Chapter 3: Water vapour

3.1 The global water cycle

H2O is the only matter that can be present at ambient conditions under its three phases:
water vapour, liquid water and ice.

Fig.3.1: Phases and phase changes of H20

97.4% of the water on Earth is assembled in the oceans, 2.6 % are on the continent,
either on the surface or in the underground, and only 10-3 % are in the atmosphere.
Nevertheless, these 0.001% are the essential link in the global water cycle. Fig. 3.2 gives
some estimates on the reservoirs and fluxes involved.
The reservoirs (Fig. 3.2) are given in 103 km3, and estimate the water masses available
in the ocean (1.4 109 km3), in the glaciers (28 106 km3), in the surface water (lakes,
rivers, ..) (3 105 km3), in the ground water (8 106 km3), in the atmosphere (13 103km3)
and in the biosphere (103 km3). The arrows indicate the net fluxes, with their orders of
magnitude in 103 km3 yr-1.
The largest flux corresponds to the evaporation of water from the oceans where the
major part of the evaporation takes place in the tropical oceans. However, a significant
part of the evaporated water condenses, forms clouds and rains close to the evaporation
site. Thus, only 40 103 km3 yr-1 are transported away from the vapour sources,
condenses over the continent and waters, thus, the land. Even though the precipitation
flux over lands is only about 1/3 of the precipitation flux over the ocean, the watering is
sufficient to allow a diversified vegetation to develop. A significant part of the
precipitated water evaporates again, another part feeds the water reservoirs, and the
excess runs off and re-joins the oceans.
Viewing the evaporation processes on the molecular level, it occurs when the flow of
individual water molecules away from the water body exceeds the return flow to the
water from the air. The actual amount of evaporation that takes place is a rather
complex function of five different parameters:

• Energy availability: The flow of molecules away from the water body requires a
certain amount of energy. This energy can be thermal, i.e. evaporation increases
with increasing temperature and the photons of the solar radiation contribute an
important amount to this energy.

A.I. Flossmann 11
 Fig.3.2: The global water cycle; reservoirs are given in 103 km3 and fluxes in 103 km3 yr-1.

• Reduction in atmospheric pressure: The molecules can leave the water surface
more easily if the counteracting atmospheric pressure force is smaller.
• Humidity: When the air layer above the water surface is relatively dry and far
from the saturation state, the vapour gradient between water surface and
atmosphere is significant. This steep gradient reduces the return flow of
molecules to the water body. In calm conditions, however, vapour will rapidly
build up in the air layer, saturate it and the gradient will rapidly disappear.
• Presence of wind: Strong winds will constantly remove the moist layer from the
water surface and, thus, maintain a steep gradient of water vapour and high
evaporation rates.
• Water availability: Through open surfaces, water is easily accessible and
maximum evaporation rates can be achieved. If the water is present in the soil,
the vegetation or animals and humans, evaporation is still taking place. However,
it is regulated by pores or stomata, and is, thus, called transpiration.

Commonly, PET (potential evapotranspiration) is the evaporation rate, which will occur
from an open water surface, while AET (actual evapotranspiration) is the amount of
water vapour formed from “resisting” surfaces. PET=AET over the ocean, e.g., while
AET<<PET in the subtropical deserts, e.g.

3.2 The saturation concept

As already suggested above, there is a limit to the quantity of water in the gaseous
phase. This limit becomes evident through a little experiment: a vacuum is generated
inside a box. Then, liquid water is introduced into the box. Initially, the entire liquid is
instantaneously vaporized. After a certain quantity, part of the water remains liquid,
and any new quantity of water added will not increase the amount of vapour generated.
If more molecules are vaporized, other molecules from the vapour will condense. This
causes a stable number of vapour molecules in the gas phase, resulting in a vapour

A.I. Flossmann 12
pressure called “saturation vapour pressure” esat. Only by increasing temperature, the
amount of vapour molecules, and the value of the saturation vapour pressure will
increase.

