PREDICTION OF ARRIVAL TIME OF CORONAL MASS EJECTIONS USING THE ONSET OF GEOMAGNETIC STORM

0
61

TABLE OF CONTENTS

Title                                                                                                                            Page

Title page                                                                 i

Certification page                                                                              ii

Approval page                                                                               iii

Dedication                                                                                           iv

Acknowledgement                                                                            v

Table of Contents                                                                                   vi

List of Tables                                                                             ix

List of Figures                                                                                  x

List of Appendices                                                                             xiv

Abstract                                                                                                        xv

CHAPTER ONE: INTRODUCTION

  1.      General Introduction                                                              1
    1.      The Earth’s Atmosphere                                                                     2
      1. The Thermal Structure of the Earth’s Atmosphere              3
      1. The Earth’s Magnetic Field.                                       6
    1.       The Ionosphere                                                                            7
      1. Structure of the Ionosphere                             8
    1.       Solar Radiation and the Earth’s Atmosphere          8
    1.       Geomagnetic Storm                                                     11
      1. The Disturbance Storm Time (Dst) Index                12
      1. Effects of Geomagnetic Storm on Earth’s Atmosphere  13
    1.       Coronal Mass Ejections (CMEs)                  15
      1. Causes of Coronal Mass Ejections                          16
      1. Coronal Mass Ejections Effects on Earth’s Magnetosphere 16
      1. Solar Flares and Coronal Mass Ejections               17
    1.       The Solar Activity Cycle                                                  18

Effects  of Solar Activity Cycle on the Earth’s Ionosphere    20

  1.      Solar Wind                                                                 22

     Purpose of Study                                                       23

CHAPTER TWO: LITERATURE REVIEW

2.1 Review of Coronal Mass Ejections (CMEs) Arrival Time            24

2.2 Review of CMEs and Geomagnetic Storm                            26

2.3 Review of CMEs and Solar Activity                         26

2.4 Review of CMEs and Solar Flare.                                   27

CHAPTER THREE: SOURCES, THEORY AND METHODS OF DATA ANALYSIS

  •     Sources of Data                                                         29
    • Coronal Mass Ejections (CMEs) data                         29
    • Geomagnetic storm Data                                                  30
    •     Theory  of Method of Data Analysis                          41       
      • Coronal Mass Ejections Arrival model                           41
      • Empirical Coronal Mass Ejections Arrival (ECA) Models   41
      • Theory of Gopalswamy et al. (2000) Model: Constant Acceleration or Deceleration                                 42
  • Theory of Gopalswamy et al. (2001) Model: Cessation  of Acceleration before IAU.                                                                                42
  • Theory of Vrsnak and Gopalswamy (2002) Model: Aerodynamic Drag.                  42
    • Theory of  the Modified Coronal Mass Ejection Arrival (ECA) Model 43
    •     Method of Data Analysis                                    45

3.3. 1     Linear Regression Analysis.                                                      45

3.3.2      Coefficient of Correlation                                         45

3.3.3     Method of Analysis of CMEs Arrival Time             46

3.3.4     Method of Analysis of CMEs and Solar Wind Velocity        46

3.3.5  Method of Analysis of CMEs and Solar Activity Cycle 46

3.3.6   Method of Analysis of CMEs on Geomagnetic Storm       46

CHAPTER FOUR: RESULTS AND DISCUSSION

4.1   Prediction of Arrival time of CMEs Events.                              47

4.2   Influence of Solar Wind Velocity on CMEs Transit Time.      55

4.3   Effects of Solar Activity Cycle on CMEs Transit Time       66

4.4   Effects of CMEs on Geomagnetic Storm      80

CHAPTER FIVE: CONCLUSION AND RECOMMENDATION

5.1 Conclusion                                                                              82

5.2 Recommendation                                                           83

     References                                                                                      84

     Appendix                                                                                     88

