1. Basics:
In addition to temperature, humidity, i.e., the water vapor content of the air, is a meteorologically important quantity. This becomes understandable when one considers that water in its various forms is involved in a large number of meteorological phenomena. This applies not only to clouds, fog, and the many types of precipitation, whose formation, as well as evaporation, also requires enormous amounts of energy, but also to the emission and absorption of long-wave radiation, for which the water vapor content of the air is essential.
2. Humidity measurements
Depending on the diverse range of problems in which humidity plays a role, there are a number of humidity measurements.
a) The Water vapor pressure e L is the partial pressure of water vapor in the air. It is standardized in Pa (Pascal). In meteorology, especially in literature, the pressure unit mbar (millibar) is used, but this has not been used since 1978. The millibar is replaced by the hectoPascal ( 1 mbar = 100 Pa = 1 hPa). The older pressure units mm Hg or Torr are no longer permitted (1 Torr = 1.3332 mbar = 133.32 Pa).
Under normal conditions, the vapor pressure e L the saturation vapor pressure E not exceed, since eL = E Condensation occurs. E is a pure function of temperature and, in particular, does not depend on air pressure. The fundamental physical equation that describes the dependence of the saturation vapor pressure on temperature is the Claudius-Clapeyron equation, known from thermodynamics.
[1] dE / dT = (r/(ΔV • T))
This is ΔV the specific volume change during the phase transition from water to water vapor (or from ice to water vapor) and r the corresponding specific phase transition heat (in J/kg). Neglecting the volume of the liquid/solid phase compared to that of the gas phase, one can use the ideal gas equation for water vapor for V = 1/pw, and obtains
[2] dE / dT = Er ( R w • T2 (2)
where R w the gas constant for water vapor is ( 461.4 J kg -1 K -1 ).
If r were constant, this equation could be easily integrated, but this is not the case. As can be easily illustrated by a Carnot cycle along the phase boundary curve water/water vapor (or ice/water vapor),
[3] r(T) = r (T 0 ) - (c w - c pW ) (T - T 0 ).
T 0 is a (in principle arbitrary) reference temperature, and c w (c pw ) is the specific heat capacity of liquid water (water vapor). c w > c pw r decreases with increasing temperature.
Inserting (3) into (2), we get
dE / dT = Er ( R w • T 2 •r(T 0 )-(c w -C pW ) (T - T 0 ) (4)
Assuming constant specific heat capacities, this equation can also be integrated
ln(E / E 0 ) =(r (T 0 )+T 0 (c w - c pw) )/R w [(1/T 0 ) - (1/T)] -[(c w -c pw )/R w ]ln(T/T 0 )
or E = E 0 [T 0 /T]((c w -c pw )/R w ) • exp[( r (T 0 )+T 0 (c w - c pw ))/R w ) • [(1/T 0 ) - (1/T)] ]
If you set
|
T0 = |
273.15 K, |
|
R w = |
461.4 J kg -1 K -1 , |
|
c w = |
4186.8 J kg -1 K -1 , |
|
c pw = |
1850 J kg -1 K- 1 and |
|
r(T 0 )= |
2,501•10 6 J kg -1 |
one gets
E = 6.1078 hPa[273.15/T] 5.072 • exp [6804.75[3.661•10 -3 - (1/T)]]
Unfortunately, cw and cpw also depend somewhat on the temperature, so that formula (6) becomes inaccurate at higher temperatures. Therefore, in practice, empirical formulas (the so-called Magnus formulas) derived from precise laboratory measurements are usually used. The following are the Magnus formulas for the saturation vapor pressure over Water (validity range 0 °C -100 °C), above supercooled water (validity range -50 °C - 0 °C) and about EiS (validity range -50 °C - 0 °C ).
|
[( 22.4429 •
e] / (27244 + e)] |
In these numerical equations, E in hPa, if one θ(°C ) . They refer to the vapor pressure that is in equilibrium with a flat surface of pure water (ice). Above ice, the saturation vapor pressure, except for the value at 7.4 •10 -3 °C (triple point), lower than over a surface of (supercooled) water at the same temperature. An indication of E(θ) should provide the following table:
|
θ(ªC) |
:-30 |
-20 |
-10 |
0 |
10 |
20 |
30 |
°C |
|
E w : |
0.51 |
1.25 |
2.86 |
6.11 |
12.29 |
23.42 |
42.49 |
hPa |
|
E E : |
0.38 |
1.03 |
2.60 |
6.11 |
|
|
|
hPa |
b) The Dew point θ d is the temperature whose saturation vapor pressure over water E w (θ d ) just equal to the actual steam pressure e L (θ L ) . When referring to ice, this is called the frost point.