Fig. 3.3: A vaporization in a vacuum will result in a saturation vapour pressure, as a function of
temperature

In order to describe the equilibrium condition between two phases of the same matter,
the two variables of state: p (pressure) and T (temperature) are generally used. They
are convenient, as easily controlled. Thermodynamics proposes a number of state
functions to describe a process. The free enthalpy G(p,T) is most adapted to study the
problem of phase transitions, as a function of p and T.
The total free enthalpy G of a matter present in any two phases with masses M1 and M2,
resp. , can be described by the sum of the two specific free enthalpies g1(p,T) and g2(p,T)
of each phase:

𝐺 𝑝, 𝑇 = 𝑀! 𝑔! 𝑝, 𝑇 + 𝑀! 𝑔! 𝑝, 𝑇 = 𝑀! 𝑔! 𝑝, 𝑇 + 𝑀 − 𝑀! 𝑔! (𝑝, 𝑇)

Introducing the molar fraction of phase 1: x1=M1/M

𝐺(𝑝, 𝑇)
𝑔 𝑝, 𝑇, 𝑥 = = 𝑥 𝑔! 𝑝, 𝑇 − 𝑔! (𝑝, 𝑇) + 𝑔! (𝑝, 𝑇)
𝑀

The state of the system, thus, depends on T, p, and x. For the two phases to exist in
equilibrium at a fixed pressure and temperature, the specific free enthalpy g(p,T,x) has
to be at a minimum and obey:

!"
= 0 => 𝑔! 𝑝, 𝑇 = 𝑔! (𝑝, 𝑇) (3.1)
!" !,!

This equality of the two specific free enthalpies confirms a relationship p=p(T) between
pressure and temperature for the equilibrium condition. For the condition of the H2O
water and vapour phases being in equilibrium, this means:

𝑒 !"# = 𝑒 !"# (𝑇)

For a state T+ΔT and p+Δp, where the phases are still in equilibrium, Eq.(3.1) can be
written as
𝑔! 𝑝 + Δ𝑝, 𝑇 + Δ𝑇 = 𝑔! (𝑝 + Δ𝑝, 𝑇 + Δ𝑇)

A.I. Flossmann 13
or
𝑔! 𝑝, 𝑇 + 𝑑𝑔! = 𝑔! 𝑝, 𝑇 + 𝑑𝑔!
or with Eq.(3.1)
𝑑𝑔! 𝑝, 𝑇 = 𝑑𝑔! (𝑝, 𝑇)

which can be developed around it’s variables of state:

𝜕𝑔! 𝜕𝑔! 𝜕𝑔! 𝜕𝑔!

𝑑𝑝 + 𝑑𝑇 = 𝑑𝑝 + 𝑑𝑇
𝜕𝑝 !
𝜕𝑇 ! 𝜕𝑝 !
𝜕𝑇 !

Thermodynamics allows to identify the specific volume v and specific entropy s through:

𝜕𝑔 𝜕𝑔
=𝑣 ; =−𝑠
𝜕𝑝 !
𝜕𝑇 !
and yields for water with p=esat:
𝑑𝑒 !"# 𝑠! − 𝑠!
=
𝑑𝑇 𝑣! − 𝑣!

Introducing the specific latent heat of phase transition at constant pressure and
temperature:
𝑙!" = 𝛿𝑄!,! = 𝑇 𝑠! − 𝑠! = ℎ! − ℎ!
yields the equation of Clausius – Clapeyron:

!! !"# !!"
= (3.2)
!" !(!! !!! )

All first order equilibrium states between two phases of the same matter are described
by a Clausius-Clapeyron equation of the type (3.2). The specific latent heat needs to be
adapted to the process in question, and is a function of temperature:

process phases value in kJ/kg at T=0°C

lv evaporation liquid/vapour 2501 (2258 at T= 100°C)
ls sublimation ice/vapour 2835
lf fusion ice/liquid 334
Table 3.1: values of the specific latent heat of H2O

Table 3.1 summarizes different values of latent heat of H2O at T=0°C. They are defined
positive, when the phase transition takes place from the state with less entropy (e.g.
liquid: v1) to the state with more entropy (e.g. vapour: v2).
The temperature dependency of latent heat can be estimated, using the expressions for
specific enthalpy:
ℎ! 𝑇 = ℎ! 𝑇! + 𝑐!" 𝑇 − 𝑇!
ℎ! 𝑇 = ℎ! 𝑇! + 𝑐! 𝑇 − 𝑇!
ℎ! 𝑇 = ℎ! 𝑇! + 𝑐! 𝑇 − 𝑇!

where cw and ci are the heat capacities of liquid water and ice (cw=4218 J kg-1 K-1;
ci=2106 J kg-1 K-1) and cpv is the specific heat of vapour at constant pressure.

