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Geomagnetic turbulence during the solar storm of 15-25 May 2005 1

Geomagnetic turbulence during the solar storm of

15-25 May 2005

Chapter 1

Introduction

This investigatory work analyses the turbulence in geomagnetic field during

solar storms. Our mother planet Earth has a magnetic field of its own. This field of

intrinsic origin is primarily dipolar in nature. The geomagnetic field forms a shroud

around it which was known as the magnetosphere. This field is historically significant

owing to the role of the magnetic compass in exploration of the planet (Figure 1.1).

Figure 1.1 The Earth’s magnetic field enabled travellers to find direction with

the use of the compass

The magnetosphere is that area of space, around the Earth, that is

controlled by the Earth's magnetic field. This near-Earth space is full of

streaming particles, electromagnetic radiation, and constantly changing electric

and magnetic fields. All these things constitute the magnetosphere (Figure 1.2).


Figure 1.2 The stream particles originating from the Sun entering the Earth’s

magnetosphere

The Sun is our nearest star and the source of energy for life on Earth. It is

about 150 million km away (93 million miles), a distance which sunlight covers

in 8 minutes, whereas the distance to the moon is only 1.3 light-seconds. The Sun

is about 300,000 times heavier than Earth and rotates around its axis (viewed

from the orbiting Earth) in about 27 days. A high resolution image of the sun is

seen in Figure 1.3.


Figure 1.3 A full disc image of the Sun captured by NASA’s STEREO mission

The Sun also has its own magnetic field which is known as the

Interplanetary Magnetic Field (IMF). The IMF is carried by the solar wind to the

planets of the Solar System. Solar wind is the plasma of charged particles

(protons, electrons and heavier ionized atoms) coming out of the Sun in all

directions at very high speeds, an average of about 400 km/sec. It is responsible

for the anti-sunward tails of comets and the shape of the magnetic fields around

the planets.

The Solar magnetic field is expansive and goes beyond any of the planets

and hence the term “Interplanetary Magnetic Field”. The magnetic field of the

Sun is carried by the solar wind which comes out from the Sun. The solar wind

and magnetic field are twisted into a spiral by the Sun's rotation.

The control of the magnetospheric features by the interplanetary

magnetic field (IMF) embedded in the solar wind is well established. This control

is widely interpreted as evidence for magnetic interconnection between the IMF

and the magnetosphere. The coupling between the two critical elements

discussed above determines to large extent the real-time space weather


conditions experienced by us. Space weather refers to conditions on the Sun and

in the solar wind, Earth's magnetosphere, ionosphere, and thermosphere that

can influence the performance and reliability of space-borne and ground-based

logical systems and can endanger human life of health. Figure 1.4 below

represents the solar terrestrial interactions.

Figure 1.4 The interaction of the solar wind with the Earth’s magnetosphere

Space weather refers to the state of the space environment and is usually

expressed in terms of the behaviour of energetic particles, as well as in changes

in electric and magnetic fields. We are mostly interested in conditions in near-

Earth space, though space weather is important throughout the solar system.

Geomagnetic storms are major disturbances of the magnetosphere that occur

when the interplanetary magnetic field turns southward and remains southward

for an prolonged period of time. During a geomagnetic storm's main phase,


which can last as long as two to two and a half days in the case of a severe storm,

charged particles in the near-Earth plasma sheet are energized and injected

deeper into the inner magnetosphere. Figure 1.5 below shows the aurora or

northern/southern lights illuminating the horizon.

Figure 1.5 The particles in the solar wind ionise the air molecules in the Polar

Regions the energy which eventually appear as the auroral lights

The significance of space weather lies in its potential impact on man-

made technologies on Earth and in space, for example, on satellites and

spacecraft, electricity power grids, pipelines, radio and telephone

communications and on geophysical exploration. Space weather also has

implications for manned space flight, both in Earth orbit and further out into

space.

Today there are a number of man-made and natural systems, which are

affected by space weather. It impacts satellites, astronauts and aircraft in the


upper atmosphere; can disrupt communications and navigation systems; and can

damage power grids, pipelines and even basic Earth systems.

When a satellite (Figure 1.6) travels through an energized environment

during geomagnetic storms, the charged particles striking the spacecraft cause

various portions of it to be differentially charged, leading to the damage (and

possibly failure) of the satellite's electronic systems.

