Vapour pressure of water#Accuracy of different formulations

There are many published approximations for calculating saturated vapor pressure over water and over ice. Some of these are (in approximate order of increasing accuracy):

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|August-Roche-Magnus (or Magnus-Tetens or Magnus) equation

| $P\; =\; 0.61094\; \backslash exp\backslash left(\backslash frac\{17.625\; T\}\{T\; +\; 243.04\}\backslash right)$

| Temperature {{mvar|T}} is in °C and vapour pressure {{mvar|P}} is in kilopascals (kPa). The coefficients given here correspond to equation 21 in Alduchov and Eskridge (1996).{{cite journal |last1=Alduchov |first1=O.A. |last2=Eskridge |first2=R.E. |title=Improved Magnus form approximation of saturation vapor pressure |journal=Journal of Applied Meteorology |volume=35 |issue=4 |pages=601–9 |year=1996 |doi=10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2 |bibcode=1996JApMe..35..601A |url=https://digital.library.unt.edu/ark:/67531/metadc693874/ |doi-access=free }}

See also discussion of Clausius-Clapeyron approximations used in meteorology and climatology.

|-

| Tetens equation

|$P\; =\; 0.61078\; \backslash exp\backslash left(\backslash frac\{17.27\; T\}\{T\; +\; 237.3\}\backslash right)$

|{{mvar|T}} is in °C and  {{mvar|P}} is in kPa

|-

|The Buck equation.

|$P\; =\; 0.61121\; \backslash exp\; \backslash left(\backslash left(\; 18.678\; -\; \backslash frac\{T\}\; \{234.5\}\backslash right)\backslash left(\; \backslash frac\{T\}\; \{257.14\; +\; T\}\; \backslash right)\backslash right)$

|{{mvar|T}} is in °C and {{mvar|P}} is in kPa.

|-

|The Goff-Gratch (1946) equation.Goff, J.A., and Gratch, S. 1946. Low-pressure properties of water from −160 to 212 °F. In Transactions of the American Society of Heating and Ventilating Engineers, pp 95–122, presented at the 52nd annual meeting of the American Society of Heating and Ventilating Engineers, New York, 1946.

|colspan=2|(See article; too long)

|}

Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapor pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005):

:

A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). The analysis here shows the simple unattributed formula and the Antoine equation are reasonably accurate at 100 °C, but quite poor for lower temperatures above freezing. Tetens is much more accurate over the range from 0 to 50 °C and very competitive at 75 °C, but Antoine's is superior at 75 °C and above. The unattributed formula must have zero error at around 26 °C, but is of very poor accuracy outside a narrow range. Tetens' equations are generally much more accurate and arguably more straightforward for use at everyday temperatures (e.g., in meteorology). As expected,{{huh|date=August 2023}} Buck's equation for {{mvar|T}} > 0 °C is significantly more accurate than Tetens, and its superiority increases markedly above 50 °C, though it is more complicated to use. The Buck equation is even superior to the more complex Goff-Gratch equation over the range needed for practical meteorology.

For serious computation, Lowe (1977){{cite journal |first=P.R. |last=Lowe |title=An approximating polynomial for the computation of saturation vapor pressure |journal=Journal of Applied Meteorology |volume=16 |issue= 1|pages=100–4 |year=1977 |doi=10.1175/1520-0450(1977)016<0100:AAPFTC>2.0.CO;2 |bibcode=1977JApMe..16..100L |doi-access=free }} developed two pairs of equations for temperatures above and below freezing, with different levels of accuracy. They are all very accurate (compared to Clausius-Clapeyron and the Goff-Gratch) but use nested polynomials for very efficient computation. However, there are more recent reviews of possibly superior formulations, notably Wexler (1976, 1977),{{cite journal |first=A. |last=Wexler |title=Vapor pressure formulation for water in range 0 to 100°C. A revision |journal= Journal of Research of the National Bureau of Standards Section A |volume=80A |issue=5–6 |pages=775–785 |year=1976 |doi=10.6028/jres.080a.071|pmid=32196299 |pmc=5312760 |doi-access=free }}{{cite journal |first=A. |last=Wexler |title=Vapor pressure formulation for ice |journal= Journal of Research of the National Bureau of Standards Section A |volume=81A |issue=1 |pages=5–20 |year=1977 |doi=10.6028/jres.081a.003|doi-access=free |pmc=5295832 }} reported by Flatau et al. (1992).{{cite journal |last1=Flatau |first1=P.J. |last2=Walko |first2=R.L. |last3=Cotton |first3=W.R. |title=Polynomial fits to saturation vapor pressure |journal=Journal of Applied Meteorology |volume=31 |issue=12 |pages=1507–13 |year=1992 |doi=10.1175/1520-0450(1992)031<1507:PFTSVP>2.0.CO;2 |bibcode=1992JApMe..31.1507F |doi-access=free }}

Examples of modern use of these formulae can additionally be found in NASA's GISS Model-E and Seinfeld and Pandis (2006). The former is an extremely simple Antoine equation, while the latter is a polynomial.{{cite web |last1=Clemenzi |first1=Robert |title=Water Vapor - Formulas |url=http://mc-computing.com/Science_Facts/Water_Vapor/Formulas.html |website=mc-computing.com}}

In 2018 a new physics-inspired approximation formula was devised and tested by Huang {{cite journal|last1=Huang|first1=Jianhua|title=A Simple Accurate Formula for Calculating Saturation Vapor Pressure of Water and Ice

|journal=Journal of Applied Meteorology and Climatology

|volume=57

|issue=6

|year=2018

|pages=1265–72.

|url=https://www.jstor.org/stable/26500764}} who also reviews other recent attempts.

File:Vapor Pressure of Water.png. Graphics shows triple point, critical point and boiling point of water.]]

• Dew point
• Gas laws
• Lee–Kesler method
• Molar mass

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• {{cite web |title=Thermophysical properties of seawater |date=20 February 2017 |work=Matlab, EES and Excel VBA library routines |publisher=MIT |url=http://web.mit.edu/seawater/}}
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• {{cite journal |last1=Murphy |first1=D.M. |last2=Koop |first2=T. |title=Review of the vapour pressures of ice and supercooled water for atmospheric applications |journal=Quarterly Journal of the Royal Meteorological Society |volume=131 |issue=608 |pages=1539–65 |year=2005 |doi=10.1256/qj.04.94 |bibcode=2005QJRMS.131.1539M |s2cid=122365938 |url=https://zenodo.org/record/1236243 |doi-access=free }}
• {{cite book |first=James G. |last=Speight |title=Lange's Handbook of Chemistry |publisher=McGraw-Hil |edition=16th |year=2004 |isbn=978-0071432207 |url-access=registration |url=https://archive.org/details/langeshandbookof70edlang }}

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• {{cite web |first=Holger |last=Vömel |title=Saturation vapor pressure formulations |date=2016 |publisher=Earth Observing Laboratory, National Center for Atmospheric Research |location=Boulder CO |url=http://cires1.colorado.edu/~voemel/vp.html |archive-url=https://web.archive.org/web/20170623040102/http://cires1.colorado.edu/~voemel/vp.html |archive-date=June 23, 2017 |url-status=dead}}
• {{cite web |title=Vapor Pressure Calculator |publisher=National Weather Service, National Oceanic and Atmospheric Administration |url=https://www.weather.gov/epz/wxcalc_vaporpressure}}

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Category:Thermodynamic properties

Category:Atmospheric thermodynamics