Chapter – I Introduction and Outline of Introduction and Outline of Introduction and Outline of Introduction and Outline of

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Chapter I

Introduction and Outline of Research work

1.1 The Earth’s Atmosphere

The Earth’s Atmosphere is the gaseous envelope surrounding the planet.

In one way or another, it influences everything we see and hear—it is intimately

connected to our lives. Air is with us from birth, and we cannot detach ourselves

from its presence. In the open air, we can travel for many thousands of

kilometers in any horizontal direction, but should we move a mere eight

kilometers above the surface, we would suffocate. We may be able to survive

without food for a few weeks, or without water for a few days, but, without our

atmosphere, we would not survive more than a few minutes. Just as fish are

confined to an environment of water, so we are confined to an ocean of air.

Anywhere we go, it must go with us. It determines the environment in which we

live. It shields us from hazardous short-wave radiations from the sun, from

gamma rays through to the ultraviolet. It controls the temperature on the surface

that sustains our life on earth. We must be concerned about both its fragility and

variability, as they could affect the very core of our daily life.

Benjamin Franklin observed that ‘some are weatherwise, some are

otherwise’. Many of us fall into the latter category. Perhaps this is not surprising,

because the behavior of the atmosphere is quite complex. Yet everyday we all

make decisions which are influenced by the weather. For this reason we should

understand something of how the atmosphere works. When we speak of the

‘earth’s atmosphere’, we mean the combination of the gases and particles that

surround the globe. Compared with the size of the earth it is merely a thin skin

(like fuzz surrounding a peach) but in reality, it has a nominal thickness of about

500 km. Within this distance four distinct layers occur which are characterized

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by alternating temperature decrease and increase. Although our life is directly

linked to the processes occurring in the troposphere, the atmosphere operates as

a single entity and there are regions of the atmosphere that show very sensitive

response to change. Human activities affect the atmosphere by pollution since

the beginning of industrial revolution. This man-made anthropogenic forcing

influence the atmosphere not only in the troposphere, its influence is detectable

even in the thermosphere, up to heights of several hundred kilometers above

surface, and changes climate in the whole atmosphere [1] Life on Earth is more

directly affected by climate change near the surface than in the middle and upper

atmosphere, but as the story of the Earth’s ozone layer illustrates, changes at

higher levels of the atmosphere may be important for life on Earth, as well [2].

The investigation of these strategic regions is important to understand the factors

involved in atmospheric variability. New understanding will lead to better

models, and more accurate prediction which can affect our survival.

A convenient method of classifying the Earth’s atmosphere is to use its

vertical temperature structure. The vertical temperature structure is unlike the

vertical pressure structure which decreases in height continuously from the

ground up into space. Temperature alternates from the ground upwards between

decreasing and increasing layers (see Figure 1.1), giving rise to four distinct

regions. These regions in increasing height are termed the troposphere,

stratosphere, mesosphere and thermosphere.

The varying shape of the temperature structure is due to the combined

effects of solar irradiation, atmospheric dynamics and atmospheric photo-

chemistry. Sunlight is absorbed at the surface of the Earth, and then re-emitted at

infra-red wavelengths. Water vapour and clouds can absorb some of this infra-

red radiation, as can CO2 and other “greenhouse gases”. This causes the

“greenhouse effect”, where the Earth’s surface and the layer of air adjacent to it

are 20-30 K higher than the blackbody temperature of the Earth as detected from

space.

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A static planetary atmosphere can be described by four major properties:

Pressure (P), density (ρ), temperature (T) and composition. Since these are not

independent, but are related by the gas law:

PV = NRT (1.1)

It is not necessary to specify all of them. Mainly basing on the chemical

composition, temperature and dominant physical processes atmosphere is

characterized into different regions named as “spheres” and the boundaries

between them as “pauses”.

The atmosphere is conveniently divided into four layers based on its

thermal structure as displayed in Figure (1.1).

1) Troposphere (from ~0 km to ~15 km)

2) Stratosphere (from ~15 km to ~50 km)

3) Mesosphere (from ~50 km to ~90 km)

4) Thermosphere (~90 km to ~ 400 km)

1.1.1 Troposphere

This first layer above the Earth’s surface contains 90% of the Earth’s

atmosphere and 99% of the water vapor. The gases in this region are

predominantly molecular Oxygen (O2) and molecular nitrogen (N2).

Temperature in this region rapidly and almost linearly decreases with altitude,

from an average of 291 K at the surface to a minimum value about 218 K at the

top, which defines its upper boundary, tropopause. The rate of change of

temperature with height is about -6.5 K km-1 in the troposphere. The spatial and

temporal variation of the surface emission and absorption causes turbulence and

convective cells in the troposphere. The negative temperature gradient means

that an air parcel that cools adiabatically due to its expansion as it rises can still

be warmer than its surroundings. Since the air parcel is warmer than the

surrounding air it will continue to rise, leading to a strong mixing of the

troposphere due to this convective process. The region where temperature stops

decreasing and starts increasing or vice versa is called ‘pauses’. The “tropos”,

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which means “turning” in Greek. It is an appropriate name, because air in the

troposphere constantly undergoes convection. The heat that initiates movement

in the tropopause comes primarily from reflected IR radiation from the earth’s

surface. The radiation heats air at the base of the troposphere. This air then rises,

and cold air sinks to take its place. This movement causes most weather

phenomena, so the troposphere can also be thought of as the “weather layer”.

Atmospheric weather is a state of the atmosphere at any given time and

place. Weather occurs because our atmosphere is in constant motion. Weather

changes every season because of the earth’s tilt when it revolves around the Sun.

Some determining factors of weather are temperature, precipitation, fronts,

clouds, and wind. Other more sever conditions are hurricanes, tornadoes, and

thunderstorms. Clouds and storms form when pockets of air rise and cool [3].

1.1.2 Stratosphere

The stratosphere begins above the tropopause and is defined as the height

where the temperature starts to increase with increasing height. This increase in

temperature with height is due to the absorption of ultraviolet (UV) solar

radiation by ozone [4]. Temperatures range from about 220 K at about 20 km, up

to about 270 K at about 50 Km. This positive temperature gradient inhibits

convection (this region is mostly mixed by turbulence), resulting in the

stratosphere being a very stable and highly stratified region of the Earth’s

atmosphere.

It is so named because it doesn’t convect and thus remains stable and

stratified. The stratosphere doesn’t convect and mix with underlying

troposphere, because at the tropopause hotter (less dense) air already lies on top

of cooler (denser) air. The heating which results from the absorption of UV by

ozone is greatest at about 50 km, defining the stratospause. Most of the ozone in

earth’s atmosphere resides in the stratosphere.

Ozone extends roughly from 10 to 80 km. It is being produced between

the 30 and 60 km levels by reaction between atomic and molecular oxygen [O2].

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Atmospheric circulation transports ozone down to the 25 km level where

maximum density occurs, the ozone layer. It absorbs all solar ultra-violet rays of

wavelength < 2900 A0 and partially absorbs between wavelengths 2900 & 3600

A0. That UV energy absorption results in the temperature in the upper half of the

stratosphere increasing until the stratopause.

1.1.3 Mesosphere

The temperature again decreases in the interval, called the mesosphere.

The mesosphere (meaning middle sphere) lies between about 50 km and 90 km.

The mesosphere does not absorb much solar energy and thus cools with

increasing distance from the hotter stratosphere below. Heat flows toward this

level by conduction from above and is removed by radiation in the IR by CO2,

visible airglow, and by downward eddy transport into the mesosphere. This

decrease in temperature with height continues until the coldest part of the

atmosphere is reached at about 90 km, defining the mesospause, where

temperatures can fall below 188 K. Mesopause is the coolest region in the entire

atmosphere of the earth. Eddy transport is important below 100 km. This process

is capable of transferring heat from the thermosphere to the mesosphere, and

derives its energy from wind motions. However, a discrepancy in the polar

mesopause region which is observed to be warmer in winter than in summer.

This region is heated in winter by the recombination of atomic oxygen

transported from greater heights by a slow downward motion of the air.

