# Guest Post “Calculating Moist Enthalpy From Usual Meteorological Measurements By Francis Massen

Francis Massen, in response to the posts,

Comment On The Northeast Heat Wave

Further Information On The Role Of Water Vapor In Measuring Heat By Francis Massen

has graciously prepared a write up of how to compute the moist enthalpy of surface air. Francis websites include http://meteo.lcd.lu/; http://computarium.lcd.lu/; and http://bmb.lcd.lu/

Calculating Moist Enthalpy From Usual Meteorological Measurements By Francis Massen

Abstract: This short article shows how to compute the moist enthalpy from usual meteorological measurements of dry temperature, air pressure and relative humidity. The result is used to add a plot of moist air enthalpy to the other near-live graphs shown by meteoLCD, the meteorological station of the LCD, Diekirch, Luxembourg

1. Sensible heat of dry air

The sensible heat of dry air is defined as Ha = Cp*T [ref. 3] with Cp usually taken as 1.005 when Ha is given in [kJ/kg] and temperature T in [°C].

Here we will use for Cp the following expression, valid for temperatures higher than 0 °C and lower than 60 °C, as given by PADFIELD [ref.2]

Ha = 1.007*T – 0.026          0 °C < T < 60 °C                                                         [eq.1]

2. Heat content of water vapor at temperature T

The heat content of water vapor is the sum of the latent heat of vaporization and the sensible heat of water vapor:

Hv =  q*( L + 1.84*T) [ref. TET]                                                                               [eq.2]

Where L = heat of vaporization = 2501 kJ/kg at 0°C

and 1.84*T = sensible heat of water vapor in kJ/kg

The sensible heat term of eq.3 (1.84*T) is very often considered negligible and omitted.

Note:L is a function of temperature, becoming slightly smaller with increasing T; for values between 0°C and 50°C one can use the linear interpolation L(T) = 2502 – 2.378*T computed by the author from a table with enthalpy values given by YHCHEN [ref.4]: The linear fit is excellent with R2 = 0.9998.

Combining eq.2 with L(T) gives:

Hv = q*(2502 – 0.538*T)    with Hv in kJ/kg and T in °C                [eq.3]

3. Total enthalpy of moist air

Total enthalpy of moist air is the sum of Ha and Hv:

H = Ha + Hv = (1.007*T -0.026) + q*(2502 – 0.538*T)                       [eq.4]

with H in kJ/kg, T in °C and specific humidity q in kg/kg

The problem with this formula is that the specific humidity q is usually not measured by a standard meteorological equipment which commonly measures relative humidity.

4. Finding q from measured dry bulb temperature, relative humidity and atmospheric pressure

PIELKE [ref.3] and the AOMIP website [ref.1] give the following formula for the specific humidity q:

where ea = vapor pressure in [Pa] and pa = atmospheric pressure in [Pa].
Attention: pa is the true air pressure, not the barometric pressure reduced to sea level!

Dividing numerator and denominator by ea gives:

Relative humidity is the fraction of water vapor pressure to saturated water vapor pressure, usually multiplied by 100 to give a percent value:

RH = 100* ea/esat  →  ea = RH/100*esat

There are many different formulas relating esat to temperature. We will use the expression given in AOMIP [ref.1] and valid up to 40°C:

with saturated water vapor pressure esat in [Pa] and temperature T in °C.

Equations 4, 6 and 7 contain only T, RH and pa, which are parameters measured by practically every standard weather station. Together they can be used to calculate the enthalpy of moist air by a single (albeit unwieldy) formula: [eq.8]

This expression is valid for temperatures 0°C < T < 40°C. Units: H[kJ/kg], T[°C], pa[Pa]

5. A practical example

The author has used eq.8  in GNUPLOT to display near-live plots of the moist enthalpy at meteoLCD, Diekirch, Luxembourg (see http://meteo.lcd.lu/today_01.html). The following figure shows the situation for the week from 10 to 16th July 2010. Sensible heat is shown by the blue bottom curve; the difference between the upper red curve ( = moist enthalpy) and the blue curve corresponds to the latent heat.

Technisolve Software has a website with an online moist air calculator, which is very handy for a quick validation check of individual values: http://www.coolit.co.za/airstate/airmoistobject.htm References

 AOMIP: Atmospheric Forcing Data – Humidity

http://efdl.cims.nyu.edu/project_aomip/forcing_data/atmosphere/humidity.html

 PADFIELD, Tim: Conservation Physics

 PIELKE, Roger, Sr., WOLTER, Klaus: The July 2005 Denver Heat Wave: How unusual was it ?. National Weather Digest, vol.31, no. 1, July 2007

http://pielkeclimatesciencesci.files.wordpress.com/2009/10/r-313.pdf

 TET (The Engineering Toolbox)

http://www.engineeringtoolbox.com/enthalpy-moist-air-d_683.html

 YHCHEN: Calculation of Enthalpy Changes

www.ntut.edu.tw/~yhchen1/Chap.%2023.pdf

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