Chapter 2

First Principles of Meteorology

Contents
2.1 General Aspects of Meteorology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.2 Vertical Structure of the Temperature and Conditions of Atmospheric Stability . . . . . . . . 70
2.2.1 Dry Vertical Temperature Lapse Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.2.2 Wet Vertical Temperature Lapse Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.2.3 Temperature Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.3 Atmospheric Variability – Air Masses – Fronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.3.1 Air Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.3.2 Classification of Air Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.3.3 Fronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.3.4 Wave Cyclone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.4 Turbulence – Equations for the Mean Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2.5 Statistical Properties of Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.6 Atmospheric Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.6.1 Temperature Season Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.6.2 Temperature Daily Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.6.3 Heating of the Earth’s Surface and Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.6.4 Distribution of Temperature in the Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.7 Humidity in the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.7.1 Mathematical Expressions of Humidity in the Atmosphere . . . . . . . . . . . . . . . . . . . . 102
2.7.2 Dew Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.7.3 Clouds in the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.7.4 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.7.5 Study of Precipitation Scavenging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.8 Applications and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Abstract The second chapter examines general aspects of meteorology including

conditions of atmospheric stability in conjunction with the vertical temperature
lapse rate. It also studies large-scale weather changes which are related to changes
in pressure systems. Air masses have different thermodynamic characteristics based
on their origin and the morphology of the surfaces above which they move.
A classification of the air masses is created, together with a mathematical descrip-
tion of the statistical properties of the air masses’ transport. Furthermore, the
temperature and humidity variability in the atmosphere is studied. Finally the
clouds in the atmosphere and general aspects of precipitation are also studied.

M. Lazaridis, First Principles of Meteorology and Air Pollution, 67

Environmental Pollution 19, DOI 10.1007/978-94-007-0162-5_2,
# Springer Science+Business Media B.V. 2011
68 2 First Principles of Meteorology

2.1 General Aspects of Meteorology

The study of atmosphere dynamics is subsumed under the science of meteorology.

The atmosphere contains thousands of chemical species in trace quantities (ppm to
ppt levels) (Finlayson Pitts and Pitts 1986; 2000). Therefore the troposphere can be
viewed as a huge container that includes gaseous and particulate matter pollutants.
The atmosphere is a dynamic system with continuous exchange of its gaseous
components between the atmosphere and the earth’s surface, including the vegeta-
tion and the oceans. Emissions of pollutants are transported into the atmosphere at
long distances from their sources. The dynamic of the atmosphere and the chemical
reactivity of the pollutants, as well as the size of particulate matter, determine their
residence time and their effects on humans and ecosystems (Seinfeld and Pandis
2006). Table 2.1 presents the different spatial scales of pollutant transport in the
atmosphere and related physico-chemical processes.
Figure 2.1 presents the different time and length scales related to atmospheric
processes ranging from molecular diffusion to climatic impacts. In the atmosphere
the chemical composition of atmospheric species can be divided into four main
groups, namely sulfur, nitrogen, carbon and halogen containing compounds
(Finlayson-Pitts and Pitts 1986; Seinfeld and Pandis 2006). Of course there are
chemical compounds in the above groups that include atoms from other groups such
as compounds that include both sulphur and carbon atoms. The chemical com-
pounds which are emitted into the atmosphere eventually are removed and there
exists a cycle for these compounds. This cycle is called biogeochemical cycle of the
compound. The term “air pollution” is used when chemical compounds emitted
from mainly anthropogenic activities are at concentrations above their normal
ambient levels and have measurable effects on humans and ecosystems. In addition,
Fig. 2.1 shows the time and spatial scales related to air pollution, turbulence, clouds,
weather and climate.
Understanding of the complex sequence of events starting from the emissions of
air pollutants to the atmosphere with human health effects as a final event is
necessary for the prognosis of potential risk to humans from specific chemical
compounds and mixtures of them (see Fig. 2.2). Furthermore, understanding of the
chemical composition/size distribution characteristics of particulate matter (PM)
and the chemical reactivity of gaseous pollutants together with their indoor-outdoor

Table 2.1 Spatial scales of pollutant transport in the atmosphere and related phenomena
Examples of physical and chemical processes in the
Scale Dimension atmosphere
Molecular << 2 mm Molecular diffusion
scale
Microscale 2 mm–2 km Industry emissions, clouds
Mesoscale 2–2,000 km Cloud coalesce, storms, air pollution at urban centers
Synoptic scale 500–10,000 km Low and high pressure systems, ozone hole in the Antarctica
Global scale > 10,000 km Decrease of stratospheric ozone, planetary wind systems
2.1 General Aspects of Meteorology 69

Energy

Time
10 min 1 h 6h 2d 20 d 1y 10 y
Length
scale
Global Climate 1000 km
Regional Arctic
scale
(trans- 100 km
boun
Mesoscale dary)
(sea breeze)
10 km
Plumes
(clouds)
1 km

Turbulence
0.1 km

Fig. 2.1 Time (s), energy and length (m) scales in the atmosphere and related phenomena

Source Elimination
Emissions Bioavailability Accumulation
Transformation

Transport Accumulation Human Biologically Early

Potential Dose Internal
and in Contact : Effective Expression at
to the Body Dose
Transformation Environment Exposure Dose Dose zone

Health
Effect

Fig. 2.2 Schematic representation of the complex sequence from emissions of air pollutants to
health effects (Adapted from Lioy 1990)

characteristics and their relation to human exposure and internal dose are necessary
steps for the quantification of human exposure to air pollutants.
Many problems of air pollution occur on several scales, such as the acidification
problem which extends from the mesoscale to a regional scale. The majority of air
pollution episodes occur in the lower part of the atmosphere, which is called the
planetary boundary layer as discussed in Chapter 1. This layer is defined as the
lowest part of the troposphere which is affected from the surface forces in time
70 2 First Principles of Meteorology

scales of 1 h or lower. The structure of the boundary layer is not static but dynamic
and contains usually the first 1,000 m from the Earth’s surface.

2.2 Vertical Structure of the Temperature and Conditions

of Atmospheric Stability

Meteorology examines the movement of air molecules in the atmosphere. Atmo-

spheric stability is examined under the conditions in which there is a small
displacement of an air volume with the application of an external force. In the
case that the external force results in bringing the air volume to its original position
prior to its displacement, then there are stable conditions in the atmosphere. On the
contrary, if the external force brings the air volume away from the original position,
there are unstable conditions.
Stability in the atmosphere is dependent on the vertical profile of temperature
and humidity of ambient air. Warm air has lower density than cold air and therefore
it is lighter. A similar situation occurs for humid air which has lower density than
dry air and therefore is lighter. Consequently, a warmer or more humid air volume
than the surrounding ambient air is characterized as unstable and will ascend into
the atmosphere. On the contrary, an air volume that is colder or drier than the
surrounding ambient air is characterized as stable and will descend into the atmo-
sphere until it reaches equilibrium.
The stability conditions in the atmosphere are related to the atmosphere’s ability
to mix and spread out pollutants. These conditions determine also the turbulent
conditions in the atmosphere and the cloud formation.
Atmospheric air absorbs less heat than the Earth’s surface due its lower heat
capacity. Therefore the layer of the atmosphere which is closer to the Earth’s
surface receives more energy, and consequently more heat, than the above layers.
Due to the heating these layers of air become lighter than the above layers and are
lofted above with consequent expansion and cooling. Since this air volume expan-
sion occurs at small time intervals without significant heat exchange with the
surrounding air environment, it is an adiabatic process. Of course the process is
not pure adiabatic since the air masses are not thermally insulated. However, since
the expansion of the air masses happens quickly and the heat exchange with
conduction and radiation is slow, the process of adiabatic expansion in the atmo-
sphere is assumed. Therefore, when an air mass is moved to an area with lower
pressure it is adiabatically expanded and cooled. On the contrary, when an air mass
is moved to an area with a higher atmospheric pressure it is contracted adiabatically
and heated. Indeed, observations have shown the importance of adiabatic processes
in the atmosphere in relation to weather.
In the International Standard Atmosphere (ISA) the temperature is decreased
with height at a rate of 0.65
C/100 m. This rate is called the temperature lapse rate.
The determination of the temperature lapse rate is presented in the following sub-
sections.
2.2 Vertical Structure of the Temperature and Conditions of Atmospheric Stability 71

2.2.1 Dry Vertical Temperature Lapse Rate

The calculation of the temperature lapse rate for a volume of dry air is examined
here assuming adiabatic expansion as discussed earlier. The first law of thermody-
namics can be expressed as:

dU ¼ dQ þ dW; (2.1)

where, U, Q and W are the internal energy of the air volume, its heat and produced
work respectively. The internal energy is given from the expression

dU ¼ Cu dT; (2.2)

where, Cu is the thermal capacity of the system at constant volume. The expression
which gives the work is given by

dW ¼ p dV: (2.3)

The law of ideal gasses can be also expressed as

pV ¼ m R T =Mair ) dðpV Þ ¼ m R dT =Mair ¼ p dV þ V dp (2.4)

where m is the air mass.

Since adiabatic conditions occur: dQ ¼ 0.
Combining equations (2.1) to (2.4) it can be found that

m R dT m R T dp m R dT dT m R T =Mair p
Cu dT ¼ V dp  ¼  ) ¼ : (2.5)
Mair Mair p Mair dp Cu þ mR=Mair

In Chapter 1 the change of pressure versus height was described with the
dz ¼  R T . With the combination of the hydrostatic equa-
Mair g p
hydrostatic equation: dp
tion and equation (2.5) it can be concluded that:

dT mg g
¼ ¼ ^ ; (2.6)
dz Cu þ mR=Mair cu þ R=Mair
^
where c is the thermal capacity at constant volume per unit mass. Finally, it can be
u ^ ^
dz ¼  ^ since c  c ¼ Mair .
g
written that dT R
cp p u
The ratio ^g for dry air is equal to 0.976
C/100 m, has the symbol G and is called
cp
dry lapse rate.
If L is the dominant lapse rate in the atmosphere, then the following cases of
stability exist for the volume of air:
72 2 First Principles of Meteorology

L ¼ G, neutral
L > G, unstable
L < G, stable

Usually, unstable conditions exist in the first 100 m from the Earth’s surface on a
sunny day. Neutral conditions exist at day or night with clouds and wind and stable
conditions near the Earth’s surface at night.
Figure 2.3 shows examples of different stability conditions in the atmosphere.
The solid and semi-continuous lines refer to the lapse rates of the air volume under
study and the atmosphere respectively. The circle denotes the air volume under study
and its position in the atmosphere. At this position the air volume temperature is equal
to the atmosphere’s temperature. Unstable conditions occur when the temperature of
the rising air volume is higher than the temperature of the surrounding air. In this
case the air volume will accelerate upwards. Stable conditions occur when the
temperature of the rising air volume is lower than the temperature of the surrounding
air. In this case the air volume tends to return to its initial position of equilibrium.
Neutral conditions prevail when the temperature of the rising air volume is the same
as the temperature of the surrounding air. In this case the air volume follows the
movement of the surrounding atmosphere.
At the upper part of the Fig. 2.3 is shown a relative gravitational example for the
stability conditions where a ball is located at the top of a hill (unstable condition), at
Air
Air

Air

ma
ma

ma

ss
ss

ss
Altitude

Altitude

Altitude

ent
En

En

m
v

viro
iro

iron
nm

nm

Env
en

ent
t

Temperature Temperature Temperature

(Unstable) (Neutral) (Stable)