Abstract

Predicting the arrival time of Coronal Mass Ejections (CMEs) with a lower value of average error between the predicted and the observed transit time is very crucial in space weather forecast. We proposed a modified Empirical Coronal Mass Ejection Arrival (ECA) model to predict the arrival time of twenty eight (28) CMEs from the sun to the earth. We tested the modified model by using data obtained from coronagraph observations of Large Angle Spectrometric coronagraph on aboard the Solar and Heliospheric Observatory (SOHO/LASCO) CME catalogue from the period of 1998-2012. To ascertain the accuracy of our model, we employed the three Empirical Coronal Mass Ejection arrival (ECA) models of Gopalswamy to our data points. The average error obtained between the CMEs transit time and models predicted  transit time with their  fractional errors were 4.27 hours and 0.10 for the modified model; 10.41hours and 0.23 for the VG2002 model; 12.3hours and 0.29 for G2001 model; 14.46 hours and  0.34 for the G2000 model. Other analyses revealed that Solar wind speed and solar activity cycle have significant influence on CMEs transit time.  Solar wind speed and CMEs speed at 1AU have been observed to have contributed to the magnitude of geomagnetic storm. Our modified model has proved to be effective in prediction of arrival time of CMEs. This least average error obtained between CMEs transit time and the model’s predicted transit time and the fractional error was much lower than all the existing models. It is our recommendation that future work be carried out employing our modified model with a view to confirming its accuracy.

CHAPTER ONE

INTRODUCTION

  1.  General Introduction

Coronal mass ejections (CMEs) are massive burst of solar materials (clouds of plasma and magnetic fields) that shoot off the Sun’s surface and released into space. Over a distance of a few solar radii, CMEs may accelerate up to a speed of 300 and subsequently propagate through the solar wind away from the Sun (Mostl et al., 2014 ;Yashiro et al., 2001)

CMEs are known to be the major cause of severe geomagnetic disturbances which is often referred to as space weather (Zhang et al., 2001; Cheng et al., 2014; Cyr et al; 2000; Tripathi et al., 2005). There are several space weather phenomena which tend to be associated with or are caused by geomagnetic storm. These include: Solar Energetic Particles (SEP) events (hazardous to Humans), Geomagnetically Induced Currents (GIC) which cause damages to satellites and electricity grid, ionospheric disturbances which may lead to radio and radar scintillation, disruption of navigation by magnetic compass and aurora displays at much lower latitudes than normal (Baker and John 2008).

Researchers have been able to continuously monitor the Sun using both full disk images and coronagraphs. With the launch of the solar and heliospheric observatory (SOHO), studies of the evolution of CMEs have been carried out which primarily focused on observations by the Large Angle and Spectrometric Coronagraph (LASCO) on board SOHO. Studies were also devoted to the in situ identification of CMEs near the Earth by Advanced Composition Explorer (ACE) that samples particles from the Sun as they stream toward the planet Earth. The Solar Dynamic Observatory (SDO) focuses on solar atmosphere. Other information and the properties of CMEs come from signatures of CMEs in time series of plasma and magnetic field measurement (in situ) in the interplanetary medium especially at 1AU (AU is the astronomical unit of measurement of sun-earth distance) where they are usually referred to as interplanetary CMEs (ICMEs). Combining observations at 1AU with those of the Sun, then permits a close link between solar events and its interplanetary manifestations.

Most of the studies carried out to predict the arrival time of CMEs from the Sun to the Earth have been with a lot of assumptions regarding the geometry and evolution of CMEs in the Inter Planetary (IP) medium. Many works have been done by many researchers in this regard in predicting the arrival time of CMEs to 1AU using different models. Predicting the arrival time of CMEs with a minimal error has been a major issue in the field of Heliophysics, because the average error between the observed transit time and predicted transit time obtained in all the result of the models so far are still very large. There is need for a lower value between the predicted and observed transit time.

Predicting the arrival time of CMEs with minimal average error will help serve as a practical way of getting advanced warning of solar disturbances heading towards the earth, save billions of currency that would have been used to repair or replace damaged satellites and power grids, identify communication problems, help high altitude flight management and make provisions for renewable energy sources to protect the Earth against a black out.

