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Chapter – I
Introduction and Outline of
Research Work
Chapter I
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 photochemistry. 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 infrared 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, photoabsorption 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 atmosphereionosphere 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 layers1. 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 × 108
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-20o 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 nearequatorial 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 EarthSolar-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].
24
Chapter I
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,
25
Chapter I
in addition to the geostrophic balance between the latitudinal pressure gradient
and the Coriolis force.
The hydrostatic balance is given as:
∂p
= −ρ g
∂z
(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 = ρ RT
(1.3)
where R is the gas constant per unit mass. Integration of Equation (1.2) with the
aid of Equation (1.3) yields
∂z
)
H
(1.4)
Ts
∂z
exp(− ∫
)
T
H
(1.5)
p ( z ) = p s ex p( − ∫
p(z) = ρs
where ps , ρ s and Ts 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}
H=
RT
g
(1.6)
Then, the geostrophic balance is expressed as:
u
=
g
v
g
−
=
w = 0
1
f ρ
∂ p
∂ y
(1.7)
1
f ρ
∂ p
∂ x
(1.8)
(1.9)
26
Chapter I
where f = 2Ω sin φ 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:
∂ ug
g ∂T
∂T
(
)= −
(
,−
, 0)
∂z T
∂x
fT ∂ y
(1.10)
where u g = ( u g , v g , 0) 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 latitudeheight 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
27
Chapter I
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
4
The atmosphere is said to be in radiative equilibrium when the incoming solar
radiation balances the outgoing terrestrial radiation.}
28
Chapter I
Figure 1.6 Schematic latitude-height cross sections for CIRA86 zonal mean
temperature (°K) in January (top) and July (bottom).
29
Chapter I
Figure 1.7 Schematic latitude-height cross sections for CIRA86 zonal mean
winds (ms-1) in January (top) and July (bottom).
30
Chapter I
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 crosssection 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
31
Chapter I
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
Few days
Inertia/ buoyancy and
Rossby-gravity
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,
32
Chapter I
du
P
+ Ω × u = ∇( + Φ ) _ Dv
dt
ρ
(1.11)
the equation of mass continuity,
∂p
= − ρ∇.u
∂t
(1.12)
the first law of thermodynamics,
 dT
 dt
ρ cv 

 dρ 
 = RT 
 + ρ J − Dk

 dt 
(1.13)
and the ideal gas equation,
p = ρ RT
(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,
d
∂
= + u.∇
dt ∂t
(1.15)
is the total time derivative, where
u.∇ =u
∂
∂
∂
+v +w
∂x
∂y
∂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,
∂
∂
=
∂x a sin θ∂λ
and
∂
∂
=
∂y a∂θ
(1.17)
On substituting Equation 1.17 in Equation 1.16, we get,
u.∇=u
∂
∂
∂
+v
+w
a sin θ∂λ
a∂θ
∂z
(1.18)
33
Chapter I
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, cv is the specific heat at
constant volume, Dv , Dk 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
= −ρ g
∂z
(1.19)
∂u
1 ∂p
− 2Ωv cos θ = −
∂t
ρ a ∂θ
(1.20)
∂v
1
∂p
+ 2Ωu cos θ = −
∂t
ρ a sin θ ∂λ
(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.
34
Chapter I
Equations 1.11 to 1.21 give a closed set of equations of u , p , ρ and T , when
D = 0 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.
u = u 0 + u ′ ). Its averaged flow u0 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:
u = u 0 + u ′ ; v = v′ ; w = w′ ; T = T0 + δ T ; p = p0 + δ p ; δ p = ρ 0 + δρ
(1.22)
where T0 is the background temperature, p0 is the background pressure,
ρ 0 is the background density, δ T is the temperature perturbation, δ p is the
pressure perturbation, and δρ is the density perturbation. In these linearized
equations the mean zonal wind u0 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:
35
Chapter I
{u′, v′, w′, δ T , δ p, δρ} = {uˆ, vˆ, wˆ , Tˆ , pˆ , ρˆ ei ( sλ −σ t ) }
(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
ω 4 − ω 2 c 2 ( k x 2 + k z 2 ) + (γ − 1) g 2 k z 2 + ω 2 γ 2 g 2 4 c 2 = 0
(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 k x and k z are the wavenumbers in the horizontal and vertical
directions.
In the absence of gravity ( g = 0 ), the above dispersion relation is reduced
to c = ω (k x 2 + k z 2 )1/ 2 = ωλ 2π , 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 k x purely real. k x must be real in
order to represent a wave that can propagate longer distances horizontally
without attention. It is found that either the k z is purely imaginary or it takes the
form (k z + i 2 H ) with k z real.
36
Chapter I
When k z is purely imaginary, the wave does not have vertical phase
propagation, and is termed as “surface wave”. When
kz
takes the
form (k z + i 2 H ) , the wave propagates upward and has amplitude which increases
upward with height (h) as exp(h 2 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 Ta ; the other, constituting “gravity waves”,
processes periods greater than a limiting value Tg . These limits are given by
Ta = 4π c gγ and Tg = 2π c g (γ − 1)1/ 2 . Typical numerical values of Ta and Tg 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 he in a
motionless basic state is
∂u′ ∂t − fyv′ + ∂φ ′ ∂x = 0
∂v′ ∂t + fyu′ + ∂φ ′ ∂y = 0
(1.25)
∂φ ′ ∂t + ghe (∂u ′ ∂x + ∂v′ ∂y ) = 0 .