Figure 1.6 A high intensity magnetic burst from the Sun could destroy

satellites in orbits crippling all services based on satellite technology

Furthermore, as technology has allowed spacecraft components to

become smaller, their miniaturized systems have become increasingly

vulnerable to the more energetic solar particles, which can cause physical

damage to microchips and change software commands in satellite-borne

computers. Increased solar activity can also cause the atmosphere to heat and

expand. For satellites in low-earth orbit, this atmospheric change can exert

increased drag on the satellites, causing them to slow down and change orbit.

Unless low-Earth-orbit satellites are routinely boosted to higher orbits, they

slowly fall, and could eventually burn up in Earth's atmosphere.


Space weather conditions can also be hazardous to humans in space.

Astronauts (Figure 1.7) are normally well protected by the shelter of the space

station. However, when they venture outside their protective space station, they

are vulnerable to the same high doses of particles or radiation as the space

station itself. In reality, however, the radiation risk to astronauts is quite small if

they work within the Earth's magnetic field and wear layers of protective

clothing.

Figure 1.7 Astronauts also face the risk of high intensity radiation during

extreme solar events, especially when they venture outside of their space

stations

Solar proton events can also produce elevated radiation aboard aircraft

(Figure 1.8) flying at high altitudes and over long distances. For example, during

air travel from New York City to Tokyo, passengers and crew could be exposed to

levels of radiation equalling that of a chest X-ray during an intense solar

radiation storm. The most intense solar flares, on the other hand, can be as

injurious to humans as the low-energy radiation from a nuclear blast. The

penetration of high-energy particles into living cells — measured as radiation


dose — can lead to chromosome damage and potentially cancer, while larger

doses can be fatal. Although the likelihood of these risks is small, monitoring of

solar proton events by satellite can help reduce the threats of human exposure.

Figure 1.8 Airline passengers will be exposed to strong radiation fields in the

event of a magnetic storm

During an ionospheric storm, some radio frequencies are absorbed and

others are reflected, leading to rapidly fluctuating signals and unexpected

propagation paths. Although TV and commercial radio stations are little affected

by solar activity; ground-to-air, ship-to-shore, Voice of America, Radio Free

Europe and amateur radio are frequently disrupted. High frequency radio wave

communication is most affected because this frequency depends on reflection

from the ionosphere to carry signals over great distances.


Figure 1.9 Radars show incorrect positioning during a magnetic storm

Therefore radio operators using high frequencies rely on solar and

geomagnetic alerts to keep their communication circuits up and running.

Likewise, some search and rescue, military detection or early-warning systems

are also affected by solar activity. Specifically, over-the-horizon radars bounce

signals off the ionosphere in order to monitor the launch of aircraft and missiles

from long distances. During geomagnetic storms, this system can be severely

hampered by radio clutter.

The accuracy of navigation systems using very low frequency signals

depends on knowing the altitude of the ionosphere's lower boundary. Some

airplanes and ships use these very low frequency signals (Figure 1.9) to

determine their positions. During solar events and geomagnetic storms,

however, the altitude of the ionosphere's lower boundary can change rapidly,

thus introducing errors of up to several kilometres. If navigators are alerted that

a proton event or geomagnetic storm is in progress, they can switch to a backup

navigation system. Likewise, global positioning systems (Figure 1.10) operate by

transmitting radio waves from satellites to the ground, ships, aircraft or other


satellites and therefore are also sensitive to ionospheric changes due to

geomagnetic storms.

Figure 1.10 GPS systems map incorrectly during magnetically disturbed

periods

Geomagnetic storms are harmful to electrical transmission equipment,

and damage to transformers and transmission lines (Figure 1.11) can leave

entire grids without power. By receiving geomagnetic storm alerts and warnings,

power companies can act to minimize damage and power outages.


Figure 1.11 Electric transmission lines sustain large scale damage in the event

of strong magnetic disturbance

Rapidly fluctuating geomagnetic fields can induce currents into pipelines

(Figure 1.12) carrying valuable fuels. Once this happens, flow meters in the

pipeline can transmit erroneous flow information, and the corrosion rate of the

pipeline can be dramatically increased. Therefore, pipeline managers routinely

receive space weather alerts and warnings to help them maintain an efficient and

long-lived system.