Fig. 2.3 Graphical representation of the relation between the temperature and the height for an air
volume for unstable, neutral and stable conditions in relation to the surrounding atmosphere
(environment) (Adapted from Hanna et al. 1981)
2.2 Vertical Structure of the Temperature and Conditions of Atmospheric Stability 73

a Air parcel cooler than surrounding air

T2
1000
Actual air T2
temperature
Altitude (m)

profile b) Air parcel

1000
m sinks back down
a) Air parcel
9.8 ºC
pushed upward
Dry
adiabatic
rate T1
0 Air parcel at same
Temperature T1 temperature as
surrounding air
An air parcel

c) Air parcel
keeps rising!
T2
1000 T2
Dry
adiabatic
Altitude (m)

rate b) Air parcel

warmer than
5.4 ºC
surrounding air
Actual air a) Air parcel
1000
temperature m pushed upward
profile

T1
Air parcel at same
0
Temperature temperature as
T1
surrounding air
An air parcel

Fig. 2.4 The relation of the temperature versus height for an air volume for (a) stable and
(b) unstable conditions (Adapted from Hemond and Fechner-Levy 2000)

a flat surface (neutral condition) and at the base of a valley (stable condition).
Another representation of the unstable and stable conditions in the atmosphere is
shown in Fig. 2.4.
A more widely accepted methodology for the calculation of atmospheric stability
has been introduced by Pasquill. The methodology is based on measurements of the
wind speed at a height of 10 m and intensity of the Sun’s radiation during the day and
cloud cover during the night (Table 2.2). However, a more practical approach is the
use of a radiosonde for determination of the vertical profile of several meteorological
parameters such as temperature and pressure.
74 2 First Principles of Meteorology

Table 2.2 Stability conditions in the atmosphere using the Pasquill methodology
Day Night
Incoming sun’s radiation intensity Cloud cover
Wind velocity at height of 10 m (m/sec) High Medium Low >4/8 <3/8
<2 A A-B B - -
2–3 A-B B C E F
3–5 B B-C C D E
5–6 C C-D D D D
>6 C D D D D
A Very unstable
B Moderate unstable
C Slightly unstable
D Neutral (it is applied for conditions of total cloud cover both day and night)
E Slightly stable
F Moderate stable

Table 2.3 Equivalence of stability classes with the methodologies of the vertical
temperature change and the Pasquill methodology
Vertical temperature
Stability class change dT (
C/100 m) Pasquill class
Unstable dT < 1 A+B+C
Neutral 1  dT < 0 D
Slightly Stable 0  dT < 1 E
Stable dT  1 F

Another methodology for determination of stability classes is based on exami-

nation of the vertical temperature profile. This methodology is used widely for the
application of Gaussian models and the equivalence of this stability class method-
ology with the Pasquill methodology is presented in Table 2.3.

2.2.2 Wet Vertical Temperature Lapse Rate

When the air contains water vapor, the thermal capacity c^p of air has to be
corrected. If wu is the ratio of the mass of water vapor to the mass of dry air in a
0
specific air volume, then the new thermal capacity coefficient c^p is given by the
expression:

c^p 0 ¼ ð1  wu Þ^
cpa þ wu c^pu (2.7)
0
cpa and therefore c^p >^
where, c^pu >^ cpa . The symbol a refers to air and u to water vapor.
Therefore the rate of cooling of rising humid air inside a cloud is smaller than
that of dry air. The humid air volume will continue to rise until the partial pressure
of the water vapor becomes equal to the equilibrium water vapor pressure.
2.2 Vertical Structure of the Temperature and Conditions of Atmospheric Stability 75

This condition will lead to the condensation of water vapor. If DHu is the heat of
sublimation, then the release of heating due to the condensation of water vapor is
given by the expression

dQ ¼ DHu m dwu : (2.8)

Following the same derivation as in the case of dry air, using the first law of
thermodynamics, it can be concluded that

m R T dp m R dT
Cu dT ¼ DHu m dwu þ 
Mair p Mair


mR m R T dp
) Cu þ dT ¼ DHu m dwu þ
Mair Mair p

with a final result being

dT g DHu dwu
¼  : (2.9)
dz c^p c^p dz

The term dwdz has negative value for a rising volume of air where water vapor
u

condensation takes place inside Therefore the cooling rate of a humid air inside
clouds is lower than that of dry air. The reason is that with the increase of height the
percentage of water vapor is decreasing due to its condensation. The term dw dz is
u

dependent on temperature since the equilibrium vapor pressure of water vapor is

increasing considerably with the temperature.

2.2.3 Temperature Inversion

As we have examined in Chapter 1, on many occasions the temperature of air

instead of decreasing with height increases at some places in the atmosphere. This is
called temperature inversion. The atmosphere is in stable equilibrium inside the
inversion layer and therefore it does not favor vertical movements of air. The
temperature inversion may result in increased concentration of air pollutants at
the lower layers of the atmosphere.
There are three main factors which may result in the occurrence of thermal
inversions:
l The cooling of lower atmospheric layers (radiation or surface inversion).
l The adiabatic warming of descending air (subsidence inversion).
l Horizontal transport of warm or cold air.
A typical profile of a plume during a subsidence inversion is shown in Fig. 2.5
and in the case of radiation inversion in Fig. 2.6. The layer which extends from the
76 2 First Principles of Meteorology

Inversion height
Altitude

Temperature
profile

Temperature

Fig. 2.5 The plume from the lower chimneys is trapped inside the inversion, whereas, the plume
from the tall chimney which is located above the inversion is rising, mixing and transported

Temperature
profile

Top
Inversion
layer
Base

Mixing
depth
Altitude

Temperature

Fig. 2.6 The inversion height is not allowing the escape of gaseous pollutants under it. If the
inversion height is becoming lower, then the mixing height is reduced and the pollutants are
trapped in a smaller air volume
2.3 Atmospheric Variability – Air Masses – Fronts 77

Earth’s surface up to the base of the inversion layer is called the mixing layer.
The height of this layer is called the mixing height.
It can be noted that the relatively unstable air below the inversion allows vertical
mixing of air pollutants up to the base of the inversion layer. The stable air in the
inversion layer does not allow vertical mixing inside the inversion layer and acts as an
obstacle to the pollutant entrainment upwards. If the inversion moves upwards, then
the height of the mixing layer is increasing and the pollutants will mix in a bigger air
volume and, on the other hand, if the inversion moves downwards then the mixing
height will be lower and the pollutants will be concentrated in a smaller air volume.
In the latter case the concentration of pollutants is increasing and in urban areas may
lead to concentrations above the health limits. Since the atmosphere tends to be
usually more unstable during the afternoon and more stable in the morning, then there
is higher mixing height at the afternoon and lower early in the morning.

2.3 Atmospheric Variability – Air Masses – Fronts

Weather changes of large scale are related to changes of the pressure systems. The
first step for weather prognosis is given by the Scandinavian School of meteorology
which realized the importance of the formation and transport of High and Low
pressure systems. The next step was the discovery of the characteristics of the air
masses and front zones, the areas in which air masses are met with different
thermodynamic characteristics. This led to a more detailed study of the air masses
which form the basis for the weather phenomena.
Generally the meteorological conditions which are persistent in an area at
specific time are dependent on the characteristics of the air masses which pass
above this region or from the interactions of two different air masses which meet
there. Therefore the weather above a region is quite uniform with small differences
which are due to local morphological characteristics of the region such as the
topography, the vegetation and distribution of land and sea.

2.3.1 Air Masses

Air masses are large bodies of atmospheric air which have similar properties of
temperature and humidity distribution. It is possible for the diameter of an air mass
to be larger than 1,500 km, covering large continental and ocean regions. Its height
may reach the tropopause. With the air masses is accomplished the general atmo-
spheric circulation and the transport of large quantities of heat from the equator to
the poles. Inside an air mass, important factors are its humidity content, its temper-
ature and especially the temperature change with height. The quantity of humidity
influences the cloud type and consequently the rain quantity. The vertical tempera-
ture distribution affects the stability of the air mass.
78 2 First Principles of Meteorology

In order for an air mass to attain similar temperature and humidity character-
istics, it is necessary to remain for several days stagnant above a region which also
has similar characteristics. This region is called the source of the air mass. At which
degree the air mass attains the characteristics of the source region is dependent on
its residence time and the temperature difference between the initial air temperature
and the temperature of the region’s surface. The air mass during its residence above
the region becomes at a certain degree homogeneous. Under the influence of wind
flow the air mass starts to move and retains during its transport at high degree the
characteristics of its regional source.
From a thermodynamic point of view the air masses are classified in two
categories, the warm and cold ones. The warm air masses are warmer than the
surface above which they are transported and for this reason are becoming colder at
their base and are also stable. The freezing of air masses is more effective on the
layers which are contiguous to the surface and extends slowly above, mainly due to
turbulent movements and not due to heat transfer. This is also the reason for the
formation of temperature inversions. When the winds are weak there are often
formations of mist and dew, whereas, with stronger winds there is the formation of
low clouds (Stratus), below the upper limit of the temperature inversion.
Cold air masses are colder than the Earth’s surface and for this reason receive
heat from below. The heating of those layers which are located close to the surface
results in a sudden drop of their temperature versus height. This temperature
drop results also in an increased temperature lapse rate and therefore unstable
conditions and enhanced ascending air movements. If these cold air masses contain
sufficient quantities of humidity or if they are supplied with humidity from the
warmer layers below, then there is a formation of clouds of vertical development
which also results in intense rainfall.

2.3.2 Classification of Air Masses

The classification of air masses is based on the following criteria:

l The source of the air mass. Air transported above oceans absorbs humidity and
tends to be saturated in the lower layers. On the contrary, continental air masses
remain dry since there is not enough water quantity for evaporation on the
surface.
l The trajectory which is followed above the Earth’s surface. The polar air which
is transported at lower latitudes is receiving heat from below and becomes
unstable. On the contrary, the tropical air which is transported at higher latitudes
becomes more stable since it becomes colder at its base.
l If the air is characterized as diverging or converging. An air mass which is
affected from the divergence of air at a high pressure system at the Earth’s
surface will move downwards at a low rate and converted to a warmer, drier and
2.3 Atmospheric Variability – Air Masses – Fronts 79

Fig. 2.7 The descending air, Air flows

which is resulted from Air flows upwards
divergence at the surface is downwards
stable, whereas the ascending
air which is resulted from
convergence at the surface is
unstable
Divergence Convergence

HIGH LOW

more stable air mass. On the contrary, an air mass which is affected from the
convergence of air at a low pressure system at the Earth’s surface will move
upwards and will be converted to a colder and more unstable air mass (Fig. 2.7).
Based on the above characteristics one can distinguish two main categories
of air:
l Polar air masses at high geographical latitudes and
l Tropical air masses at low geographical latitudes.
These two basic categories are further divided into continental and ocean masses
based on whether the air mass moves above a continent or a sea as follows:
l Polar Maritime air (Pm)
l Polar Continental air (Pc)
l Tropical Maritime air (Tm)
l Tropical Continental air (Tc)
In addition to the above basic air masses, there are also the Arctic masses.
Sources of the arctic masses are the arctic regions close to the poles. These are
cold air masses through all seasons and especially during winter. The behavior and
alteration of the arctic air masses that intrude at lower latitudes is dependent on the
part of the Earth’s surface above which they are transported. In general if they are
transported above oceans, then the lower layers become warmer and receive large
quantities of water vapour. This results in the formation of unstable clouds of
vertical development and extension of the weather characteristics in larger areas.
Transport above cold continental areas results in stable air masses with mild
weather characteristics, the main feature being intense cold.