1.2 The Earth’s Atmosphere.

The Atmosphere of the Earth is a layer of gases surrounding the planet Earth that is retained by Earth’s gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention (greenhouse effect) and reducing temperature extremes between day and night (the diurnal temperature variation).

The atmosphere has a mass of about 5.15×1018 kg. The common name for breathing gases and those involved in photosynthesis is air. By volume, dry air contains 78% Nitrogen, 20.9% oxygen (Zimmer, 2013), 0.93% Argon, 0.039 Carbon dioxide. According to National Oceanic and Atmospheric Administration (NOAA), (2006); the major constituent of dry air by volume is given in Table 1.1

The atmosphere becomes thinner and thinner with increasing altitude, with no definite boundary between the atmosphere and outer space. Although air content and atmospheric pressure vary at different layers, air suitable for the survival of terrestrial plants and animals is found in the Earth’s troposphere.

1.2.1 The Thermal structure of the Earth’s Atmosphere.

In general, air pressure and density decrease with altitude in the atmosphere. The general pattern of the temperature/altitude profile is constant and recognizable through means such as balloon soundings. The temperature behavior provides a useful metric to distinguish between atmospheric layers.

The troposphere is the lowest layer of the Earth’s atmosphere. It extends from the Earth’s surface to an average height of about 12km, although this altitude actually varies from about 9km at the poles to 17km at the equator. The temperature in the troposphere decreases as altitude increases, dropping from about 17oC to -52oC (Subbiondo, 2004). This is because it is mostly heated through energy transfer from the surface. Thus, the lowest part of the troposphere is typically the warmest section of the troposphere. This promotes vertical mixing the troposphere is denser than all its overlying atmospheric layers because a larger atmospheric weight sits on top of the troposphere and causes it to be most severely compressed. It is primarily composed of Nitrogen (78%) and Oxygen (21%) with only small concentrations of other trace gases. Nearly all atmospheric water vapor or moisture is found in the troposphere, so it is the layer where most conventional aviation activity takes place.

The stratosphere is the second –lowest layer of the Earth’s atmosphere. It is bounded by the stratopause. The stratosphere contains the ozone layer. In this layer, the temperature rises with increasing altitude. The rise in temperature is caused by the absorption of ultraviolet radiation (UV) radiation from the Sun by the ozone layer which restricts turbulence and mixing. The troposphere is bounded above by the tropopause, a boundary marked by stable temperature. The stratospheric temperature profile creates very stable atmospheric conditions so that the stratosphere lacks the weather-producing air turbulence that is so prevalent in the troposphere.  

The mesosphere is the third highest layer of the Earth’s atmosphere, occupying the region above the stratosphere and below the thermosphere. It extends from the stratosphere an attitude of about 50km to the menopause at 80-85km above the sea level. Temperature drops in increasing attitude to the mesopause; it is the coldest region on Earth. According to State and Gardner (2010), the average temperature of the mesopause is around 85oC (-120oF or 190K).The mesosphere is also the layer where most meteors burn up upon atmospheric entrance. It is too high above the Earth to be accessible by jet-powered aircraft and too low to support satellites and orbital or sub-orbital spacecraft. It is mainly accessed by rocket-powered aircraft and unmanned sounding rockets.

The Thermosphere is the second-highest layer of Earth’s atmosphere, it extends from the mesopause (which separates it from the mesosphere) at an altitude of about 80km up to the thermopause at an altitude range of 500-l,000km.The lower part of the thermosphere from 80km to 550km above the Earth’s surface contains the atmosphere. In this region temperature increases with altitude. This is due to the extremely low density of its molecules. The temperature of this layer can rise as high as l,727°C (Subbiondo,2004).The air is rarefied that an individual molecule travels an average of 1 kilometer between collisions with other molecules.

