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.

For a dilute saturated vapour with constant latent heat $L$ in a dry atmosphere, set $x=R_A/c_{pA}$, $ϵ=R_A/R_B$ and $\beta =L/(R_B{T}_s)$. Its mass path is $W=ϵe_s(T_s)e^{\beta }{E}_1(\beta )/(gx)$. Substituting $y=\beta e^{x\zeta }$ in the log-pressure column integral proves this identity. For $\beta \gg 1$, $W\sim c_{pA}{T}_s{e}_s(T_s)/(gL)$ with relative correction $-1/\beta +O({\beta }^{-2})$.

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.