Figure 1.12 Long distance pipe lines stand the risk of bursting and fire from

geomagnetically induced currents during magnetic storms

Many animals with true navigation have magnetite, the mineral used in

basic compasses, within a select group of cells. The magnetite reacts to the

Earth's magnetic field, giving the animal internal cues to identify north. There is a

growing body of evidence that changes in the geomagnetic field affect biological

systems.

The most closely studied of the sun's biological effects has been the

degradation of homing pigeons (Figure 1.13) navigational abilities during

geomagnetic storms. Pigeons (and other migratory animals, such as dolphins and

whales) have internal biological compasses composed of the mineral magnetite

wrapped in bundles of nerve cells, which are often much less effective during

space weather events.


Figure 1.13 Animals are found to lose their sense of direction during solar

magnetic events

The sun is the heat engine that drives the circulation of our atmosphere.

Although it has long been assumed to be a constant source of energy, recent

measurements of this solar constant have shown that the base output of the sun

can vary by up to two tenths of a percent over the 11-year solar cycle and

temporary decreases of up to one-half percent have been observed. Atmospheric

scientists say that this variation is significant and can modify climate over time.

Evidence of this can be seen in almost all geographic phenomena (Figure 1.14)

like variations of plant growth, stratospheric wind directions near the equator

and ozone depletion, etc, which corresponds to solar cycles.


Figure 1.14 All processes that take place in the biosphere from climate to

evolution of life are influenced by variability of the magnetosphere

Temporal variations are characteristic of the geomagnetic field observed

at various ground stations. The objective of the current investigatory project is to

categorise high latitude geomagnetic stations based on their susceptibility to

interplanetary magnetic field (IMF) disturbance originating from the sun.

This work employs vertical variance analysis to examine the coupling

between these two distinct magnetic fields i.e. the IMF and the geomagnetic

fields. The geomagnetic field observations from 30 different geomagnetic

stations are analysed.


Chapter 2

Geomagnetism

The magnetic nature of the earth has been known for quite a long time.

Various effects of this magnetic field around the earth were also known. This

field is primarily of dipolar nature. It has been studied and mapped with a fair

degree of accuracy. Figure 2.1 below depicts an approximate current picture of

the geomagnetic field.

Figure 2.1 The Earth behaves like a magnet with its magnetic N-S axis slightly

tilted at an angle to the geographic axis

This magnetic field resembles a dipole as if a giant bar magnet was

embedded inside. However, the axis of the dipole is not aligned with the

rotational axis of the earth. Neither is it centred in the earth.


The magnetic dipole axis of the earth is tilted about 11½° from the

rotation axis. This means the magnetic north pole and the geographic North Pole

are not in the same place. The magnetic poles of the earth are defined as the

location of the strongest vertical magnetic field. This places the magnetic north

pole just west of northern Greenland (about 80° N 70° W) and the magnetic

south pole near the coast of Antarctica south of Australia (about 75° S 150° E), as

the following diagram shows. The magnetic equator is defined as the line around

the earth where the magnetic field is horizontal, or parallel to the earth’s surface.

It does not circle the earth as a smooth line like the geographic equator, but

instead it meanders north and south, as shown in Figure 2.2 below.

Figure 2.2 The figure shows the alignment of the magnetic equator across the

globe

The total geomagnetic field vector generally represented as F is mostly

resolved into components for convenient comprehension and research as shown

in Figure 2.3. The geomagnetic field vector is described by the orthogonal

components X (northerly intensity), Y (easterly intensity) and Z (vertical


intensity, positive downwards. The horizontal intensity is H. Inclination (or

dip) I is the angle between the horizontal plane and the field vector, measured

positive downwards. Declination (or magnetic variation) D is the horizontal

angle between true north and the field vector, measured positive eastwards).

Declination, inclination and total intensity can be computed from the orthogonal

components using the equations

Where, H is given by

.

Figure 2.3 The vector components of the geomagnetic field

The strength of the field at the Earth's surface ranges from less than 30

micro-teslas (0.3 gauss) in an area including most of South America and South

Africa to over 60 micro-teslas (0.6 gauss) around the magnetic poles in northern

Canada and south of Australia, and in part of Siberia. Its value at Trivandrum is

0.38 gauss which is used in local calculations.