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1.1.4 Thermosphere

The outermost layer of the atmosphere, the “thermosphere”, contains very

little of the atmosphere’s gas (less than 1 %). In the thermosphere, photo-

absorption by various chemical species leads to a string increase in temperature

with height. The main source of heat in this region is the absorption of extreme

UV radiation by atomic oxygen. A large proportion of the air is ionized by the

solar extreme UV radiation and X-rays, and so the action of electric and

magnetic fields is important for its dynamics.

Most of the heat liberated in the thermosphere is removed by downward

conduction so that the temperature increases upward. Finally, the heat

conductivity becomes so good that the region of the upper thermosphere is

maintained in a nearly isothermal condition at a relatively high temperature

(1000-2000 K). Because the thermosphere has so little gas, it contains very little

heat, even though it registers a high temperature.

The temperature achieves a constant value at ~600 km and above as the

gas density becomes extremely less and the particles follow ballistic orbits. This

region is called the exosphere and is the outermost layer of earth’s atmosphere-

ionosphere system. Lower thermosphere acts as a heat sink. Although some heat

is lost by radiation in the IR and visible ranges, eddy transport is probably the

principal means of removing heat from the thermosphere, being more rapid than

molecular conduction at levels below the turbopause (upper layer of mesopause).

Molecular conduction could not carry heat through the temperature minimum at

the mesopause; also that the temperature gradient is too small in the upper

mesosphere. According to the eddy transport theory, the bulk of the heat

absorbed in the thermosphere is transported down to the mesosphere and

deposited at heights around 50 km.

Depending upon the mixing of atmospheric species, atmosphere is also

subdivided as,

1) Homosphere and

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2) Heterosphere.

1.1.5 Homosphere

The troposphere, stratosphere and mesosphere constitute the homosphere

(Gk. homos = same) in which the composition of the atmosphere is more or less

uniform throughout. The densities of gases in these lower three layers of the

atmosphere are enough that moving atoms and molecules frequently collide. For

this reason, atmospheric scientists refer to the troposphere, stratosphere and

mesosphere together as the “homosphere”.

1.1.6 Heterosphere

In contrast, atoms and molecules in the low-density thermosphere collide

so infrequently that this layer does not homogenize. Rather, gases separated into

distinct layers based on composition, with the heaviest (nitrogen) on the bottom,

followed in succession by oxygen, helium and at the top, hydrogen, the lightest

atom. To emphasize this composition, atmospheric scientists refer to the

thermosphere as the “heterosphere”. The physical and chemical processes that

underline the meinel band emissions in the airglow are important aspects of

coupling between the thermosphere and the mesosphere.

1.1.7 Exosphere

At about 500 km, the neutral densities become so low that collisions

become unimportant and hence the upper atmosphere can no longer be

characterized as fluid. This transition altitude is called the exobase, and the

region above it is called the exosphere.

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1.1.8 Magnetosphere

Finally, there is the magnetosphere, the region in which the earth’s

magnetic field controls the dynamics of the atmosphere. It is difficult to define a

lower limit, since the movement of ionization is geo-magnetically controlled at

all heights above about 150 km but the magnetosphere certainly includes the

whole atmosphere above the level at which ionized constituents become

predominant over neutral constituents i.e., at about 150 km.

Magnetopause or the boundary of the magnetosphere lies at about ten

earth radii on the day side of the earth and at a greater distance on the night side.

1.2 Ionosphere

The term ionosphere was first used by Sir Robert Watson-Watt in a letter

to the secretary of the British Radio Research Board in 1926. The expression

came into wide use during the period 1932-34 when Watson-Watt, Appleton,

Ratcliff and others used it in papers and books. Before the term ‘ionosphere’

gained a worldwide acceptance, it was called the Kennelly-Heaviside layer, the

upper conducting layer and ionized upper atmosphere [5].

The Earth’s ionosphere is a partially ionized gas that envelops the Earth

and in some sense forms the interface between the atmosphere and space. Since

the gas is ionized it cannot be fully described by the equations of the neutral

fluid dynamics. On the other hand, the number density of the neutral gas exceeds

that of the ionospheric plasma and certainly neutral particles cannot be ignored.

Therefore the knowledge only of two «pure» branches of physics: classical fluid

dynamics and plasma physics is not sufficient. In addition to atmospheric

dynamics, space physics, ion chemistry and photochemistry are necessary to

understand how the ionosphere is formed and buffeted by sources from above

and below and to deal with production and loss processes [6]. The ionosphere is

a part of the upper atmosphere having enough electrons and ions to effectively

interact with electromagnetic fields. As a conduction media, it plays an

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important role in the global electric circuit. Presently, the altitude of the

ionosphere is between 50 and 1000 km. Some authors propose higher values for

the upper boundary but usually the higher altitudes are regarded as the earth’s

plasmasphere because at these altitudes the earth’s atmosphere becomes fully

ionized plasma [7, 8]. The maximum concentration of ionized part in the earth’s

atmosphere (ionosphere) is between 250 and 500 km depending on geophysical

conditions. The physical and chemical processes responsible for ionosphere

formation are very different at different altitude levels which provide the layered

structure of the ionosphere [9].

1.2.1 Ionospheric Formation

Ionosphere is mainly produced by a process called ionization that takes

place in the ionosphere region due to solar ultraviolet radiation having a

wavelength shorter than 102.7 nm, which is effectively absorbed by atmospheric

molecules and atoms. There are other sources of ionization such as solar X-rays,

solar cosmic rays and energetic particles precipitating at high latitudes. Figure

1.2 shows the ionosphere height structure and the main source of the ionization

for every layer of the ionosphere [10]. Ionospheric layers are subdivided into

two or more layers and it is dependant on the time of day and geophysical

conditions [9, 11].

The sun’s extreme ultraviolet light and X-ray emissions encountering

gaseous atoms and molecules in the atmosphere can impart enough energy for

photoionisation to occur, thereby producing positively charged ions and free

electrons. A secondary ionizing force of lesser importance is cosmic radiation. A

counteracting process in the ionosphere is recombination, in which the ions and

electrons join again producing neutral atoms and molecules.

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Fig 1.2 Ionosphere structure on day and night time with the sources of

ionospheric ionization [9].

In the lower regions of the ionosphere, free electrons can combine with

neutral atoms to produce negatively charged ions. This process is called

attachment. However, due to different molecules and atoms in the atmosphere

and their differing rates of absorption, a series of distinct regions or layers of

electron density exist. These are denoted by letters D, E, F1 and F2 and are

usually collectively referred to as the bottom side of the ionosphere. The part of

the ionosphere between F2 layer and the upper boundary of the ionosphere is

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termed the topside of the ionosphere. It is the F2 layer where usually the

maximum electron density occurs as a consequence of the combination of the

absorption of the extreme ultraviolet light and increase of neutral atmospheric

density as the altitude decreases. The F1 layer disappears in winter time, when

the solar zenith angle is higher than in summer time (when the F1 layer is

consistently present).

Now we will see in detail the ionospheric layers-

1. D Region

The lower boundary for penetration of solar radiation having wavelength

shorter than 102.5 nm at the height of 90 km but Lyman-α radiation (λ=121.6

nm) can ionize the minor component of the neutral atmosphere NO having

very low ionizing potential and forming NO+ ions at the heights of 60 – 90

km [9]. In this layer, the primary source of ionization is cosmic radiation which

is same for day and for night. At night, the electrons gets attached to atoms

and molecules forming negative ions that cause the D layer to disappear

and at day, as a consequence of sun’s radiation, the electrons tend to

detach themselves from the ions causing the D layer to re-appear. As a

consequence, at the altitude of about 60 to 70 km, the D layer electrons

are present at day but not at night causing a distinct diurnal variation in the

electron density. The typical values for the noon time electron densities of the D

layer at the mid-latitude region are in the range of 6.1 × 108 to 13.1 × 10

8

electron/m3 according to the solar activity. The lower part of D layer is referred

to as the C layer [10, 12]. where the cosmic radiation is the only source of

ionization compared to the middle, and upper part of the D layer; where both the

cosmic radiation and X-ray emissions are present.

