8.1.4 Water

The scale height of water, h_w, which results from a fast evaporation/condensation process, is small (typically 2 km) compared to the equilibrium scale height h_o= 8.4 km. At h = 2.5 km, the altitude of the Plateau de Bure, the water vapor column density N_w (or w, ``amount of precipitable water'', when expressed in g.cm^-2, or cm of water) is normally reduced by a factor of 3-4, with respect to sea level. This factor, as we have seen, is strongly modulated by the local temperature gradient. w is lower in the presence of a low altitude inversion layer which reduces the vertical turbulence and traps most of the water well below the observatory.

The value of w on a site can be estimated directly by measuring the air pressure p_tot (in mbar), temperature T (in K) and relative humidity RH (in percent), and using the formulas 8.7 and 8.11 adapted for water (the air pressure p is replaced by the partial water vapor pressure e):

$$w [\mathrm{mm}]= \rho_ w[\mathrm{gm}^{-3}] h_w [\mathrm{km}] %$$ (8.16)

$$\rho_w [\mathrm{gm}^{-3}]= {\frac{e M_w}{RT}} = 216.5 e [\mathrm{mbar}] /T [\mathrm{K}]$$ (8.17)

e is related to e_s(T), the water vapor pressure in saturated air, by:

$$e = RH\cdot e_s/{100}$$ (8.18)

e_s is a rather complex function of T, for which an approximate analytical expression, as well as tabulated values, can be found in the literature (see e.g. [Queney 1974], p.120). To the zero order, it can be expressed by:

$$e_s [mbar] \simeq 6 (T/273)^{18}$$ (8.19)