The similarity of the geomagnetic field to that of a bar magnet is but

superficial. The magnetic field of a bar magnet, or any other type of permanent

magnet, is created by the coordinated spins of electrons and nuclei within the


atoms. The Earth's core, however, is hotter than 1043 K, the Curie point

temperature at which the orientations of spins within iron become randomized.

Such randomization causes the substance to lose its magnetic field. Therefore the

Earth's magnetic field is caused not by magnetized iron deposits, but mostly by

electric currents in the liquid outer core.

Figure 2.4 A schematic showing the electric currents in the liquid core of the

Earth giving rise to the geomagnetic field

Convection of molten iron (Figure 2.4) within the outer liquid core, along

with a Coriolis effect caused by the overall planetary rotation, tends to organize

these "electric currents" in rolls aligned along the north-south polar axis. When

conducting fluid flows across an existing magnetic field, electric currents are

induced, this in turn creates another magnetic field. When this magnetic field

reinforces the original magnetic field, a dynamo is created which sustains itself.

This is called the Dynamo Theory and it explains how the Earth's magnetic field

is sustained.


Chapter 3

The Interplanetary Magnetic Field (IMF)

The Sun is a yellow main sequence star comprising about 99% of the total

mass of the Solar System. It is a near-perfect sphere, with an oblateness

estimated at about 9 millionths, which means that its polar diameter differs from

its equatorial diameter by only 10 km (6 mi). As the Sun exists in a plasmatic

state and is not solid, it rotates faster at its equator than at its poles. This

behaviour is known as differential rotation. The period of this actual rotation is

approximately 25 days at the equator and 35 days at the poles. However, due to

our constantly changing vantage point from the Earth as it orbits the Sun, the

apparent rotation of the star at its equator is about 28 days. The centrifugal

effect of this slow rotation is 18 million times weaker than the surface gravity at

the Sun's equator. The tidal effect of the planets is even weaker, and does not

significantly affect the shape of the Sun. The Figure 3.1 below presents an

approximate structure of the sun.

Figure 3.1 A schematic showing the structure of the sun


The Sun has a strong dipolar magnetic field of around 50 gauss, a field

100 times stronger than that of the Earth. This dipolar nature is especially true

during the period called the solar minimum.

However, during the years around solar maximum (2000 and 2001 are

good examples) spots appear on the face of the Sun. Sunspots are places where

intense magnetic loops - hundreds of times stronger than the ambient dipole

field - emerge through the photosphere. Sunspot magnetic fields dominate over

the underlying dipole. Consequently, the solar magnetic field near the surface of

the star becomes tangled and complicated. The Figure 3.2 below shows a 3

dimensional picture of the sun with its magnetic field.

Figure 3.2 A representative diagram of the solar magnetic field

extending into space

The Sun's magnetic field isn't confined to the immediate vicinity of our

star. The solar wind carries it throughout the solar system. Out among the

planets we call the Sun's magnetic field the "Interplanetary Magnetic Field" or

"IMF." Figure 3.3 below shows the solar wind originating from the Sun.


Figure 3.3 A satellite photograph of the Sun with a vector superimposition of

the solar wind velocity

Because the Sun rotates (once every 27 days) the IMF has a spiral shape

called the "Parker spiral" after the scientist who first described it. The parker

spiral is shown in Figure 3.4.

Figure 3.4 The spiral shape of the IMF as seen in the Parker spiral

The interplanetary (heliospheric) current sheet is a three-dimensional

form of a Parker spiral that results from the influence of the Sun's rotating


magnetic field on the plasma in the interplanetary medium. It is shown in Figure

3.5

Figure 3.5 The heliospheric current sheet

Along the plane of the Sun's magnetic equator, the oppositely directed

open field lines run parallel to each other and are separated by a thin current

sheet known as the "interplanetary current sheet" or "heliospheric current

sheet". The current sheet is tilted (because of an offset between the Sun's

rotational and magnetic axes) and warped (because of a quadrupole moment in

the solar magnetic field) and thus has a wavy, "ballerina skirt"-like structure as it

extends into interplanetary space. The “Ballerina skirt” structure is shown below

in Figure 3.6.