A.I. Flossmann 14
 𝑙! 𝑇 = 𝑙! 𝑇! + (𝑐!" − 𝑐! )(𝑇 − 𝑇! )
𝑙! 𝑇 = 𝑙! 𝑇! + (𝑐!" − 𝑐! )(𝑇 − 𝑇! )
and 𝑙! 𝑇 = 𝑙! 𝑇 − 𝑙! (𝑇)

with T0=273.15K as the temperature of the triple point.

In eq (3.2), when one phase is water vapour, generally the specific volume of the
condensed phase can be neglected with respect to the vapour phase, and the vapour
phase at saturation is assumed as a perfect gas (see Eq. 2.1):

𝑅! 𝑇
𝑣! = 𝑣! =
𝑒 !"#,!

Under these assumptions, Eq. (3.2) becomes:

𝑑 𝑙! (3.3)
ln(𝑒 !"#,! ) =
𝑑𝑇 𝑅! 𝑇 !

Fig. 3.4 displays the dependence of the saturation vapour pressure with respect to the
temperature, as detailed in Eq.(3.3).
If water vapour is vaporized in the air, and not in a vacuum as assumed above, then the
derivation still holds. However, the pressure of water vapour becomes the partial
pressure, following Dalton’s law (compare Eq. 2.1).

Consequently, evaporation, as described in chapter 3.1 cannot accumulate infinitely

water vapour in the air. There exists a saturation partial pressure of water vapour
esat in the atmosphere, which is a monotonically increasing function of temperature. The
warmer the temperature, the more molecules can enter the vapour phase before
saturation occurs. Inversely, when temperature decreases, condensation has to occur in
the saturated atmosphere, in order not to exceed the saturation partial vapour pressure.

The same reasoning applies to the equilibrium between the vapour and the ice phase,
described by
! !!
ln 𝑒 !"#,! = ! !
!" !!

Fig. 3.4: Saturation vapour pressure over liquid (upper light blue) and over ice (dark blue) as a
function of temperature

A.I. Flossmann 15
represented also in Fig.3.4. The equilibrium curve between ice and vapour below 0°C is
presented here together with the liquid supercooled curve.The concept of a saturation
state of water vapour in the atmosphere is essential for cloud physics and is used to
derive a certain number of humidity measures.

3.3 Humidity measures

In order to quantify humidity in the atmosphere, either absolute or relative measures

are used. Absolute measures quantify the amount of vapour molecules in the
atmosphere, while the relative measures define the humidity state with respect to the
saturation state.

3.3.1 Absolute measures

3.3.1.1 partial vapour pressure

The partial vapour pressure of water vapour e, given in Pa (or in hPa=102 Pa),
characterize the amount of vapour evaporated from liquid or solid surfaces.

3.3.1.2 absolute humidity

The absolute humidity (or vapour density) is the amount of water vapour per unit
volume of air (in kg m-3):
1 𝑒 𝑅! 𝑒 𝑒
𝜌! = = = = 0.622
𝑣! 𝑅! 𝑇 𝑅! 𝑅! 𝑇 𝑅! 𝑇

3.3.1.3 specific humidity

The specific humidity is the ratio of the mass of vapour per total mass in (kg kg-1):

!
𝑀! 𝑀!
𝑞 = ! ≈
𝑀 + 𝑀! + 𝑀! + 𝑀! 𝑀! + 𝑀!

When neglecting the presence of liquid water and ice, and using Eq. (2.1), yields:
𝑒 𝑒
𝑞! = 0.622 ≈ 0.622
𝑝 − 0.378 𝑒 𝑝

3.3.1.4 mixing ratio

The mixing ratio is the ratio of mass of water vapour per mass of dry air in (kg kg-1):
𝑀! 𝑒
𝑟 = ! = 0.622
𝑀 𝑝!

or
𝑒 𝑒
𝑟 = 0.622 ≈ 0.622
𝑝−𝑒 𝑝

3.3.1.5 approximations
Combining the equations yields:
𝑟
𝑞! =
1+𝑟

A.I. Flossmann 16
or
𝑞!
𝑟=
1 − 𝑞!
and for small values of r and qv (in the atmosphere the values for both vary between 0
and 0.05):
𝑟 ≈ 𝑞!

