Formulas for various atmospheric variables

There are numerous formulas available for computing atmospheric variables. These are a few that I have used for years. There are many more modern ones available and quite a few books of tables but these suffice for most engineering purposes.

In all cases, you should check a few of your computed values against tabular values just to be sure you have entered the formula correctly or that I have typed the formulas below correctly.

 

T = dry bulb temperature (C or F)
T_d = dewpoint temperature (C or F)
T_w = wetbulb temperature (C or F)
r = relative humidity (may be either decimal or in percent)
e = actual vapor pressure (usually millibars, mb, but can be in mm or inches of Hg)
e_s = saturation vapor pressure of the air over liquid water (usually millibars, mb, but can be in mm or inches of Hg)
e_i = saturation vapor pressure of the air over ice (usually millibars, mb, but can be in mm or inches of Hg)
w = mixing ratio (mass of water vapor per mass of dry air, usually g/g or kg/kg)
q = specific humidity (mass of water vapor per mass of moist air, usually g/g or kg/kg)

 

From Bosen (1958);

if r is a decimal and T & T_d are in F, then A = 173
if r is a decimal and T & T_d are in C, then A = 112

T_d = (A + 0.9*T)r^0.125 - A + 0.1*T
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From Bosen (1960:275); T (F) and e_s in inches Hg
e_s = (0.0041T + 0.676)⁸ - 0.000019Abs(T + 16) + 0.001316
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From LaMoreux (1962:27) ; T, T_d (F) and e_s in inches Hg
e_s = exp(15.674 - 7482.6/(T + 398.36))
T_d= -[7482.6/(ln(e) - 15.674)] - 398.36
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From Anderson(1968); all in F

T_w = T-(T-T_d)(0.12+0.008T)
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From Murray(1967); e_s (mb) T&T_d (C)

e_s = 6.1078 EXP [17.2693882T/(T+238.3)]

e_i = 6.1078 EXP [21.8745584T(-273.16)/(T-7.66)]

T_d=238.3*ln(e/6.1078)/[17.2693882 - ln(e/6.1078) ]
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From Hess(1959) e and p must be in the same units

w = 0.622e/(p-e)

q = 0.622e/(p-0.378e)

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e = e_s*r where r is decimal
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The relations of Murray are preferred. Errors will be less than one percent over -25C<T<50C
Bosen will be < 1.6 percent over 0F < T < 100F at sea level

 

Several of these formulas are available on the El Paso NWS or the Birmingham,AL NWS Web Page. You may also want to use this spreadsheet.

 

References

Anderson,E.A.,1969. Development and testing of snow pack energy equations. Water Resources Research 4:27

Bosen,J.F.,1958.An approximation formual to compute relative humidity from dry bulb and dewpoint temperature. Monthly Weather Review 86:486.

Bosen,J.F.,1960. Formula for the approximation of saturation vapor pressure over water. Monthly Weather Review 88:275-276.

Hess,T.1959. Introduction to theoretical meteorology. Holt,Rhinehart and Wilson

LaMoreux,Wallace W.,1962. Modern evaporation formulae adapted to computer use. Monthly Weather Review 90:26-28.

Murray,F.W.,1967.On the computation of saturation vapor pressure. J. of Applied Meteorology pp 203-204.

Wlhelm,Luther R., 1976. Numerical calculation of psychrometric properties in SI units. Trans. ASAE 19(2):318-321.