2.3.3 Fronts

We pointed out previously that air masses have different thermodynamic charac-
teristics based on their source of origin and the morphology of the surfaces above
which they move. When two air masses with different characteristics come in
80 2 First Principles of Meteorology

contact, they mix very slowly and form an inhomogeneous surface whose vertical
profile is called a frontal surface. The cross section of this surface with the Earth’s
surface is called a front.
The frontal surfaces have small depth and are steep in relation to the horizon,
with the warmer mass always being above the colder one. The most important
fronts are the following:

2.3.3.1 Polar Front

At the mid-latitudes, polar cold air masses collide with tropical warm ones. The
separation zone between these tropical and polar air masses is called a polar front.
The position of the polar front is variable. The strong polar air moves the warm
tropical air at some places whereas, in some other places the polar front declines at
northern positions due to pressure from the tropical air. As a result the polar front
has a corrugated form as shown in Fig. 2.8.
However, the polar front seldom is found as a continuous zone encompassing the
whole hemisphere as shown in Fig. 2.8. There are locations around the hemisphere
where the transition between the polar and tropical air masses is so smooth that the
dividing curve does not appear. Therefore the polar front is not continuous,

Fig. 2.8 Semi-hemispheric view of the polar front

2.3 Atmospheric Variability – Air Masses – Fronts 81

especially during the summer period in the northern hemisphere where the front is
pressed northerly of the 60
parallel. During winter the polar front that is located
usually at medium latitudes moves south and invades the tropical zones.

2.3.3.2 Cold Front

Even though the polar front represents a main zone of discontinuity in each
hemisphere, fronts can be formed at any location on Earth if there is a coalescence
of air masses with different thermodynamic characteristics. During the meeting of
the air masses, two types of fronts are formed, the warm and cold fronts.
When two air masses (a cold and a warm one) come in contact and move so that
the cold mass displaces the warm mass, then the surface that divides them is called a
cold frontal surface. A side view of a cold front is shown in Fig. 2.9.
In a cold front, the warm mass which is located at the lower layers moves slower
than the cold air. Therefore the cold air which moves quicker and penetrates through
the lower levels of the warm air, causes a violent vertical upward movement. It has to
be noted that the warm air is ascending at both warm and cold fronts and is responsible
for the weather changes. It is furthermore interesting to refer to the characteristics of
the warm and cold fronts, since their dynamics determine the extent of cloud coverage,
the intensity and duration of rain and finally the direction and velocity of the wind.

47
1005 1003
25 46
04
10

23 1008 21
20
52 1
45

1013 1006
25 42
1010 39 50 1006 55
21 31 39 1009
44
26 34 50

1011 51 1009
41 49
1014 1010
37
1011 53
54 50
53
54 1011

Fig. 2.9 Surface weather associated with a cold front. The dark band denotes the region of the
weather phenomena
82 2 First Principles of Meteorology

The peak of a cold frontal surface in relation to the Earth’s surface is close to 1/50
and the frontal weather covers a narrow region ranging from 30 to 50 miles. The
physical process which occurs for the formation of the cold front is related with the
movement of warm air which is transported faster than the warm air and, because it is
heavier, is located under it. Therefore the warm air which is lighter has an upward
movement along the frontal surface. During the upward movement process it is
cooled adiabatically due to expansion and reaches saturation. Furthermore there is
a condensation process and cloud formation. Since the ascending warm mass is
transported quickly, there is formation not only of stratocumulus clouds but also of
clouds of vertical development (storms). The weather phenomena which are related
with a cold front are intense (intense rain, storms, hail) and of small time scale.
The distribution of clouds as well rain is dependent on the atmosphere’s stability
and the humidity percentage of the rising warm air. The limit between the two air
masses on the Earth’s surface is depicted in meteorological maps as a line with a
blue shading and solid triangles which point towards the moving front. The cold
front moves quite quickly.

2.3.3.3 Warm Front

When two air masses (warm and cold) are in contact and moving so that the warm
mass forces the cold mass to move, then the surface which divides them is called a
warm frontal surface. The intersection of this surface with the Earth’s surface is
called a warm front (Fig. 2.10). Since the warm air mass is lighter, it ascends above
the cold air and cools adiabatically resulting in extended condensation.

Fig. 2.10 Surface weather associated with a warm front

2.3 Atmospheric Variability – Air Masses – Fronts 83

In a warm front the presence of warm air at the upper atmospheric layers
prevents the mixing of air masses vertically. The presence of warm air masses
that are rich in humidity and that move above cold air masses has as a result a
volume increase in air mass and the formation of clouds and rain with gradual
cooling of the air. At the warm fronts there is the formation of extended cloud layers
and storms with the scavenging of chemical compounds which are inside them.
Transport from the lower layer is not easy due to the absence of clouds.
The gradient of the warm front in relation to the surface is close to 1/100. The warm
air, since it is lighter, is moving faster than the cold air and is ascending above it along
the warm frontal surface. During its ascent the warm air is getting colder adiabatically
and after the saturation point starts the condensation process with the formation of
extended cloud layers. The width of these cloud layers extends between 100 and
300 miles and its length may extend 1,000 miles. Since the gradient of the warm front
is small, then the upward movement of the warm air masses occurs slowly. The warm
air masses are characterized by stable conditions due to the uniformity of the temper-
ature and relative humidity characteristics inside them, and the clouds which are
formed are stratocumulus. These clouds are very extensive geographically and give
rain over a range up to 2,000 miles which may be light or medium in intensity but has
long duration. In special cases the warm air can be unstable so there is a possibility of
formation of clouds with vertical development (storms).
The limit on the Earth’s surface between the two air masses is depicted in the
meteorological maps as a red line with semi-circles which show the movement
direction of the warm front. In Table 2.4 are presented the main characteristics of

Table 2.4 Characteristics of warm and cold fronts

Characteristics Cold front Warm front
Distribution of air masses The cold air mass press the The warm air mass ascends
warm air mass above the cold air mass
and pushes it away
Gradient of the frontal Large gradient (1/50) Small gradient (1/100)
surface (in relation to
the surface)
Weather phenomena Intense weather Moderate weather
phenomena (storms, phenomena (weak to
strong winds, strong moderate rain,
rain etc.) moderate winds)
Band of weather Close to 150 km (100 km 400 km (or more) The
phenomena front of the cold front weather phenomena
and 50 km behind it) occur before the warm
front
Duration of the weather Small duration Large duration
phenomena
Symbol Solid blue line with Solid red line with half
triangles along the front circles along the front
showing its direction of showing its direction of
movement movement
84 2 First Principles of Meteorology

Cold air

Warm air

Fig. 2.11 Stationary front at a weather surface map

the warm and cold fronts. These characteristics can be modified to a larger extent
since they are dependent on many parameters, such as the season, the thermody-
namic characteristics of the air masses, the humidity content of the warm air mass
and others.

2.3.3.4 Stationary Fronts

When warm and cold air masses are in contact but are not moving and therefore
neither of them is tending to displace the other, then the intersection of their
dividing surface with the Earth’s surface is called a stationary front (see Fig. 2.11).
The wind is moving parallel to the stationary front and the weather conditions at
these fronts are similar to the warm fronts. However, they have weaker intensity
and can cover a larger area. The stationary fronts can remain for several days or
weeks and their exact weather conditions are difficult to be forecast. In surface
maps they are depicted with a solid line which has red arrows and blue semi-circles.

2.3.3.5 Occluded Fronts

Cold fronts move with higher velocity in relation to warm fronts and as a result the
warm region (the area between the cold and warm fronts) is reduced and finally the
cold front catches up and overtakes a warm front with the formation of an occluded
front. This can occur at the final stages of a wave cyclone. In the formation of an
occluded front, three air masses are involved and their position vertically is
dependent on their temperature difference (Fig. 2.12)
The occluded front is depicted with a line on which triangles (blue) and hemi-
circles (red) denote the direction of the front movement.
The clouds that accompany an occluded front are dependent on the clouds which
were present at the warm and cold fronts. Severe weather conditions may occur at
2.3 Atmospheric Variability – Air Masses – Fronts 85

Warm air

Colder air Cold air

Fig. 2.12 Vertical structure of an occluded front

the first stages of the formation of an occluded front due to the unstable air mass
which is forced to move upward. However, this stage lasts only for a short time
interval.

2.3.4 Wave Cyclone

The low barometric conditions at the middle latitudes are developed at regions
where there is a formation of fronts. The fronts are formed due to the general
atmospheric circulation close to the Earth’s surface.
The process starts with a stationary front, where the cold air is located north and
the warm south. A front has the properties of a wave. Due to the front tilt there is a
formation of an initial oscillation at the intersection between the front and the
surface. Thus the warm air forms a cavity inside the cold air. The pressure starts to
drop at the top of the cavity and starts the formation of a cyclonic movement of air.
The low pressure system which is formed and is accompanied with frontal move-
ments (warm and cold front) is called a wave cyclone. When the wave cyclone is
formed it is moving in an easterly direction, passing successively through stages as
depicted in Fig. 2.13 until its dissolution (life cycle of a wave cyclone).
The first stationary front is divided into a warm and a cold front and the low
system which accompanies it starts to deepen. The sector between the warm and cold
fronts is called a warm sector. The whole system moves eastward and the pressure at
the centre of the low system continues to decrease. The transport velocity of a wave
cyclone is equal to the velocity of the geostrophic wind in the warm region.
A continuing pressure drop causes convergence inside the low system and
consequently an upward flow. This upward flow forms due to adiabatic cooling of
water condensation and other weather phenomena. The weather conditions are
discussed in the sections related to warm and cold fronts. As the air of the warm
sector ascends in conjunction with the quick arrival of the cold front, a narrow area
of the warm sector develops. Then the cold front occupies the warm section and the
two fronts are combined. The combination starts at the Earth’s surface. The front
which is formed from the above process is the occluded front. Finally, the baromet-
ric low gradually disappears.
86 2 First Principles of Meteorology

a b c
H
Cold
Cold
Warm L Cold
Cold Stationary front
L
front
Warm Warm Weather Warm
zone
N H

d e f
Occluded
front
L
L Cold L

Cold Cold
Cold Stationary
front
Warm Warm

Fig. 2.13 A life cycle of a wave cyclone

2.4 Turbulence – Equations for the Mean Values

Turbulence characterizes the atmospheric boundary layer; but, due to the complex
structure and variability of the layer, a deterministic description of its turbulence is
difficult. A description of turbulence can, however, be constructured through its
statistical properties. A suitable methodology is to divide the flux into turbulent and
non- turbulent terms. An example is the calculation of the changes in small spatial
and temporal changes, where the equations are expanded to average and instant
values. This methodology is known in the literature as Reynolds analysis since it
was developed by Osborne Reynolds.
As an example, the gaseous number concentration can be divided as the sum of
the average and instant values:
0
N ¼NþN (2.10)

where, N is the average gaseous concentration (molecules/(m3 s)) and N0 is the

instant value. The average concentration is calculated with integration of time and
volume:
Z tþDt Z xþDx Z yþDy
Z zþDz   
1
N¼ N dz dy dx dt: (2.11)
Dt Dx Dy Dz t x y z

The atmospheric flux is turbulent. Turbulent flux does not have specific forms but
exhibits a random behavior in relation to time. These random changes of velocity
give changes to the rates of change of momentum, heat and mass which are higher
2.5 Statistical Properties of Turbulence 87

u
u'
u

N
N N?