So the following applies: E w (θ d ) = e L (θ L ).
c) The absolute humidity a is the density of water vapor, i.e. the mass of water vapor per unit volume. The correct expression for absolute humidity is kg-m -3 . To make handy
To obtain numerical values, a is usually given in gm -3 From the gas equation a = ρ w = eL /R W • T you can use the formula
a = 0.795 • e L / [l + (θ/273)] (10)
It gives a in gm -3 (or possibly -) if one e L in hPa and θ(°C) uses.
d) The specific humidity s is the ratio of the mass of water vapor to the total mass of humid air of the same volume. This is equivalent to the ratio of the corresponding
the densities, so s = ρ w /(p L + p w ). Using the gas equation and R L /R w = 0.623 follows
s = (0.623 • e L ) / (p - 0.377 • e L ),
where p and e L can be specified in any (same) units, s is a pure number; however, it is usually expressed in g-kg -1 = 10 -3 stated. Because e L «p Equation (11) can be translated to a very good approximation into
5 = 623 • (e L /p) g/kg
transform.
e) The Mixing ratio m is the ratio of the mass of water vapor to the mass of water vapor-free air of the same volume. From this definition follows
m = .(623 • e L ) / (p - e L)
Regarding the units, what was said before for s applies. Approximately m = s , so that the approximate formula (12) can be used.
That two such similar sizes as s and m used simultaneously is due to the fact that some laws are easier to s , some easier with m For most practical purposes, s and m equal. Both are typical meteorological humidity quantities. As ratios of masses in the same volume, their value does not change with changes in pressure and temperature of the humid air. Thus, unlike the other humidity quantities, they do not change, especially with vertical displacements of an air parcel, and are therefore invariant under many meteorologically significant processes (e.g., adiabatic ascent).
f) The Saturation deficit E L - e L ., also called steam hunger, is sometimes used to advantage in considerations related to evaporation. However, it is also not a measure of the
Water vapor content of the air such as
G) the relative humidity f. This gives the ratio of the current water vapor pressure e L to the saturation vapor pressure E L above water (!) at air temperature t L to.
f = (e L / E L ) = 100 • (e L / E L )
f is usually expressed in %. Its frequent use is probably due in no small part to its ease of measurement. Sometimes you also need the
h) relative satiety deficit E L / e L
(E L / e L )/E L = 1 - f(15)
ie the addition of f to 1
i) Finally, two quantities should be mentioned here that can be considered as moisture quantities, even if they are not direct indications of the moisture content: The Wet bulb temperature t` and the Equivalent temperature r fla.
In addition to temperature, humidity, i.e. the water vapor content of the air, is a meteorologically important parameter. This becomes understandable when one considers that in a large number of meteorological
3. Humidity measurement method
The large number of moisture measurement quantities corresponds to a barely smaller number of moisture measurement methods, some of which allow the direct measurement of one or the other of the above-mentioned quantities.
a) Unfortunately, there is no simple and good method for directly determining the vapor pressure e L . The Rüdorff bottle , in which the air to be examined is led into a bottle and the water vapor is removed by adding a desiccant, so that the pressure drop is equal to e should be, yields inadequate values due to pressure and temperature changes during the measurement and thus has more of a demonstration object character. Likewise, experiments with water vapor-permeable but air-impermeable films (cellophane) have so far produced unsatisfactory results. With some justification, one could include the methods mentioned under b), e), and f), in which the vapor pressure of the sensor is equal to that of the air at equilibrium.
b) If a non-hygroscopic surface is slowly cooled further and further below the air temperature, then finally after reaching the dew point t d A fogging with condensation may occur, which disappears when warmed up. One might expect that the temperature at the beginning of fogging and the temperature at the disappearance of fogging would be equal to the dew point temperature. t d In reality, the former lies below, the latter above t d . For most cases, it is sufficient to use the mean of both readings as Δd The simple measuring principle has led to the construction of many types of Condensation hygrometers (dew point mirrors) However, their measurement accuracy often fell short of expectations. This is due, among other things, to the difficulties in producing the necessary non-hygroscopic surface. The best results were achieved with polished metal surfaces (especially gold). Below 0 °C, where the dew point method would be of particular interest due to the increasing errors of other humidity measurement methods, it is sometimes difficult to decide whether the condensation is (supercooled) dew or frost. Finally, the fact that the passing air is by no means homogeneous in terms of its humidity, because moister and drier air sections alternate, results in inaccuracies.