Since the Earth is located sometimes above and sometimes below the

rotating current sheet, it experiences regular, periodic changes in the polarity of

the IMF. These periods of alternating positive (away from the Sun) and negative

(toward the Sun) polarity are known as magnetic sectors.


Figure 3.6 The ballerina skirt structure of the IMF with the magnetic field

lines shown in blue

The IMF is a vector quantity with three directional components, two of

which (Bx and By) are oriented parallel to the ecliptic. The third component-Bz -is

perpendicular to the ecliptic and is created by waves and other disturbances in

the solar wind. When the IMF and geomagnetic field lines are oriented opposite

or "anti-parallel" to each other, they can "merge" or "reconnect," resulting in the

transfer of energy, mass, and momentum from the solar wind flow to

magnetosphere The strongest coupling-with the most dramatic magnetospheric

effects- occurs when the Bz component is oriented southward. The IMF is a weak

field, varying in strength near the Earth from 1 to 37 nT, with an average value of

around 6 nT.

Since the solar wind is in plasma form. It is highly electrically conductive

so that magnetic field lines from the Sun are carried along with the wind. The

dynamic pressure of the wind dominates over the magnetic pressure through

most of the solar system (or heliosphere), so that the magnetic field is pulled into

an Archimedean spiral pattern (the Parker spiral) by the combination of the

outward motion and the Sun's rotation. Depending on the hemisphere and phase

of the solar cycle, the magnetic field spirals inward or outward; the magnetic

field follows the same shape of spiral in the northern and southern parts of the


heliosphere, but with opposite field direction. These two magnetic domains are

separated by a current sheet (an electric current that is confined to a curved

plane). This heliospheric current sheet has a similar shape to a twirled ballerina

skirt, and changes in shape through the solar cycle as the Sun's magnetic field

reverses about every 11 years.

The plasma in the interplanetary medium is also responsible for the

strength of the Sun's magnetic field at the orbit of the Earth being over 100 times

greater than originally anticipated. If space were a vacuum, then the Sun's 10-4

tesla magnetic dipole field would reduce with the cube of the distance to about

10-11 tesla. But satellite observations show that it is about 100 times greater at

around 10-9 tesla. Magnetohydrodynamic (MHD) theory predicts that the motion

of a conducting fluid (e.g. the interplanetary medium) in a magnetic field induces

electric currents which in turn generate magnetic fields, and in this respect it

behaves like a MHD dynamo.


Chapter 4

Geomagnetic storms and solar flares

A geomagnetic storm is a temporary disturbance of the Earth’s

magnetosphere caused by a solar wind shock wave and/or cloud of magnetic

field that interacts with the Earth's magnetic field. The increase in the solar wind

pressure initially compresses the magnetosphere. The solar wind's magnetic

field interacts with the Earth’s magnetic field and transfers an increased energy

into the magnetosphere. Both interactions cause an increase in plasma

movement through the magnetosphere (driven by increased electric fields inside

the magnetosphere) and an increase in electric current in the magnetosphere

and ionosphere.

A solar flare is an intense burst of radiation coming from the release of

magnetic energy associated with Sunspots. They are seen as bright areas on the

Sun and last from mere minutes to several hours. Geomagnetic storms often

occur in tandem with solar flares.

The Dst index is derived from the low latitude geomagnetic stations and is

considered a measure of the ring current formed around the Earth from the

trapped solar wind. The H component of the geomagnetic field from the stations

of Hermanus, Kakioka, Honolulu, and San Juan are averaged for arriving at the Dst

index. The Dst value is determined using Equation for N number of stations, H

being the horizontal component of the magnetic field disturbance at a given

station, Hq the same component over the quietest days, and θ the station latitude.

∑=

−=

N

n

q

st

HH

ND

1 cos

1

θ

The Dst index value is closely related to the prevailing conditions in the

IMF. The direction of the north-south component of the interplanetary magnetic

field (IMF) for the most part regulates the growth and decay of the ring current

and consequently the Dst.


The variation of the Dst index during storm time and quiet and its

correlation with geomagnetic field are investigated here. Time periods during

which the Dst index typically falls below -50nT are designated as geomagnetic

storms. The Dst value is proportional to the total energy of the ring current

particles and for this reason, it is considered a reasonable measure of the

strength of a geomagnetic storm. The features of a typical storm are shown in

Figure 4.1.