3.3.2 the saturation values

The saturation state over liquid water or over ice of the atmosphere are described by

𝑒 !"#,! and 𝑒 !"#,!

In the literature, approximated formulas for the saturation vapour pressures can be
found. An example is the formula of Magnus, which gives:

!! (!!!! )
𝑒 !"# 𝑇 = 𝑒 !"# 𝑇! 10 !! !(!!!! ) (3.4)

with bwv=234.9K, biv=265.5K, dwv=7.4475, div=9.5, 𝑒 !"#,! 𝑇! = 𝑒 !"#,! 𝑇! =6.11 hPa,

T0=273.15K, for liquid water and ice, resp.
Using the appropriate constants yields the saturation vapour pressure over water and
ice, resp.

Another formula was proposed by Tetens:

𝑇 − 𝑇!
𝑒 !"#,! 𝑇 = 𝑒 !"#,! 𝑇! exp 17.502
𝑇 − 32.19
and
𝑇 − 𝑇!
𝑒 !"#,! 𝑇 = 𝑒 !"#,! 𝑇! exp 22.587
𝑇 + 0.7

Their use allow to calculate also:

! !"#,!
𝑞 !"#,! ≈ 𝑟 !"#,! ≈ 0.622 (3.5)
!
𝑒 !"#,!
𝑞 !"#,! ≈ 𝑟 !"#,! ≈ 0.622
𝑝

3.3.3 virtual temperature

Eq. (2.1) reads:
𝑀! 𝑅! 𝑀! 𝑅!
𝑝 = 𝑝! + 𝑒 = 𝜌! 𝑅! 𝑇 + 𝜌! 𝑅! 𝑇 = 𝑇+ 𝑇 = 𝜌! 𝑅! 𝑇
𝑉 𝑉
with
𝑀! + 𝑀!
𝜌! =
𝑉
and
! ! !! !! ! !! !! !!!!
𝑅! = = (3.6)
! ! !! ! !!!

A.I. Flossmann 17
The appearance of a “gas constant” Rh that is a function of the variable vapour content r
is not very useful. Consequently, using Rd instead of Rh is more convenient which defines
a new temperature Tv called virtual temperature:

𝑅! 𝑇 = 𝑅! 𝑇!

which can be determined when using Rv/Rd=1.608:

1 + 1.608𝑟
𝑇! = = 𝑇 ! ! ≈ 𝑇(1 + 0.608𝑟) (3.7)
1+𝑟

using (1+ε)-1≈1-ε, for ε small.

The virtual temperature corresponds to the temperature until which dry air has to be
heated to have the same density as humid air (at p and V constant). Note that a given
volume V of humid air has a lower density than the same volume of dry air, at T and p
constant. This is due to the lower molecular weight of water as compared to dry air
(compare chapter 2.1). The virtual temperature is usually on the order of one degree
above the regular temperature.

3.3.4 Relative measures

Instead of using absolute measures for humidity, often it is more convenient to use
relative measures. These are relative to the saturation state and describe the state of the
atmosphere with respect to the deviation from saturation.

3.3.4.1 Relative humidity

The most widely used relative measure for moisture is relative humidity:

𝑒
𝑅𝐻 = ∙ 100
𝑒 !"#,!

The ratio of the partial pressures of the actual state of the air and the saturation state is
a measure smaller or equal than unity. Generally, this value is multiplied by 100 to
give values of relative humidity in %. Using the relationship between e and qv, yields
also:
𝑟 𝑞!
𝑅𝐻 ≈ !"#,! ∙ 100 ≈ !"#,! ∙ 100
𝑟 𝑞

One can also define the relative humidity over ice:

𝑒 𝑟 𝑞!
𝑅𝐻! = !"#,! ∙ 100 = !"#,! ∙ 100 ≈ !"#,! ∙ 100
𝑒 𝑟 𝑞

Due to the different values of the saturation vapour pressure over liquid water and over
ice, the resulting relative humidities are not identical.