Modern measurement technology has, however, found ways to reduce these errors by using thin, plate-shaped measuring elements to significantly reduce inertia, by automatically sequentially heating and cooling (some of which are inductive, eddy current heating), by photoelectrically detecting fogging, and by ensuring rapid air exchange. Several companies have developed fully automated devices using modern electronics, but these cannot be widely used, not least because of the costs.
c) With Absorption hvrometers the direct measurement of absolute humidity a For this purpose, the air to be examined is passed through vessels (U-tubes, cylinders) containing highly hygroscopic substances (H 2 SO 4 on pumice stone, CaP 2 O 5 CI 2 , ), which absorb the water vapor; from the increase in weight of the measuring tubes and the volume of air flowing through, a results directly. The method is very accurate if sufficient care is taken, but it is very laborious, so that it is restricted to laboratory experiments and is not used in practical service.
d) The saturation vapor pressure E L over pure water is - as already mentioned above - given by Equation (7) and the following table and is a pure function of temperature. If the water is contained in other substances or if such substances are dissolved in water, the resulting vapor pressure eL is given by
e L = f•E L (16)
given, where f < 1 is usually a factor that is practically independent of temperature and depends only on the water content of the substance. In vapor pressure equilibrium with the surrounding air, the f The water content of the sensor substance is a measure of the relative humidity, the definition of which according to Eq. (14) is identical to (16). Of course, the measuring element must be at air temperature. If the water content of such substances is measured, which can of course also be done indirectly via other properties dependent on the water content, the relative humidity is initially obtained. f and from it and the air temperature the vapor pressure e L . A whole series of moisture measurement methods is based on this possibility.
The obvious method of measuring water content by weighing has been used several times in individual studies, as has the observation of volume changes in a suitably selected series of solutions with different water contents. A far more important role, however, is played by the water content (and thus by f ) dependent swelling. Despite extensive investigations, including with new types of plastics, the first moisture measuring element, namely the defatted human hair (Saussure 1783) , have not yet been displaced. This changes its length by about 2.5% between 0 and 100% relative humidity, whereby the relationship between the relative change in length X , and the relative humidity f however, is not linear.
|
f: |
0 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
% |
|
X |
0 |
21 |
39 |
53 |
64 |
73 |
79 |
85 |
90 |
95 |
100 |
% |
This relationship applies to hair treated with the conventional method, which degreases the tissue without damaging it. Newer treatment methods produce different characteristics, some of which are more linear.
By mechanically magnifying the change in hair length, it can be easily read as a deflection on a scale divided approximately equally in % relative humidity. One of the most common types of hair hygrometer is the Koppe hygrometer. In this case, the hair is freely clamped in a frame. One end is wound around a roller, which moves the pointer. The other end is fixedly adjustable, so that the reading can be adjusted to match the true humidity at a given point on the scale. The saturation point serves as the calibration point. The air around the hair can be saturated by inserting a frame covered with wet gauze into the device and closing it. Saturation then occurs immediately, and the pointer can be set to 100%.
For further testing, the wrapping and gauze can be removed and the reading at medium humidity levels (room) compared with another humidity meter. A correction table may need to be prepared.
Next to the Koppe hygrometer Other types are, of course, also used. For measurements in small rooms, the Diem hair hygrometer is often very useful. Can-shaped dial hygrometers, which also display the temperature (polymeters), allow the absolute humidity to be read off at the intersection point of the two dials in a diagram, among other things. Since relative humidity is an indicator of the water content of goods such as wood, grain, tobacco, etc., dial hygrometers were constructed for this purpose.