The exosphere is the outermost layer of the Earth’s atmosphere. It extends from the exobase, which is located at the top of the thermosphere at an altitude of about 700km above sea level to about 10,000km. The exosphere merges with the emptiness of outer space, where there is no atmosphere. The layer is mainly composed of extremely low densities of hydrogen, helium and several heavier molecules including nitrogen, oxygen and carbon dioxide closer to the exobase. The atoms and molecules are so far apart that they can travel hundreds of kilometers without colliding with one another. Since the exosphere no longer behaves like a gas, the particles constantly escape into space. The free moving particles follow ballistic trajectories and may migrate in and out the magnetosphere or the solar wind.

The Earth’s magnetic field, also known as the geomagnetic field is the magnetic field that extends from the Earth’s interior to where it meets the solar wind, a stream of charged particles emanating from the Sun. The Earth’s magnetic field is generated by electric currents in the convection currents due to heat escaping from the core. The Earth’s magnetic field changes overtime because it is generated by a geodynamo. Near the surface of the Earth, the geomagnetic field can be approximated by the magnetic dipole positioned at the centre of the Earth and tilted at an angle of about 11.50 with respect to the rotational axis of the Earth.

A typical procedure for measuring its direction is the use of compass to determine the direction of magnetic North. Its angle relative to true North is the declination (D) or variation. Facing magnetic North, the angle the field makes with the horizontal is the inclination (I) or dip. The intensity (F) of the field is proportional to the force it exerts on a magnet. Another common representation is in X (North), Y (East) and Z (Down) coordinates.

F is the total field. The magnitude of the field projected in the horizontal plane is H. The Declination (D), inclination (I), and total intensity F can be computed as shown below.

D =                                                                                            (1.1)

I  =                                                                                            (1.2)

H =                                                                                          (1.3)

F =                                                                                            (1.4)

The Earth’s magnetic field serves to deflect most of the solar wind, whose charged particles would otherwise strip away the ozone layer that protects the Earth from harmful ultraviolet radiation (Schlermeler, 2005).

1.3      The Ionosphere.

The ionosphere is a region of the upper atmosphere, from about 85km to 600km altitude that is ionized by solar and cosmic radiations. The ionosphere is of major importance because among other function, it influences radio propagation to distant places on the Earth, and between satellites and the Earth. Most of the ionosphere is electrically neutral but when solar radiation strikes the chemical constituents of the atmosphere, electrons are dislodged from atoms and molecules to produce the ionospheric plasma. This occurs in the Sun light side of the Earth, and only the shorter wavelength solar radiation (the extreme ultraviolet and X-ray part of the spectrum) are energetic enough to produce this ionization.

Ionization depends primarily on the Sun and its activity. The amount of ionization in the ionosphere varies greatly with the amount of radiation received from the Sun. Therefore there is diurnal (time of day) effect and a seasonal effect. The local winter hemisphere is tipped away from the Sun, thus there is less received solar radiation. The activity of the Sun is associated with Sunspot cycle, with more radiation occurring with more Sunspots. Radiation received also varies with geographical location (polar, aurora zones, mid-latitudes and equatorial regions).

There are also mechanisms that disturb the ionosphere and decrease the ionization. There are disturbances such as solar flares and the associated release of charged particles into the solar wind which reaches the Earth and interacts with its geomagnetic field.

1.3.1 Structure of the Ionosphere.

The ionosphere is divided into three layers namely the D, E and F with the term “Layer” referring to the ionization within a region. Figure 1.3 shows the various layers of the ionosphere and their predominant ion populations

The D layer is the lowest Layer covering altitude between 50km and 90km. The ionization here is due to Lyman series-alpha hydrogen radiation at a wavelength of 121.5nm ionizing Nitric Oxide (NO). With high solar activity, hard-X rays (wavelength< 1nm) may ionize molecular Nitrogen (N2) and oxygen (O2) during the night, cosmic rays produce a residual amount of ionization. Recombination is high in the D layer.

Fig 1.3 Structure of the Ionosphere (Schunk, 2009)

The net ionization effect is low but loss of wave energy is great due to frequent collisions of the electrons. High frequency (HF) radio waves are not reflected by the D layer. The absorption is small at night but greatest about mid day.