3.3.4.2 dew point and frost point

Cooling humid air approaches its vapour pressure to the value of the saturation vapour
pressure. Finally, at T=τ, the saturation value is reached, and dew is forming. If the

A.I. Flossmann 18
corresponding temperature is lower that 0°C, the point is called frost point τi, as frost is
formed. Dew and frost point can be calculated using e.g. Magnus formula (3.4):

𝑑!
𝜏 = 𝑇! − 𝑏! 𝑒 +1
lg !"# − 𝑑!
𝑒 𝑇!

For bv and dv the appropriate values for water or ice have to be used.
Using eq. (3.2) for water and ice allows calculating the ratio of dew point temperature
and frost point temperature close to T0:

!! ! ! !"#,! !! (!! )
= = = 0.89 (3.8)
! ! ! !"#,! !! (!! )

This approximation is only valid close to T0. For other temperatures, the temperature
dependence of the latent heat needs to be taken into account.

3.4 How to measure humidity

3.4.1 In-situ measurement techniques

To measure atmospheric humidity, commonly a psychrometer is used. It consists of
two identical mercury-in-glass thermometers mounted side by side. The bulb of one
thermometer is wrapped in a muslin sleeve. This sleeve is soaked in distilled water, and
a reservoir of water next to the thermometer assures that it stays wet. The dry-bulb
thermometer measures actual air temperature T. Water vaporizes from the muslin
sleeve into the air, and evaporative cooling lowers the wet-bulb temperature Tw. The
drier the air, the greater the evaporation and the lower the reading will be on the wet-
bulb thermometer compared to the dry-bulb one. The temperature difference between
the two thermometers is called wet-bulb depression, and can be estimated using the 1st
principle of thermodynamics and some assumptions. The 1st principle of
thermodynamics reads:
𝑑𝑈 = 𝛿𝑄 + 𝛿𝑊
or
𝑑𝐻 − 𝑉𝑑𝑝 = 𝛿𝑄

where U is internal energy and H=U+pV is enthalpy. Q and W are the heat added to the
system and the volume work done to the system (δW=-pdV).
Applying 1st principle to the psychrometer, it can safely be assumed that the evaporation
process is isobaric (dp=0) and adiabatic (δQ=0). Then, the equation becomes dH=0 or
dh=0, using specific enthalpy.
Quantifying the evaporation process occurring between an initial state and a final state
in equilibrium allows calculating the variation of enthalpy.
The amount of vapour necessary results from liquid water present initially. The process
can thus be idealized by two separate steps: the humid air around the bulb decreases in
temperature from T to Tw, while a part of the liquid water experiences a phase transition
to the vapour. The amount of liquid water necessary corresponds to reaching the
saturation vapour pressure esat,w(Tw).

A.I. Flossmann 19
Fig.3.5: Schematic display of the psychrometer processes

The variation of the enthalpy can, thus, be written as the variation due to the 2 steps:

𝑑ℎ = 𝑑ℎ!""#$%& + 𝑑ℎ!!!"# !!!"#$ = 0

0 = 𝑐! 𝑑𝑇 + ℎ!"#$%& − ℎ!"#$"%& 𝑑𝑞!

where cp is the specific heat at constant pressure and dqv is the amount of vapour
necessary to increase the qv(T) to qsat(Tw):

𝑑𝑞! = 𝑞 !"# 𝑇! − 𝑞! (𝑇)

With the use of the definition of latent heat:

𝑐! 𝑇! − 𝑇 + 𝑙! 𝑞 !"# 𝑇! − 𝑞! 𝑇 =0

and with Eq. (3.5):

! !.!""
𝑇 − 𝑇! = !! !
𝑒𝑠𝑎𝑡 (𝑇𝑤 ) − 𝑒 (3.9)
!

an equation for the wet bulb depression results. This equation can be transformed into
an equation for the vapour pressure e:

𝑝 𝑐𝑝
𝑒 = 𝑒𝑠𝑎𝑡 𝑇𝑤 − (𝑇 − 𝑇𝑤 )
0.622 𝑙𝑣

Assuming cp as the specific heat of dry air and neglecting the specific heat of water
vapour:
!!,! ! ! !!!,! ! ! !!,! !!!,! !
𝑐! = = ≈ 𝑐!,! + 𝑐!,! 𝑟 ≈ 𝑐!" (3.10)
! ! !! ! !!!

with cpd=1.0035 J g-1 K-1 and cpv=2.080 J g-1 K-1, and assuming that l12≈l12(T0), a constant
can be defined:
𝑐!"
𝐴! = = 0.65 10!! 𝐾 !!
0.622 𝑙!!