Fig. 2.14 Actual, average and instant values for the velocity and gaseous concentration. Every
point in the horizontal axis depicts variations at specific time and space values

by several orders of magnitude in relation to the molecular diffusion. During

turbulent flux there is a continuous conversion of the kinetic energy to internal
energy. The energy source in turbulent dispersion is the shear flux in the flux field.
If ui(t) is the instant value of the velocity of a molecule, then the average velocity
value versus time is given by the expression
Z to þt
1
ui ¼ lim ui ðtÞ dt: (2.12)
t!1 t to

Since the velocity is not exactly constant versus time, the average velocity can be
expressed as
Z tþt=2  0 0
1
ui ðtÞ ¼ ui t dt : (2.13)
t tt=2

Figure 2.14 shows the time series of velocity u and the gaseous concentration N,
depicting the difference between average and instant values.

2.5 Statistical Properties of Turbulence

Turbulence is a characteristic of the atmospheric boundary layer and due to its non -
deterministic nature its description is formulated with the help of statistics. In this
section statistical methods for the study of turbulence are examined.
Turbulence has a spectrum analogous to the colour spectrum of light after
passing through prism. Similar analysis is performed for the description of the
colour spectrum and turbulence such as the contribution of different components of
flux to the total turbulent kinetic energy. Figure 2.15 shows an example of the
function of the probability density for temperature in the atmospheric boundary
layer. It is important to understand that variations of different components in the
atmosphere make necessary their statistical evaluation.
88 2 First Principles of Meteorology

1400
a
1200

1000

800

600

400

200

0
–0.8 – 0.6 – 0.4 – 0.2 0 0.2 0.4 0.6

Fig. 2.15 Typical form of the function of the probability density for temperature fluctuations in
the atmospheric boundary layer (x-y plane at z ¼ 389 m). The y-axis denotes frequency of
occurrence, and the units of the x-axis are degrees Kelvin. Mean temperature is 301 K (Adapted
from Housiadas et al., 2004)

The function for the mean value constitutes one of the main functions which will
be examined. There are several ways to examine the mean value of a function.
These include mean values of time t ð Þ, space s ð Þ, and from the ensemble e ð Þ
(Stull 1997). Therefore for a variable A(t,s) that is function of time (t) and space (s),
the following expressions for discontinuous and continuous conditions can be used:

P
N1 RP
t
AðsÞ ¼ N1 Aði; sÞ or t
AðsÞ ¼ P1 Aðt; sÞ dt; (2.14)
i¼0 t¼0

P
N1 RS
s
AðtÞ ¼ N1 Aðt; jÞ or s
AðtÞ ¼ 1S Aðt; sÞ ds; (2.15)
j¼0 t¼0

P
N1 RE
e
Aðt; sÞ ¼ N1 Ai ðt; sÞ or e
A ðtÞ ¼ E1 Aðt; eÞ de: (2.16)
i¼0 t¼0

A statistical criterion for the variation of data around its mean value is the
dispersion coefficient which is defined as

1 X
N 1
2
s2A ¼ Ai  A : (2.17)
N i¼0
2.5 Statistical Properties of Turbulence 89

The dispersion coefficient is a good measure of the variations inside the bound-
ary layer. Another coefficient which is used more often for groups of measurements
can be defined as

1 X N 1
2
s2A ¼ Ai  A ; (2.18)
N  1 i¼0

where the instantaneous variations can be written as

a0i ¼ Ai  A: (2.19)

Finally we can write as a result,

1 X
N 1
0
s2A ¼ a 2 ¼ a0 2 : (2.20)
N i¼0 i

In addition, a coefficient can be defined for the intensity of turbulence for an

average velocity value Uas

I ¼ sU =U: (2.21)

The covariance coefficient denotes the correlation between variable A and B:

1 X
N 1


covar ðA; BÞ  A i  A Bi  B : (2.22)
N i¼0

Using the Reynolds methodology (ðA BÞ ¼ A B þ a0 b0 ) for the average value,

then the following expression is derived for the covariance (covar(A,B)):

1 X
N 1
0 0
covar ðA; BÞ  a b: (2.23)
N i¼0 i i

As an example for the covariance coefficient, we examine the case that the
coefficient A is the temperature (T) and B is the vertical velocity component w.
On a warm summer day the warmer air ascends (positive T0 and w0 ) and the colder
air descends (negative T0 and w0 ). This denotes that the product w0  T0 is positive
and therefore the temperature and vertical velocity components change co-instan-
taneously. Figure 2.16 shows the vertical fluctuations of the velocity at the surface
x – y for a typical situation of the atmospheric boundary layer, whereas, Fig. 2.17
shows the vertical fluctuations of the velocity at the surface y – z.
The normalized covariance (rAB) can be defined as

a0 b0
rAB  : (2.24)
sA sB
90 2 First Principles of Meteorology

5000

4500

4000

3500

3000

2500
m

2000

1500

1000

500

0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
m

Fig. 2.16 Instantaneous w-fluctuations (m) in the x-y plane at z ¼ 190 m (middle of domain)
(Adapted from Housiadas et al., 2004)

1100

1000

900

800

700

600
m

500

400

300

200

100

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
m

Fig. 2.17 Instantaneous w-fluctuations (m) in the y-z plane at x ¼ 2,500 m (middle of domain).
(Adapted from Housiadas et al., 2004)
2.5 Statistical Properties of Turbulence 91

The coefficient rAB has values which range between +1 and 1.When two
variables change in the same manner, then rAB ¼ 1. When the variables change
in opposite ways, then rAB ¼ 1.
The kinetic energy of mass m is given by the expression Ek ¼ 1/2 m u2, where u
is the velocity. The kinetic energy per unit mass is written as Ek/m ¼ 1/2 u2. The
kinetic energy of flux can be divided into two terms, one which is related to the
mean velocity and one which is related to the turbulence. Therefore the expression
for the mean kinetic energy can be written as

MKE 1  2
¼ U þ V2 þ W2 ; (2.25)
m 2

where U, V, W are the three components of the mean velocity.

The expression for the turbulent kinetic energy can be written as

TKE 1  0 2
¼ u þ v0 2 þ w0 2 ; (2.26)
m 2
where, u0 , u0 and w0 are the three components of the instantaneous velocity.
Furthermore we study the flux concept in the atmosphere, which is defined as the
transport of a quantity per unit surface and unit time. In the boundary layer there is
usually a study of flux of mass, heat, humidity, momentum and pollutants. As an

example for the mass we define the pollutant flux ( M ) which is expressed in units
Kgair  m
m2 s : The kinematic flux is defined as M ¼ rair (units s ). Furthermore the vertical
M

kinematic heat flux due to turbulent flux (vertical kinematic eddy heat flux) is defined
0
as w0 y where y is the temperature. Another quantity that is important in the study of
atmospheric flux is stress, which is actually a force that can produce a deformation of
a body. Pressure is a kind of stress which is applied in fluids under equilibrium. The
Reynolds stress for a fluid in turbulent movement is given by the expression

tReynolds ¼ r u0 w0 ðReynolds stressÞ (2.27)

or can be expressed as



@Ui @Uj 2 @Uk
tij ¼ m þ þ mB  m dij ; (2.28)
@xj @xi 3 @xk

where, mB is the viscosity coefficient and m is the dynamic viscosity coefficient.

The tensor of the Reynolds stress is symmetric and is given as
2 3
u 0 u0 u0 v 0 u0 w0
4 u0 v0 v0 v0 v0 w0 5 (2.29)
u0 w 0 v0 w0 w0 w0
92 2 First Principles of Meteorology

where u, v, w are the air velocities in the three directions.

A typical value of the kinematic coefficient of the Reynolds stress in the
atmosphere is 0.05 m2/s2. The Reynolds stress is a characteristic property of the
flux and not of the medium.
In addition the Reynolds stress at directions x, y and z can be expressed as

txz ¼ r u0 w0s ; ðviscous stressÞ (2.30)

tyz ¼ r v0 w0s ; (2.31)

with a total Reynolds stress

  h i1=2
tReynolds  ¼ t2 þ t2 : (2.32)
xz yz

Finally the friction velocity u* can be written as

h i
2 1=2  
¼ tReynolds =r:
2
u2  u0 w0s þ v0 w0s (2.33)

2.6 Atmospheric Temperature

2.6.1 Temperature Season Variability

The Sun is the largest heat source in our solar system and of course also for the
Earth. Heat is an energy form that is dependent on the composition of materials and
can be moved to other bodies or can be transferred to other energy forms.
The Earth spins on its own axis (with a period of one day – 24 h) and at the same
time revolves with a velocity of thousands of kilometers per hour around the sun
with elliptical trajectory (with a period close to 365 days) (Fig. 2.18). The direction
of rotation is anticlockwise and has a velocity of several 100 kilometers per hour.
This is the reason that sun, moon and stars rise in the east and decline in the west.
Since the Earth performs an elliptical orbit around the sun, the distance between
Sun – Earth changes during the year. Earth is closer to the Sun in January (distance
of 147 million km) than in June (distance of 152 million km). At the Northern
Hemisphere the average temperature in June is higher than that of January and thus
the change of seasons is determined by the quantity of the Sun’s energy which
reaches the earth. The quantity of radiation from the Sun which reaches the earth’s
surface is determined from the angle that radiation strikes the surface and the time
period that the sun radiates at a specific latitude.
2.6 Atmospheric Temperature 93

N
Autumnal equinox
September 22

Winter
solistice Summer
December 21 solistice
N N June 21
SUN

S231/2º
661/2º

Earth's orbit

Vernal equinox
N March 20

Fig. 2.18 Earth’s orbit around the Sun. During this movement the Earth is rotated around an axis
which has an angle of 23 ½
from its vertical axis The rotation axis is constant during the year. The
result is that in June, when the northern hemisphere is turned towards the Sun, there is more direct
light and longer duration of the day there. This results in warmer weather, compared to December
when the northern hemisphere is turned away from the Sun

Tro Tro
pic pic
of C of C
anc anc
er. er
Tro Rays of Tro
pic Equ pic Equ
of C ato Sunlight of C ato
apr r apr r
Pol icor Pol icor
ar C n ar C n
ircle ircle

a b

Fig. 2.19 Earth’s direction (a) 21st June (b) 21st December

Figure 2.19 shows also the earth’s direction in relation to the Sun’s radiation
during 21st June and 21st December. On 21st June the Sun’s radiation strikes the
earth vertically at 231/2
north (N) (Tropic of Cancer). On 21st December the
darkness lasts for 24 h for all areas above 661/2
north (N) and 661/2
south (S).
When the Sun’s radiation penetrates the atmosphere, a part of it is absorbed or
scattered from the atmospheric gasses, whereas another part is reflected from
clouds. This means that the greater is the thickness of the atmosphere which
the Sun’s radiation has to penetrate, the higher is the possibility that the radiation
will be absorbed or scattered. This occurs during summer and high latitudes such as
94 2 First Principles of Meteorology