The E layer is the middle layer, covering 90 to 180 km above the Earth’s surface. Ionization here is due to soft X-Rays (1-10 nm) and far ultraviolet (UV) Solar radiation ionization of molecular oxygen (O2). This layer can reflect radio waves having frequencies lower than about 10 MHz. Within the E region, is the normal E layer produced by solar radiation and sporadic layers designated Es. During intense sporadic E events, the Es layer can reflect frequency up to 50 MHz and higher. The Es layer is characterized by small thin clouds of intense ionization which can support reflection of radio waves up to 225 MHz. At night the E-layer disappears because the primary source of ionization is no longer present.

The F layer lies between 180 and. 1,000 km. The F layer can be separated into two layers F1 and F2 during the day (Hines et al.  1965 and Ratcliff, 1960). At higher altitude, the number of oxygen ions decreases and higher ions such as hydrogen and helium become dominant. The extreme ultraviolet (UV, 10-100nm) solar radiation ionizes atomic oxygen. During the day, two layers can be distinguished, a small layer known as F1 and above it is a more highly ionized dominant layer called F2. At night they merged at the level of F2 layer which is also called the Appleton layer. This region reflects radio waves with frequencies up to about 35 MHz. 

1.4   Solar Radiation and the Earth’s Atmosphere

The atmosphere may seem to be completely transparent to solar radiation, but there are dynamic interactions occurring constantly that result in a complex and delicately balanced system crucial to the continuation of life forms on Earth. The atmosphere acts as a filter, absorbing and reflecting portions of the electromagnetic spectrum such as ultraviolet region, that are harmful to humans and other life forms. It also provides a natural “green house effect” maintaining the temperatures and climates in which life forms on Earth have evolved to` survive. The atmosphere controls amount of solar radiation reaching the surface of the Earth and regulates the amount of radiation from the Earth escaping into space. Slight changes in the concentrations of certain gases may upset the balance of reactions and be detrimental to life.

Absorption is the process by which radiant energy is transferred to matter. If the matter is gas, radiation can affect it in a number of ways. The ways it can absorb energy depends on the size and complexity of the gas molecule. The gas molecule can be rotated and a variety of vibratory modes can be excited depending on the nature of the molecule. If the energy is strong enough the molecule can be splitted apart. Each mode of energy absorption occurs at a specific narrow band of the solar spectrum. Gases, therefore, are not like black bodies that absorb equally and completely at all wavelengths. Rather, they absorb only at specific, often narrow ranges of wavelengths.

 Diatomic molecules such as nitrogen and oxygen (most of our atmosphere) can absorb energy by increasing the vibration of the bond between the two atoms. If the energy absorbed is great enough it may break the bond resulting in two freewheeling oxygen or nitrogen atoms traveling at high speeds. Thus, we have (Schneider, 1989):

               O2 + ultraviolet light = O + O                                                                   (1.5)   

Nitrogen absorbs only in the extreme ultraviolet of which there is very little in the Sun’s radiation. Oxygen absorbs more strongly than nitrogen and over a wider range of wavelengths in the ultraviolet. Oxygen molecules are therefore splitted into oxygen atoms in the highest regions of the atmosphere. By an altitude of about 100 kilometers much of the radiation that is energetic enough to do this breaking of molecular bonds is used up and this process diminishes. Hence there is heating of the uppermost atmosphere (fast moving atoms of nitrogen and oxygen) and as the altitude decreases to about one hundred kilometers the atmosphere cools. This is because there is little absorption of solar energy and consequently little heating of the atmosphere so the temperature reaches a minimum.