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 − σ t )] are considered.
The three equations can be combined into a single equation for the latitudinal
structure V ( y ) of v′ , given by
37
Chapter I
d 2V dy 2 + {− k σ (df dy ) − k 2 + (σ 2 − f 2 ( y )) ghe }V = 0
(1.26)
The quantity in bracket ‘{ }’ is designated l 2 ( 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 σ 2 = ghe (k 2 + l 2 ) is that for gravity waves.
Case 2. Midlatitude f-plane:
f = f 0 = constant. The index of refraction is
again
is
constant.
Frequency
related
to
horizontal
wavenumbers
by σ 2 = f 0 2 + ghe (k 2 + l 2 ) = σ 2 IG . The Coriolis parameter f 0 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 f 0 . 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 f 0 and df dy by the constant β . The resulting dispersion relation
38
Chapter I
may be written as σ 2 − β kghe σ = f 0 2 + ghe (k 2 + l 2 ) . For each value of k , l , there
are now three different real values of frequency σ , 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 f 0 . For these roots, β kghe σ << σ 2 and a good first
approximation is obtained by neglecting the term that is inversely
proportional to σ , yielding σ 2 = f 0 2 + ghe (k 2 + l 2 ) = σ 2 IG . 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 f 0 .
2. Low-frequency Rossby waves
This second class of waves is limited to frequencies much less than f 0
in magnitude. For these oscillations, σ
2
< < β k g he
and the σ 2 term
in equation may be neglected to obtain good approximation to the
dispersion relation given by σ = − β k ( k 2 + l 2 + f 0 2 ghe ) = σ R . These
Rossby waves are westward traveling, with σ < 0 . Because σ << f 0 , 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.
39
Chapter I
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 σ f 0 . Near the equator this scaling
breaks down because ‘ f ’ varies considerably changing sign from northern to
southern hemisphere. Although, f 0 =0 is appropriate for tropical waves, the ratio
σ f 0 then
becomes
meaningless.
Hence,
applying
equatorial
β plane
approximation (in which the Coriolis parameter f = β y , where β = 2Ω a , and Ω
is the angular velocity of earth) and non-dimensionalizing by taking the units of
length and time as L = ( ghe )1/ 4 β −1 2 and T = ( ghe ) −1/ 4 β −1/ 2 for simplification, we get
the structure equation with k ′ = kL , y′ = y / L , and σ ′ = σ T as
d 2V dy′2 + {(− k ′ σ ′ − k ′2 + σ ′2 ) − y′2 }V = 0
(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 Vn ( y′) = Cn H n ( y′) exp(− y′2 / 2) where Cn is an arbitrary constant
determined from the value of Vn ( y′) at a finite specified value of y′ . H n ( y′) is the
nth order Hermite polynomial, the accompanying dispersion relation is
− k ′ σ ′ − k ′2 + σ ′2 = 2n + 1 , 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 σ ′2 << k ′ / σ ′ , the dispersion relation σ ′2 = k ′2 + 2n + 1 (for
40
Chapter I
integer ‘n’) describes the behaviour of inertia gravity waves which are present in
the
high
frequency
limit.
When σ ′2 << k ′ / σ ′ ,
the
dispersion
relation
σ ′ = − k ′ /(k ′2 + 2n + 1) 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 σ ′ = k ′ . 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
41
Chapter I
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 sunsynchronous 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 dU dt + 2πΩ × U = g − 1 ρ∆ψ , where ψ the
potential function. The motion also satisfies the continuity equation, adiabatic
42
Chapter I
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 χ = divU 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
χ s ,l = ∑∑ Rmn (r )Θ min (θ ) exp[im(2π t / Ts ,l + λ )]
(1.28)
where Rmn (r ) is the altitude structure function of a particular latitudinal mode,
which is (by implication) the same at all latitudes, Θmn (θ ) is the latitude
structure function of a particular latitudinal mode which is (by implication) the
same at all heights, Ts ,l 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 Θmn
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 n = m = 2 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
43
Chapter I
negative modes have n = 1, 2, 3, etc. corresponding to hn = −∞, −12.2, −1.79 km
etc., respectively; and the diurnal positive modes have
n = 1, 2, 3, etc.
corresponding to hn = 0.698, 0.240, 0.121 km etc., respectively. Positive and
negative symmetric modes have (n − m + 2) and (n − m − 1) zeroes respectively
and positive and negative antisymmetric modes have (n − m + 2) and (n − m + 1)
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
44
Chapter I
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 Ri = N 2 (du dz ) 2 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 Ri < 0.25 . 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
45
Chapter I
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 AZ in the atmosphere.
This AZ 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. AZ is
converted into AE . Generally, a situation prevails in which warm air rises and
cold air sinks in x-p plane. AE is converted into K E .
AZ → AE → K E
The storehouse of AZ is continuously fed by differential heating of
different latitude zones for which solar heating is the ultimate cause. K E 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.
46
Chapter I
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, 74.2oE ) and Tirunelveli (8.7oN, 77.8oE), 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.
47
Chapter I
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