Abstract. A simplified set of equations is derived systematically below for the interaction of large scale flow fields and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model, have the form of a shallow water equation and an equation for moisture coupled through a strongly nonlinear source term. This source term, the precipitation, is of relaxation type in one region of state space for the temperature and moisture, and vanishes identically elsewhere in the state space of these variables. In addition, the equations are coupled nonlinearly to the equations for barotropic incompressible flow. Several mathematical features of this system are developed below including energy principles for solutions and their first derivatives independent of relaxation time. With these estimates, the formal infinitely fast relaxation limit converges to a novel hyperbolic free boundary problem for the motion of precipitation fronts from a large scale dynamical perspective. Elementary exact solutions of the limiting dynamics involving precipitation fronts are developed below and include three families of waves: fast drying fronts as well as slow and fast moistening fronts. The last two families of waves violate Lax's Shock Inequalities; nevertheless, numerical experiments presented below confirm their robust realizability with realistic finite relaxation times. From the viewpoint of tropical atmospheric dynamics, the theory developed here provides a new perspective on the fashion in which the prominent large scale regions of moisture in the tropics associated with deep convection can move and interact with large scale dynamics in the quasi-equilibrium approximation.Key words. tropical atmospheric dynamics, equatorial waves, tropical convection, moisture, hyperbolic PDE, nonlinear relaxation equations, hyperbolic free boundary problems MSC 2000 subject classifications: 86A10 Meteorology and atmospheric physics 35L67 PDE of hyperbolic type, Shocks and singularities IntroductionOne of the striking observational discoveries over the last few decades is the profound impact of the interaction of water vapor and planetary scale dynamics in the tropics on monthly, seasonal, and even decadal prediction of weather and climate in the midlatitudes [21]. Contemporary comprehensive computer models (known as general circulation models or GCM's) are currently incapable of adequately resolving or parameterizing these interactions on time scales appropriate for seasonal prediction as well as climate change projections [38]. Given the complexity of contemporary GCM's, one important theoretical thrust in the atmospheric science community is the development of simplified models for the parameterization of the interaction of moisture and large scale dynamics which retain fidelity with crucial features of the observational record ([9] [26]). Observations show that moisture-coupled large scale waves in the atmosphere often move at speeds that are much slower than the dry gravity wave speed ([21], [40]); the theoretical predi...
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 for only a small fraction of the entropy production. This behavior is directly related to the fact that the convective heat transport is mostly due to the latent heat transport. In such cases, moist convection acts more as an atmospheric dehumidifier than as a heat engine. The amount of work available to accelerate convective updrafts and downdrafts is much smaller than predicted by studies that assume that moist convection behaves mostly as a perfect heat engine.
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 Earth's 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.
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 the two circulations can be explained by the atmospheric transport of water vapor. In particular, the enhanced mass transport on moist isentropes corresponds to a poleward flow of warm moist air near the earth's surface in midlatitudes. This low-level poleward flow does not appear in the zonally averaged circulation on dry isentropes, as it is hidden by the presence of a larger equatorward flow of drier air at same potential temperature. However, as the equivalent potential temperature in this low-level poleward flow is close to the potential temperature of the air near the tropopause, it is included in the total circulation on moist isentropes. In the tropics, the situation is reversed: the Hadley circulation transports warm moist air toward the equator, and in the opposite direction to the flow at upper levels, and the circulation on dry isentropes is larger than that on moist isentropes.The relationship between circulation and entropy transport is also analyzed. A gross stratification is defined as the ratio of the entropy transport to the net transport on isentropic surfaces. It is found that in midlatitudes the gross stability for moist entropy is approximately the same as that for dry entropy. The gross stratification in the midlatitude circulation differs from what one would expect for either an overturning circulation or horizontal mixing; rather, it confirms that warm moist subtropical air ascends into the upper troposphere within the storm tracks.
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