Figure 4.1 Plot of ΔH-variation during a typical magnetic storm showing

phases of the event.

The conventional definition of a storm includes three phases. The initial

phase involves an abrupt increase in the H component of geomagnetic field

known as the SSC (Sudden Storm Commencement) of arbitrary time duration.

The main phase is marked by a distinct fall in the H component value extending

for a few hours. This phase is followed by recovery phase that extends from a few

to tens of hours. Ring current intensification beyond a threshold is integral to

geomagnetic storms.

Geomagnetic field measurements made by ground based magnetometers

picked up unusual disturbances after the prominent solar flare of 1 September

1859. A magnetic storm was recorded at ground stations within the span of a day

following the flare. Later, explicit association was confirmed between solar

eruptions and geomagnetic field. Geomagnetic storms that impacted the


magnetosphere during of 15-25 May 2005 and 17-24 March 2015 is shown in the

Dst plots in Figures 4.2 and 4.3 respectively.

Figure 4.2 The Dst indices for May 2005 showing a geomagnetic storm during

which the index dropped to -247nT on 15 May 2005.

The drop in Dst indices are indicative of the compression that occurred for

the magnetospheric cavity during the events of solar origin. During both these

events, a gradual recovery of Dst is observed marking the withdrawal the

pressure exerted by the solar wind in course of time.

Figure 4.3 The Dst indices dropped to -223nT during March 2015 showing the

magnetospheric disturbance during the investigated geomagnetic storm.

The turbulence that is induced in the geomagnetic field by such events is

subjected to detailed analysis in this work.


Chapter 5

The Vertical Variance Method

The first indication of a possible correlation between observed solar

phenomenon and geomagnetic field measurements made by ground based

magnetometers was obtained during the prominent solar flare of 1 September

1859 [Carrington, 1859]. A magnetic storm as intense as no other was recorded

at ground stations within the span of day following the flare. Even though

Carrington did not dare to relate these events on cause and effect terms, later

authors like Hale [1931] and Newton [1943] have put down in no uncertain

terms solar eruptions and geomagnetic field disturbances as associated

phenomena. Investigations have further resulted in wide acceptance of the fact

that energy transfer occurs from the solar wind to the magnetosphere through

the mechanism of magnetic reconnection [Dungey, 1961].

As already mentioned, the IMF and horizontal component of earth’s

magnetic field consists of transient variations. An acceptable relationship that

yields the geomagnetic field strength observed at a station for a certain value of

the incident IMF has not yet been realized.

This project uses new mathematical index called the Vertical Variance

(VV) index [Abraham et. al, 2010], which can exactly quantify the amount of

temporal variations in any time series. The index being of daily nature,

aberrations from quiet-time Sq variations is minimal. The analysis of

interplanetary and observed geomagnetic field variations using the VV index

immediately yields empirical relations between the two. It is also observed that

the elucidated relationship is specific to each ground based station and hence can

be used for categorizing observatories on that basis.

The development of the VV index followed from the attempts of the

authors to precisely determine the degree of disturbance in various time series

data sets. The VV index is intended to assign to a time dependent function

varying within specified temporal end points, an exact numerical reckoning


which expresses the amount of fluctuations in the data. The versatility of the VV

Index lies in the fact that it can be applied to both IMF and geomagnetic data thus

enabling a comparison of the contained fluctuations.

Defining the VV index for any data set consisting of values x(t), xi and xi+1

being adjacent data values of x corresponding to adjacent time values ti and ti+1;

n

ttxx

xx

indexVV

n

i iiii

ii∑

= ++

+

−+−

−

=1

2

1

2

1

2

1

)()(

)(

,

where,)(

)(

1

12

ii tt

TTn

−

−=

+

.

T2 and T1 are the extreme time limits of the period for which the index is being

determined. In order to understand the behaviour of the index, it may be noted

that, if x(t) is plotted against t, considering unit change along the time axis, the

numerator in summation appears as the vertical change in the plot while the

denominator in the summation appears as the hypotenuse. The gauge of the

vertical change gives the name to the index while the denominator serves to

normalize the index.