Sometimes, the constant is expressed as its inverse: Cl=1/Al=1550 K, called “Sprung”-

constant. For ice, the constant becomes:

𝑐!"
𝐴! = = 0.57 10!! 𝐾 !!
0.622 𝑙!!

A.I. Flossmann 20
with a “Sprung”-constant of Ci=1757 K. The ratio between the two constants gives again
a factor of 0.89, as already documented for the different between dew and frost point
(compare Eq.(3.6)). Thus,
𝑝
𝑒 = 𝑒 !"#,! 𝑇! − (𝑇 − 𝑇! )
𝐶!
and
𝑝
𝑒 = 𝑒 !"#,! 𝑇! − (𝑇 − 𝑇! )
𝐶!

Tables for the web bulb depression in terms of relative humidity and dew point can be
found in the appendix.

Note :
cvd=5/2 Rd = 717 J kg-1 K-1 => cpd-cvd=Rd (eq. of Mayer)
cpd=7/2 Rd

If the air temperature is 20°C and the wet bulb depression is 5°C, then the relative
humidity is 58%. If there is no-wet-bulb depression, the air is saturated and the relative
humidity is 100%.

An instrument that is less accurate than a psychrometer is the hair hygrometer. As the
name implies, this instrument uses hair as the humidity sensor. Hair lengthens slightly
as the relative humidity increases and shrinks with humidity decrease. The typical
length change of hair is on the order of 2.5% for relative humidity ranging from 0% to
100%. Usually, a sheaf of blond human hair is connected to a pointer, allowing the
reading of RH in percent. When the pointer draws a curve on a clock-driven drum, the
instrument is called a hygrograph. It allows recording continuously the fluctuations in
relative humidity with time.

Chilled mirror dew point hygrometers are some of the most precise instruments
commonly available. These use a chilled mirror and optoelectronic mechanism to detect
condensation on the mirror surface. The temperature of the mirror is controlled by
electronic feedback to maintain a dynamic equilibrium between evaporation and
condensation on the mirror, thus closely measuring the dew point temperature.

For applications where cost, space, or fragility is relevant; other types of electronic
sensors are used, at the price of a lower accuracy. In capacitive humidity sensors, the
effect of humidity on the dielectric constant of a polymer or metal oxide material is
measured.

In resistive humidity sensors, the change in electrical resistance of a material due to

humidity is measured. Typical materials are salts and conductive polymers. Resistive
sensors are less sensitive than capacitive sensors - the change in material properties is
less, so they require more complex circuitry. The material properties also tend to
depend both on humidity and temperature, which means in practice that the sensor
must be combined with a temperature sensor. This type of hygrometer used e.g. in
radiosondes (see chapter 5.1)

A.I. Flossmann 21
3.4.2 Remote sensing measurement techniques
All remote sensing methods rely on the fact that water vapour scatters and absorbs
radiation at different wavelengths in so-called absorption-bands (compare chapter 14).
The amount of radiation absorbed is proportional to the amount of vapour in the
pathway between the radiative emission source and the receptor. Consequently, all
these methods give integrated quantities along the path that is covered.
Numerous remote sensing instruments are currently space-borne on Earth-orbiting
satellites. They use different wavelengths, that present different advantages and
disadvantages.

The Air Mass Corrected Differential Optical Absorption Spectroscopy (AMC-DOAS), e.g.
on GOME or SCIAMACHY, is a method to retrieve total water vapour column amounts
from spectral measurements in the visible wavelength region around 700 nm. Because
data in the visible spectral range are analysed, the AMC-DOAS method is only applicable
to measurements on the dayside and to (almost) cloud-free ground scenes. A significant
advantage of the AMC-DOAS method is that the derived water vapour columns do not
depend on additional external information, like a calibration using radio sonde data
which is often used in the microwave spectral region. The AMC-DOAS water vapour
columns therefore provide a completely independent data set.

