Olivier Pauluis

Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part I: Maximum Work and Frictional Dissipation

Abstract The entropy budget of an atmosphere in radiative–convective equilibrium is analyzed here. The differential heating of the atmosphere, resulting from surface heat fluxes and tropospheric radiative cooling, corresponds to a net entropy sink. In statistical equilibrium, this entropy sink is balanced by the entropy production due to various irreversible processes such as frictional dissipation, diffusion of heat, diffusion of water vapor, and irreversible phase changes. Determining the relative contribution of each individual irreversible process to the entropy budget can provide important information on the behavior of convection. The entropy budget of numerical simulations with a cloud ensemble model is discussed. In these simulations, it is found that the dominant irreversible entropy source is associated with irreversible phase changes and diffusion of water vapor. In addition, a large fraction of the frictional dissipation results from falling precipitation, and turbulent dissipation accounts fo...

Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part II: Latent Heat Transport and Moist Processes

In moist convection, atmospheric motions transport water vapor from the earth’s surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes. The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.

The Global Atmospheric Circulation on Moist Isentropes

The global atmospheric circulation transports energy from the equatorial regions to higher latitudes through a poleward flow of high-energy and -entropy parcels and an equatorward flow of air with lower energy and entropy content. Because of its turbulent nature, this circulation can only be described in some averaged sense. Here, we show that the total mass transport by the circulation is twice as large when averaged on moist isentropes than when averaged on dry isentropes. The additional mass transport on moist isentropes corresponds to a poleward flow of warm moist air near Earths surface that rises into the upper troposphere within mid-latitudes and accounts for up to half of the air in the upper troposphere in polar regions.

Frictional Dissipation in a Precipitating Atmosphere

Abstract The frictional dissipation in the shear zone surrounding falling hydrometeors is estimated to be 2–4 W m−2 in the Tropics. A numerical model of radiative–convective equilibrium with resolved three-dimensional moist convection confirms this estimate and shows that the precipitation-related dissipation is much larger than the dissipation associated with the turbulent energy cascade from the convective scale. Equivalently, the work performed by moist convection is used primarily to lift water rather than generate kinetic energy of the convective airflow. This fact complicates attempts to use the entropy budget to derive convective velocity scales.

The Global Atmospheric Circulation in Moist Isentropic Coordinates

Abstract Differential heating of the earth’s atmosphere drives a global circulation that transports energy from the tropical regions to higher latitudes. Because of the turbulent nature of the flow, any description of a “mean circulation” or “mean parcel trajectories” is tied to the specific averaging method and coordinate system. In this paper, the NCEP–NCAR reanalysis data spanning 1970–2004 are used to compare the mean circulation obtained by averaging the flow on surfaces of constant liquid water potential temperature, or dry isentropes, and on surfaces of constant equivalent potential temperature, or moist isentropes. While the two circulations are qualitatively similar, they differ in intensity. In the tropics, the total mass transport on dry isentropes is larger than the circulation on moist isentropes. In contrast, in midlatitudes, the total mass transport on moist isentropes is between 1.5 and 3 times larger than the mass transport on dry isentropes. It is shown here that the differences between ...

It is not the entropy you produce, rather, how you produce it

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earths environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will ‘adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate’. Our aim in this ‘outside view’, invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical–chemical systems and also systems governed by the ‘laws’ of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.

A Statistical Generalization of the Transformed Eulerian-Mean Circulation for an Arbitrary Vertical Coordinate System

AbstractA new method is derived for approximating the mean meridional circulation in an arbitrary vertical coordinate system using only the time-mean and zonally averaged meridional velocity, meridional eddy transport, and eddy variance. The method is called the statistical transformed Eulerian mean (STEM) and can be viewed as a generalization of the transformed Eulerian mean (TEM) formulation. It is shown that the TEM circulation can be obtained from the STEM circulation in the limit of small eddy variance. The main advantage of the STEM formulation is that it can be applied to nonmonotonic coordinate systems such as the equivalent potential temperature. In contrast, the TEM formulation can only be applied to stratified variables. Reanalysis data are used to compare the STEM circulation to an explicit calculation of the mean meridional circulation on dry and moist isentropic surfaces based on daily data. It is shown that the STEM formulation accurately captures all the key features of the circulation. Th...

Water vapor and mechanical work: A comparison of Carnot and steam cycles

Abstract The impact of water vapor on the production of kinetic energy in the atmosphere is discussed here by comparing two idealized heat engines: the Carnot cycle and the steam cycle. A steam cycle transports water from a warm moist source to a colder dryer sink. It acts as a heat engine in which the energy source is the latent heat of evaporation. It is shown here that the amount of work produced by a steam cycle depends on relative humidity and is always less than that produced by the corresponding Carnot cycle. The Carnot and steam cycles can be combined into a mixed cycle that is forced by both sensible and latent heating at the warm source. The work performed depends on four parameters: the total energy transport; the temperature difference between the energy source and sink; the Bowen ratio, which measures the partitioning between the sensible and latent heat transports; and the relative humidity of the atmosphere. The role of relative humidity on the work produced by a steam cycle is discussed in...

Thermodynamic Consistency of the Anelastic Approximation for a Moist Atmosphere

Abstract The primary goal of this paper is to validate the use of the anelastic approximation for fluids with a complex equation of state such as moist air or seawater. The anelastic approximation is based on a leading-order expansion of the equations of motion for a compressible fluid in terms of density. Its application to atmospheric flows has been based on a dry framework that treats phase transitions as an external energy source. However, cloudy air is more accurately described as a two-phase fluid in which condensed water and water vapor are in thermodynamic equilibrium. Thermodynamic equilibrium reduces to three the number of state variables necessary to describe the thermodynamic state of moist air, and leads to a discontinuity in the partial derivatives of the equation of state at the saturation point. A version of the anelastic approximation for a moist atmosphere is derived here by considering the atmospheric density as a small perturbation from a moist-adiabatic reference profile, and using mo...

Boundary Layer Dynamics and Cross-Equatorial Hadley Circulation

The behavior of the Hadley circulation is analyzed in the context of an idealized axisymmetric atmosphere. It is argued that the cross-equatorial Hadley circulation exhibits two different regimes depending on the depth of the planetary boundary layer and the sea surface temperature gradient in the equatorial regions. The first regime corresponds to a classic direct circulation from the summer to winter hemisphere. The second regime differs in that the return flow rises above the boundary layer in the winter hemisphere and crosses the equator within the free troposphere. This equatorial jump is associated with a secondary maximum in precipitation on the winter side of the equator. The transition between these two regimes can be understood through the dynamical constraints on the lowlevel flow. Strong virtual temperature gradients are necessary for the return flow to cross the equator within the planetary boundary layer. However, the mass transport driven by such a temperature gradient is highly sensitive to the thickness of the boundary layer. For a weak temperature gradient or a shallow boundary layer, the return flow is prevented from crossing the equator within the the boundary layer and, instead, must do so in the free troposphere. These dynamical constraints act equally in a dry and a moist atmosphere. However, a comparison between dry and moist simulations shows that the equatorial jump is much deeper in a moist atmosphere. This is interpreted as resulting from the feedbacks between the large-scale flow and moist convection, which results in establishing a very weak gross moist stability for the equatorial jump.