In general, meteorological instruments do not measure either the amount of water in the atmosphere or the relative humidity. Instead, they measure
The odd thing is that relative humidity has little to do with cloud formation, and even less with rain. It seems intuitively obvious that clouds form when the relative humidity is 100% .. but they don't. In fact, they tend to evaporate at even higher water concentrations.
Equally odd is the fact that water won't freeze until about -38°C even though it melts at about 0.01°C.
100% relative humidity is defined over a flat area of water where both the water and the air have the same temperature. In a cloud, the temperature of the water and the surrounding air are about the same - but the water is in small drops. As a result, at 100%RH it is easier for a small drop to lose a water molecule than it is for it to gain one. However, once the size crosses some threshold, the drop will suck up all the available water and make rain.
For clouds to form at 100%RH, there needs to be something that changes the balance. The "technical" term for this is "dust". Over oceans, this could be salt crystals; over a desert, silica. Air pollution may also help. In a cloud chamber, cosmic rays cause a liquid (usually alcohol or water) to condense.
Without getting into the details, the point is that clouds form in a range
of relative humidities - not just when
When a liquid is cooled below its freezing point, it is referred to as super cooled. In the atmosphere, super cooled water is fairly common. (Think freezing rain. Sometimes this is just rain hitting a very cold surface. But it can also be super cooled rain that freezes on contact.)
Ice will form at a higher temperature if there is something to start the process - dust is the common suspect.
The relative humidity over ice is different than over liquid water. This is usually explained by observing that a certain amount of energy is required to evaporate water and that, for ice to sublime, it requires additional energy equivalent to the amount needed to raise the temperature to the triple point and the latent heat needed to convert it to the liquid state. However, reality is a bit more complicated, depending also on the crystal type (amorphous, cubic, or hexagonal) and the existence of sharp points (think snowflake vs sleet).
And of course, the computed RH values are over a large surface, and the stuff that falls has lots of small surfaces. Therefore, 100%RH is just a guideline for ice formation, not when it must occur.
The Celsius temperature scale was originally calibrated using 2 points - the freezing and boiling points of water - defined as 0°C and 100°C respectively. Today there is only one calibration point, the triple point at 0.01°C. The second point at 100°C is no longer used. However, it is still necessary to use 2 points to define the temperature scale. Assuming the second point to be absolute zero (0.0 K), and that it can be determined by the gas law, places the boiling point at 99.974°C at 1 atm (1013.25 mbar).
From Review of the vapour pressures of ice and supercooled water for atmospheric applications by D. M. Murphy and T. Koop, 29 Dec 2006
The vapour pressure of both ice and liquid water at the triple point is
Pt = 611.657 ± 0.01 Pa at temperature Tt = 273.16 K
(Guildner et al. 1976, Vapor pressure of water at its triple point. J. Res. Natl. Bur. Stand., 80A, 505–521)
According to the International Union of Pure and Applied Chemistry, Subcommittee on Calibration and Test Materials, 1975, p 1449 (pdf p 12), the saturation partial pressure of water is (was) 0.6111 kPa at 273.16 K. The notes for the related section indicate that
The other major source of uncertainty is the fact that the equations model pure water with no dissolved salts or gases. Since that is not representative of the atmosphere, there is an "Enhancement Factor" to produce actual values - the error is about 0.5% near sea level and decreases with decreasing total pressure. For example, at 0°C, Buck gives the saturation partial pressure over liquid Water as 6.1121 mbar, corrected to 6.1360 mbar at 1,000 mbar total pressure - 6.1202 mbar at 250 mbar total pressure.
At any rate, these are some of the reasons it is difficult to find a "correct" equation or to evaluate any work (think climate model) that uses relative humidity.
Other references use additional algorithms.
My programs implement
It is difficult to calibrate equations that fit a bunch of data points.
In the original definition - water freezes at 0°C and boils at 100°C.
However, both of those values depend on the total pressure. In general, both should be defined at 1013.25 hPa (101,325 Pa).
Also, the "freezing" calibration point has been replaced with the triple point - 0.01°C (273.16 K).
Of the 20 formulas I've used for liquid water, only one has a partial pressure of 1013.25 hPa at 100°C and 4 have a partial pressure of 611.657 Pa at 273.16 K. (7 at 611.657 ± 0.01 Pa). Of these, the "best" appear to be the ones from HylandWexler and Sonntag because they nearly intersect both calibration points. The Seinfeld and Pandis formula is also pretty good since it nearly intersects the old calibration points.
