How does it work
For given ambient temperature T and relative humidity RH, the Dewpoint Calculator solves
the defining Equation (1) for the Dewpoint temperatur 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
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Dewpoint Tdp
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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.
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| Dewpoint Versus Temperature Curve for RH=5% |
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Frostpoint Tfp
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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.
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Boiling point
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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.
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Relative Humidity
RH
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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:
In practice, RH is often measured directly and propagated through weather reports.
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Saturation Vapor Pressure
Pvs
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The intensity at which water vapor will evaporate from water
(Pressure over liquid water) or from ice (Pressure over ice).
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.
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Chilled Sensor Hygrometer
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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.
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Capacitive RH Hygrometer
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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.
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Temperature Scale
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The Dewpoint Calculator uses the traditional temperature scales
Deg.C = Deg.K - 273.15 and
Deg.F = 9/5 Deg.C + 32.
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Interpolation Formulas
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There are a great deal 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.
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Newton's Method
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To solve an equation of the form
f(x)=y for x, Newton's Method computes the iterates xn
starting at a suitable initial guess x0. If the problem is not ill-conditioned, iterates
will converge quickly to the solution x.
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