Figure 5.1 An illustrative diagram showing the application of the vertical

variance index to four different trial data sets


The panels in Figure 5.1 demonstrate the application of the vertical

variance to four different sets of illustrative data. The four panels give the VV

index values of four different plots. The end points are the same for all the four

sets of data for the function value x(t), plotted on the y-axis (with a minimum of

zero and a maximum of five). The end points are also the same in all the four data

sets for the time variation t, plotted along the x-axis (with a minimum of zero and

a maximum of four). The data sets are so chosen to facilitate easy comparison.

The first plot in the top left panel of Figure 5.1 which shows a symmetric

function variation whose VV index is 0.928. This data set is used as a standard

case. Both the bottom panels of the figure show a structure variation to the lower

part of the plot shown in the standard case. The bottom left panel represents an

increased gradient in its lower portion and a decreased gradient in the upper

portion of the plot as compared to the standard plot. Similarly, the bottom right

panel represents a decreased gradient in its lower portion and an increased

gradient in the upper portion of the plot as compared to the standard plot. It is

can be seen that the index is reduced by the same difference to 0.848 in both the

cases. On the other hand, the data represented in the top right panel plot

contains more fluctuations within the same end points as compared to the

standard plot data. It can be noted that the VV index for this data is 0.980 which

is significantly higher than for the standard plot data. The comparison between

the four sets of data plotted in Figure 1 highlight the suitability of the VV index

in furnishing a measure of the disturbance in a time series data.

Applying specifications to the index to suit the current investigation

involving actual magnetic field data, )( 1 ii tt −+

is equated to the unit of time used.

Then; )( 12 TTn −= , the number of time units in the interval for which the index

is determined. While determining the VV index for individual days; ,1440=n the

number of minutes in the span of a day.


Then the equation for the index is streamlined to the form below.

1440

)(1

)(

)(1

2

1

2

1∑

= +

+

−+

−

=

n

i ii

ii

xx

xx

nTindexVV .

During the data processing stage, )( 1 ii xx −+

is simply the difference between the

magnetic field strength data values for successive minutes.

This work however utilises the vertical variance without

normalising it as an index using the denominator in the above equation. The

division by 1440 is also not performed. However, normalisation is done for the

determined vertical variance by dividing with the largest value for the analysed

days.


Chapter 6

The Vertical Variance Analysis and Results

The vertical variance analysis proceeds to obtain the variances for

individual days using 1-minute observations. The VV is determined for

geomagnetic field data for the stations of Chichijima (CBI) and Leirvogur (LRV)

for the days of 15-25 May 2005 during which a geomagnetic storm impacted the

magnetosphere. The World Data Centre (WDC), Kyoto has provided the absolute

1-minute geomagnetic field data for events in units of nano-Teslas.

The VVs are determined on a daily basis. Since at least 1440 data

elements have to be processed rigorously to find the VV index of each day,

suitable computational packages like MS excel and Matlab are used in

determining these values. The monthly average of these VVs for each station is

separately determined and the results are tabulated in Table 6.1-6.2. The VV

being a measure of the disturbance in the geomagnetic field, a higher value of the

VV indicates a highly disturbed geomagnetic field.

Dates VV (x)VV (x)-

NormalisedVV (y)

VV (y)-

NormalisedVV (z)

VV (x)-

Normalised

04-May-05 701.490 0.306 683.260 0.304 0.063 0.294

05-May-05 673.590 0.294 839.860 0.373 0.068 0.316

06-May-05 775.840 0.338 866.420 0.385 0.080 0.370

07-May-05 1043.400 0.455 1246.400 0.554 0.087 0.404

08-May-05 1560.800 0.680 1480.200 0.658 0.124 0.575

09-May-05 1017.600 0.443 921.620 0.409 0.076 0.350

10-May-05 897.940 0.391 906.420 0.403 0.072 0.331

11-May-05 1052.500 0.459 887.470 0.394 0.068 0.314

12-May-05 904.340 0.394 1045.000 0.464 0.070 0.323

13-May-05 1014.300 0.442 1110.900 0.494 0.100 0.463

14-May-05 848.730 0.370 802.880 0.357 0.068 0.314

15-May-05 2294.800 1.000 2250.700 1.000 0.216 1.000

16-May-05 935.940 0.408 1164.900 0.518 0.079 0.366

17-May-05 1073.100 0.468 837.610 0.372 0.069 0.322

Table 6.1 The table gives the vertical variance of Chichijima station for the

days of 4 -17 May 2005.


