Wv: Precipitable Water (or water vapor path) [kg m-2]
Wv/rho_l = 単位底面積の気柱の中に含まれる水蒸気が全て凝結して気柱の底にたまったら、水の高さはどのくらいになるか。
rho_l: density of liquid water [kg m-3]
rho_v: density of water vapor [kg m-3]
rho_a: air density [kg m-3]
q_v: specific humidity [kg kg-1]
p: pressure [Pa] or [kg m-1 s-2]
p0: surface pressure, corresponding to z =0
\begin{align*}
\begin{split}
W_v=\int_{0}^{\infty} \rho_v dz \\
=\frac{1}{g}\int_{p}^{p_0} \frac{\rho_v}{\rho_a} dp \\
=\frac{1}{g}\int_{p}^{p_0} q_v dp
\end{split}
\end{align*}
数式の変換 → https://texclip.marutank.net/
Curry and Webster (p.115)
Ref
Curry and Webster, Thermodynamics of Atmospheres and Oceans, Academic Press.
PW = 1 kg m-2 => 10^(-3) mの高さの水柱 = 1 mm
1 kgの水の体積 = 1000 cm3 = 10^(-3) m3