contrast, typical estimates of the kinetic energy dissipation in the atmosphere are between 2 and 5 Watts per meter square. The difference between the Carnot upper limit and the generation of kinetic energy can be attributed to the hydrological cycle, and in particular to two key aspect of the Earth atmosphere: (1) it rains, and (2) the atmosphere is mostly dry.
Let’s start with the role of rain. A typical droplet of rain forms a few kilometers up in the atmosphere before falling to the Earth’s surface. If this droplet were in free fall, its velocity would reach over 100 mph – that would make make Belgium unlivable. Instead, raindrops are slow down by the aerodynamical drag exerted by the surrounding air and only reach a terminal velocity of a few mph. This drag is a dissipative processes. We used satellite data to estimate it and found a number of about 1.2 Watt per meter square, about the same order of magnitude as the wind dissipation (Pauluis and Dias, 2013).
Second, the Earth’s atmosphere is quite dry, primarily because of its active hydrological cycle. Consider that, despite the fact that two third of the Earth are covered by Oceans, its averaged relative humidity is about 70%. This is atmospheric circulation acts as a dehumidifier that continuously removes water vapor: moist air rises and forms clouds, loses water through precipitation and is then brought back to the surface with a much lower water content. From a thermodynamic point of view, this dehumidification can be thought of as a chemical reaction in which one reactant (water vapor) is transformed into a product (liquid water) against its natural inclination (i.e. liquid water evaporates in unsaturated air). In the technical jargon, the Gibbs free energy of the product is larger than that of the reactant. More importantly, this process reduces the amount of kinetic energy that can be produce (Pauluis, 2010).
Sadi Carnot, 1824: “Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance” Librairie Bachelier, 118pp.
Pauluis, O., and J. Dias. “Satellite Estimates of Precipitation-Induced Dissipation in the Atmosphere (Vol 335, Pg 953, 2012).” Science 339, no. 6117 (January 18, 2013).
Pauluis, Olivier. “Water Vapor and Mechanical Work: A Comparison of Carnot and Steam Cycles.” Journal of the Atmospheric Sciences 68, no. 1 (September 3, 2010): 91–102. https://doi.org/10.1175/2010JAS3530.1