1. basics:
Besides temperature, humidity, i.e. the water vapor content of the air, is a meteorologically important variable. 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, the formation of which, like evaporation, involves the conversion of enormous amounts of energy, but also to the emission and absorption of long-wave radiation, for which the water vapour content of the air is essential.
2. measured humidity values
According to the many different problems in which air humidity plays a role, there is a whole range of humidity measurements.
a) The water vapour pressure eL is the partial pressure of water vapour in the air. It is specified in Pa (Pascal) according to the standard. In meteorology - especially in the literature - the pressure unit mbar (millibar) is used, but 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 vapour pressure eL cannot exceed the saturation vapour pressure E because condensation occurs when eL= E. E is a pure function of temperature and does not depend on air pressure in particular. The basic physical equation describing the dependence of the saturation vapour pressure on the temperature is the Claudius-Clapeyron equation known from thermodynamics.
1] dE / dT = (r/(ΔV - T))
ΔV is the specific volume change during the phase transition from water to steam (or from ice to steam) and r is the corresponding specific phase transformation heat (in J/kg). If the volume of the liquid/solid phase is neglected compared to that of the gas phase, the ideal gas equation for water vapor can be used for V = 1/pw, and the following is obtained
2] dE / dT = Er ( Rw - T2 (2)
where Rw is the gas constant for water vapour ( 461.4 J kg-1K-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 vapour (or ice / water vapour)
3] r(T) = r (T0) - (cw- cpW) (T - T0).
T0is a (in principle arbitrary) reference temperature, and cw(cpw) is the specific heat capacity of the liquid waterS (water vapor). Because cw > cpw, r decreases with increasing temperature.
If (3) is inserted into (2), the following results are obtained
dE / dT = Er ( Rw - T2-r(T0)-(cw-CpW) (T - T0) (4)
Assuming constant specific heat capacities, this equation can also be integrated
ln(E / E0) =(r (T0)+T0(cw - cpw))/Rw[(1/T0) - (1/T)] -[(cw-cpw)/Rw]ln(T/T0)
or E = E0[T0/T]((cw-cpw)/Rw) - exp[( r (T0)+T0(cw - cpw))/Rw) - [(1/T0) - (1/T)] ]
If one sets
T0= 273.15 K,
Rw = 461.4 J kg-1 K-1,
cw= 4186.8 J kg-1K-1,
cpw=1850 J kg-1K-1 and
r(T0)=2.501-106 J kg-1
one, you get
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 temperature, so that formula (6) becomes inaccurate at higher temperatures. In practice, empirical formulas (the so-called Magnus formulas), which were obtained from precise laboratory measurements, are therefore mostly used. The Magnus formulae for the saturation vapour pressure above water (validity range 0 °C - 100 °C), above supercooled water (validity range -50 °C - 0 °C) and above EiS (validity range -50 °C - 0 °C) are given below.
[( 22.4429 •Water (0 °C -100 °C)
E = 6,1078 - e [(17,0809 -e)/( 234-175+e)] (7)
Undercooled water:
E = 6.1078 - e [(17.8436 - e) / (245,425+e)]
Ice(-50 °C-0 °C)
E = 6,1071- ee] / (27244 + e)]
In these numerical value equations, E is given in hPa if θ(°C )is used. They refer to the vapour pressure that is in equilibrium with a flat surface of pure waterS (ice). Above ice, the saturation vapour pressure is lower than above a surface of (supercooled) water at the same temperature, apart from the value at 7.4 -10-3 °C (triple point). The following table is intended to provide a reference point for E(θ):
θ(ªC) :-30 -20 -10 0 10 20 30 °C
Ew:0.51 1.25 2.86 6.11 12.29 23.42 42.49 hPa
EE: 0.38 1.03 2.60 6.11 hPa
b) The dew point θd is the temperature whose saturation vapour pressure over water Ew(θd) is just equal to the real vapour pressure eL(θL). When referring to ice, one speaks of the frost point.