in the Scandinavian countries. The Sun in these countries is never very high on the
horizon and therefore the radiation must penetrate a quite thick atmospheric layer
before it reaches the Earth’s surface. Also due to high cloud content of the
atmosphere the radiation is scattered effectively before it reaches the ground.
The seasons are determined from the quantity of the Sun’s radiation which
reaches the planet, which is determined from the duration of the day and the incident
angle of the Sun’s radiation. As a result the higher latitudes lose more radiation
(from the emitted radiation at the higher wave length of the Earth’s surface) than
what they receive (short wave length of the Sun’s radiation). On the contrary, at
lower latitudes there is a higher quantity of Sun’s radiation which reaches the Earth
than is emitted from it. Due to the global wind circulation that results from this
temperature difference there is a transport of heat from the lower to higher latitudes.
As shown in Figs. 2.18–2.19, on 21st June the Sun’s radiation has a maximum at
the Earth’s surface at latitude 30
N. This day the Sun is located above the latitude
23 1/2
N (Tropic of Capricorn). The reason that the maximum of incident energy is
at latitude 30
N and not at latitude 23 1/2
N is due to two reasons. First, the
duration of day at the area of 30
N is larger than the area 23 1/2
N on 21st June.
Secondly the area close to the point 30
N is characterized by desert areas, clear sky
and dry air, whereas at the area 23 1/2
N the climate is more humid with clouds
which reflect the Sun’s radiation.
After the 21st of June the sun is lower at noon in the sky and the summer days
become shorter. With the beginning of September there is the start of autumn.
On September 22nd the Sun is located above the equator. On this date, except at the
poles, the day and night have the same duration (autumnal equinox). At the north
pole the Sun appears on the horizon for 24 h and then disappears from the horizon
for 6 months. At other latitudes in the north hemisphere after the 22nd September
the Sun at noon appears gradually lower in the sky and the day lasts fewer hours.
On 21st December, which is 3 months after the autumnal equinox, the north
hemisphere is directed farther from the Sun compared to the previous period. The
nights are long and the days are short. This is the shortest day of the year (winter
solstice) and it is the astronomical start of winter. This day the Sun shines directly
above latitude 23 1/2
S (Tropic of Capricorn). It is located at its lower position at
the middle of the day and its radiation passes through a large portion of the
atmosphere and affects a large portion of the Earth’s surface.
On 20th March there is the astronomical start of spring and it is the vernal
equinox. This day the Sun shines directly above the equator, whereas at the north
pole the Sun appears on the horizon after being 6 months absent. The following
period the days last longer and there is warmer weather in the north hemisphere.
After 3 months, 21st June, the sun’s radiation reaches a maximum. It is obvious
that even though the sun’s radiation is more intensive during June, the warmest
period appears a few weeks later during July or August. The reason is that during
June the outgoing radiation from earth is smaller than the incoming and there is no
thermal equilibrium. When a thermal equilibrium is achieved, there is the highest
temperature in the atmosphere and this is achieved a few weeks after the 21st June.
The same situation occurs during winter when the outgoing energy from the
2.6 Atmospheric Temperature 95

Balance Balance

Surplus
Deficit Deficit
Radiation per Year

Surplus Heat Energy Transferred by

Atmosphere and Oceans to higher
latitudes

90 60 30 0 30 60 90
North Latitude South

Fig. 2.20 The average annual incoming solar radiation (grey line) absorbed by the earth and the
atmosphere compared with the average emitted infrared radiation from the earth and the atmo-
sphere (Adapted from Ahrens 1994)

atmosphere is higher than the incoming and the temperature decreases. Since the
outgoing radiation is higher than the incoming then for a few weeks after 21st
December there is the coldest period mainly during January and February.
Whereas in the whole planet there is energy equilibrium between the absorption
and emission of solar radiation, this is not valid at every latitude. Figure 2.20 shows
the energy equilibrium at different latitudes.
The temperature is expressed in degrees, which are subdivisions of thermal
scales. The best known and most used are the Celsius centigrade scale (
C) and
the Fahrenheit scale (
F) which is used mainly in the United States and finally the
Kelvin scale (K) which is used mainly for scientific purposes. Thermal energy is
observed in the system Earth – atmosphere with the following forms:
l As absolute heat which can be measured with the help of thermometers and
l As latent heat which occurs during specific physical processes related to the
phase changes of water (evaporation, condensation etc.).
As discussed earlier, the main source of heat for the Earth and its atmosphere is
the Sun, since the energy from the Earth’s interior is negligible. It has been
calculated that if there was no contribution from the Earth’s interior its mean
temperature would be reduced by less than 0.1
C. Therefore the short length
Sun’s radiation affects the planet’s temperature and controls, together with the
long length radiation, the temperature on the Earth’s surface. The processes of heat
exchange (between warm and cold regions) at the lower atmospheric layers due to
uneven heating of the earth’s surface are the main reasons for the formation of
weather phenomena inside the atmosphere.
96 2 First Principles of Meteorology

2.6.2 Temperature Daily Variability

The intensity of the Sun’s radiation which is received from the Earth’s surface is
dependent on the Sun’s position. During a sunny day the radiation intensity has a
simple variation with maximum close to noon. During a day without clouds and
turbulent atmosphere the air temperature varies with the minimum a few minutes
after the Sun’s rise and maximum 2–3 h after the noon hour. As shown in Fig. 2.21
during a normal day without clouds the upward part of the daily variation of the
temperature has higher gradient compared to the downward part, since during the
night there is no great loss of thermal radiation.
During the daily temperature variation in air the upper layer of the Earth’s
surface absorbs and emits the Sun’s radiation, which is responsible for the temper-
ature changes. During the night there is often a temperature inversion with an
increase of the temperature versus height since there is cooling of the Earth’s
surface with the emission of electromagnetic radiation with large wave length.
The difference between the maximum and minimum temperature during a day is
called daily thermal width. This is larger above the mainland and smaller above the

Daily Temperature profile

Maximum
Temperature

Minimum

Incoming Solar
Radiation

Outgoing Earth
Radiation
Energy rate

12 2 4 6 8 10 Noon 2 4 6 8 10 12
Time
Sunrise Sunset

Fig. 2.21 Daily changes of the temperature and incoming and outgoing radiation. When the
incoming Sun’s energy is higher than the outgoing energy then the air temperature increases.
Contrary when the outgoing energy is higher than the incoming then the air temperature decreases.
(Adapted from Ahrens 1994)
2.6 Atmospheric Temperature 97

seas due to the larger heat capacity of water. Its value decreases gradually from
equator to poles as the latitude increases.
In the northern hemisphere, over a year’s time, the temperature of air in
temperate regions shows a simple variation. The maximum occurs most of the
time above mainland during July and above sea during August. The minimum is
observed above mainland during February and above sea during March.
The difference between the mean temperature of the warmest and coldest month
of a year is called annual thermal width. This is larger above mainland and smaller
above sea and increases from the equator to the poles.
The first classification of climate is based on the annual thermal width:
l Tropical moist, when the annual width is smaller than 10
C.
l Temperate, when the annual width is between 10
C and 20
C and
l Moist mid-latitude climates with severe winters, when it is larger than 20
C.
A detailed characterization of climate is demonstrated by the Köppen classifica-
tion system (Ahrens 1994).
The air temperature is the most important climatic component and the most
important parameter for climate classification. Meteorologists and climatologists
examine temperature values at different elevations inside the atmosphere. When
someone refers to air temperature, they mean the temperature in shadow inside a
special shelter (meteorological cage) and at height 1.5–2.0 m above ground.
For mainly climatological reasons the air temperature in a given location can be
described with the following parameters:
l Average daily temperature (Tday ) which is defined from the expression
P
24
Td ¼ 24
1
ThðiÞ where Th(i) is the hourly value (i ¼ 1, 2, 3. . ., 24). This expres-
i¼1
sion is used when the meteorological station has the capability of hourly
temperature measurements. The expression which is used by the World Meteo-
rological Organization for the calculation of Td is: Td ¼ 14 ðT06 þ T12 þ 2T18 Þ,
(where 06, 12 and 18 are the time in UTC – Universal Time Coordination). The
use of this expression is adopted in cases where there is need to have direct
comparison between the meteorological values in an extensive geographical
area. For climatological use the data have to be extended for at least a period
of 30 years.
l Absolute maximum (Tmax) and minimum (Tmin) value of the air temperature
which occurs during a whole day (24 h).
l Average monthly temperature (Tmo ) which can be calculated from the expres-
Pv
sion Tmo ¼ v1 TdðiÞ , where v is the number of days during the month.
i¼1
l Daily thermal width. This is defined as the difference between the maximum and
minimum temperature value (M.T.V.) during 24 h: MTV ¼ Tmax - Tmin.
l Yearly temperature width (Y.T.W.). This is defined as the difference between
the average air temperature of the coldest month and the average temperature of
the warmest month during the year: Y.T.W. ¼TmoðwarmÞ - TmoðcoldÞ
98 2 First Principles of Meteorology

June
December

W
4:30
7:30

S N

7:30 E 4:30

Fig. 2.22 Variability of the Sun’s orbit at mean geographical widths at the northern hemisphere
(Adapted from Ahrens 1994)

Figure 2.22 shows the trajectory of the Sun at middle latitudes in the northern
hemisphere during a year. During winter the sunrise starts at the south-east and the
sunset occurs at south-west. During summer the sunrise occurs in the northeast and
the sunset in the northwest. Consequently a house with windows facing south
receives more light than a house with windows facing north. The same applies
more intensively for mountainous regions. Regions which are oriented to the south
receive more light and as a result tend to be warmer and drier than regions which are
oriented to the north. This has a direct effect on the flora of the region. Vineyards
which are located at areas oriented to the south produce a better quality wine.
On the contrary plants which withstand cold are located at areas oriented to the
north. The architecture of houses is also affected from the position of the sun and
considerable benefits for energy consumption are derived from an appropriate
orientation of houses and the rational use of windows (bioclimatic architecture).
Another example is the operation of ski resorts which have a north orientation.

2.6.3 Heating of the Earth’s Surface and Heat Conduction

Radiation from the sun is the main heat source for the Earth’s surface. The heating
of the surfaces and their temperature is dependent on a number of parameters such
as:
l The special heating (heat capacity) of a surface. By the term heat capacity is
meant the quantity of heat that is needed to increase the temperature of one gram
2.6 Atmospheric Temperature 99

of a given material by 1
C. Since the heat capacity of water is twice that of the
ground, then more heat is needed in order to increase the temperature of a water
surface by 1
C compared to the ground. As a result the ground becomes heated
(or cooled) more quickly compared to the sea. In comparison with the sea, the
ground is warmer during the day but it is cooler during the night.
l The absorbency of a surface. Everybody that receives a quantity of radiation
absorbs part of its energy. The percentage of absorption is dependent on the
body’s nature and the radiation.
l The reflectivity of a surface. If the total amount of the sun’s radiation is reflected
from a surface, there is no absorption or transformation to thermal energy. The
surfaces of snow and water have high reflectivity and are not heated, such as
surfaces with low reflectivity (e.g. cultivated areas, dense jungle etc.).
l The conductivity of a surface. The ocean streams transport large quantities of
heat (inside oceans) through the water movement. With this process the sea is
heated to a larger depth compared to the mainland.
l The cloud cover of a surface. A factor which plays a significant role in the
temperature of surfaces is the cloud cover, which during the day does not allow
penetration of the Sun’s radiation to the Earth’s surface (Fig. 2.23). This results
in a reduction of the Earth’s temperature. Therefore the air which is in contact
with the Earth’s surface will receive lower heating during the day. During the
night the cloud cover results in the opposite phenomenon since it does not allow
part of the thermal energy which it receives from the Earth to escape to space.
The atmosphere under clouds experiences lower cooling and therefore higher
temperatures occur.
The thermal energy is spread from one body to the next or re-distributed inside a
body in different ways. Some of these mechanisms are:
l The radiation. All bodies emit energy in the form of electromagnetic radiation.
Higher temperatures result in smaller wave length of the radiation. Consequently
the wave length of the Sun’s radiation is smaller than the re-emitted radiation
from the Earth’s surface which is much colder than the Sun’s surface.