Figure 6.1 The figure shows the increased turbulence in all the components of

the geomagnetic field of Chichijima station, which is especially noticeable on 15

May 2005.

It is evident from Table 6.1 and Figure 6.1 that there is transfer of

turbulence from the solar wind to the geomagnetic field during the storm of May

2005. The geomagnetic storm is clearly visible in the Dst variation seen in Figure

4.2. Two events are observed in the Figure 4.2, a small dip in Dst around 7-8 May

2005 and a clear storm starting on 15 May 2005. Both these events are reflected

in Figure 6.1 in the form of peaks in the vertical variance.

It can also be noted from Table 6.1 that absolute value of the variance is

much higher in the X-component clearly showing the direct coupling of the solar

phenomenon to the component. Turbulence is lower in the Y- component and

least in the Z-component of the geomagnetic field.


Dates VV (x)VV (x)-

NormalisedVV (y)

VV (y)-

NormalisedVV (z)

VV (x)-

Normalised

04-May-05 4030.8 0.329 4131.6 0.360 1.3 0.063

05-May-05 2363.0 0.193 2386.7 0.208 0.8 0.036

06-May-05 2747.8 0.225 2621.5 0.228 0.9 0.043

07-May-05 5639.9 0.461 5661.4 0.493 2.9 0.139

08-May-05 12234.0 1.000 11480.0 1.000 12.7 0.610

09-May-05 8146.6 0.666 7935.2 0.691 4.6 0.221

10-May-05 7427.6 0.607 7101.5 0.619 7.4 0.355

11-May-05 5708.6 0.467 5640.7 0.491 3.1 0.148

12-May-05 7268.4 0.594 7081.2 0.617 4.0 0.191

13-May-05 7833.9 0.640 7767.6 0.677 5.7 0.272

14-May-05 3893.3 0.318 3624.3 0.316 1.0 0.048

15-May-05 10881.0 0.889 10535.0 0.918 13.9 0.667

16-May-05 11104.0 0.908 11409.0 0.994 20.9 1.000

17-May-05 9292.9 0.760 9719.5 0.847 7.4 0.354

Table 6.2 The table gives the vertical variance of Leirvogur station for the

days of 4 -17 May 2005.

Figure 6.2 The figure shows the increased turbulence in all the components of

the geomagnetic field of Leirvogur station noticeable around 8th and 15th May

2005.


The general observations are similar for the vertical variance of the

Leirvogur station. However, the Table 6.2 shows that the absolute values of the

vertical variances of the station are much higher compared to Chichijima station.

This can be attributed to the higher geomagnetic latitude of Leirvogur station

(68.85 N) compared to the Chichijima station (18.87 N). The conclusions of this

investigation are listed out as follows.

• Geomagnetic storms are visible in the form of Dst variations.

• Vertical variance (VV) is a measure of the turbulence in the geomagnetic

field.

• The turbulence of the geomagnetic field (in all components) is clearly

observed during the period of geomagnetic storms at various ground

based stations.

• The turbulence is most visible in the X-component of geomagnetic field,

less visible in the Y-component and least in the Z-component.

• The turbulence is higher at higher geomagnetic latitudes relative to lower

latitudes.

The investigations in this work have brought forth results with significant

bearing on the effect of solar storms on Earth’s magnetic field.


References

Abraham, A., G. Renuka, and L. Cherian (2010), Interplanetary magnetic field–

geomagnetic field coupling and vertical variance index, J. Geophys. Res., 115,

A01207, doi:10.1029/2008JA013890.

Carrington, R.C. (1859), Description of a singular appearance seen in the sun on

September 1, 1859. Mon. Not. R. Astron. Soc., XX, 13.

Dungey, J. W. (1961), Interplanetary magnetic field and the auroral zones, Phys.

Res. Lett., 6, 47.

Hale, G. E. (1931), The spectrohelioscope and its works, part III, Solar eruptions

and their apparent terrestrial effects, Astophys. J., 73, 379.

Newton, N. H. (1943), Solar flares and magnetic storms, Mon. Not. R. Astron. Soc.,

103, 244.

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