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2. E Region

E-region of the ionosphere is formed under the action of solar ultraviolet

radiation within the band 80<λ<102.8 nm. The most important among them are

the lines Lβ=102.6 nm and CIII=97.7 nm ionizing O2, as well as soft X-ray. The

main ionized components are O2 and N2, and main ions O2+ and NO

+, which are

formed from O2+ and N2

+ as a result of ion-molecular reactions. The main

mechanism of the charged particles loss is the dissociative recombination of the

molecular ions with the electrons [9].

The E layer is free from disturbances unlike the D and F layers and is

only present at day. The E layer does not completely vanish at night, however,

for practical purposes it is often assumed that its electron density drops to zero at

night. The atmosphere is rare and only two body collisions occur, so atomic

ions cannot recombine easily with electrons; however molecular ions do

recombine easily. The overall effect is that the positive ions are mostly

molecular.

Inside the E region very thin-patched layers could be formed. This

formation is called the sporadic E layer and designated as Es. The formation of

these layers is due to convergence of the vertical flux of long living metallic

ions. The thickness of sporadic E-layer changes from several hundred meters up

to a few kilometers [12].

3. F Region

The F-region of the ionosphere is divided into two layers i.e. F1 and F2.

I) F1 Layer

The F1 layer appears as a bending point on the vertical profile of

electron concentration between the E and F2 layers at the height of 160 – 200

km. It rarely develops in the distinct maximum appearing more often near 180

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km. Its formation owes to solar ultraviolet radiation within the band 10< λ < 90

nm. The main ionized components are N2 and O and to a lesser extent O2 [9].

The F1 layer is more likely to appear during summer daytime conditions

of summer and during nighttime it is the cavity between the E and F2 layers,

named as the valley in ionospheric physics. It is more pronounced during the

summer than during the winter months for low solar sunspot numbers and for

periods with ionospheric storms.

II) F2 Layer

According to the plasma density the F2 layer is the most dynamical and

most dense layer of the ionosphere. Here, depending on the geophysical

conditions the main ionosphere maximum is located at the altitude of between

210 and 500 km. It includes the small part of the bottom ionosphere from 200

km up to peak density, and the whole topside ionosphere from the peak up to

1,000 - 2,000 km.

It is formed due to the solar emission in the range 10< λ <90 nm. The

main ionized species are the atomic oxygen, but N2 and O2 also play

important roles in the atom-ion interchange process leading to the loss of

electrons by dissociative recombination. The main difference between the

F2 layer and other ionospheric layers is that the ionization loss velocity is

proportional to the ion concentration whereas in other layers it is

proportional to the square of the ion concentration.

1.3 Major Geographic Regions of the Ionosphere

There are three major regions of the global ionosphere. These are the

high-latitude, mid latitude and equatorial regions. In this section, the main

characteristics of the individual regions are briefly described.

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1.3.1 Low Latitude Ionosphere

The low-latitude ionosphere (0° to 30°) is unique in that the magnetic

field is nearly horizontal, so that zonal electric fields produced by the

neutral wind dynamo during magnetically quiet times can transport the

plasma vertically through the E×B drift. This quiet-time vertical drift is

upward during the daytime, causing plasma to drift to higher altitudes

from where it diffuses down along magnetic fields due to the pressure

gradient and gravity to higher latitudes creating two plasma crests on either

side of the magnetic equator. Since the plasma is transported from the

magnetic equator to higher latitudes, a density trough is formed centered on the

magnetic equator with two density crests around 15o-20

o magnetic latitude to

the northern and the southern hemispheres. This unique latitudinal

distribution of the plasma/ionization density is called the equatorial ionization

anomaly (EIA) or the equatorial anomaly for short and the effect of transporting

the plasma from the magnetic equator to higher latitudes is referred as the

equatorial plasma fountain [13, 14]. The EIA was first described by

Appleton [15] in a widely available Western journal so that it is often

called the Appleton anomaly [16]. Fig. 1.3 illustrates the equatorial plasma

fountain i.e. Appleton anomaly.

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Fig. 1.3 Diagram illustrates that the equatorial plasma fountain [17].

1.3.2 Mid-Latitude Ionosphere

The mid-latitude ionosphere (30°-60°) is the least variable and

undisturbed among the different ionospheric regions. It is usually free of the

effect imposed by the horizontal magnetic field geometry peculiar to the

equatorial region. Also, this is the region from where one can have most of

the ionospheric observations available due to the fact that most of the

ionospheres sensing instruments are located in the countries situated in the

mid-latitude region. Fig. 1.4 gives detail of major geographic regions of the

ionosphere.

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Fig. 1.4 Major geographic regions of the ionosphere [18].

1.3.3 High-Latitude Ionosphere

In addition to photon ionization and collisional ionization is another

source of ionization in the high-latitude region (above 60°). The main reason for

this is the fact that the geomagnetic field lines are nearly vertical in this region

leading to the charged particles descending to E layer altitudes (about 100 km).

These particles can collide with the neutral atmospheric gases causing local

enhancements in the electron concentration, a phenomenon which is

associated with auroral activity. Auroral activity can also be regarded as

the interaction between magnetosphere, ionosphere and atmosphere. The

auroral zones are relatively narrow rings situated between the northern and

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southern geomagnetic latitudes of about 64 and 70 degrees, respectively. In

general, the intensity and the positions of the auroral ovals are related to

geomagnetic disturbances. The ovals extend towards the equator with increasing

levels of geomagnetic disturbance.

1.4 Ionospheric Disturbances

Ionospheric disturbances can result from solar disturbances and natural

activity disturbances. The ionospheric disturbances are associated directly or

indirectly with the solar and natural activity.

1.4.1 Geomagnetic Storms

A geomagnetic storm is a temporary intense disturbance of the earth's

magnetosphere. During a geomagnetic storm the F2 layer will become unstable,

fragment and may even disappear completely. Geomagnetic storms usually

occur in conjunction with the ionospheric storms and can be caused by solar

flares, high speed solar wind stream (coronal holes) and sudden disappearing of

filaments. Geomagnetic storm originated from solar-flare usually starts with a

sudden commencement as an initial phase. On the other hand, a high speed solar

wind stream induced geomagnetic storm is expected to start with a gradual

commencement with storms tending to reoccur every 27 days or so following the

sun’s rotation [19, 20].

1.4.2 Lightning

Lightning can cause ionospheric perturbations in the D-region according

to one of the two ways. The first is through Very Low frequency (VLF) radio

waves launched into the magnetosphere. These so-called ‘whistler’ mode waves

can interact with radiation belt particles and cause them to precipitate onto the

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ionosphere, adding ionization to the D-region. These disturbances are called

Lightning-induced Electron Precipitation (LEP) events.

1.4.3 Ionospheric Scintillation

Small-scale structures in the electron content of the ionosphere range

from a few meters to a few kilometers in extent which can cause both refraction

and diffraction effects on the electromagnetic waves propagating through the

ionosphere. Refraction is associated with the bending of the electromagnetic

waves which takes place when the wave front moves obliquely across two media

with different propagation velocities. However, bending can also take place

when the electromagnetic waves pass by an obstacle such as a localized

ionospheric disturbance [12, 21]. As a consequence of refraction and diffraction,

the wave front becomes crinkled giving rise to amplitude and phase fluctuations

of the signal. These fluctuations caused by small-scale ionospheric structures are

called ionospheric scintillations [22].

1.5 Geomagnetic Index

Magnetic activity indices describe the variation in the geomagnetic field

caused by these irregular current systems.

1.5.1 Kp Index

Geomagnetic disturbances can be monitored by ground-based magnetic

observatories recording the three magnetic field components. The global Kp

index is obtained as the mean value of the disturbance levels in the two

horizontal field components observed at 13 selected subauroral stations. The

name Kp originates from planetary index.