The following applies: Ew(θd) = eL(θL).
c) The absolute humidity a is the density of water vapour, i.e. the mass of water vapour per unit volume. The correct indication of the absolute humidity is kg-m-3. To get handy
To obtain numerical values, a is usually given in g-m-3. From the gas equation a = ρw = eL /RW - T one can obtain the formula
a = 0.795 - eL / [l + (θ/273)] (10)
...to the other side. It gives a in g-m-3 (or mgl-) if eL is used in hPa and θ(°C).
(d) The specific humidity s is the ratio of the mass of water vapour to the total mass of humid air of the same volume. This is equivalent to the ratio of the corresponding
the densities, so s = ρw/(pL + pw). Using the gas equation and RL/Rw = 0.623 follows
s = (0,623 - eL ) / (p - 0,377 - eL),
where p and eL can be given in any (equal) units, s is a pure number; but it is usually given in g-kg-1 = 10-3. Because of eL "p, eq. (11) can be approximated very well in
5 = 623 - (eL /p) g/Kg
to reshape.
(e) The mixing ratio m is the ratio of the mass of water vapour to the mass of air free of water vapour of the same volume. From this definition follows
m = .(623 - eL) / (p - eL)
Regarding the units, the same applies as previously mentioned in s. Approximately m = s, so that the approximate formula (12) can be used.
The fact that two such similar quantities as s and m are used at the same time is due to the fact that some laws are easier to write with s, some easier to write with m. For most practical purposes s and m are the same. Both are typical meteorological moisture quantities. As ratios of masses in the same volume, their value does not change with changes in pressure and temperature of humid air. In contrast to the other humidity variables, they do not change, especially during vertical displacements of an air parcel and are therefore invariant during many meteorologically significant processes (e.g. adiabatic ascent).
f) The saturation deficit EL - eL. also called steam hunger, is sometimes used to advantage in considerations related to evaporation. However, it is just as little a measure for the
Water vapour content of the air like
(g) the relative humidity f. This indicates the ratio of the current water vapour pressure eL to the saturation vapour pressure EL above water (!) at the air temperature tL.
f = (eL / EL) = 100 - (eL / EL)
f is usually given in %. It owes its frequent use probably not least to its simple measurement. Sometimes you also need the
(h) relative saturation deficit EL / eL
(EL / eL)/EL = 1 - f(15)
i.e. the addition of f to 1
(i) Finally, at least two quantities should be mentioned here which, although they are not direct indications of moisture content, can be regarded as moisture quantities: The wet bulb temperature t` and the equivalent temperature flat.
Apart from temperature, humidity, i.e. the water vapour content of the air, is a meteorologically important variable. This becomes understandable if one considers that with a large number of meteorological
3. moisture measuring method
The large number of moisture measured variables corresponds to a scarcely smaller number of moisture measuring methods, some of which allow the direct measurement of one or other of the above-mentioned variables.
a) Unfortunately there is no simple and good method for the direct determination of the vapour pressure eL. The Rüdorff bottle, in which the air to be examined is fed into a bottle and the water vapour is extracted by introducing a desiccant so that the pressure drop should be equal to e, provides inadequate values because of the pressure and temperature changes during the measurement and thus has more the character of a demonstration object. Similarly, experiments with films that are permeable to water vapor but impermeable to air (cellophane) have not yet yielded satisfactory results. With some justification, 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, could be counted among them.
b) If a non-hygroscopic surface is slowly cooled further and further below the air temperature, then finally, after reaching the dew point td, condensation will occur which disappears again when heated. One could expect that the temperature at the beginning of the fogging and the temperature at the disappearance of the fogging would be equal to the dew point temperature td. In reality, the former is below and the latter above td. In most cases it is sufficient to take the average of both readings as Δd. The simple measuring principle has led to the construction of many types of condensation hygrometers (dew point piezometers), but their measuring accuracy often did not meet expectations. This is partly due to the difficulties in producing the necessary non-hygroscopic surface. The best experience was made with polished metal surfaces (especially gold). Below 0 °C, where the dew point method would be of particular interest because of the increasing errors of other moisture measurement methods, the decision whether the mist is (undercooled) dew or frost sometimes causes difficulties. Finally, the fact that the air passing by is by no means homogeneous in terms of humidity, because more humid and drier air parts alternate, results in inaccuracies.