Land
Land

Fig. 2.23 The cloud cover reduces the warming of the Earth’s surface during day and its freezing
during the night
100 2 First Principles of Meteorology

l The conductivity. The thermal energy can be conducted inside a body or from
one body to the other with contact through conductivity. For example iron is a
good conductor of heat, whereas the wood or air are poor heat conductors. An air
molecule which is in contact with the Earth’s surface is heated through conduc-
tivity. This is an important factor for creation of the weather phenomena.
l The heat transfer. A moving body of air transports also its thermal energy. The
heat transfer occurs vertically and horizontally inside the atmosphere and this
process is the most important for the weather phenomena.
a. Vertical heat transfer: An air mass which is heated on the Earth’s surface
starts to expand and then becomes less dense and ascends. With its uplift it
expands adiabatically and transfers its thermal energy at upper atmospheric
layers.
b. Horizontal heat transfer: An air mass moves horizontally to fill the gap of
air which is created from the vertical movement of another air mass. This air
mass which is moving horizontally transports together its thermal energy and
humidity.

2.6.4 Distribution of Temperature in the Air

The temperature distribution of air above a region (small, large or even above the
whole globe) is described with isothermal curves (lines with the same temperature
along them).
The most important factors which control the temperature distribution in air are:
l The season and the latitude
l The distribution of land and sea
l The vegetation and general nature of the surface
l The elevation
l The slope of the Earth’s surface
l The existence of snow or ice on the surface
l The cloud cover
l The prevailing winds and
l The sea streams.
Each of these parameters acts in a different manner and therefore the air
temperature does not decrease smoothly from the equator to the poles. The highest
temperatures are not observed at the equator but at latitudes 10
–20
south and
north from it. This is due to the fact that at the equator there are extensive clouds
and rainfall.
An important factor is the geographical distribution of land and sea. During
summer the land is warmer than the sea. The temperature increases mainly above
land. During winter the land is colder than the sea and therefore lower temperatures
2.7 Humidity in the Atmosphere 101

are observed above land at higher latitudes (e.g. North Canada, Siberia, Greenland).
Winds have a great influence on temperature distribution at different locations.
Therefore the west winds in northern temperate zones transport warm ocean air
masses to the west regions of Europe and America and cold air masses to the east
regions of America and Asia.
The constant ocean currents finally influence considerably the temperature distri-
bution. These are moving to the poles carrying warm water to colder regions, whereas
the currents moving to the equator transport cold water masses to warmer regions.

2.7 Humidity in the Atmosphere

The term humidity refers to the water vapour which is contained in the atmosphere
at a specific time. The air humidity is a very important parameter since it determines
the cloud formation and the rain formation.
The atmosphere and especially troposphere contains water vapour at variable
quantities which come mainly from water evaporation. The quantity of water vapour
that the air contains is specific and is dependent directly on the air temperature.
When the air contains the maximum quantity it is called saturated. When only a
part of the maximum quantity is contained, then it is called unsaturated. The term
humid air is often used when there is an elevated amount of water vapour in the
atmosphere. The term dry air is used in the absence of water vapour.
The water in the atmosphere is not only in the vapour phase but it exists also in
the liquid phase (cloud, rain) and in the solid (snow, drizzle). It is known that in the
atmosphere there is a water cycle. The water enters the air through evaporation
from all the water surfaces and especially from oceans. Therefore huge quantities of
water evaporate from the Earth’s surface and are moved higher in the atmosphere
and are condensed forming extensive cloud layers. Further, the clouds are trans-
ported to other regions and through wet deposition the water comes back to the
Earth’s surface.
Taking into account that 23 of the planet are covered by water, millions of tons of
water are evaporated daily and are moved to the upper troposphere in the form of
water vapour. The 84% of water vapour originates from oceans whereas the other
16% originates from lakes, rivers, wet surfaces, vegetation and the expiration of
animals.
Every year the planet receives from water precipitation (e.g. rain, snow) 400 km3
of water. An equal quantity is introduced to the air through evaporation. Of the total
water precipitated on the Earth’s surface, close to 100 km3 precipitate on land and
the other 300 km3 on oceans and water surfaces. Evaporation of 400 km3 water into
the atmosphere during 1 year requires 3  1029 cal. This energy corresponds to 23%
of the total energy which the Earth receives during a year from the sun.
The water in the atmosphere can change from one phase to another and for the
water condensation the atmosphere has to be saturated (relative humidity equal to
100%). However in specific cases there is no condensation even at relative humidity
102 2 First Principles of Meteorology

above 100%. This is due to the absence of a sufficient number of available

condensation nuclei in the atmosphere. Without these nuclei, a relative humidity
close to 420% is required in order for condensation to occur. Existence of sufficient
condensation nuclei will lower the relative humidity required for condensation to
100%. With the presence of nuclei of sodium chloride the necessary relative
humidity for condensation is close to 97%, whereas for sulphur oxide or phosphate
oxide nuclei the relative humidity drops to 80%. Therefore in industrial regions the
dense fog is a consequence of the existence of a large number of condensation
nuclei. To the contrary, the number of condensation nuclei drops at higher eleva-
tions in the atmosphere.
As the water vapour condenses onto condensation nuclei, droplets or ice crystals
form and with time their size increases. The formation of droplets or ice crystals is
dependent on the temperature and pressure. At higher elevations where the temper-
ature is far below 0
C and the pressure is also low, the water exists in the liquid
phase. This is an unstable condition which is called super critical melting. When
this unstable condition of water is disturbed by the passage of an aircraft, there is an
immediate icing of the water droplets above the airframe and the wings which has
consequences for the flight. Water at super critical melting exists at temperatures up
to 15
C and, though less often, at 40
C. The most dangerous region is between
0
C and 15
C.
Generally the percentage of water vapour which comes from water evaporation
from the soil is about 15% of the total water vapour which exists in air. The other
85% comes from the oceans. It is surprising to think that if the total amount of water
in the atmosphere precipitated simultaneously onto the Earth’s surface, it would
cover the whole surface of the planet to a height of 2.5 cm.
Figure 2.24 shows the average spatial distribution of rainfall in Europe during
the period 1940–1995. Lower values are observed in Southern Europe.

2.7.1 Mathematical Expressions of Humidity in the Atmosphere

The term humidity refers to the water content inside air. We present here some
different methodologies that can describe this phenomenon.

2.7.1.1 Absolute Humidity (B)

Absolute humidity b is defined to be the ratio of a mass of water vapour to the air
volume in which the mass is contained. Absolute humidity denotes the density of
water inside an air volume and usually is expressed as grams of vapour inside a
cubic meter of air. For example if the water vapour inside a cubic meter of air
weights 25 g, then the absolute humidity b of air is 25 g/m3.
The air volume changes with fluctuations of its elevation due to differences in air
pressure. This results in changes in absolute humidity even though the quantity of
2.7 Humidity in the Atmosphere 103

–30 ° –20 ° –10 ° 0° 10 ° 20 ° 30 ° 40 ° 50 ° 60 ° 70°

Average annual
precipitation,
60 °
1940-1995

–30 °
mm
60° 1 - 300
300 - 500
60°
500 - 800
800 - 1.000
1.000 - 1.600
1.600 - 4000
50 ° No data
Outside data
50°
coverage

50°

40 °

–10 °

0° 10 ° 20 ° 30 ° 40 °

Fig. 2.24 Map of the spatial distribution of precipitation (mm) in Europe in the period 1940–1995

water vapour inside the volume remains constant. For this reason the term absolute
humidity is not often used in atmospheric sciences.

2.7.1.2 Specific Humidity (Q)

Specific humidity q is the ratio of the water vapour of the mixture divided by the
total air mass and is expressed as water vapour grams per gram of humid air.

2.7.1.3 Mixing Ratio (R)

Mixing ratio is the ratio of water vapour to the mass of dry air.

2.7.1.4 Relative Humidity (RH)

Relative humidity of the atmospheric air is called the ratio of the water vapour mass
which is contained in a specific air volume to the mass of the water vapour in the
same volume under saturation conditions at the same pressure and temperature
conditions. The relative humidity is actually the ratio of water vapour pressure to its
equilibrium pressure at the same temperature. Therefore the relative humidity can
be expressed as
104 2 First Principles of Meteorology

pH 2 O
RH ¼ 100 ; (2.34)
po H2 O

where the multiplication by 100 occurs since RH is expressed in percentage.

The relative humidity is an important parameter which is involved directly in the
daily life of humans. An example is the study of the transfer of cold outdoor air to
indoors. Dry arctic air incorporates small quantities of water vapour. Saturated air at
temperature 25
C includes only 0.5 g of water vapour per 1 kg air. When this air is
introduced indoors at temperature 20
C, then its capacity to incorporate water
vapour increases by 29 times to the value 14.7 g/Kg. This results in relative
humidity indoors of

0:5 g=Kg
RH ¼ 100  ¼ 3% (2.35)
14:7 g=Kg

Low levels of humidity have direct results on the quality of life indoors. Plants
which exist indoors become dry due to the fast evaporation of the humidity from the
soil. Furthermore, human skin becomes dry, there are effects on the nose and the
larynx, and bacteria can be more easily introduced into the body.
High values of relative humidity on warm days during summer result in respira-
tory problems for sensitive members of the population, especially older people and
children. When the temperature is high, the main path for lowering of body
temperature is through sweating. In the case of low air humidity, evaporation of
sweat from the skin occurs quickly and the temperature feels lower than its actual
value. In the case of high air humidity, sweating is difficult and the body cannot
easily reduce its temperature.

2.7.2 Dew Point

The dew point denotes the temperature at which the air has to be cooled without
changes of pressure and humidity in order to have saturation. The dew point is an
important parameter which is used for the prognosis of ice and fog. At ground level
there is no considerable variation of atmospheric pressure and as a result the dew
point corresponds to the humidity quantity in air. High values of the dew point
indicate a high humidity content and low values of the dew point indicate low
humidity content.
The difference between the air temperature and the dew point indicates if the
relative humidity is high or low. When the air temperature and the dew point are
equal the relative humidity is 100%. This occurs during a snow storm. But the air in
a desert area, where there is a large difference between the air temperature and the
dew point, has quite low relative humidity. It is interesting to note that the desert air
with a higher dew point contains more water vapour than the air in a snowstorm.
2.7 Humidity in the Atmosphere 105

There are different phenomena, other than the dew phenomenon, which are
related directly with the water vapour condensation. An example is fog formation.
When water vapour condenses, visibility is reduced due to growth in size of the
atmospheric particles. The size of the fog droplets further increases when the relative
humidity is high and the droplets become visible. When the visibility is reduced to
less than 1 km, a cloud appears close to the Earth’s surface and this is called fog.
The air above urban areas is usually polluted with elevated concentrations of
airborne particles. Therefore the fog above urban areas is denser than above the sea
under the same atmospheric conditions. Examples include the dense fog which was
formed above London in the 1950s. The fog was so dense that the Sun’s rays could
not penetrate the air and it was necessary to use lamps during the day. The fog can
be acid when there are interactions with gaseous pollutants such as sulphur and
nitrogen oxides. Furthermore, acid fog has negative consequences to the public
health and especially to people with breathing problems.
Fog is formed during evaporation processes, when cold air comes into contact
with warm quantities of water vapour. The fog consists of small droplets which are
produced from the water vapour condensation at layers of air close to the Earth’s
surface. A fog is therefore a cloud which is formed in stable layers of air and its base
is usually the Earth’s surface.
Necessary conditions for the occurrence of fog are:
l small difference between temperature and due point (large relative humidity)
l presence of condensation nuclei
l weak surface winds
l cold Earth’s surface with warm and humid air above or warm sea and cold air above.
Usually the fog is formed in coastal areas where the humidity is elevated and
also in industrial areas where there is increased concentration of airborne particles
which serve as condensation nuclei.
The occurrence of fog is a result of two main phenomena:

2.7.2.1 The Evaporation of Water at Cold Air

One phenomenon is called evaporation fog and occurs close to the sea surface (or
lake), when the air temperature is very low and there is a large temperature difference
between sea and air. Its formation is due to the quick evaporation of the sea (or lake)
water, and its surface resembles the view of a large boiler that emits large quantities of
vapor which are condensed quickly inside the cold air. The layer of fog is small and
seldom reaches 30 m and also the visibility changes are highly variable.

