Factor 1000 in mixing ratio formula I am seeing two different formulas for the mixing ratio, which differ by a factor 1000. To be more specific:
$w = 0.622 \cdot (e/p)$
and
$w = 1000 \cdot 0.622 \cdot (e/p)$
where $e$ and $p$ are the water vapour pressure and the atmospheric pressure, respectively.
I assume the factor 1000 has to do with the fact that the mixing ratio is theoretically a ratio of masses, so probably the numerator can be expressed in grams and has to be converted to kilograms, but I'm confused because I don't see masses in these formulas.
What's the difference between the two ?
The factor of 1000 may be related to the expected units. The mass 'units' can be found in the derivation.
The full derivation of mixing ratio goes like this
$$w=\epsilon\frac{e}{P}$$
since, by the ideal gas law,
$$e=\rho_vR_vT$$
and
$$P_d=\rho_dR_dT$$
then the mixing ratio is expressed as
$$w=\epsilon\frac{\rho_vR_vT}{\rho_dR_dT}=\epsilon\frac{\rho_vR_v}{\rho_dR_d}$$
Since $\epsilon=\frac{R_d}{R_v}=0.622$ (see above hyperlink),
$$w=\frac{\rho_v}{\rho_d}$$
To return back to the question 'what is the difference between your two equations?' The units reported are $g/g$ and $g/kg$ for the first and second equations, respectively.