Wavelength in the near IR are used also, e.g. by Moderate Resolution Imaging
Spectroradiometer (MODIS) on board of the satellites Terra and Aqua, e.g. Since the
MODIS water vapour retrieval relies on observations of water vapour attenuation of
near Infrared (IR) solar radiation reflected by surfaces and clouds, it is sensitive to the
presence of clouds. The frequency and the percentage of cloud free conditions at mid-
latitudes is only 15-30% on average, limiting the usefulness of this spectrometer in
certain regions.

Fig. 3.6: Water vapour field over the

Indian Ocean from MODIS-Terra from
April 18, 2000; Credit: Scientific
Visualization Studio, NASA Goddard
Space Flight Center,
http://visibleearth.nasa.gov/
view.php?id=54126

Another approach is to use wavelengths in the microwave region, such as Advanced

Microwave Sounding Unit (AMSU) on the NOAA polar orbiting satellites. The advantage
of this method resides in the fact that clouds do not influence microwave radiation.
Retrieval in this spectral range work in all–sky situations as long as the background
emission is known to be low, like over ocean areas.

Yet another method for estimating the amount of water vapour in the atmosphere is
linked to the exploitation of the signals propagating from GPS satellites to ground-based

A.I. Flossmann 22
GPS receivers, which are delayed by atmospheric water vapour. This delay is
parameterized in terms of a time-varying zenith wet delay (ZWD), which is retrieved by
stochastic filtering of the GPS data. Given surface temperature and pressure readings at
the GPS receiver, the retrieved ZWD can be transformed into an estimate of the
integrated water vapor (IWV) overlying that receiver. The emerging GPS networks offer,
thus, also the possibility of observing the distribution of water vapour.

Yet, another method to obtain integrated information of water vapour is the use of
Raman lidars, equipped with a water vapour channel. The Raman scattering is a weak
scattering phenomenon of light from a molecular medium. In the Raman scattering
mechanism, also known as inelastic scattering process, the scattered radiation is shifted
from the exciting radiation by an amount that is unique to the scattering molecule. Since
the vibrational energy shift is different for each type of molecule, Raman scattering can
be used to sense specific constituents in the atmosphere. Raman scattering is a weaker
interaction than Rayleigh scattering, with a cross-section that is typically three orders of
magnitude smaller. Because of the weak nature of Raman scattering, lidars using Raman
principle have ben optimized for nighttime investigation of the atmosphere.
All techniques deployed on satellites are also used on the ground or on other airborne
platforms (planes, balloons, ..).

Exercises:

1.) For a station where p=1000 hPa, T= 10°C and RH=70% calculate dew point
temperature, partial pressure, mixing ratio, virtual temperature and saturation
mixing ratio.

2.) For a station where T=15°C, r=6.22 g kg-1 and RH=50% calculate dew point
temperature, pressure and saturation vapour pressure.

3.) Which three parameters allow to calculate all other humidity measures:
a) pressure, dew point temperature and mixing ratio
b) pressure, dew point temperature and saturation mixing ratio
c) pressure, temperature and mixing ratio
d) vapour pressure, mixing ratio and dew point temperature

4.) Derive qv=0.622 e/(p-0.378e)

5.) Derive the equation for the virtual temperature Tv.

6.) Consider a horizontal cylinder thermally in equilibrium with the outside

temperature where one side is closed with a piston gliding without friction. The
cylinder is filled with humid air with T=15°C; p=1000hPa; RH=50%.

Determine the dew point temperature.

Which will be the dew point temperature and the relative humidity if the air
inside the cylinder is heated to 20°C?

A.I. Flossmann 23
 Then, the temperature in the cylinder is decreased to 1°C. Which will be the dew
point temperature and the relative humidity?

Eventually condensed liquid water is eliminated. Then, the temperature is

restored to the initial value to T=15°C. Which will be the dew point temperature
and the relative humidity?

A.I. Flossmann 24