Methodology

For given ambient temperature T and relative humidity RH, the Dewpoint Calculator solves the defining Equation (1) for the Dewpoint temperature Tdp.

The solving is done numerically using Newton's Method and by initially guessing the ambient temperature as the dewpoint. The algorithm must be able to evaluate the saturation vapor pressure of water at arbitrary temperatures, and therefore relies on interpolation formulas for this quantity.

At freezing conditions (sub-zero Deg. C temperatures), the Dewpoint Calculator uses the saturation vapor pressure over ice, thus computing the frostpoint.

Glossary

Dewpoint Tdp
If a body is exposed to moist air and then cooled down, water will condense on its surface when the temperature drops below the dewpoint temperature. At freezing conditions, both dewpoint (now the dew is super-cooled water) and frostpoint can coexist.
Note: For a fixed relative humidity, neither dewpoint nor frostpoint depend on the atmospheric pressure. However, if a moist air sample is pressurized at a constant temperature and at a constant absolute humidity, both the relative humidity and the dewpoint will rise.
Dewpoint Versus Temperature Curve for RH=5%

Frostpoint Tfp
Corresponding to the dewpoint for freezing conditions, the frostpoint is the temperature at which ice will form on the cool body. The frostpoint for liquid water is slightly higher than the dewpoint. Because the formation of ice depends on a certain amount of impurity on the surface of the body, however, you may still experience dew at subzero temperatures.

Boiling point
The temperature at which the vapor pressure equals atmospheric pressure (about 101kPa at sea-level). Below the boiling point, the atmospheric pressure (which equals the pressure inside the water) will prevent evaporation inside the water body. At the boiling point, the water body becomes physically unstable in that vapor bubbles will start to form.

Relative Humidity RH
Degree of saturation of water in air. At a RH of 100%, the air is saturated and attains its most moist state. At a RH of 0%, no water is present. Relative humidity is defined by Equation (1) as a function of ambient temperature T and dewpoint Tdp only, and therefore does not depend on air pressure or altitude:
Pvs(Tdp)=RH Pvs(T). Equation (1)
In practice, RH is often measured directly and propagated through weather reports.

Saturation Vapor Pressure Pws
The intensity at which water vapor will evaporate from water(Pressure over liquid water) or from ice (Pressure over ice). The vapor pressure of a system, at a given temperature, for which the vapor of a substance is in equilibrium with a plane surface of that substance's pure liquid or solid phase; The saturation vapor pressure is a function of temperature only. It can be measured directly, is recorded in Steam Tables, and can be evaluated with the help of interpolation formulas.

Vapor Pressure Pw
For a vapor mixed with other vapors or gases, it is that vapor's contribution to the total pressure (i.e., its partial pressure). In meteorology, vapor pressure is used almost exclusively to denote the partial pressure of water vapor in the atmosphere.

Actual Mixing Ratio
Also called the Humidity Ratio, is measured in grams of water per kilogram of dry air. The calculator will show the Saturation Mixing Ratio in grams of water per kilogram of dry air of a given temperature, if the Relative Humidity input value is set to 100%. The equation is:
x = 0.62198 pw / (pa - pw) Equation (2)
pw = partial pressure of water vapor in moist air (kPa, psi) and
pa = atmospheric pressure of moist air (kPa, psi)
Chilled Sensor Hygrometer
Technique to directly measure the dewpoint by chilling on object (e.g. a mirror) to the point of condensation. Sensors of this type are quite accurate, but are expensive to operate and have a low response rate.

Capacitive RH Hygrometer
Type of sensor most commonly used to measure atmospheric humidity. These type of sensors have a typical accuracy of about 2% to 5% at RH between 10% and 90%. For very low or very high humidity, accuracy can be lower.

Temperature Scale
The Dewpoint Calculator uses the traditional temperature scales
Deg.C = Deg.K - 273.15, and Deg.F = 9/5 Deg.C + 32.

Interpolation Formulas
There are a great number of interpolation formulas for the saturation vapor pressure Pvs(T). These formulas are of varying accuracy and have different ranges of validity. The Dewpoint Calculator uses the formula put forward in 1997 by IAPWS, the International Association for the Properties of Water and Steam, see below. It is very accurate for 273.15 K < T < 647.096 K, with the relative accuracy never exceeding 0.06%. For details, please consult the source code.

Newton's Method
To solve an equation of the form f(x)=y for x, Newton's Method computes the iterates xn
xn+1 = xn + (y-f(xn))/f'(xn), Equation (2)
starting at a suitable initial guess x0. If the problem is not ill-conditioned, iterations will converge quickly to the solution x.

Resources

Last modified by Wolfgang Kühn on 2010-03-12 and Tom Legbandt on 2011-07-28
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