An Introduction to Lightning

Lightning has been striking the Earth since before humans first set foot on the planet. In fact, the occurrence of lightning is so common that before you finish reading this sentence, lightning will have struck the Earth more than 100 times. At any given instant approximately 2,000 thunderstorms are roaming the Earth’s atmosphere, and they strike the Earth with lightning flashes 100 times per second.

The main constituents of air in the Earth’s atmosphere are nitrogen (78 %), oxygen (20 %), noble gases (1 %), carbon dioxide (0.97 %), water vapor (0.03 %), and other trace gases. Because of the ionization of air by the high-energy radiation of cosmic rays and radioactive gases generated from the Earth, each cubic centimeter of air at ground level contains approximately ten free electrons. In general, air is a good insulator, and it can retain its insulating properties until the applied electric field exceeds approximately 3 × 10⁶ V/m at standard atmospheric conditions (i.e., T = 293 K and P = 1 atm). When the background electric field exceeds this critical value, air is converted very rapidly into a conducting medium, making it possible for electrical currents to flow through it in the form of sparks. Let us now consider the basic processes that make possible the conversion of air from an insulator into a conductor and the different types of discharge that take place in air under various conditions.

The goal of this chapter is not to provide a reference for the theory of electricity and magnetism. The study of the physics and effects of lightning flashes entail certain elements of electricity and magnetism that are used to describe various interactions. Some of the equations of electromagnetic theory that will be used either directly or indirectly in the book are presented here. For a complete treatment of the subject the reader is referred to Refs. [1] and [2].

Based mainly on the way in which the atmospheric temperature varies with height, Earth’s atmosphere is divided into several radial sections. The way in which the air temperature of Earth’s atmosphere varies as a function of height is depicted in Fig. 4.1. Observe that as height increases from ground level, initially the temperature decreases with height, reaches a minimum value at a certain height, and then starts to increase. The height where the temperature starts to increase again is called the tropopause. The height of the tropopause is not constant around the globe. In tropical regions, its height is approximately 12 km and in temperate regions approximately 9 km. The region below the tropopause is called the troposphere. As we will see later, all thunderstorm activity around the globe takes place in the troposphere. With increasing altitude from the tropopause the temperature starts to increase (it could also remain more or less stable over tens of kilometers), and the next inversion point where the temperature starts to decrease with height is called the stratopause. The region between the stratopause and the tropopause is called the stratosphere. This tendency for the temperature to increase with height is broken again with increasing altitude at a height known as the mesopause. The region between the mesopause and the stratopause is called the mesosphere. As we will see later, all three of these regions of the atmosphere – troposphere, stratosphere, and mesosphere – take part in activities related to lightning flashes. Indeed, it is the troposphere where thunder clouds and lightning flashes manifest themselves, but their effects are felt in both the stratosphere and the mesosphere, and these indirect effects manifest in various forms and are called upper atmospheric lightning flashes (a description of these electrical events is given in Chap. 19). But it should be understood that these are not independent events but are always related to the action of lightning flashes taking place in the troposphere. The way in which these indirect effects are manifested depends on the electrical characteristics of the atmosphere and the gas density.

Almost everyone is familiar with cumulus clouds (Fig. 5.1a), which look like a piece of floating cotton, with a sharp outline and a flat bottom. When a growing cumulus resembles the head of a cauliflower, it is called a cumulus congestus (Fig. 5.1b). When conditions are just right, cumulus congestus continues to grow vertically, and the result is cumulonimbus, the thundercloud (Fig. 5.1c). It is a giant heat engine that converts the energy of the Sun into the mechanical energy of air currents and the electrical energy of lightning.

Many theories have been advanced to explain the generation of electrical charge in thunderclouds [1]. However, one theory has withstood the test of time, and the current consensus is that the mechanism proposed by this theory is the dominant one for charge separation in thunderclouds. This mechanism is based on the collision of graupel and ice crystals in a cloud.

As we saw in Chap. 2, the initiation of an electric discharge requires the electric field in the air to increase beyond a critical electric field, which depends on the air density. At sea level this critical electric field is approximately 3 × 10⁶ V/m. The critical electric field necessary for electrical breakdown decreases with atmospheric density, and at a height of approximately 5 km the value of this field is approximately 1.5 × 10⁶ V/m. It is important to note that these values of the electric fields are applicable in clear air devoid of particles. However, the presence of small particles in air can decrease the background electric field necessary for electrical breakdown due to field enhancement. For example, a spherical particle in a background electric field of strength E gives rise to an electric field that varies as 3E cos θ on its surface (Fig. 7.1). Thus, the maximum electric field on the surface of the sphere is 3E. If the particle has a pointed shape, then the field enhancement will be higher. It is important to recognize that to create an electrical breakdown, it is not sufficient for the electric field to reach the critical value at a point. The electric field should increase above the critical value over a critical region so that the electron avalanche process can be initiated. A thundercloud contains a variety of small particles, such as water droplets, ice crystals, and graupel, and their presence will reduce the background electric field necessary for electrical breakdown to a value on the order of 500 kV/m. However, only rarely are such high electric fields observed inside thunderclouds. Measurements conducted inside thunderclouds consistently show typical electric field values of the order of 100–150 kV/m [1]. These values are significantly below the values necessary for electrical breakdown. The question is how the electric fields necessary for an electrical breakdown are achieved inside thunderclouds and what the significance is of an overall electric field of approximately 100–150 kV/m in the breakdown process.