The Kp index is a measure of irregular variations of the cartesian

components of the earth’s magnetic field (X, Y and Z). These irregular

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variations are associated with the geomagnetic field disturbances measured in

gamma (nT). Nearly 13 observatories lying between 46 and 63 degrees north and

south geomagnetic latitude determine their own integer K ranging from 0 to 9

for each 3 hour period of the day based on the measured ranges in the

geomagnetic field components. A particular K scale is adopted for each

observatory but the scale differs from observatory to observatory. The planetary

3 hour Kp index is designed to give a global measure of geomagnetic activity

and computed as an arithmetic mean of the K values determined at 13

observatories. The Kp index has zero (quiet geomagnetic activity) to 9 (greatly

disturbed geomagnetic activity).

1.5.2 Disturbance Storm Time Index (Dst Index)

The hourly Dst is a geomagnetic index which monitors the world wide

magnetic storm level. It expressed in nT and based on the average value of the

horizontal component of the earth's magnetic field measured hourly at four near-

equatorial geomagnetic observatories. Negative Dst values indicate a magnetic

storm in progress. The negative deflections in the Dst index are caused by the

storm time ring current which flows around the earth from east to west in the

equatorial plane. The ring current results from the differential gradient and

curvature drifts of electrons and protons in the near earth region and its strength

is coupled to the solar wind conditions. There is an eastward electric field in the

solar wind which corresponds to a southward interplanetary magnetic field

(IMF). There is significant ring current injection resulting in a negative change

to the Dst index. Thus, by knowing the solar wind conditions and the form of the

coupling function between solar wind and ring current and an estimate of the Dst

index can be possible.

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1.6 Energy Sources and Heat Transport

The atmosphere is set into motion by various external and internal energy

sources. However, the transformation of these sources into heat and the

momentum of atmospheric gas is a complicated process that depends on the

physical and chemical conditions of the atmosphere. Minor constituents like

ozone or ionospheric plasma play important roles in transferring solar energy

into heat and momentum. In the following section, a few important external

sources which are assumed to be responsible for the direct transfer of heat and

momentum into the atmosphere are briefly outlined.

1.6.1 Solar Irradiance

Solar radiation reaching the earth is the main energy source of the Earth-

Solar-Atmosphere system. As the solar photons penetrate the atmosphere, they

undergo collisions with the atmospheric gas and are progressively absorbed and

scattered. In the thermosphere, the absorbed solar energy is split between

photoelectrons and ions (photo ionization) resulting in stored chemical energy.

This energy is transferred to the neutral gas through elastic and inelastic

collisions of the photoelectrons with the neutrals and through heating by

recombination. Thermal conductivity redistributes the heat downward.

In the lower and middle atmosphere (bellow 100 km), molecular heat

conduction can be ignored, but the solar heat input is more difficult to interpret

for the following reasons [23].

I. Water vapour and carbon dioxide (CO2) absorb infrared radiation of

terrestrial origin.

II. The lower and middle atmospheres are optically thick to the IR radiation,

so that radiation transport becomes important.

III. Scattering by molecules and aerosols is dependent upon their size and

density.

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IV. Clouds scatter and absorb light. Moreover they transport latent heat and

redistribute the solar heat input.

V. Solar heat input is dependent upon highly complicated ozone chemistry

which varies temporally and spatially (see Figure 1.5).

1.6.2 Solar Wind Energy

The flowing gas of the sun, carrying mainly photons and electrons, blown

radially outward through interplanetary space is called the solar wind. This solar

wind is embedded in an interplanetary magnetic filed which interacts with the

earth’s magnetosphere. Some solar wind particles deposit a significant amount

of energy in the upper atmosphere [23] and are responsible for the high latitude

increases in E-region (100-200 km) ionospheric density and auroral electrojets

accompanied by thermospheric heating. Their subsequent effects may penetrate

further into the atmosphere.

In addition to the external sources of atmospheric wave motion, internal

or indirect sources have to be considered as they account for all physical and

chemical processes in the multi-component atmospheric gas. We briefly outline

the internal sources relevant to the large scale motion in the mesosphere and

lower thermosphere (MLT) region in the following subsections.

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Figure 1.5 Measurements made on board the NASA Space shuttle illustrates

the marked variability of ozone. This figure can be found on the web site

http://ssbuv.gsfc.nasa.gov/o3imag.html [24].

1.6.3 Eddy Viscosity and Heat Conduction

The steady influx of solar heat generates atmospheric wave motion of all

scales. In the absence of dissipation, the kinetic energy of the atmospheric flow

would increase beyond bound. Molecular viscosity provides such dissipation.

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However, its direct effect on large scale motion is negligible at lower and middle

atmospheric heights.

Effective heat transport within the atmospheric gas is governed by

turbulence. A cascade of turbulent eddies transfer ordered heat from larger scales

to the smaller scales, until molecular heat conduction eventually converts the

ordered heat into unordered internal energy of the gas. However, molecular heat

begins to dominate only above the turbopause near 110 km altitude.

At heights above 200 km, the collisions between ions and neutrals result

in frictional drag and hence transfer a sufficient amount of momentum so that

the neutral energy is dissipated. However, ion neutral interactions become

significant above 100 km and therefore the dissipative effects on ion drag are not

expected to affect the middle atmosphere region.

1.6.4 Latent Heat

The atmosphere is never completely saturated with water vapour so that

liquid water from oceans and from the surface of continents continuously

evaporates. Winds and turbulence transport this water vapour away from its

source. The water vapour may condense and form clouds, particularly, when

subjected to up-drafts which bring the water vapour in to the region of lower

temperatures below the saturation limit. During condensation, the latent heat of

vapourization is transferred to the atmosphere and acts as a local heat source.

The same amount of heat is removed from the atmosphere if the cloud droplets

evaporate again, for example in down-draft winds. Precipitation removes the

water content from the atmosphere and hence from the energy balance. Freezing

or melting of ice particles add or subtract the latent heat of melting to the energy

balance.

Local variations of latent heat are of minor importance in global scale

dynamics, but deep convective activity in the tropics produces a significant and

large scale latent heating and thus acts as an additional source for atmospheric

(diurnal) tidal variability in the MLT region [25].

Chapter I

25

1.6.5 Newtonian Cooling

Water vapour, ozone and carbon dioxide absorb and emit infrared

radiation. The heat budget of the lower and middle atmosphere therefore

strongly depends on the infrared radiative transfer. Radiative loss processes

dominate the cooling of the atmosphere and is described as a Newtonian cooling

heat sink. The infrared cooling reaches its maximum around 50 km and has some

effect on the diurnal tide in the 80-100 km height region.

1.7 Circulation of Middle Atmosphere

The middle atmosphere extends from about 10-100 km and comprises

stratosphere, mesosphere and lower thermosphere. The circulation of the middle

atmosphere of the earth is driven by an unequal distribution of net radiative

heating. As noted before, the major features of the middle atmosphere

temperature structure are controlled by the emission and absorption of radiation.

Absorption of ultraviolet solar radiation by ozone leads to the high temperature

around 50 km; emission from the 15 µm infrared band of carbon dioxide is the

main cause leading to cold temperatures at the mesopause. Solar radiation

absorbed by atomic and molecular oxygen leads to the rapid increase of the

temperature above the mesopause. The radiative heating by ozone is a function

of solar incident flux, hence the intensity shows large seasonal and latitudinal

variation. The difference in heating between the northern and southern

hemispheres causes the general circulation of the middle atmosphere. The

intensity of the heating attains its maximum and minimum in the summer and

winter polar regions.

The large scale circulation of the middle atmosphere can be treated as

approximately two-dimensional in latitude φ and height z . The primary factor in

the formation of the general circulation is the hydrostatic balance in the vertical,

Chapter I

26

in addition to the geostrophic balance between the latitudinal pressure gradient

and the Coriolis force.