Descending below eighty kilometers the atmosphere is heated by another process. Here the atmosphere gets denser (thicker) with decreasing altitude; the molecules of oxygen and nitrogen are closer together. If the bond of an oxygen molecule is broken and the two atoms go flying off, there is a higher likelihood that one of these atoms will strike an oxygen molecule. If it does it may form an ozone molecule. Above 50 kilometers the heating is primarily due to the break up of oxygen molecules by ultraviolet radiation with wavelengths between 0.12 and 0.18 μm, while between 50 kilometers and 10 kilometers the heating is due to the absorption by ozone of ultraviolet radiation with wavelengths between 0.18 and 0.34 μm.

Both the breaking up of oxygen molecules above fifty kilometers and ozone molecules at fifty kilometers and below cause heating of the atmosphere.

1.5 Geomagnetic Storm.

A geomagnetic storm is a temporary disturbance of the Earth’s magnetosphere caused by a solar wind shock wave which interacts with the Earth’s magnetic field. The increase in the solar wind pressure initially compresses the magnetosphere and 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 movement of plasma through the magnetosphere (driven by increased electric field inside the magnetosphere) and an increase in electric current in the magnetosphere and ionosphere.

A typical geomagnetic storm has three phases namely an initial phase, a main phase and a recovery phase (Gonzalez et al., 1994) as shown in Figure 1.4. The initial phase is characterized by Disturbance Storm Time (Dst) increasing by 20 to 50nT lasting from minutes to hours. The initial phase is also referred to as a storm sudden commencement (SSC). Not all geomagnetic storms have an initial phase and not all sudden increases in Dst are followed by a geomagnetic storm. The main phase of a Geomagnetic storm is defined by Dst decreasing to less than -50nT. The main phase can last for about 2 to 8 hours.

During the main phase of a geomagnetic storm, electric current in the magnetosphere creates magnetic force which pushes out the boundary between the magnetosphere and solar wind. Disturbance in the interplanetary medium which drives the geomagnetic storm may be due to a solar coronal mass ejection (CME) or a high stream (Co-rotating interaction region or CIR) of the solar wind originating from a region of weak magnetic field on the Sun’s surface (Bern, 2000).

The recovery phase is the period when the disturbance changes from its minimum value to its quiet time value. The period of the recovery phase may be as short as 8 hours or as long as eight days. The frequency of geomagnetic storm increases and decreases with the Sunspot or solar cycle. CME driven storms are more common during the maximum of the solar cycle and CIR driven storms are more common during the minimum of the solar cycle.

There are several space weather phenomena which tend to be associated with or are caused by a geomagnetic storm. These include: Solar Energetic Particle (SEP) events, Geomagnetically induced Currents (GIC), ionospheric disturbances which cause radio and radar scintillation, disruption of navigation by magnetic compass and aurora displays at much lower latitudes than normal.

1.5.1 The disturbance storm time (Dst) Index. 

The disturbance storm time index (Dst) is a measure of geomagnetic storms. It is expressed in nanotesla and is based on the average value of the horizontal component of the Earth’s magnetic field measured hourly at four near- equatorial geomagnetic observatories. The disturbance shows the effect of the globally symmetrical westward flowing high altitude equatorial ring current which causes the “main phase” depression worldwide in the H- component field during large storms. The use of the Dst as an index of storm strength is possible because the strength of the surface magnetic field at low latitudes is inversely proportional to the energy content of the ring current which increases during geomagnetic storm.

In the case of a classic magnetic storm, the Dst shows a sudden rise corresponding to the storm sudden commencement and then decreases sharply as the ring current intensifies. Once the interplanetary magnetic field (IMF) turns northward again and the ring current begins to recover, the Dst begins a slow rise back to its quiet time level. Other currents contribute to the Dst; most importantly is the magnetopause current. The Dst index is corrected to remove the contribution of this current as well as that of quiet time ring current.

Kaur and Kumar (2005) classified the size of geomagnetic storm as follows:

Intense          Dst   ≤   -100nT.

Major           -50nT   >   Dst   >  -100nT   .

Minor             20nT >   Dst   >   -50nT.

PREDICTION OF ARRIVAL TIME OF CORONAL MASS EJECTIONS USING THE ONSET OF GEOMAGNETIC STORM