Rayleigh-Benard convection with phase changes in a Galerkin model

The transition to turbulence in Rayleigh-Benard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused to the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in steady state, in oscillating recharge-discharge regime or turbulent in dependence on the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.Comment: 30 pages, 14 Postscript figure

Isentropic Analysis of Convective Motions

This paper analyzes the convective mass transport by sorting air parcels in terms of their equivalent potential temperature to determine an isentropic streamfunction. By averaging the vertical mass flux at a constant value of the equivalent potential temperature, one can compute an isentropic mass transport that filters out reversible oscillatory motions such as gravity waves. This novel approach emphasizes the fact that the vertical energy and entropy transports by convection are due to the combination of ascending air parcels with high energy and entropy and subsiding air parcels with lower energy and entropy. Such conditional averaging can be extended to other dynamic and thermodynamic variables such as vertical velocity, temperature, or relative humidity to obtain a comprehensive description of convective motions. It is also shown how this approach can be used to determine the mean diabatic tendencies from the three-dimensional dynamic and thermodynamic fields. A two-stream approximation that partitions the isentropic circulation into a mean updraft and a mean downdraft is also introduced. This offers a straightforward way to identify the mean properties of rising and subsiding air parcels. The results from the two-stream approximation are compared with two other definitions of the cloud mass flux. It is argued that the isentropic analysis offers a robust definition of the convective mass transport that is not tainted by the need to arbitrarily distinguish between convection and its environment, and that separates the irreversible convective overturning fromoscillations associated with gravity waves

A Theory for the Lower-Tropospheric Structure of the Moist Isentropic Circulation

A theoretical model describing the structure of the dry and moist isentropic circulations in the lower troposphere is derived. It decomposes the meridional flow in the troposphere into three contributions: a dry equatorward flow, a cold moist equatorward flow, and a warm moist poleward flow in the mixed layer. The model is based on observations of the meridional mass fluxes joint distribution in potential temperature and equivalent potential temperature. It updates an existing model of the dry circulation by emphasizing the role of moisture in the mixed layer. The model is used to derive an expression for the ratio of moist to dry circulation strengths and this expression is used to assess the influence of surface thermodynamics on the circulations. It predicts that the moist circulation should be between 1.5 and 2 times as strong as the dry circulation and that this relative strength should not increase indefinitely with increasing surface temperature variability. The model also yields an expression for the ratio of total meridional heat fluxes to meridional sensible heat fluxes. This expression indicates that while an increase in the total heat fluxes occurs when surface temperature variability increases (via an increase in latent heat flux), it cannot increase indefinitely. The results suggest that changes in surface thermodynamic conditions must be constrained to constrain changes in the meridional overturning circulation associated with a warming climate

Tropical and Subtropical Meridional Latent Heat Transports by Disturbances to the Zonal Mean and Their Role in the General Circulation

The spectrum of meridional latent heat transport in the tropics and subtropics by disturbances to the zonal mean during all seasons is analyzed. The transport is divided into stationary and transient planetary- and subplanetary-scale eddy contributions. The stationary transport is largest in the subtropical lower troposphere and dominates the overall transport during summer. It is of planetary scale and the zonal scale of the transport corresponds to the number of subtropical anticyclones. The transient transport is large from the surface up to the midtroposphere and from the tropics to subpolar latitudes. It is dominated by the subplanetary-scale contribution during all seasons. Westward (eastward)- propagating waves dominate the transport in the tropics (subtropics and midlatitudes). The analysis reveals that, while the total eddy meridional latent heat transport is seamless from the deep tropics to the pole, it represents the sum of transport by distinct dynamical features. The role of the eddy meridional latent heat transport in the moist isentropic circulation is assessed using the statistical transformed Eulerian mean formulation, which converts the eddy transports into streamfunctions. The addition of the eddy latent heat streamfunction to the Eulerian mean plus eddy sensible heat streamfunction increases the mass transport by a factor of 2–3 in the subtropics and midlatitudes. The eddy transport is found to dominate the transport across the subtropical boundary. During Northern Hemisphere summer there is virtually no circulation in the absence of eddy latent heat transport. The results highlight the important role of latent heat transport by subtropical anticyclones and tropical and baroclinic waves in the general circulation

Moist Recirculation and Water Vapor Transport on Dry Isentropes

An analysis of the overturning circulation in dry isentropic coordinates using reanalysis data is presented. The meridional mass fluxes on surfaces of constant dry potential temperature but distinct equivalent potential temperature are separated into southward and northward contributions. The separation identifies thermodynamically distinct mass fluxes moving in opposite directions. The eddy meridional water vapor transport is shown to be associated with large poleward and equatorward mass fluxes occurring at the same value of dry potential temperature but different equivalent potential temperature. These mass fluxes, referred to here as the moist recirculation, are associated with an export of water vapor from the subtropics connecting the Hadley cell to the midlatitude storm tracks. The poleward branch of the moist recirculation occurs at mean equivalent potential temperatures comparable to upper tropospheric dry potential temperature values, indicating that typical poleward-moving air parcels can ascend to the tropopause. The analysis suggests that these air parcels ascend on the equatorward side of storm tracks by following moist isentropes reminiscent of upright deep convection, while on the poleward side their moist isentropes are indicative of large-scale slantwise convection. In the equatorward branch, the analysis describes typical air parcels that follow their dry isentropes until they get injected into the boundary layer where they are subsequently moistened. The moist recirculation along with the mean equivalent potential temperature of its poleward and equatorward components are used to recover an approximate overturning circulation on moist isentropes from which it is shown that the moist recirculation accounts for the difference between the meridional circulation averaged on dry and on moist isentropes