The hydrostatic balance is given as:

p

gz

ρ∂= −

∂ (1.2)

where p , ρ and g are the pressure, density and gravitational acceleration. The

pressure p can be expressed as density ρ and temperature T through the

equation of state for an ideal gas:

p RTρ= (1.3)

where R is the gas constant per unit mass. Integration of Equation (1.2) with the

aid of Equation (1.3) yields

( ) exp( )s

zp z p

H

∂= − ∫ (1.4)

( ) e x p ( )ss

T zp z

T Hρ

∂= − ∫ (1.5)

where sp , sρ and sT are the constant reference pressure1, density and

temperature. H is the atmospheric scale height2 and is given by

1 usually taken as 1000 mb

2 In middle atmosphere studies it is common to let H=7 km

RT

Hg

= (1.6)

Then, the geostrophic balance is expressed as:

1

g

pu

f yρ

∂= −

∂ (1.7)

1

g

pv

f xρ

∂=

∂ (1.8)

0w = (1.9)

Chapter I

27

where 2 sinf φ= Ω is the Coriolis parameter determined by the earth’s rotation

rate, Ω and latitude, φ . By differentiating Equations 1.7 and 1.8 with respect to

z, and considering Equations 1.2 and 1.3, the thermal wind equation is expressed

as:

( ) ( , , 0 )gu g T T

z T fT y x

∂ ∂ ∂= − −

∂ ∂ ∂ (1.10)

where ( , , 0)g g gu u v= is a geostrophic wind. The thermal wind equation 1.10

relates the vertical shear of the geostrophic wind components to the horizontal

temperature gradients.

Using the thermal wind equation, the pole to pole temperature gradient

results in zonal winds that increase in magnitude with height, and which are

eastward in the winter hemisphere and westward in the summer hemisphere.

This situation is demonstrated in Figures 1.6 and 1.7 which shows a latitude-

height section of zonal mean temperature and mean zonal winds in January and

July from the CIRA3 model. Negative and Positive latitudinal gradients of

temperature around 40-50 km altitudes are seen (see Figure 1.6) in the northern

winter (January) and northern summer (July), respectively, where the absorption

of UV by the ozone is large.

Figure 1.7 shows a similar distribution of the CIRA86 zonal mean wind

in the middle atmosphere. It is found that eastward and westward winds at mid

latitude increase up to the height of 50-70 km, which is explained by the thermal

wind equation (1.10). Another pronounced feature of Figure 1.7 is the decrease

in zonal wind above 70 km and the reversal of wind direction at around the

mesopause (80-100 km). Furthermore, the temperature distribution in this height

range, which shows that the temperature in the summer polar region is lower

than that in the winter polar region in Figure 1.6, is not explained in terms of

radiative equilibrium4. Hence, dynamical processes due to atmospheric waves

are believed to produce a drag on the mean zonal wind and to cool (heat) the

summer (winter) polar region. The role of gravity wave breaking is recognized

Chapter I

28

as the most important among the various dynamic processes which have been

studied theoretically [26-33] and experimentally [34-40].

3Committee on Space Research International Reference Atmosphere

4The atmosphere is said to be in radiative equilibrium when the incoming solar

radiation balances the outgoing terrestrial radiation.

Chapter I

29

Figure 1.6 Schematic latitude-height cross sections for CIRA86 zonal mean

temperature (°K) in January (top) and July (bottom).

Chapter I

30

Figure 1.7 Schematic latitude-height cross sections for CIRA86 zonal mean

winds (ms-1) in January (top) and July (bottom).

Chapter I

31

Another noticeable feature in Figures 1.6 and 1.7 is the asymmetry

between the northern and southern hemispheres. If the middle atmosphere is

homogenous and symmetrical between the hemispheres, the latitudinal cross-

section in January should coincide with July conditions. However, Figure 1.6

shows that the temperature profiles at high latitude in the stratosphere and

mesosphere are different between the winters in the northern and southern

hemisphere. Also the mean zonal wind in Figure 1.7 shows remarkable

difference of the winter eastward wind both in amplitude and location between

the northern hemisphere and southern winters; the maximum eastward wind

occurs at lower height and higher latitude, and the peak intensity is stronger in

the southern winter than in the northern winter. These differences are thought to

be due to atmospheric waves. Investigation of the differences in wave activity

between hemispheres is an important subject for the observational study.

1.8 Atmospheric Waves

The earth’s atmosphere has an important dynamical property of

supporting wave motions. Atmospheric waves are excited when air is disturbed

from equilibrium. The presence of one or more restoring forces opposes the

disturbances and supports local oscillations in the field variables such as

pressure, temperature and wind. Atmospheric waves play major roles in

maintaining the zonal mean momentum and temperature budget as well as the

ozone budget. In the middle atmosphere, atmospheric waves with various

periods such as gravity waves (few min. to few hours), atmospheric tides (24 hr,

12 hr, 8 hr, …) and planetary waves (≥ 1 day) are superimposed on mean winds.

The atmospheric waves can be classified based on their restoring mechanisms.

Table 1.1 summarizes different types of waves along with their periods and

restoring mechanisms.

As these waves propagate upward, their wave amplitudes tend to increase

with height as the background density decreases so that wave energy is

conserved. The waves saturate when their amplitudes become too large and

Chapter I

32

transfer their energy and momentum to the mean flow. Turbulence is generated

through either convective or dynamic instabilities. Therefore, a study of

interactions of atmospheric waves with mean winds and waves has become as

important as investigations of excitation, propagation and dissipation of single

waves. We, therefore, briefly review atmospheric waves in the following

subsection.

Table 1.1: Different types of waves, their periods and restoring mechanisms

No.

Wave type

Time period

Restoring force

1 Acoustic-gravity Few min. to few hours Compressibility/buoyancy

2 Inertia-gravity Several hours Inertia/ buoyancy

3 Kelvin Few days Inertia/ buoyancy

4 Rossby Few days Planetary vorticity gradient

5 Mixed

Rossby-gravity

Few days Inertia/ buoyancy and

Planetary vorticity gradient

1.8.1 Basic State

The mixture of gases in the lower and middle atmosphere can be treated

as a single ideal gas of constant molecular weight M. The three fundamental

physical processes which describe motions in the atmosphere are the

conservation of mass, energy and momentum. Here, we will examine only the

basic equations, for there are many works dealing with the fluid dynamics and its

detailed derivations [23,41].

The basic hydrodynamic and thermodynamic laws governing the motion

of atmospheric gas may be represented by

the equation of motion,

Chapter I

33

( ) _u v

du PD

dt ρ+Ω× = ∇ +Φ (1.11)

the equation of mass continuity,

.up

tρ

∂= − ∇

∂ (1.12)

the first law of thermodynamics,

v k

dT dc RT J D

dt dt

ρρ ρ = + −

(1.13)

and the ideal gas equation,

p RTρ= (1.14)

where t is the time, u is the full wind velocity vector ( ), ,u v w , with its

components directed to the east (u ), north ( v ), and upward (w ). Moreover,

u.d

dt t

∂= +∂

∇ (1.15)

is the total time derivative, where

x

u. =u v wy z

∂ ∂ ∂+ +

∂ ∂ ∂∇ (1.16)

Atmospheric waves with large horizontal scale, approximately ten thousand km,

such as atmospheric tides and planetary waves, have to be discussed taking into

account the earth’s sphericity. In spherical coordinates,

sinx a θ λ

∂ ∂=

∂ ∂ and

y a θ∂ ∂=

∂ ∂ (1.17)

On substituting Equation 1.17 in Equation 1.16, we get,

sin

u. =u v wa a zθ λ θ

∂ ∂ ∂+ +

∂ ∂ ∂∇ (1.18)

Chapter I

34

where θ is colatitude, Ω is the vector of Earth’s rotation, λ is the longitude, z is

altitude, a is the Earth’s radius, p is the pressure, ρ is the atmospheric density,

T is the temperature, Φ is the gravitational potential, vc is the specific heat at

constant volume, ,v kD D are the dissipation terms and J is the thermo tidal

heating term.

The horizontal momentum equation (1.11) expresses the balance between

zonal acceleration, the Coriolis force, and the external forces. The continuity

equation (1.12) expresses conservation of mass. The thermodynamic equation

(1.13) states that the time rate change of temperature is balanced by adiabatic

cooling or heating which results from the expansion or compression of air as it

rises or sinks, and by solar heating and long wave cooling. The equation 1.14 is

an equation of state for an ideal gas.

