This is a really simple problem, and for some reason my brain isn't comprehending an equivalency. Are atmospheric mixing ratios logarithmic? This is within the context of Meteorology. \(RH=\frac{r}{r_s}\) \(r = \epsilon \frac{e}{p-e}\approx \epsilon \frac{e}{p}\) \(r_s = \epsilon \frac{e_s}{p-e_s}\approx \epsilon \frac{e_s}{p}\) \(RH=\frac{r}{r_s}\approx\frac{\frac{e}{p}}{\frac{e_s}{p}}\approx\frac{e}{e_s}\) \(e=6.11* exp{\frac{Lm_v}{R*}(273.15^{-1} - (273.15+T)^{-1})}\) This is correct? Mathematically I can't see why not, it just doesn't feel intuitive that the two ratios would be equivalent. Are they in actuality not?
