CHAPTER 3:: HUMIDITY AND MOISTURE
Introduction
There are several variable used to characterize atmospheric water vapor. Different techniques for
quantifying water vapor provide direct measurements of certain variables. Before discussing these
techniques, it is useful to review the basic quantities used to quantify moisture and to show the
interrelationship amount these variable.
Water vapor
Water vapor pressure is the partial pressure exerted by water vapor
molecules in an atmospheric volume. To illustrate vapor pressure, the
concept of equilibrium vapor pressure considers a closed container shown
to the left. This picture illustrates a liquid water surface that is included in
a container with a vacuum in the column above the water surface. As
water vapor molecules evaporate from the surface the vapor pressure will
increase. As this pressure increases, there will be condensation of water
vapor molecules at the surface. The condensation rate will increase as the
vapor pressure increases. At the point where the evaporation rate is equal
to the condensation rate, we define the vapor pressure as the equilibrium or saturation vapor pressure. If
now, the temperature of the system is increased, the evaporation rate will increase and the vapor pressure
will increase again until a new equilibrium pressure will be obtained. Thus, as temperature increases the
saturation vapor pressure increases. If one were to plot this relationship, shown would look like what is
shown in the figure below.
SVP Curve
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Thus saturation vapor pressure es is a function of temperature, such that es(T). The vapor pressure
e of an air parcel is the measure of the moisture content, while the saturation vapor pressure is a function of
temperature. The ideal gas law provides the relationship between e, and water vapor density ρv as
(4.1)
e   v RvT
where Rv is the specific gas constant for water vapor (461 J K-1 kg-1). The relationship between saturation
vapor pressure es and temperature is given by the Clausius-Clapeyron equation as
des
 e
 v s
(4.2)
dT Rv T 2
where
 v is the latent heat of vaporization or enthalpy of vaporization. It decreases slowly with
temperature and has a value of 2.5*106J kg-1 at 0oC and a value of 2.25*106J kg-1 at 100oC. At 0oC es =
6.108mb and at 100oC es=1013.25mb. For small intervals of temperature around some reference
temperature and es value, the Clausius-Clapeyron equation can be integrated assuming a constant value of
 v . This gives us

es
 exp  v
eso
 Rv
 1
1


 TKo TK



(4.3)
where in this expression temperature is in Kelvin and quantities subscripted with a o are reference values.
An empirical expression for es as a function of temperature that is valid for temperatures from -60oC to
40oC is given by Bolton (1980) as
17 .67T 
(4.4)
es of T  6.112 mb exp 

T
  243 .5 
where T in this expression is in oC, this expression can also be inverted to give
T
243.5 ln es  440.8
19.48  ln es
(4.5)
Other Humidity Variables
Dewpoint, Td, is the temperature to which air would have to be cooled isobarically to reach saturation. This
process can be seen that
 17.67TD 