For planetary scale motions the vertical velocity,w , is small compared to

the horizontal. Also the vertical acceleration and Coriolis force are small

compared to that gravity and vertical pressure gradient force. These conditions

are consistent with the motion being in hydrostatic equilibrium i.e. only the

vertical pressure gradient and the gravitational acceleration are retained in the

vertical equation of motion. The equation 1.11 simplifies to

p

gz

ρ∂= −

∂ (1.19)

1

2 cosu p

vt a

θρ θ

∂ ∂− Ω = −

∂ ∂ (1.20)

1

2 cossin

v pu

t aθ

ρ θ λ∂ ∂+ Ω = −

∂ ∂ (1.21)

Other following approximations were made in Equations 1.11 to 1.14

I. The atmosphere is assumed to be thin compared to the radius of the earth.

II. The gravitational acceleration g is assumed to be constant.

III. The earth is assumed to be spherical.

IV. The earth’s topography is ignored.

V. The gas constant, R , is equal to 237 Joule kg-1K

-1.

Chapter I

35

Equations 1.11 to 1.21 give a closed set of equations of u , p , ρ and T , when

0D = i.e. in an inviscid and adiabatic atmosphere. However, a direct analytic

solution for this set of equations is difficult to obtain, because they are

complicated non-linear equations. One most commonly used method for

obtaining the solutions of the basic equations is the perturbation method, where

the wave structure of the atmosphere is separated into the mean flow, which is

independent of longitude, and departures from the mean flow or eddies (e.g.

0u u u′= + ). Its averaged flow 0u generally changes slowly with time. Planetary

waves of all scales (eddies) represent the deviations from the mean flow.

Wave oscillations are considered as linearized perturbations about the

basic state, i.e. quadratic and higher order terms in u′ are neglected. In this

approximation (a) the waves are considered as decoupled from each other, (b)

wave amplitudes are small compared to the background flow, and (c) the time

evolution of the background fields is long compared to the wave motions.

Planetary waves and tides in middle atmosphere have wave amplitudes which

rarely exceed 10 % of the basic state, and therefore often fulfill this condition.

Hence equations 1.11 to 1.14 can be linearized using the following assumptions:

0u u u′= + ; v v′= ;w w′= ; 0T T Tδ= + ; 0p p pδ= + ; 0pδ ρ δρ= + (1.22)

where 0T is the background temperature, 0p is the background pressure,

0ρ is the background density, Tδ is the temperature perturbation, pδ is the

pressure perturbation, and δρ is the density perturbation. In these linearized

equations the mean zonal wind 0u is included, whereas meridional winds are

neglected. Mean meridional motions are weak in comparison to mean zonal

winds below 175 km in the earth’s atmosphere and therefore neglected in the

above equations.

It is then possible to find a general solution of any time dependent

disturbance by linearly superimposing waves of different periods and different

horizontal structures. The steady state solutions of the linearized equations (1.22)

are assumed to be of the form:

Chapter I

36

( )ˆ ˆˆ ˆ ˆ ˆ, , , , , , , , , , i s tu v w T p u v w T p e λ σδ δ δρ ρ −′ ′ ′ = (1.23)

where σ is the wave frequency and s is the zonal wave number.

1.8.2 Gravity waves

Acoustic waves are essentially high frequency longitudinal waves

satisfying the equation of motion in which the air-inertia is balanced only by the

pressure gradient forces. When the force of earth’s gravity and force due to

pressure gradient are comparable with the compressibility forces, the resultant

waves are called ‘acoustic-gravity waves’ or simply gravity waves. These waves

are not purely longitudinal because gravity produces a component of the air

particle motion that is transverse to the propagation direction. They have periods

of few minutes to few hours and wavelengths of tens to hundreds of kilometers.

In the theory of the propagation of acoustic gravity waves, the process is

assumed to adiabatic. The dispersion relation for gravity waves is

4 2 2 2 2 2 2 2 2 2 2( ) ( 1) 4 0c k k g k g cz zxω ω γ ω γ− + + − + = (1.24)

ω is the angular frequency of the wave, c is the speed of sound, γ is the

ratio of specific heats for the atmospheric gas, g is the acceleration due to

gravity and xk and zk are the wavenumbers in the horizontal and vertical

directions.

In the absence of gravity ( 0g = ), the above dispersion relation is reduced

to 2 2 1/ 2( ) 2x zc k kω ωλ π= + = , which is the dispersion relation for a sound wave.

In this relation, the phase velocity is independent of direction. If gravity is

included, no solution can be arrived at with xk purely real. xk must be real in

order to represent a wave that can propagate longer distances horizontally

without attention. It is found that either the zk is purely imaginary or it takes the

form ( 2 )zk i H+ with zk real.

Chapter I

37

When zk is purely imaginary, the wave does not have vertical phase

propagation, and is termed as “surface wave”. When zk takes the

form ( 2 )zk i H+ , the wave propagates upward and has amplitude which increases

upward with height ( )h as exp( 2 )h H , and is termed as “internal wave”.

The dispersion relation suggests that two classes of waves can exists for

which ω can be real. One class, comprising “acoustic waves”, processes periods

2π ω less than a limiting value aT ; the other, constituting “gravity waves”,

processes periods greater than a limiting value gT . These limits are given by

4aT c gπ γ= and 1/ 22 ( 1)gT c gπ γ= − . Typical numerical values of aT and gT for

the mesospheric conditions are 4.4 and 4.9 minutes, respectively.

1.8.3 Effects of rotation: Inertia gravity waves and Rossby waves

As the frequency of oscillation approaches f , the effect of Coriolis force

needs to be taken into account in the equation of motion. The linearized form of

the horizontal structure equations for a fluid system of mean depth eh in a

motionless basic state is

0u t fyv xφ′ ′ ′∂ ∂ − + ∂ ∂ =

0v t fyu yφ′ ′ ′∂ ∂ + + ∂ ∂ = (1.25)

( ) 0et gh u x v yφ′ ′ ′∂ ∂ + ∂ ∂ + ∂ ∂ = .

Here φ ′ represents the temporal and horizontal structure of the geopotential

fluctuations on pressure surfaces or pressure fluctuations on height surfaces. The

Coriolis parameter is taken to be a function of y (Beta-plane approximation).

Because all coefficients are independent of x and t, solutions with zonal

wavenumber k and frequency σ proportional to exp[ ( )]i kx tσ− are considered.

The three equations can be combined into a single equation for the latitudinal

structure ( )V y of v′ , given by

Chapter I

38

2 2 2 2 2( ) ( ( )) 0ed V dy k df dy k f y gh Vσ σ+ − − + − = (1.26)

The quantity in bracket ‘ ’ is designated 2 ( )l y and represents an index of

refraction that changes with latitude. We will now consider different cases

involving different assumptions on Coriolis parameter ( )f .

Case 1. Nonrotating plane: f = 0. Here the index of refraction is constant and

the dispersion relation 2 2 2( )egh k lσ = + is that for gravity waves.

Case 2. Midlatitude f-plane: f = 0f = constant. The index of refraction is

again constant. Frequency is related to horizontal wavenumbers

by 2 2 2 2 2

0 ( )e IGf gh k lσ σ= + + = . The Coriolis parameter 0f places lower bound on

the frequency for these inertia gravity waves at large horizontal scales. If the

horizontal scales are large enough and the vertical scale is small enough that

pressure gradients are negligible, σ approaches 0f . This anticyclonic circulation

is called inertial oscillation. Fluid parcels orbit anticyclonically in an attempt to

conserve their linear inertia in an absolute reference frame, but are constrained to

reside on a horizontal surface. On the other hand, at small scales (large k, l), the

gravity wave characteristic dominates. If σ =0, the motion will be steady and

nondivergent and it is geostrophically balanced by pressure gradients.