On the computation of moist-air specific thermal enthalpy

The specific thermal enthalpy of a moist-air parcel is defined analytically following a method in which specific moist entropy is derived from the Third Law of thermodynamics. Specific thermal enthalpy is computed by integrating specific heat content with respect to absolute temperature and including the impacts of various latent heats (i.e., solid condensation, sublimation, melting, and evaporation). It is assumed that thermal enthalpies can be set to zero at $0$ K for the solid form of the main chemically inactive components of the atmosphere (solid-$\alpha$ oxygen and nitrogen, hexagonal ice). The moist thermal enthalpy is compared to already existing formulations of moist static energy (MSE). It is shown that the differences between thermal enthalpy and the thermal part of MSE may be quite large. This prevents the use of MSE to evaluate the enthalpy budget of a moist atmosphere accurately, a situation that is particularly true when dry-air and cloud parcels mix because of entrainment/detrainment processes along the edges of cloud. Other differences are observed when MSE or moist-air thermal enthalpy is plotted on a psychrometric diagram or when vertical profiles of surface deficit are plotted.Comment: Paper accepted for publication (January 2014) in the Quarterly Journal of the Royal Meteorological Society (39 pages, 12 Figures, 7 Tables

Moist static energy: definition, reference constants, a conservation law, and effects on buoyancy

Atmospheric thermodynamic variables are commonly computed under approximations. Although exact formulas are available, they are rarely used. This paper addresses some potential issues arising when using approximate formulas by taking the moist static energy as an example. An important conclusion is that the temperature dependence of latent heat must be taken into account. We also demonstrate that the zero-point energies of various species do not affect the moist static energy budget. The use of an exact formula for moist static energy increases its surface value by 15 K for a typical tropical sounding. However, the change of the parcel buoyancy by using the exact formula is less dramatic, although not negligible. Calculating, for example, the CAPE for convection parameterization, the use of an exact formula is likely not be critical for the practical purposes, but quantitative discrepancies can be as large as 50–200 J/kg

The key physical parameters governing frictional dissipation in a precipitating atmosphere

Precipitation generates small-scale turbulent air flows the energy of which ultimately dissipates to heat. The power of this process has previously been estimated to be around 2-4 W m-2 in the tropics: a value comparable in magnitude to the dynamic power of the global circulation. Here we suggest that this previous power estimate is approximately double the true figure. Our result reflects a revised evaluation of the mean precipitation path length Hp. We investigate the dependence of Hp on surface temperature,relative humidity,temperature lapse rate and degree of condensation in the ascending air. We find that the degree of condensation,defined as the relative change of the saturated water vapor mixing ratio in the region of condensation, is a major factor determining Hp. We estimate from theory that the mean large-scale rate of frictional dissipation associated with total precipitation in the tropics lies between 1 and 2 W m-2 and show that our estimate is supported by empirical evidence. We show that under terrestrial conditions frictional dissipation constitutes a minor fraction of the dynamic power of condensation-induced atmospheric circulation,which is estimated to be at least 2.5 times larger. However,because Hp increases with surface temperature Ts, the rate of frictional dissipation would exceed that of condensation-induced dynamics, and thus block major circulation, at Ts >~320 K in a moist adiabatic atmosphere.Comment: 12 pp, 2 figure

Present and Last Glacial Maximum climates as states of maximum entropy production

The Earth, like other planets with a relatively thick atmosphere, is not locally in radiative equilibrium and the transport of energy by the geophysical fluids (atmosphere and ocean) plays a fundamental role in determining its climate. Using simple energy-balance models, it was suggested a few decades ago that the meridional energy fluxes might follow a thermodynamic Maximum Entropy Production (MEP) principle. In the present study, we assess the MEP hypothesis in the framework of a minimal climate model based solely on a robust radiative scheme and the MEP principle, with no extra assumptions. Specifically, we show that by choosing an adequate radiative exchange formulation, the Net Exchange Formulation, a rigorous derivation of all the physical parameters can be performed. The MEP principle is also extended to surface energy fluxes, in addition to meridional energy fluxes. The climate model presented here is extremely fast, needs very little empirical data and does not rely on ad hoc parameterizations. We investigate its range of validity by comparing its performances for pre-industrial climate and Last Glacial Maximum climate with corresponding simulations with the IPSL coupled atmosphere-ocean General Circulation Model IPSL_CM4, finding reasonable agreement. Beyond the practical interest of this result for climate modelling, it supports the idea that, to a certain extent, climate can be characterized with macroscale features with no need to compute the underlying microscale dynamics.Comment: Submitted to the Quarterly Journal of the Royal Meteorological Societ