2.7.2.2 The Freezing of Humid Air

The fog which is formed with freezing of humid air can be divided into different
categories such as radiation fog, advection fog, mixing fog and sea smoke. Different
106 2 First Principles of Meteorology

mechanisms are responsible for these effects. For example the radiation fog is formed
during the night without clouds, with a light wind, when a thin layer of humid air is
located close to the Earth’s surface and under a layer of dry air. The thin layer of
humid air does not absorb adequate infrared radiation from the Earth’s surface and
freezes quickly, while and at the same time it freezes the dry air above. When the
temperature equals the dew point, then the condensation of water vapor starts and
consequently also the formation of droplets and the fog formation. The interested
reader can consult the book by Ahrens (1994) to study the different forms of fog.

2.7.3 Clouds in the Atmosphere

We explained previously that adiabatic processes together with ascending warm air
from the surface results in its expansion and cooling. The unsaturated air mass is
cooled adiabatically with a rate close to 1
C/100 m. When the air is colder, it
contains smaller quantities of water vapour. Therefore the air mass which ascends
and becomes cooler has also an increase of its relative humidity. At the height at
which the temperature of the air mass is equal to the dew point (when the relative
humidity reaches 100%) the excessive water vapour starts to condense with the
formation of small droplets. The formed droplets coagulate and forms larger
droplets. Note that an average rain droplet consists of about 103 water droplets.
Finally a very extensive number of water droplets form a cloud.
The cloud formation occurs with: (1) radiation of heat from an air mass to the
environment, (2) with the air transport to a cooler region and (3) adiabatic rise of an
air mass. Figure 2.25 shows the steps in the formation of clouds during adiabatic
cooling of warm air masses from the Earth’s surface.
As the saturated air mass continuous to rise it will be further cooled with increase
of the quantity of water droplets and the cloud size. The temperature lapse rate is
not equal to the dry lapse rate since the air mass receives the latent heat which is
released from the water vapour during the condensation process. Therefore the
temperature drop of the ascending saturated mass is close to 0.5
C/100 m which is
known as wet lapse rate.
It is accepted that most clouds are formed with adiabatic cooling which occurs
inside air masses when they ascend inside the atmosphere. The ascending move-
ment of air masses is due to:
l The vertical air transport after intense surface heating,
l The impact of air masses on mountains,
l The convergence of air masses due to barometric systems,
l The movement of air at the warm and cold fronts.
For the formation of clouds it is not enough to have only adiabatic cooling but it
is necessary that condensation nuclei exist in the atmosphere. The water vapour
condensation can occur on the surface of soluble (such as NaCl) or insoluble
particles (such as dust or diesel particles) and on ions in the atmosphere.
2.7 Humidity in the Atmosphere 107

I. Patch of ground, warmed II. Warm air bubble

by sun, heats overlying air. begins to rise.

rising cloud
air bubble
dew point

III. Air bubble detaches IV. Air bubble cools to dew

and continues to rise. point and cloud forms.

temperature
IV. Air in cloud rises
of surrounding
at wet adiabatic lapse rate.
air
Altitude (ft)

wet
adiabatic dew point,
lapse rate cloud forms

II., III. Air bubble rises at dry

dry 5.4 ºF adiabatic lapse rate.
adiabatic
1000 ft I. Air near ground warmed by
lapse rate
radiation-absorbing surface.
Temperature

Fig. 2.25 Schematic representation of cloud formation in the atmosphere with adiabatic cooling
of a warm air volume from the Earth’s surface (Adapted from Hemond and Fechner 2000)

2.7.4 Precipitation

The term precipitation refers to all condensation products of water that fall from the
atmosphere as rain, snow, hail and soft hail. The formation of precipitation inside
clouds is determined from the air temperature and the turbulence conditions in the
atmosphere. Precipitation is one of the most important meteorological and climato-
logical parameters. During precipitation a factor which is important to be studied is
the water quantity that drops on a surface and is referred to as rainwater. This
108 2 First Principles of Meteorology

quantity expresses the rainwater height (more commonly referred to as depth) on a

horizontal surface and is measured with a rain-gauge. Another useful parameter in
climatology is the rain intensity which expresses the resulting rainwater height per
unit time. Internationally the measurement unit of rainwater height is mm or cm.
For example 1 mm rainwater expresses a water quantity of 1 kg water per 1 m2
surface.
In respect to the droplet size and precipitation conditions, rain has different
names such as “shower” which is produced from clouds of vertical development
and has sudden starts and stops as well as abrupt changes in intensity. Drizzle is
characterized by small and many droplets which are suspended and follow the air
currents.
For the study of the water precipitation in a region it is necessary to consider the
following parameters:
l Average Monthly Precipitation (A.M.P.): The average total water precipitation
per month (T.P.). For example the average total water precipitation in January in
the period 1959–2004 is equal to the summation of the total January precipita-
tion per year divided by the total number of observation years:

T:P:ðJAN1959Þ þ T:P:ðJAN1960Þ þ ::::::::::::: þ T:P:ðJAN2004Þ

A:M:P:ðJANÞ ¼
46
(2.36)

l Total maximum precipitation of 24 h (T.max.P.24 h): The maximum water

precipitation during 24 h. The maximum water precipitation is observed and
logged during 24 h in a period of 1 month for the total number of observation
years. This value is possible to be characterized as extreme and it is important to
know the year that it occurred. The T.max.P.24 h has to be considered for the
occurrence of floods.
l Average Precipitation Days (A.P.D.): The average number of days in a month at
which there is water precipitation. The minimum water amount which is neces-
sary to precipitate in order to be considered as water precipitation is different
among countries but are generally close to 0.1 mm. For example for the
calculation of the average precipitation days of January in the period
1959–2004 are equal to the summation of the precipitation days per year divided
by the total number of observation years:

P:D:ðJAN1959Þ þ P:D:ðJAN1960Þ þ ::::::::::::: þ P:D:ðJAN2004Þ

A:P:D: ¼
46
(2.37)

The atmosphere is a dynamic system and changes in the form of precipitation

can occur during transport from its origin to the Earth’s surface. Figure 2.26 shows
some physical processes which can be associated with precipitation.
2.7 Humidity in the Atmosphere 109

Altitude

snowflakes

water droplets

sleet pellets

–10 C 0C 10 C

Fig. 2.26 Snowflakes originating from a cloud can melt during their downward movement when
they encounter a warm layer of air and after can freeze again and form sleet pellets when they meet
a colder air layer

2.7.5 Study of Precipitation Scavenging

There are several ways for precipitation to occur as discussed in the current chapter.
The most common ones are through rainfall and snowfall. The flux of gasses and
particles from the atmosphere to the Earth’s surface through rain can be defined as
(Seinfeld and Pandis 2006)

i
Wgas=rain ¼ Lig Ci;gas ; (2.38)

i
Waeros=rain ¼ Lip Ci;part ; (2.39)

where Lig and Lip are the scavenging coefficients for the components i for the
gaseous and particulate phase respectively. The total scavenging Fbc(t) (Kg m2
h1) under clouds, when the concentration of the pollutants exists in a horizontally
homogeneous atmosphere, is Cg(z,t); then it results that
Z h
Fbc ðtÞ ¼ Lg ðz; tÞ Cg ðz; tÞ dz; (2.40)
0
110 2 First Principles of Meteorology

where h is the height of the cloud base and Lg is the scavenging coefficient which is
dependent on time (s1). The total scavenging is the sum of the scavenging inside
the clouds (washout) and under the clouds (rainout). For a homogeneous atmo-
sphere under the clouds it can be written that
Z h
Fbc ðtÞ ¼ Cg ðtÞ Lg ðz; tÞ dz ¼ Lg h Cg ðtÞ; (2.41)
0

where Lg is the average value of the scavenging coefficient.

The washout ratio can be defined as

Ci;precip ðx; y; 0; tÞ
wr ¼ ; (2.42)
Ci;air ðx; y; 0; tÞ

where Ci,pecip(x,y,0,t) is the concentration of component i which is contained inside

the rain at the Earth’s surface and Ci,air(x,y,0,t) is the concentration of component i
inside the air at the Earth’s surface. Therefore the flux Fw of the wet scavenging can
be expressed as (Seinfeld and Pandis 2006)

Fw ¼ Ci;precip ðx; y; 0; tÞ po ; (2.43)

where po is the rain intensity (mm h1). For light rain the rain intensity is equal to
po ¼ 0.5 mm h1, whereas for heavy rain po ¼ 25 mm h1. Furthermore, the
velocity of wet deposition can be defined as uw ¼ Ci;air ðFx;y;0;t
w
Þ:
In meteorology the rain is defined when the descending droplets have a diameter
larger than or equal to 0.5 mm. After an intense rain there is usually better visibility
since rain is scavenging a large number of particles. The rain has also the ability to
absorb water soluble chemical components and remove them from the atmosphere.
It is important to calculate the scavenging rate of gaseous components in the
atmosphere based on knowledge of the rain’s characteristics such as density and
droplet size, as well as from the physico-chemical characteristics of the gaseous
species.
The transfer of gasses on the droplet surface can be calculated from the
expression


Wt ðz; tÞ ¼ Kc Cg ðz; tÞ  Ceq ðz; tÞ ; (2.44)

where Kc is the coefficient of mass transfer (cm s1), Cg is the concentration of the
pollutant under study in the gaseous phase and Ceq its concentration on the droplet
surface which is in equilibrium with the concentration in the aqueous phase.
Using Henry’s law we can derive that


1
Ceq ¼ Caq ; (2.45)
H
2.7 Humidity in the Atmosphere 111

where, H is Henry’s coefficient and Caq is the pollutant concentration in the aqueous
phase.
Consequently the equation (2.44) can be written as


Caq ðz; tÞ
Wt ðz; tÞ ¼ Kc Cg ðz; tÞ  : (2.46)
H

The coefficient of mass transfer from molecules in the gaseous phase to the
droplet can be calculated from the expression (Seinfeld and Pandis 2006)
"

 #
Dg rair Ut Dp 1=2 mair 1=3
Kc ¼ 2 þ 0:6 ; (2.47)
Dp mair rair Dg

where, Dp is the droplet diameter, Dg is the diffusivity in the gaseous phase, rair is
the air density, mair is air viscosity and Ut is the droplet velocity. In the above
equation the term Sh ¼ Kc Dp/Dg is the Sherwood number, Re ¼ rair Ut Dp/mair is
the Reynolds number and Sc ¼ mair/rair Dp is the Schmidt number. The concentra-
tions Caq and Cg are functions of height and time.
In addition to precipitation occurring under clouds, transport of chemical com-
ponents to rain droplets can occur inside clouds. Gaseous species such as HNO3,
NH3, and SO2 can be absorbed inside rain droplets. If the concentration of particles
inside a cloud is equal to N(Dp) then the transfer rate of a gas Wic which has larger
concentration in air than in the liquid phase (e.g., HNO3) is given by the expression
(Seinfeld and Pandis 2006)
Z 1