Case 3. Midlatitude β -plane. If latitudinal excursions of parcel trajectories are

great enough that a parcel senses a changing Coriolis parameter, steady

nondivergent flow is no longer a solution. As the beta effect influences the

dynamics, the exactly balanced solution transforms into a second class of waves

that propagate to the west (relative to the mean flow). Theses oscillations can be

studied by applying the Midlatitude β -plane approximation, replacing ( )f y by

the constant 0f and df dy by the constant β . The resulting dispersion relation

Chapter I

39

may be written as 2 2 2 2

0 ( )e ekgh f gh k lσ β σ− = + + . For each value of , ,k l there

are now three different real values of frequencyσ , which correspond to the three

time derivatives in the shallow water equations.

The wave solutions separate clearly into two distinct classes:

1. High-frequency inertia-gravity waves

Two of the roots of the above dispersion relation have frequencies

greater than 0f . For these roots, 2

ekghβ σ σ<< and a good first

approximation is obtained by neglecting the term that is inversely

proportional toσ , yielding 2 2 2 2 2

0 ( )e IGf gh k lσ σ= + + = . These two

roots are just the inertia-gravity waves. The eastward traveling waves

(σ <0) propagate with slightly higher frequency than the westward

traveling waves (σ >0). All the inertia-gravity waves oscillate with

frequency greater than 0f .

2. Low-frequency Rossby waves

This second class of waves is limited to frequencies much less than 0f

in magnitude. For these oscillations, 2

ekghσ β<< and the 2σ term

in equation may be neglected to obtain good approximation to the

dispersion relation given by 2 2 2

0( )e Rk k l f ghσ β σ= − + + = . These

Rossby waves are westward traveling, with 0σ < . Because 0fσ << , the

horizontal accelerations in Rossby waves are much smaller than the

Coriolis force and pressure gradient terms.

1.8.4 Equatorial waves-Kelvin waves, Mixed Rossby-Gravity waves

A significant advance in the dynamics of middle atmosphere has been the

identification of some waves in the near-equatorial region. Their amplitude is

maximum in the neighbourhood of the geographical equator and decreases very

fast away from the equator. Such waves are considered important for the

semiannual oscillation (SAO) in the lower mesosphere and upper stratosphere

and for quasi-biennial oscillation (QBO) in the middle and lower stratosphere.

Chapter I

40

Thses equatorial waves have important dynamical links not only in the tropics

but also in the extra-tropics through interactions with the extra-tropical waves

and meridional circulation.

Theoretical treatment on these waves by Matsuno et al., [42] has been an

important landmark. His treatment is relatively simple and straightforward; yet it

brings out essence of dynamics of the equatorial waves. The main features of

Matsuno’s solution are given below.

The Midlatitude, hedrostatic waves are characterizes by properties that

depend on the time scale of fluctuations relative to the Coriolis parameter ( f ),

that is, on the nondimensional parameter 0fσ . Near the equator this scaling

breaks down because ‘ f ’ varies considerably changing sign from northern to

southern hemisphere. Although, 0f =0 is appropriate for tropical waves, the ratio

0fσ then becomes meaningless. Hence, applying equatorial β plane

approximation (in which the Coriolis parameter f yβ= , where 2 aβ = Ω , and Ω

is the angular velocity of earth) and non-dimensionalizing by taking the units of

length and time as 1/ 4 1 2( )eL gh β −= and 1/ 4 1/ 2( )eT gh β− −= for simplification, we get

the structure equation with k kL′ = , /y y L′ = , and Tσ σ′ = as

2 2 2 2 2( ) 0d V dy k k y Vσ σ′ ′ ′ ′ ′ ′+ − − + − = (1.27)

This relatively simple governing equation has well understood solutions.

For solutions required to be confined to the tropics, V can be written in a very

simple closed form by letting the meridional domain expand to infinity. The

result is 2( ) ( ) exp( / 2)n n nV y C H y y′ ′ ′= − where nC is an arbitrary constant

determined from the value of ( )nV y′ at a finite specified value of y′ . ( )nH y′ is the

nth order Hermite polynomial, the accompanying dispersion relation is

2 2 2 1k k nσ σ′ ′ ′ ′− − + = + , which is similar to the mid-latitude dispersion relation.

The dispersion relation is a cubic equation giving a Rossby wave moving

westward and two gravity waves-one moving westward and the other moving

eastwards. When 2 /kσ σ′ ′ ′<< , the dispersion relation 2 2 2 1k nσ ′ ′= + + (for

Chapter I

41

integer ‘n’) describes the behaviour of inertia gravity waves which are present in

the high frequency limit. When 2 /kσ σ′ ′ ′<< , the dispersion relation

2/( 2 1)k k nσ ′ ′ ′= − + + describes the behaviour of mixed Rossby-gravity waves

which are in low frequency limit.

To some extent, the effect of rotation is present in the so-called gravity

waves and the effect of gravity is present in the so-called Rossby waves. Both

the solutions decrease fast, away from the equator. The solution for n = 0 has

received considerable importance in the study of dynamics of middle atmosphere

and is known as mixed Rossby-gravity wave. This westward moving wave is

connected with QBO in the lower stratosphere. It has characteristics of both the

Rossby waves (quasi-geostrophic flow) and gravity waves (cross-isobaric flow).

The second addition is the peculiar equatorial Kelvin wave. On the

equatorial β -plane, its meridional velocity is identically zero. Setting v = 0 in

the shallow water equations shows that the Kelvin wave is in geostrophic

balance in one direction but propagates zonally as a nondispersive pure gravity

wave with kσ ′ ′= . This hybrid wave propagates only towards the east. Kelvin

waves were originally named for Midlatitude oceanic waves that propagate

along a coastline with vanishing velocity component normal to the coast. In the

present case, equator exhibits corresponding characteristics of the coastline.

Kelvin wave has the characteristic feature similar to Rossby wave in that the

zonal motion is nearly geostrophic on both sides of the equator. It also has the

characteristic of gravity waves is as much as there is considerable cross-isobaric

flow.

1.8.5 Atmospheric Tides

Atmospheric tides are global scale oscillations in temperature, wind,

density and pressure at periods which are subharmonics of a solar or lunar day.

They are amongst the most dominant atmospheric waves in the MLT region.

Solar tides are primarily generated by thermal forcing due to absorption of solar

radiation by water vapour or ozone [43, 44]. Diurnal and semidiurnal tides are

Chapter I

42

normally dominant, although higher harmonics of the 24 hour periodicity are

detected, such as terdiurnal and quarter diurnal tides. They are classified into two

types, namely, migrating tides and non-migrating tides. If the longitudinal

distribution of the minor constituents such as water vapour and ozone that absorb

solar radiation and generate tides is uniform then the corresponding tide

generated follows the apparent westward movement of the sun. This sun

synchronous tide is commonly called “migrating tide”. If the distribution is

longitudinally asymmetric, the tide could not follow the sun’s apparent motion

and hence it is named as “non-migrating tide”. In addition to the sun-

synchronous tides, non migrating tides can also be generated by the local

excitation source, such as heat released through cloud convection and heat

exchange near earth’s surface [45-47]. Their amplitudes were found be stronger

over land than over sea [48]. They have been identified with shorter vertical

wavelength of around 10 km [49-54].

They have various zonal wave numbers and therefore they could

propagate both westward as well as eastward or be standing [55]. Based on the

satellite observations, Lieberman et al. [56] reported that non-migrating tides

could have larger amplitudes than migrating components and these large

amplitude non-migrating tides could cause significant time variations of diurnal

tides.

For many years, tides are known to play an important role in the

dynamics of the mesosphere and lower thermosphere (MLT). In general, tides

have amplitudes larger than other wave motions and they dominate the wind

field. They transport momentum and wave energy upward from their source

regions to the regions in which they are dissipated by various instabilities and

hence affect the mean circulation and structure of the atmosphere [57-63].

1.8.5.1 A brief outline of tidal theory

The equation of motion is 2 1U Ud dt gπ ρ ψ+ Ω× = − ∆ , where ψ the

potential function. The motion also satisfies the continuity equation, adiabatic

Chapter I

43

equation and a thermodynamic equation; the latter relates dT dt to the heat input

Q , derived from first law of thermodynamics.

