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 CALCULATING RELATIVE HUMIDITY

METEOROLOGIST JEFF HABY

Calculating the RH requires the correct equation(s). The RH is the amount of moisture in the air (via moisture mass or vapor pressure) divided by the maximum amount of moisture that could exist in the air at a specific temperature (via max moisture mass or saturation vapor pressure). RH is expressed as a percentage and has no units since the units in both the numerator and denominator are the same. The percentage is found by multiplying the ratio by 100%. The RH is NOT the dewpoint divided by the temperature. For example, if the temperature was 60 F and the dewpoint was 30 F, you would not simply take (30/60)*100% = 50% RH.

Method #1

When given temperature and dewpoint, the vapor pressure (plugging Td in place of T into Clausius-Clapeyron equation) and the saturation vapor pressure (plugging T into Clausius-Clapeyron equation) can be determined. The RH = E/Es*100%.

Clausius-Clapeyron equation

LN(Es/6.11) = (L/Rv )(1/273 - 1/T)
Es = Saturation vapor pressure
L = Latent heat of vaporization = 2.453 × 10^6 J/kg
Rv = Gas constant for moist air = 461 J/kg
T = Temperature in Kelvins

Method #2

The mixing ratio is defined as the mass of water vapor divided by the mass of dry air. In a lab setting, the lab technician could measure both the mass of water vapor and mass of dry air in an air sample. The mass of water vapor in a sample of air divided by the mass of dry air is W. The lab technician could then saturated the air (making sure temperature remains the same) and recalculate the mass of water vapor divided by the mass of dry air. This would be Ws. The RH = W/Ws*100%

To get W and Ws, use the equation:

W= (0.622*e) / (P - e) and Ws = (0.622*Es) / (P - Es)

This requires that E and Es are known. Therefore, without using the Clausius-Clapeyron equation, calculating RH outside of a lab setting is difficult.

--operational methods of calculating RH--

1. Mixing ratio can be determined using the Skew-T log-P diagram. For any pressure level, the mixing ratio is read through the dewpoint and the saturation mixing ratio is read through the temperature. By reading the mixing ratio values off the Skew-T you can determine W and Ws for any temperature and dewpoint. RH = W/Ws*100%

2. Take the temperature and dewpoint and plug them into the Clausius-Clapeyron equation. There are computer programs that will do this. The computer uses the graph of the Clausius-Clapeyron equation for all temperature and dewpoints to find RH.

3. Many textbooks have a graph or table data of saturation mixing ratio and/or saturation vapor pressure for various temperatures. Using dewpoint will either give the actual vapor pressure or actual mixing ratio while using temperature will either give the saturation vapor pressure and saturation mixing ratio (depending on if graph is showing vapor pressure or mixing ratio). RH is E/Es*100% or W/Ws*100%.