Wic ¼ Cg Kc p D2p N Dp dDp ¼ L Cg ; (2.48)
0

where L is the scavenging

 rate. A typical concentration of droplets can be given
by the expression N Dp ¼ a ebDp where a ¼ 2.87 cm4, b ¼ 2.65 cm1 at
Dp ¼ 5–40 mm. With a replacement in equation (2.48) it can be concluded that
L ¼ 0.2 s1 for a cloud which consists of 288 droplets/cm3. The above calculations
denote that the processes which transfer chemical species at droplets are very fast,
of the order of a few seconds in comparison with the transport of the chemical
species inside a cloud or with changes of the ratio of condensation and evaporation.
Several chemical species, such as SO2 are not absorbed directly from rain droplets.
Their absorption is dependent on other factors such as the presence of other
chemical species inside droplets and the pH of the water. In addition to the
absorption of gaseous species there is also absorption of particles inside clouds.
A common process is the increase of particle size through absorption of water
vapour and coagulation with other particles.
112 2 First Principles of Meteorology

2.8 Applications and Examples

Example 1. An air volume is rising adiabatically from height z1 to z2. Prove that
the relationship between temperature and pressure at two different heights in the
h iðg1Þ=g
atmosphere are TT ððzz21 ÞÞ ¼ ppððzz21 ÞÞ :

From the theory it is known that

dT m R T=Mair p
¼ ;
dp Cu þ mR=Mair

where

^ ^ R
cc¼
p u Mair

And
^
cp
g¼^ :
cu
Therefore:



dT mR mR dp dT R ^ R dp
¼ = cu þ ) ¼ = cu þ
T Mair Mair p T Mair Mair p
Z T ðz2 Þ Z pðz2 Þ



dT g  1 dp T ðz2 Þ g1 pðz2 Þ
) ¼ ) ln ¼ ln :
T ðz1 Þ T pðz1 Þ g p T ðz1 Þ g pðz1 Þ
 
T ðz2 Þ pðz2 Þ ðg1Þ=g
Finally: ¼ :
T ðz1 Þ pð z 1 Þ
If z1 is the height of the Earth’s surface and air volume, which is initially at conditions
T, p is rising adiabatically to pressure po, then the temperature y at pressure po is
 ðg1
g
Þ

given by the relation y ¼ T po p

and is called potential temperature
Example 2. Show that if the atmosphere is isothermal, then the temperature
change of the temperature of an air volume
0
which, ascending adiabatically, is
given by the expression TðzÞ ¼ To eG z=To where To and To0 are the temperatures of
the air volume and the atmospheric air at the surface respectively. G ¼ ^g :
cp
For the air volume (T0 is the air temperature and T is the temperature of the air
volume under study) we have

dp Mair g p
¼ :
dz R T0
2.8 Applications and Examples 113

For the air volume which is ascending we can write that

dz T
dT m R T=Mair p dT dp T 0
¼ ) ¼ m g
dp Cu þ mR=Mair dp cu þ m R=Mair

dz ¼ G T 0 :
which results in dT T

With the integration of the above expression it follows that


RT Rz G0z
dT
To T ¼ 0 G Tdz0 ) ln TTo ¼  TG0 z ) TðzÞ ¼ To e To
:
o

Example 3. Concentrations of two gaseous species (N1 ¼ 8 kai N2 ¼ 4)

with velocities (u1 ¼ 3 and u2¼1) have been measured at two different
points at specific times. Calculate the following variables:
0 0 0 0 0 0
N; N1 ; N2 ; u; u1 ; u2 ; u N ; u N; u N:
Using the expressions for the average and instant values it can be written that

N ¼ ðN1 þ N2 Þ=2 ¼ 6;
0
N1 ¼ N1  N ¼ 2;
0
N2 ¼ N2  N ¼ 2;
 0 0 0 0

u0 N 0 ¼ u1 N1 þ u2 N2 =2 ¼ 4;

u N ¼ u N þ u0 N 0 ¼ ðu1 N1 þ u2 N2 Þ=2 ¼ 10 :

u ¼ ðu1 þ u2 Þ=2 ¼ 1;
0
u1 ¼ u1  u ¼ 2;
0
u2 ¼ u2  u ¼ 2;

u N ¼ 6:

Example 4. A meteorological station measures with anemometers the components

U and W of the wind. Velocity measurements have been performed every 6 s for
1 min. The measurements are given in the following 10 pairs:
114 2 First Principles of Meteorology

U (m/s) 5 6 5 4 7 5 3 5 4 6,
W (m/s) 0 1 1 0 2 1 2 1 1 1.
Calculate the average value and dispersion of each component of the velocity, as
well as the correlation coefficient between U and W.
Using the expressions for the average and correlation coefficient values, the
following values can be written.

U ¼ 5 m s1

W ¼ 0 m s1

s2U ¼ 1:20 m2 s2

sU ¼ 1:10 m s1

s2W ¼ 1:40 m2 s2

sW ¼ 1:18 m s1

u0 w0 ¼ 1:10 m2 s2

r UW ¼ 0:85

From the above expressions can be concluded that the turbulence component of
velocity W is higher than the U component even if the average value for the velocity
W is zero. From the negative value of the correlation coefficient ruw it can be
concluded that the variations of the components U and W are occurring mainly in
opposite directions.
Example 5. The concentration of a gas A is equal to 10 mg m3 under a cloud.
Suppose that the washout coefficient is constant and equal to 3.3 h1. Calculate the
concentration of gas A in the atmosphere after 30 min of rain and the total flux of
the wet deposition. The cloud base is 2 km (Adapted from Seinfeld and Pandis,
2006).
The concentration variability can be expressed as

@C
¼ Wair=rain þ R þ E;
@t

where since there no emissions or chemical reactions (R ¼ 0, E ¼ 0) it can result

that
2.8 Applications and Examples 115

@C
¼ L C;
@t

where L is the washout coefficient. The solution of the equation gives

C ¼ Co eLt :

After 30 min the resulting concentration is equal to C ¼ Co  0.19 ¼ 1.9 mg m3.

Therefore, Co-C ¼ 8.1 mg m3 and the total flux for a column of 2 km is equal to
8.1  2,000 ¼ 16.2 mg m2.
Problems
2.1 It is proposed that the problem of air pollution in the city of Los Angeles can be
solved by digging tunnels in the surrounding mountains and pumping the air outside
to the surrounding areas which are mainly deserts. Calculate the energy that would
be needed for the transport of air from Los Angeles. Los Angeles covers an area of
4,000 km2 and the polluted air is located under the boundary layer which has an
average height of 400 m. The viscosity coefficient of air which is transported above
the Los Angeles area is 0.5 and the minimum energy which is required for the air flux
is equal to the energy which is consumed from the surface friction. Calculate the
energy which would be required for an air mass transport with velocity7 km/h.
Compare the result with the capacity of Hoover Dam (power station of energy
production) which is equal to 1.25  106 KWh.
2.2 The value of the vertical temperature lapse rate in an area is equal to5
C/km
and the temperature of air on the surface is equal to 20
C. If an insulated balloon
full of dry air with temperature 50
C is allowed to ascend from the surface, then
calculate the height which the balloon can reach (the balloon temperature lapse
rate is equal to gd ¼ 10
C/km).
2.3 Simultaneous measurements of the air temperature at four points A,B,G and D
which are located downwind of a mountain chain are the following:

Locations A B G D
Height (m) 1,530 1,396 690 378
Temperature (T) (oC) 6.3 6.9 11.9 14.4

Calculate the value of the vertical lapse rate between the positions (a) D G, (b) G B,
(c) B A and (d) D A. Additionally make a comparison of the mean value of the
vertical lapse rate above the mountain chain with the corresponding value of
6.5
C/km and determine the difference.
2.4 A potential temperature Y is determined under the hypothesis of adiabatic
processes. Changes in entropy can be connected with changes in temperature and
pressure with the expression



@S @S
dS ¼ dT þ dp:
@T P @P T
116 2 First Principles of Meteorology

a. Show that
c

p R dp
dS ¼ dT  :
T Ma p

b. During adiabatic conditions (dS ¼ 0) show that dY ¼ 0 and

Y ¼ const tan t  p ðg1
T
Þ:
g

2.5 In an urban area, the air temperature at 07:00 after a cloudless night in
January is equal to 0
C. The height of a temperature inversion was h ¼ 0 and its
depth d ¼ 100 m. Calculate at which height from the inversion base (surface) it will
be the same air temperature, if the value of the vertical temperature lapse rate
is  (yT/yz) ¼ 5
C/km and the intensity of the inversion is equal to 0.1
C/10m.
2.6 Calculate the concentration (mole/cm3) and the mixing ratio (ppm) of water
vapour at the Earth’s surface for temperature equal to T ¼ 298K and relative
humidity RH 50%, 60%, 70%, 80%, 90%, 95%, 99%. The water vapour pressure of
pure water (saturation pressure) versus temperature is given by the expression

poH2 O ðTÞ ¼ ps  exp½13:3185a  1:976a2  0:6445a3  0:1299a4 ;

where:

ps ¼ 1013:25mbar

and


373:15
a¼1 :
T

2.7 The prognosis of the daily atmospheric temperature structure under non-
variable conditions is examined here. In this case it is necessary to examine the
spatial temperature changes only in the vertical direction. It is assumed that the
radiation absorption from the atmosphere is negligible and the dynamic tempera-
ture y can be determined from the expression


@y @ @y
¼ K : (2.49)
@t @z @z

In the above expression it is assumed that K has a constant value. It is also assumed
that at elevated heights the temperature profile is the same with an adiabatic rate
equal to

y!0 when z ! 1: (2.50)

References 117

The temperature at the surface (z ¼ 0) is dependent on the Sun’s heat during the
day and the cooling at night is due to radiation emission. Therefore y(0,t) can be
expressed as

yð0; tÞ ¼ A cos ot: (2.51)

where A is the width of the daily variation and o ¼ 7.29 w 105 s1.
A) Show that the solution which satisfies the equations (1  3) is

yðz; tÞ ¼ A ebz cosðot  bzÞ;

pffiffiffiffiffiffiffiffiffiffiffiffi
where b ¼ o=2K . The above solution is called a steady-state solution and
describes the temperature dynamics which correspond to the influence of equa-
tion 3.
B) Show that the height H which expresses the base or the top of a temperature
inversion is given by the expression

g
sinðot  bHÞ  cosðot  bHÞ ¼ ebH :
Abb
cp

Is it possible to have more than one temperature inversion ?

Show that @y @T
@z ¼ @z þ G
where G ¼ : g
bcp
2.8 It is observed in an area that the atmospheric temperature is decreased by 14 K
between the Earth’s surface and height of 2 km above it. What is the vertical lapse
rate and how does it compare with the dry and wet lapse rate ? Calculate the
atmospheric stability conditions under the above conditions.

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Finlayson Pitts, B. J., & Pitts, J. N. (2000). Chemistry of the upper and lower atmosphere. San
Diego: Academic Press.
Hanna, S. R., Briggs, G. A., & Hosker, R. P. (1981). Handbook on atmospheric diffusion, technical
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Hemond, H. F., & Fechner-Levy, E. J. (2000). Chemical fate and transport in the environment. San
Diego: Academic Press.
Housiadas, C., Drossinos, I., & Lazaridis, M. (2004). Effect of turbulent fluctuations on binary
nucleation. Journal of Aerosol Science, 4(35), 545–559.
118 2 First Principles of Meteorology

Lioy, P. J. (1990). Assessing total human exposure to contaminants. Environmental Science and
Technology, 24, 938–945.
Seinfeld, J. H., & Pandis, S. N. (2006). Atmospheric chemistry and physics (2nd ed.). New York:
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Stull, R. B. (1997). An introduction to boundary layer meteorology (pp. 199–202). London:
Kluwer Academic Publishers.
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