Below freezing, there are 4 calibration points, but these are only used by Fukuta.
Over ice, the curve is different and there is only one calibration point - 611.657 ± 0.01 Pa at 273.16 K - and only 4 of 11 formulas intersect it.
|Computed Saturation Pressure (mbar)||
ne - no equation
Some of the sources only provide over ice or over water
|Calibration Values||6.11657||6.11657||1013.25||1013.25||The boiling point values are defined by the calibration method|
|GoffGratch||6.1071||6.1077976||1011.9447||1012.8844||-50°C to 102°C over water|
-100°C to 0°C over ice
|CIMO||6.1170373||6.1164311||1037.4672||1038.4492||Widely used in Meteorology|
|HylandWexler||6.1165702||6.1165703||1013.2464||1014.1872||Commonly used among radiosonde manufacturers and should be used in upper air applications to avoid inconsistencies.|
|Buck_manual||6.1165331||6.1165411||1012.1404||1013.0778||Buck Research Manual (1996) - They make frost-point hygrometers|
|WMO2000||ne||6.11139||993.59275||994.50492||Identical to WMO_Goff except this contains an exponent sign error|
|Fukuta||ne||6.1025599||-378825.41||-379605.02||-20°C to -35°C -- Goes negative at +21°C|
|IAPWS||ne||6.1165707||1013.2393||1014.1799|| International Association for the Properties of Water and Steam (IAPWS) Formulation 1995 |
Valid only above the triple point - 273.16 K to 647.095 K
|Seinfeld_Pandis||ne||6.116602||1012.3101||1013.25||From textbook - intersects both calibration points|
|GISS_AR4||6.1080103||6.1080091||1239.6974||1240.9521||GISS Model-E for IPCC AR4 and AR5|
|Antoine equation||ne||6.0602333||1012.4211||1013.3651||Based on Clausius-Clapeyron relation for 0 to 100°C|
99.974°C = 373.124 K
Seinfeld and Pandis claim their formula produces a value of
"The Hyland and Wexler (1983) parameterization is used for calibration of the widely used Vaisala radiosondes (Miloshevich et al. 2001), [but] is only valid above 0°C (273.15 K)." Murphy and Koop, 2006
The Fukuta algorithm, calibrated for -20°C to -35°C, is worthless above 0°C - it goes negative around +21°C.
Water becomes a super critical fluid above 373.946°C (647.10 K) - above that temperature, there is no distinction between liquid and gas.
Over liquid water
The Goff Gratch equation for the vapor pressure over liquid water covers a region of -50°C to 102°C. This work is generally considered the reference equation but other equations are in use in the meteorological community.
The equations by Hyland and Wexler, the nearly identical equation by Wexler, and the equation by Sonntag are the most commonly used equations among radiosonde manufacturers and should be used in upper air applications to avoid inconsistencies. [ref]
|The equations discussed here are mostly of interest for frost-point measurements using chilled mirror hygrometers, since these instruments directly measure the temperature at which a frost layer and the overlying vapor are in equilibrium. In meteorological practice, relative humidity is given over liquid water ... and care needs to be taken to consider this difference. [ref]|
Psat := 6.108 * exp(2.5E6 * (7.93252E-6 - 2.166847E-3/T_K)); // Latent_heat water = 2.5E6 Psat := 6.108 * exp(2.834E6*(7.93252E-6 - 2.166847E-3/T_K)); // Latent_heat ice = 2.834E6
Well, maybe it doesn't matter. For my use, it is possible that one model (algorithm) is as good as any other. With a few exceptions (such as Fukuta which gives ridiculous results outside its calibration range), the values are pretty close. Keep in mind - I don't care what the relative humidity is. I simply need to use it to determine how many water molecules are actually in a unit volume of atmosphere - expressed in parts-per-million (ppm) - which is easy to compute from the water vapor mixing ratio. My line-by-line program (not ready for distribution) uses the ppm values to compute the amount of IR radiation absorbed (or emitted) by a given parcel. I have an analysis showing the difference at 15°C.
Below 180 K (-93°C), the saturation partial pressure is so low that computations have little value. Most of them are worthless below 150 K, some even produce negative results. Because of this, and because none of the algorithms are calibrated below 238 K (-35°C), the program simply returns zero below 150 K.