Unfortunately, the hair shows some defects. Its reading can be accurately measured to within 2-3% relative humidity, provided it is repeatedly compared with a psychrometer. When exposed to dry air for a long time, it shows signs of aging, which can cause errors of up to 10%. These errors largely disappear if the hair is briefly exposed to saturated or nearly saturated air, thus "regenerating." For measurements taken outdoors, this is likely to occur almost every night anyway. Minor strains can be reversed through "regenerating," but severe strains render the hair unusable. Only clean hair works properly, so it should not be touched with fingers. Despite the small diameter (50 µm), a lower inertia is sometimes desirable, especially at low temperatures (e.g., radiosonde). Frankenberger achieved this by rolling the hair (Velox hair). However, such severe interventions, which are also possible with chemical agents, alter the characteristics and reduce the strength.
But hair also has advantages. The fact that it displays relative humidity practically independently of temperature has already been mentioned above. Its greatest advantage, however, is that its reading can be recorded using simple means, a virtue that, despite all its shortcomings, has given the hair hygrometer—and thus, perhaps not entirely justifiably, relative humidity as well—a position that is difficult to contest. Since the adjusting force of a single hair is insufficient to overcome the friction of a writing instrument, several hairs are used in bundles or harps. It should also be mentioned that the change in length can be transmitted to display and recording devices located far away from the measuring location using appropriate electrical processes (e.g., resistance sensors).
As already mentioned above, in addition to the change in length of swelling substances, other properties dependent on water content can also serve as primary measurement variables. For example, the color changes of cobalt salts, already common in simple hygroscopes, as well as the dependence of dielectric behavior on water content, were used.
e) The electrical conductivity is becoming increasingly important for measuring air humidity. In solutions of salts and the like, this depends heavily on the concentration, i.e. on the water content. Since the inherently disruptive dependence on temperature is well known, it can be eliminated mathematically or, in newer methods, even by suitable circuits. For example, the humidity measuring element in the US radiosonde is a glass strip equipped with two electrodes. Between the electrodes is a thin layer of plastic in which LiCl is embedded as a hygroscopic substance. As with hair, in equilibrium the vapor pressure of the water-containing substance is equal to that of the air. Direct measurement as an electrical quantity is a noticeable advantage, especially for the radiosonde. Of course, other suitable substances can also be used alongside LiCl.
f) Another procedure is externally similar, in which usually LiCI with a carrier substance is used. However, a heating current is sent through the hygroscopic film via the electrodes, so that the measuring element heats up and water evaporates until a concentrated LiCl solution is reached, in which crystals precipitate. At equilibrium, the vapor pressure of the concentrated LiCl solution is equal to that of air. From the temperature of the measuring element, the vapor pressure e can be determined using an empirical relationship or by calibration. Since ventilation (heat balance equation!) influences the calibration curve, it must be constant, which is usually attempted to be achieved by wind protection devices.
G) Also the Capacity change A capacitor's dielectric change in the presence of water molecules can be used to measure humidity. This is done with the "Hygrotest" used in the experiment. The dielectric in the capacitor of this humidity sensor is a
A mixture of high-polymer plastics that absorb water molecules as a function of the water vapor partial pressure. These molecules align themselves in the capacitor's field due to their inherent dipole moment (orientation polarization), thus causing a change in capacitance, which is internally converted and digitally displayed as relative humidity.
h) In all the humidity measurement methods described so far (the most common humidity measuring device), water vapor is converted into liquid water or vice versa at the measuring element. Due to the very low water content of the air at low temperatures, this leads to very long response times. This is primarily why, at present, routine radiosonde service is only able to obtain very few reliable humidity values from altitudes above 7 km. It is therefore understandable that methods are being sought which measure the water content of the air without converting it into other states. The development of methods which attempt to measure the water vapor content using selective absorption in suitable spectral ranges has already produced some considerable success. This applies not only to the determination of the total water S (water equivalent) contained in an air column using the absorption of shortwave radiation in the near infrared (< 1 µm), but also to measurements in the longwave radiation range (10 µm) and, more recently, in the cm-wave range .
i) In addition to the moisture measurement methods described so far, the psychrometer represent a distinct, widespread group of measuring instruments for the precise determination of humidity parameters. Psychrometers consist of two identical thermometers, the mercury vessel of one of which is covered with a continuously moistened gauze sock. Heat is removed from the "wet" thermometer through evaporation and consequently indicates a lower temperature than the "dry" thermometer. The temperature difference between the two thermometers is a measure of the relative humidity. The accuracy of the psychrometer depends on the underlying measurement method. A distinction is made between naturally ventilated August psychrometers and artificially ventilated hut psychrometers. The Assmann aspiration psychrometer is considered the reference instrument for testing temperature-humidity measuring instruments.