e  es o f TD  6.112mb exp 
 TD  243.5 
(4.6)
Similarly, this can be inverted to give an expression for T D as a function of vapor pressure e as
TD 
243.5 ln e  440.8
19.48  ln e
(4.7)
Relative humidity, RH, is the ration of the vapor pressure e to the saturation vapor pressure es(T), such that
RH 
e
* 100%
es
(4.8)
Where e is from the web bulb temperature and es is from the regular temperature.
Mixing ratio, r, is the ratio of the mass of the vapor mv to the mass of the dry air md in a parcel such that
m
0.622 e
r v 
(4.9)
md
pe
Specific humidity, q, is the ratio of the mass of the vapor to the total mass (mv + md) or
q
mv
m d  mv
2
(4.10)
Using the definition for w and q it can be show that
q
1
1
; r
1 r
1 q
(4.11)
Mixing ratio and specific humidity are conserved in the adiabatic descent for unsaturated air parcels. By
the definition r and q are non-dimensional, although it is common to represent these in dimensional form as
g/kg by multiplying the non-dimensional quantities by a factor of 1000. For example r = 10-2 = 10 g/kg.
Saturation mixing ratio rs and specific humidity qs can be also defined as the values a parcel would have if
it were saturated. Thus it follows that
0.622 e s
(4.12)
rs 
p  es
From these definitions it follows that the RH is
r
(4.13)
RH  *100 %
rs
This expression for RH is in common use by the meteorology community.
Enthalpy
In the absence of an external field, the enthalpy may be defined as
H  C pT  U  pV
(4.14)
where U is the internal energy (in joules), p is the pressure of the system, (in pascals), and V is the volume,
(in cubic meters). The enthalpy is an arbitrary concept but the enthalpy change ΔH is more useful because
it is equal to the change in the internal energy of the system, plus the work that the system has done on its
surroundings. The change of enthalpy can be represented by
(4.15)
H  U  pV  pV
The first law of thermodynamics can be written as
(4.16)
U  Q  W
where δQ represents the infinitesimal amount of energy attributed or added to the system, and δW
represents the infinitesimal amount of energy acted out by the system on the surroundings. Combing (4.15)
and (4.16) and representing δW as pδV, we have…/.
?
(4.16)
H  Q  Vp
For isobaric process, δp=0. (4.16) can be represented as
C p T  Q
(4.17)
where specific heat at constant pressure.
Wet bulb temperature
Wet bulb temperature, Tw, is the coldest temperature that air can be cooled to by evaporation. An
expression for Tw as a function of other humidity parameters can be derived using conservation of enthalpy
in an isobaric, adiabatic process involving either evaporation or condensation of water mass. This
conservation can be written as
c p (Ti  T f )   v (r f  ri )
(4.18)
where the subscript i indicates an initial value, the subscript f indicates a final value, and cp is the specific
heat of moist air, which can be approximated in most applications as the value for dry air (1005 J kg-1 K-1).
If liquid water is evaporated in a parcel, the parcel will cool as the water vapor mixing ratio increases. A
good rule of thumb obtained from the equation (4.18) is that if 1gram of liquid water is evaporated or
condensed isobarically in 1 kg of air, the air will cool (warm) by 1 oC as the mixing ratio increases
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(decreases) by 1 g/kg. For the determination of moisture using wet bulb temperature, the environmental
temperature and mixing ratio (i.e., dry bulb) are designated as the ambient T and r, and the final wet bulb
temperature is Tw while the final mixing ratio is rs(Tw). Thus equation (3.18) becomes
cp
rr

(T  Tw )
(4.19)
s of Tw
v
Since r 
0.622 e
, equation (4.19) can be written as
p
 cp p 
e  es of Tw  
(T  Tw )
 0.622 v 
(4.20)
where the quantity in the brackets has a value of 0.065mb K-1 at sea level and it is called the psychometric
constant (although it is not really a constant since p can vary). Further, since e  es (TD ) and T  Tw , it
follows that
e  es (Tw ) and that TD  Tw  T .
Humidity variables at T<0oC
For temperature below freezing point, the equilibrium (or saturation) vapor pressure can be
defined in two ways. One is for super-cooled water where the saturation vapor pressure is that given by the
values discussed earlier for liquid water. The other is the saturation vapor pressure with respect to ice esi.
To physically understand the difference between es and esi, consider a container with a layer of
water in the bottom as shown previously. If the water is super cooled and remains in liquid form at some
temperature below freezing, the vapor pressure is that with respect to a pure water surface and in
equilibrium the evaporation from the water surface will balance the condensation on the surface. Consider
what happens to that equilibrium, however, if the liquid water is replaced with ice at the same temperature.
Because of the increase molecular forces in the ice relative to those in the liquid, the evaporation rate will
decrease, and the condensation rate will now exceed the evaporation rate and the vapor pressure will
continue to decrease until the condensation rate decreases and again comes to equilibrium with the
evaporation rate. Thus esi will be less than es.
The saturation vapor pressure with respect to ice can be quantified using the Clausius-Claperyon
equation (4.2) where  v is replaced with the enthalpy (latent heat) of sublimation  s where
 s  ( v   f )  2.834 *10 6 J kg 1 K 1 at 0oC,
Since it follow from (4.2) that
desi des