At least modern measuring technology has found ways to reduce these errors by using thin platelet-shaped measuring elements to greatly reduce inertia, allowing cooling and heating (some of them inductive, eddy current heating) to follow one another automatically and rapidly, detecting fogging photoelectrically and ensuring rapid air exchange. From several sides, fully automatic devices have been developed using modern electronics, but - not least because of the costs - they cannot be generally used.
c) Absorption hvqmeters are used for direct measurement of absolute humidity a. For this purpose, the air to be examined is passed through vessels (U-tubes, cylinders) containing strongly hygroscopic substances (H2SO4 on pumice stone, CaP2O5CI2, ), which absorb the water vapour; the increase in weight of the measuring tubes and the volume of the air flowing through them directly gives a. Although the method is very accurate if sufficient care is taken, it is very laborious in terms of its operation, so that it is more restricted to laboratory tests and is not used in practical service.
d) The saturation vapour pressure EL over pure water is - as already mentioned above - given by eq. (7) or the following table and is a pure temperature function. If the water is contained in other substances or if such substances are dissolved in water, the vapor pressure eL then occurring is given by
eL = f-EL (16)
is given, where f < 1 is usually a factor that is practically independent of temperature and only dependent on the water content of the substance. In the vapour pressure equilibrium with the ambient air, the water content of the sensor substance, which is clearly related to f, is thus a measure of the relative humidity of the air, the definition of which is identical to (16) according to equation (14). The measuring element must, of course, have 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, then the relative humidity f is obtained first and from this and the air temperature the vapour pressure eL. A whole series of moisture measurement methods are based on this possibility.
The obvious method of measuring water content by weighing has been used several times in individual investigations, as has the observation of volume changes in a suitably selected series of solutions of different water content. By contrast, swelling, which depends on the water content (and thus on f), plays a far more important role. Despite extensive investigations, also with new types of plastics, the first moisture measuring element, namely the degreased human hair (Saussure 1783), could not yet be displaced, apart from cases with special questions. Between 0 and 100 % relative humidity, this hair changes its length by about 2.5 %, although the relationship between the relative length change X and the relative humidity f is not linear.
f:0 10 20 30 40 50 60 70 80 90 100 %
X0 21 39 53 64 73 79 85 90 95 100%
This relationship applies to hair treated according to the usual method, which degreases the tissue without attacking it. Newer treatment methods result in different characteristics, which are sometimes better linear.
By mechanically increasing the hair length change, it can be easily read off as a rash on a scale divided approximately equally in % relative humidity. One of the most common types of hair hygrometer is the Koppe hygrometer. With this instrument the hair is freely clamped in a frame. One end is wrapped around a roller which moves the pointer. The other end is permanently adjustable so that the pointer can be brought in line with the true humidity at a scale point. 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 instrument and closing it. Saturation will then occur immediately, and the pointer can be moved to the 100 %-
point can be set. For further testing you can remove the cover and gauze and compare the display at average humidity values (room) with another moisture meter. It may be necessary to make a correction table.
Besides the Koppe hygrometer, other types are of course also used. For measurements in small rooms, the hair hygrometer according to Diem is often very useful. pointer hygrometers in can form, which also indicate the temperature (polymeters), allow the absolute humidity to be read in a diagram in the case of versions with two pointers at the intersection of both, etc. Since the relative humidity is an indication of the water content of goods such as wood, grain, tobacco, etc., we have built pointer hygrometers for this purpose.
Unfortunately the hair shows some defects. Its reading can be viewed accurately at 2...3% relative humidity, provided it is repeatedly compared with a psychrometer. If left standing in dry air for a longer period of time, it shows signs of aging, which can cause errors of up to 10%. The errors largely disappear if the hair is placed in saturated or almost saturated air for a short time and thus "regenerated". In measurements in the field this should be the case almost every night anyway. Small strains can be reversed by "regeneration", strong ones make the hair unusable. Only clean hair works perfectly, so you should not touch it with your fingers. Despite the small diameterS (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 strong interventions, which are also possible with chemical means, change the characteristics and reduce the strength.
