Saturation Vapor Pressure

where ₁ 1/₁ and index 1 refers to the liquid phase and index 2 refers to the gas phase.

For an isothermal change of phase, the Clausius-Clapeyron equation has the form

d P_s/d T = L/[T · (₂-₁)]

Water vapor behaves like an ideal gas and _{2 1} for a change in state.

L 2.5 · 10³ Joules/gm

L 2.824 · 10³ Joules/gm over ice

R_w = R_*/<mw>_w = 8.3143/18.016 = 0.4615 Joules/gm/K

P_s = ₂ · R_w T

d P_s/d T = L/[T · (₂-₁)] (L · ₂)/T = (L · P_s) /(R_w · T²)

d log(e_s) = d P_s/P_s = (L/R_w) · (dT/T²)

log_e(e_s) = (L/R_w) · (dT/T²) = -(L/R_w)|T->T₀ + C = -L/(R_w · T₀) + L/(R_w· T) + C

at triple point all 3 phases can exist in equilibrium, 0.0098° C and P_s = 6.11 mB

e_s(T=T₀) = 6.11

L/R_w = 5417.12

L/(R_w T₀) = 19.8313

6.11 · exp[ L/(R_w T₀) ] = 2.504 · 10⁹

e_s(T) = 6.11 · exp[ 5417( 1/T₀ - 1/T) ] = 2.504 · 10⁹ · exp[ 5417/T ]

Undocumented fit is used in the program watsat.F (over liquid)

e_s = 2.229 · 10⁹ · exp[ -5385/T ]

Note this is the same equation as above, except that it assumes L = 2485.2 Joules/gm and T₀ = 273.15 ° K

Another undocumented fit is given (but not used) in the program watsat.F

e_s = 0.001 · exp[ a/T + b + c log(T) + d · T + e · T² ]

From Rogers and Yau, pg. 16

e_s = 6.112 · exp[ a · (T-273.16)/(T-b) ]

Murray, F.W. 1966. ``On the computation of Saturation Vapor Pressure'' J. Appl. Meteor. 6 p.204

e_s = 6.1078 · exp[ a · (T-273.16)/ (T-b) ]

Saucier, W.J. 1883. ``Principles of Meteorological Analysis'' Dover pg. 9 who uses values of Tetens (1930). Note, he used 10^{[(a'T)/(T-b')]} with T in Centigrade so to convert into the form above a = log 10 · a' and b = 273.16-b'.