dT
dT
Values for esi can be calculate from equation (4.3) where  s replaces  v . At temperatures < 0oC, we can
also define the relative humidity with respect to ice as
RH i 
e
*100%
esi
(4.21)
Thus it is possible to have condition that are unsaturated with respect to water but saturated with respect to
ice since RHi>RH. This result has important consequences for cloud physics at temperatures below
freezing point.
Frost point temperature, TF, can be defined as the temperature a parcel of air can be cooled isobarically to
form frost. If the dew-point is greater than 0oC, the frost point cannot be defined. But at temperature
where the dewpoint is <0oC, the frost point will be higher than the dewpoint. Thus, the general frost is not
formed by dew freezing, since as air cooled below freezing the frost point will be reached before the dew
point.
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Humidity Measurements
Physical principles: condensation
The above illustrates the measurement of humidity via a condensation principle. The
thermoelectric cooler will cool the mirror to the point that dew will form, so that when a light source shines
on the mirror, the optical detector would not pick it up. Then we may use a thermometer to measure the
dew point. This process can be repeated until they get a precise measurement. The advantage is that it is
capable of high accuracy; the disadvantage though is its slow repose, because of the cooling of the mirror
takes time.
Sling psychrometer
It consists of two thermometers mounted in such a way that they can be ventilated by slinging.
The bulb of one of the thermometers is covered by a muslin cloth that is wetted with distilled water. The
two thermometers are then ventilated by slinging. The temperature of the wet bulb will lower as water
from the wick is evaporated. The lower the humidity, the greater the difference between the wet and dry
bulb temperatures. The lowest that can be reached by evaporative cooling is the wet bulb temperature. The
vapor pressure at sea level is related to the we and dry bulb temperature as
mb 

e  es of Tw   0.65
(T  Tw )
K 

(4.22)
where Tw is the wet bulb temperature, T is the dry bulb temperature, and es is the saturation vapor pressure
that can be obtained from the graph above.
For accurate measurement of humidity by the wet-dry method; it is important to protect the
thermometers from radiant heat and ensure a sufficiently high speed of airflow over the wet bulb. One of
the most precise types of wet-dry bulb psychrometer was invented in the late 19th century by Adolph
Richard Aßmann (1845-1918). In this device, each thermometer is suspended within a vertical tube of
polished metal, and that tube is in turn suspended within a second metal tube of slightly larger diameter;
these double tubes serve to isolate the thermometers from radiant heating. Air is drawn through the tubes
with a fan that is driven by a clockwork mechanism to ensure a consistent speed (some modern versions
use an electric fan with electronic speed control).
One difficulty for accurate humidity measurement is under the condition when the air temperature
is below freezing. In this case, we can use a thermostatically-controlled electric heater to raise the
temperature of outside air to above freezing. In this arrangement, a fan draws outside air past (1) a
thermometer to measure the ambient dry-bulb temperature, (2) a heating device, (3) a second thermometer
to measure the dry-bulb temperature of the heated air, then finally (4) a wet-bulb thermometer. Humidity
can be determined using three temperature measurements. According to the WMO Guide, "The principle of
the heated psychrometer is that the water vapour content of an air mass does not change when it is heated.
However, since the humidity of the ambient air is calculated indirectly from three temperature
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measurements, in such a device accurate thermometer calibration is even more important than for a twobulb configuration.
Humidity measurement is among the more difficult problems in basic meteorology. Hygrometers need
regular recalibration.
Other hygrometers
Hygrometers can be made based on other mechanisms of using sensitivity of various physical
processes with water vapor as a function of relative humidity. Like electric resistance, surface resistively,
mechanical characteristics.
Hair tension hygrometer: In a simple mechanical type of hygrometer the sensing element is usually an
organic material which expands and contracts with changes in the moisture in the surrounding air. The
material used most is human hair, which elongates as relative humidity increases. It consists of a bundle of
hair that is held under a slight tension by a spring, and a magnifying linkage that actuates a pointer.
Electronic hygrometers: Modern instruments use electronic means of recording the information. The two
most common electronic sensors are capacitive or resistive sensors. Capacitive sensor: Capacitance is the
ability of a body to hold an electrical charge, or a measure of the amount of electric charge stored (or
separated) for a given electric potential. A common form of charge storage device is a parallel-plate
capacitor. The capacitive sensors sense water vapor by measuring the change in capacitance caused by the
amount of water vapor present. Resistive sensor: It normally uses a thin film that changes conductivity
according to absorbed water. The common one is polymer membrane.
Extinction of light: At certain wavelengths the absorption and scattering of light can be a strong function of
water vapor density. The Lyman alpha hydrometer:
They have fast repose and are precise, but not very accurate, because of temperature and pressure
sensitivity, plus salts may get in the way. Some times it is used in combination with slower but more
accurate sensors.
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