With necessary assumptions, the equations can be reduced to a single

differential equation, which can be solved by the method of separation of

variables. The velocity divergence Udivχ = is generally used as the dependent

variable. It is written as a function of geocentric distance r and colatitude θ (or

latitude ϕ ) , and must be periodic in longitude λ and time t . The solar ( s ) or

lunar ( l ) oscillation is written as a superposition of solutions

, min ,( ) ( )exp[ (2 / )]s l mn s lR r im t Tχ θ π λ= Θ +∑∑ (1.28)

where ( )mnR r is the altitude structure function of a particular latitudinal mode,

which is (by implication) the same at all latitudes, ( )mn θΘ is the latitude

structure function of a particular latitudinal mode which is (by implication) the

same at all heights, ,s lT is the length of the solar or lunar day and the index

m=1,2,3 for diurnal, semi-diurnal and ter-diurnal oscillations. The functions mnΘ

are known as Hough functions and can be generally written in terms of

associated Legendre functions. When the method of separation of variables is

applied to the differential equation for χ , we get an eigenvalues equation, called

‘Laplace tidal equation’. The eigenvalues have the dimensions of length and are

termed the “equivalent depths”, denoted by hn . The latitudinal structure of each

tidal mode is different. A mode is specified with the index m and latitudinal

number n . For the semi-diurnal tide, ( , )m n mode means that there are ( )n m−

zeroes for the tidal amplitude in the latitudinal range of 0 to π and n is giving

increasing integer values starting with 2n m= = so that (2, 2), (2, 3), (2, 4), (2,

5) etc. denote 2, 3, 4, 5 etc. zeroes in the latitude structure of a tidal perturbation

amplitude of semi-diurnal tide.

In case of diurnal tide, there can be negative values of hn . When the hn

values are arranged in the decreasing order of absolute magnitude, the diurnal

Chapter I

44

negative modes have 1,2,3,n = etc. corresponding to , 12.2, 1.79nh = −∞ − − km

etc., respectively; and the diurnal positive modes have 1,2,3,n = etc.

corresponding to 0.698,0.240,0.121nh = km etc., respectively. Positive and

negative symmetric modes have ( 2)n m− + and ( 1)n m− − zeroes respectively

and positive and negative antisymmetric modes have ( 2)n m− + and ( 1)n m− +

zeroes respectively between 0 and π radians of latitude. The above theoretical

treatment applies to tides in an atmosphere, which is dissipationless, does not

have background wind and is uniform in latitude and longitude in its basic

structure. It describes the basic characteristics of the tides in the atmosphere

quite well.

1.8.6 Atmospheric Instabilities

While the atmospheric waves have been characterized by a restoring force

tending to return a displaced parcel to an initial position, many atmospheric

instabilities can be described by a negative restoring force which tends to

increase the displacement of the parcel away from its equilibrium position.

1.8.6.1 Inertial instability

Inertial motions occur when the centripetal and Coriolis forces balance in

the absence of a pressure gradient. Under inertial motion, the parcels revolve

opposite to the vertical component of planetary vorticity. In the presence if shear

in zonal flow, displacements either oscillate or decay exponentially or grow

without bound. The system will be unstable, if the absolute vorticity of the mean

flow has sign opposite to the planetary vorticity. The displacements then amplify

exponentially and the zonal flow is inertially unstable. Inertial instability does

not play a major role in the atmosphere. Extratropical motions are mostly

inertially stable, even in the presence of synoptic and planetary wave

disturbances. However, the criterion for the inertial instability is violated near

Chapter I

45

the equator, where Coriolis parameter f is very small. An evidence of instability

exists in the tropical stratosphere, where the horizontal shear flanking the strong

zonal jets can violate the criterion for inertial stability.

1.8.6.2 Shear instability

Shear instability can develop when the mean flow speed varies in a

direction perpendicular to the direction of the straight flow and if the molecular

viscosity is small. Richardson number defined by 2 2( )iR N du dz= measures the

competition between the destabilizing influence of the wind shear and the

stabilizing influence represented by a real Brunt-Vaisala frequency. For inviscid

flow, shear instability develops when 0.25iR < . Large value of Richardson

number means that the wind shear is not strong enough for the displaced parcel

to gain the required energy. Small Richardson number indicates weak

stratification so that parcels can be displaced vertically without doing much

work against gravity and the displacements amplify. If a perturbation can acquire

kinetic energy from the shear of the basic state faster than it loses potential

energy by vertical displacements in stable stratification, then it gains total energy

from the basic state and amplifies. This instability mechanism can lead to

turbulence.

1.8.6.3 Barotropic and Baroclinic instabilities

These instabilities act on the synoptic and planetary-scales and they result

from a change in sign of the basic-state potential vorticity gradient, rather than a

sign change in the potential vorticity itself. Barotropic instability arises mainly

from excessive horizontal shears of flow, for example in a jet. Exchanges of

kinetic energy take place between the basic flow and the wave perturbations

through horizontal non-divergent motions. In the process, the zonal jet gets

diluted; its momentum is shared by its adjacent layers. While the zonal

Chapter I

46

momentum of the jet flow as a whole is conserved, its kinetic energy decreases.

This loss of kinetic energy by the jet is gained by the wave perturbation.

Baroclinic instability arises from a combination of vertical shear and

rotation. In a balanced state, vertical shear of horizontal wind, say of zonal wind

u, implies meridional temperature gradient. If the eastward winds increase with

height in a balanced state, temperature decreases poleward according to thermal

wind equation. There is zonal available potential energy ZA in the atmosphere.

This ZA can get accumulated in the atmosphere only upto a certain extent.

Beyond that, the equilibrium is ready to break down at the slightest provocation.

In a perturbation superimposed on this basic state, cold polar air flows

equatorward and the relatively warm sub-tropical air flows poleward so that

along a latitude circle, we have now cold and warm air side by side. ZA is

converted into EA . Generally, a situation prevails in which warm air rises and

cold air sinks in x-p plane. EA is converted into EK .

Z E EA A K→ →

The storehouse of ZA is continuously fed by differential heating of

different latitude zones for which solar heating is the ultimate cause. EK is

continuously drained out of the system by friction. Charney et al., [64] was the

first to bring out the importance of baroclinic instability, under dry adiabatic

process, in the formation of extratropical synoptical scale disturbances in the

eastward winds.

One dimensional analysis of Plumb et al., [65] showed that for eastward

upper mesospheric shear in excess of 6 m/s/km, the mesospheric jet would be

unstable, with the most rapidly growing wave having a zonal wavelength of

~10000 km and an eastward phase velocity of ~60 m/s. At mid-latitudes, this

corresponds to a zonal wavenumber of about 3 with a period around 2 days and

this can be associated with observed quasi-2-day wave. Plumb suggested that

such condition support baroclinic instability of these waves.

Chapter I

47

1.9 Outline of Research Work

The above paragraphs highlight the importance of the study of the

atmospheric wave motions of different scales that determine many of the

characteristics of middle atmosphere. They also emphasize the need for further

observations of planetary waves, tides and gravity waves in the equatorial MLT

region, since they have been sparse until recently. The subject of investigation of

this thesis concerns the medium frequency (MF) radar observations of MLT

winds and waves in the altitude region of 80-98 km from the low latitude

stations, Kolhapur (16.8oN, 74.2

oE ) and Tirunelveli (8.7

oN, 77.8

oE), in India. In

the equatorial region, radars of present kind are operational at only few other

locations that again emphasize the need for more observations from different

geographical locations. The thesis provides a detailed observational study on

both short- and long-period atmospheric motions from both the stations. The

main objectives of the study are as follows.

1. Study of the temporal behaviour of MLT mean winds.

2. Study of Intraseasonal Oscillations (ISO) in the MLT winds.

3. Study of planetary waves in the MLT winds.

4. Comparision of MLT mean winds and ISO over both the stations

Kolhapur and Tirunelveli and to see the latitudianal differences /

variability in the results.

The results obtained under the above headings / themes are presented in the

thesis.

Chapter I

48

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