= Moist-layer mass constraint in a light atmosphere
{title2=$(P-P_d)[P+(\epsilon-1)E]=\epsilon\Delta pE$}
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 $\epsilon$ be the vapor-to-background <molar mass> ratio. The vapor <mass fraction> is $\epsilon x/[1+(\epsilon-1)x]$, so <hydrostatic balance> and <mass conservation> give the displayed <quadratic equation>. Physical solutions require $x\leq1$ 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.
Back to article page
