Atmosphere

A gravitationally retained gaseous envelope of a planet. Its pressure, composition and temperature determine its radiative transfer and circulation. A pure saturated water atmosphere follows the saturation pressure along a phase coexistence curve when condensate is locally available.

The column mass of a specified constituent per unit horizontal area, $W_i=\int {\rho }_{i}dz$. Under hydrostatic equilibrium it is $g^{-1}\int q_{i}dp$, where $q_i$ is the constituent mass fraction.

Prescribe a dry adiabat for a background ideal gas A,where $R_A$ is its specific gas constant, $c_{pA}$ its constant specific heat capacity at fixed pressure, and $T_s,p_s$ the surface temperature and pressure. A dilute saturated vapour B has specific gas constant $R_B$, constant latent heat $L$, and saturation vapor pressure $e_s(T)$. Put $ϵ=R_A/R_B$ and $\beta =L/(R_B{T}_s)$.

The ideal-vapour Clausius-Clapeyron relation integrates toIts dilute vapour mass fraction is approximately $ϵe_s/p$. Under constant-$g$ hydrostatic balance, the vapour mass path is thereforeFor the second equality, set $\zeta =\log (p_s/p)$ and then $y=\beta e^{x\zeta }$. Thus the exponential integral follows from the combination of adiabatic cooling and rapidly falling saturation vapor pressure.

For $\beta \gg 1$, integration by parts gives $e^{\beta }{E}_1(\beta )\sim {\beta }^{-1}(1-{\beta }^{-1}+2{\beta }^{-2}-\cdots )$, henceThe column is weighted toward its warm lower part. Diluteness must hold throughout the column. This calculation prescribes the dry adiabat; if condensation heating changes that profile, a consistent moist adiabat is needed instead.

The temperature of a planetary surface at a specified location or averaging scale. It can differ from overlying air temperature, effective radiating temperature and spectral brightness temperature.

The mass per unit horizontal area above a level in an atmosphere. With constant gravitational acceleration, hydrostatic balance gives $m=(p_s-p_{\mathrm{top}})/g$. This relation connects an observed surface pressure to the total reservoir mass without assuming an isothermal temperature profile.

For a dry background inventory of column weight $P_d$, a mixed layer of fixed pressure thickness $\Delta p$, and saturated surface vapor partial pressure $E$, put $x=E/P$ and let $ϵ$ be the vapor-to-background molar mass ratio. The vapor mass fraction is $ϵx/[1+(ϵ-1)x]$, so hydrostatic balance and mass conservation give the displayed quadratic equation. Physical solutions require $x\le 1$ and a nonnegative upper-layer pressure. At $x=1$, $P=E=P_d+\Delta p$. A real positive algebraic root beyond that value need not be physically admissible.