By R.L. Snyder (Revised March 24, 2005)

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1 Humidity Conversion By R.L. Snyder (Revised March 24, 2005) This Web page provides the equations used to make humidity conversions and tables o saturation vapor pressure. For a pd ile o this document, click on HumCon.pd. The saturation vapor pressure tables in an MS Excel spreadsheet can be donloaded by clicking on es.xls. Barometric Pressure Barometric pressure (P) in kpa rom elevation (E L ) in m above sea level as reported by Jensen, Burman and Allen, 1990 as P E L 526. (1) Latent heat o vaporization Latent heat o vaporization (λ) in kj kg -1 rom air temperature (T) in o C λ T (2) Saturation Vapor Pressure Saturation vapor pressure over ater is the vapor pressure o the air hen the number o ater molecules condensing equals the number evaporating rom a lat surace o ater ith both the air and ater at some temperature (T). An equation or the saturation vapor pressure (e s ) over ater at temperature (T) in o C as given by Tetens (1930) as e s T exp T (3) Values o e s or T to 0 and or T 0 to 49.9 are given in Tables 1 and 2.

Barometric Pressure Barometric pressure (P) in kpa rom elevation (E L ) in m above sea level as reported by Jensen, Burman and Allen, 1990 as 293 0. 0065 P 1013. 293 E L 526.

2 When the number o ater molecules sublimating equals the number depositing onto a lat surace o ice ith both the air and ice at some temperature (T), the saturation vapor pressure (e s ) in kpa over ice at temperature (T) in o C as given by Tetens (1930) as e s T exp T (4) Values o e s or T 0 to are given in Table 3. De point and Ice point Temperature De-point temperature (T d ) in o C rom air temperature (T) in o C and relative humidity (RH) in % T d ( RH /100) ( RH 100) T T (5) Ice-point temperature (T i ) in o C rom air temperature (T) in o C and relative humidity (RH) in % T i ( RH /100) ( RH 100) T T (6) Note that the actual vapor pressure (e) is equal to the saturation vapor pressure (e d ) at the depoint temperature (T d ) and, or subzero temperatures, e equals the saturation vapor pressure (e i ) at the ice point temperature (T i ). De-point temperature (T d ) in o C rom vapor pressure (e e d ) in kpa over ater is calculated in to steps ( ) ln e b (7) b T d (8) 1 b Ice-point temperature (T i ) in o C rom vapour pressure (e e i ) in kpa over ice is calculated in to steps ( ) ln e b i (9) b T i (10) 1 b

De point and Ice point Temperature De-point temperature (T d ) in o C rom air temperature (T) in o C and relative humidity (RH) in % T d ( RH /100) 237.3 17.27 1 17.27 ( RH 100) 237.3 + T 237.

3 Psychrometric Constant Psychrometric constant (γ) in kpa o C -1 or liquid ater as a unction o barometric pressure (P) in kpa and et-bulb temperature (T ) in o C as given by Fritschen and Gay (1979) as γ ( T ) P (11) Psychrometric constant (γ ) in kpa o C -1 or ice as a unction o barometric pressure (P) in kpa and rost-bulb temperature (T ) in o C is γ ' ( T )P (12) Vapor Pressure Vapor pressure (e e d ) in kpa at the de point temperature (T d ) in o C 17.27T d e exp (13) d Td Vapor pressure (e e i ) in kpa at the subzero ice point temperature (T i ) in o C T i e exp (14) i Ti Vapor pressure (e) in kpa rom dry (T) and et-bulb (T ) temperature in C and barometric pressure (P) and kpa ( T T ) e ( T )( T T )P e e γ (15) here e in kpa is the saturation vapor pressure at the et-bulb temperature (T ) in o C. It is calculated by substituting T or T in Equation 4. Vapor pressure (e) in kpa rom dry (T) and rost-bulb (T ) temperature in C and barometric pressure (P) in kpa e e γ ' T T e T T T (16) i ( ) ( )( )P here e is the saturation vapor pressure at the rost-bulb temperature. It is calculated by substituting T in o C or T in Equation 4. Slope o Saturation Vapor Pressure Slope o Saturation Vapor Pressure ( ) in kpa o C -1 pressure (e s ) in kpa at temperature T in o C over liquid ater ith saturation vapor

00115T )P (12) Vapor Pressure Vapor pressure (e e d ) in kpa at the de point temperature (T d ) in o C 17.27T d e 0.6108exp (13) d Td + 237.

4 4098e s (17) 2 ( T ) Equivalent Temperature Equivalent temperature (T e ) in o C rom temperature T in o C, vapor pressure e in kpa and the psychrometric constant γ in kpa o C -1 T e e T + γ (18) Absolute Humidity Absolute humidity (χ) in g m -3 rom vapor pressure (e) in kpa and temperature (T) in o C 2165 e χ (19) T Table 1. Saturation vapor pressure (e s ) in kpa over a lat surace o liquid ater calculated using Tetens ormula (Equation 4) or temperature beteen 0.0 C and C. Temperature ( C)

Absolute humidity (χ) in g m -3 rom vapor pressure (e) in kpa and temperature (T) in o C 2165 e χ (19) T + 273.16 Table 1.

6 Table 2. Saturation vapor pressure (kpa) over a lat surace o liquid ater calculated using Tetens ormula (Equation 4) or temperature beteen 0 C and 49.9 C. Temperature ( C)

752 3 0.758 0.763 0.769 0.774 0.780 0.785 0.791 0.796 0.802 0.808 4 0.813 0.819 0.825 0.831 0.836 0.842 0.848 0.854 0.860 0.866 5 0.872 0.878 0.885 0.891 0.897 0.903 0.910 0.916 0.922 0.929 6 0.935 0.

7 Table 3. Saturation vapor pressure (kpa) over a lat surace o ice calculated using Tetens ormula (Equation 5) or temperature beteen 0.0 C and C. Temperature ( C) Reerences Fritschen, L.J. & Gay, L.W Environmental Instrumentation. Ne York, NY: Springer-Verlag. Jensen, M.E., R.D. Burman, and R.G. Allen, Eds Evapotranspiration and Irrigation Water Requirements. Amer. Soc. o Civil Eng., Ne York. Tetens, V.O Uber einige meteorologische. Begrie, Zeitschrit ur Geophysik. 6:

107 48 11.163 11.219 11.276 11.333 11.390 11.447 11.504 11.562 11.620 11.679 49 11.737 11.796 11.855 11.914 11.974 12.034 12.094 12.154 12.215 12.276 Table 3.

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