But the hair also has advantages. The indication of relative humidity, which is practically independent of temperature, was already mentioned above. Its greatest advantage, however, is that its indication can be registered by simple means, an advantage which, despite all its shortcomings, gave the hair hygrometer - and thus probably not quite rightly also the relative humidity - a position that is difficult to challenge. Since the adjusting force of a single hair is not sufficient to overcome the friction of a writing instrument, several hairs are used there as bundles or harps . It should also be mentioned that the change in length can be transferred to display and recording instruments far away from the measuring point by means of appropriate electrical procedures (e.g. resistance transmitters).
As already mentioned above, in addition to the change in length of swelling substances, other properties dependent on the water content can also be used as a primary measured variable. For example, the colour changes of cobalt salts, which are already common in simple hygroscopes, were used, as was the dependence of the dielectric behaviour on the water content.
e) Electrical conductivity is becoming increasingly important for measuring humidity in the air. For solutions of salts etc., it depends strongly on the concentration, i.e. the water content. Since the intrinsically disturbing dependence on temperature is well known, it can be eliminated by calculation or, in the case of newer methods, even by suitable circuitry. For example, a glass strip equipped with two electrodes is used as the humidity measuring element of the US radio probe. Between the electrodes there is a thin layer of a plastic in which LiCI is embedded as a hygroscopic substance. As with hair, in equilibrium the vapour pressure of the hygroscopic substance is equal to that of air. The direct measurement as an electrical quantity is a noticeable advantage especially for the radiosonde. Of course other suitable substances can be used in addition to LiCI.
f) Outwardly similar is another method, in which LiCI with a carrier substance is usually also used. In this case, 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 LiCI solution is obtained in which crystals are deposited. At equilibrium, the vapor pressure of the concentrated LiCI solution is then equal to that of air. The vapor pressure e can be determined from the temperature of the measuring element according to an empirical relationship or by calibration. Since the ventilation (heat balance equation!) influences the calibration curve, it must be constant, which is usually achieved by using draft shields.
g) The change in the capacity of a capacitor due to a change in the dielectric when water molecules are present can also be used to measure humidity. This is done with the "hygrotest" to be used in the experiment. The dielectric in the capacitor of this humidity sensor is a
Mixture of high polymeric plastics which absorb water molecules as a function of the partial pressure of water vapour. Due to their own dipole moment in the field of the condenser, these molecules orient themselves outwards (orientation polarisation) and thus cause a change in capacity, which is internally converted and displayed digitally as relative humidity.
h) With all humidity measuring methods described so far, the most common humidity measuring instrument is the one that converts water vapour into liquid water at the measuring element or vice versa. Due to the very low water content of the air at low temperatures, this leads to very long response times. This is the main reason why at present only few reliable humidity values can be obtained from altitudes above 7 km in routine radio probe service. It is therefore understandable that methods are sought which measure the water content of the air without converting it into other forms of state. The development of methods which attempt to measure the water vapour content by means of selective absorption in suitable spectral ranges has already led to some considerable successes. This applies not only to the determination of the total waterS (water equivalent) contained in a column of air with the aid of the absorption of short-wave radiation in the near infrared ( < 1 µm), but also to measurements in the range of long-wave radiation (10 µm) and more recently in the range of cm waves.
i) In addition to the moisture measuring methods described above, the psychrometer is a widely used group of measuring instruments for the exact determination of moisture parameters. Psychrometers consist of two thermometers of the same type, one of which has a mercury vessel covered with a continuously moistened gauze stocking. Heat is extracted from the "wet" thermometer by evaporation and as a result it shows a lower temperature than the "dry" thermometer. The temperature difference between the two thermometers is a measure of relative humidity. The accuracy of the psychrometer depends on the measurement method used. A distinction is made between naturally ventilated psychrometers after August and artificially ventilated hut psychrometers. The aspiration psychrometer according to Assmann is considered the reference instrument for checking temperature-humidity measuring devices.