The length of a lightning channel can be tens of kilometers long, and at each point on this channel there is a current flow that changes with time. Unfortunately, it is possible to directly measure only the current at the strike point of a ground lightning flash. When discussing the features of a lightning current, we are actually referring to the features of the lightning current at the strike point. In special cases the current can be measured at elevated strike points by recording the currents in lightning flashes striking airplanes in flight. It is important to note that the features of currents flowing at other points of a lightning channel could be different from that measured at ground level. The farther away the point of interest from the strike point, the larger the possible difference between the two currents. However, before giving the features of lightning currents at strike points, let us understand how the currents in lightning strikes can be measured.

Electromagnetic fields of lightning flashes are of interest both in lightning protection studies and in understanding the physics of lightning flashes. In lightning protection knowledge of the characteristics of electromagnetic fields generated by lightning flashes is necessary in estimating the voltages and currents induced in structures by lightning flashes. The features of lightning-generated electromagnetic fields are of interest in lightning physics because they can be used as a vehicle to probe the physical mechanism behind lightning flashes. They can also be used to estimate the signature of currents in lightning flashes. In this chapter the characteristics of electromagnetic fields of lightning flashes are described. First, let us consider the basic principles of the procedures used to measure both the electric and magnetic fields. The two most common techniques used to measure electric fields are the vertical antenna and the field mill [1]. In the case of magnetic fields a loop antenna is used in the measurements.

To calculate the electromagnetic fields generated by return strokes, it is necessary to know the spatial and temporal variation of the return-stroke current along the channel. Unfortunately, only the return-stroke velocity and the current generated at the channel base can be measured directly, and the way in which the return-stroke current varies along the channel must be extracted indirectly. For example, the magnitude of a current and its wave shape at different heights can in principle be extracted by studying the optical radiation. Unfortunately, the exact relationship between the return-stroke-generated optical radiation and the return-stroke current parameters are not known, and therefore only qualitative inferences can be made on the return-stroke current. The information thus obtained indicates that the return-stroke peak current decreases with height while the rise time of the current increases.

As discussed in Chap. 7, a return stroke is a potential discontinuity that propagates from ground to cloud along the leader channel. The potential ahead of the return stroke front is at cloud potential and the potential behind the return stroke front is close to the ground potential. A similar process also happens if a perfectly conducting vertical wire is charged to a given potential and the end of the wire is connected to ground. In this case, too, a potential discontinuity propagates along the conductor. The speed of propagation of the potential discontinuity in the case of the perfectly conducting wire is equal to the speed of light in air. On the other hand, the speed of propagation of the return stroke front is considerably less than the speed of light, and to date there is no consensus among researchers as to the cause of this speed reduction in the return stroke front. However, return stroke speed is an important parameter in return stroke models, and almost all the return stroke models available at present use return stroke speed as an input parameter.

Consider a radio antenna located over ground and transmitting at a given frequency. If the ground is perfectly conducting, the amplitude of the radio wave generated by the antenna decreases inversely with distance as one moves away from the antenna, i.e., the signal decreases as 1/r, where r is the distance from the antenna to the point of observation. However, if the conductivity of the ground is finite, then the amplitude of the radio wave decreases much more rapidly than the inverse distance. The higher the frequency of the wave, the higher the rate of decrease of the radio signal with distance. This attenuation of the radio signal or the electromagnetic wave by finitely conducting ground is called propagation effects. Attenuation of the electromagnetic wave results from the absorption of energy from the electromagnetic field by the finitely conducting ground. The higher the frequency of the electromagnetic field, the higher the amount of energy absorbed by the ground. Let us analyze this a bit further. Consider an electromagnetic field generated by a radio antenna tuned to a given frequency. If the ground is perfectly conducting, at any given point on the ground the electric field is perpendicular to the ground surface and the magnetic field is in the azimuthal direction (Fig. 12.1a). The direction of energy flow or the Poynting vector (i.e., E × H) of the electromagnetic field at that point is directed parallel to the ground. Now consider the electromagnetic field of a radio antenna located over finitely conducting ground. In this case, the magnetic field has the same direction as before, but the electric field is inclined to the surface of the ground (Fig. 12.1b). That is, there is a component of the electric field parallel to the ground. This component is called the horizontal electric field. The Poynting vector in this case is directed to the ground, indicating that energy is absorbed from the electromagnetic field by the ground. With increasing frequency or with decreasing ground conductivity the angle between the vertical and the direction of the electric field increases, i.e., the horizontal electric field increases. Thus, the energy absorbed by the ground increases with increasing frequency and with decreasing conductivity.

As described in Chap. 9, the magnetic field produced by the current flowing in a vertical lightning channel propagates outward with the speed of light along the ground surface and forms circular loops with the center at the point of strike (Fig. 13.1). At any given point the magnetic field is parallel to the tangent to the circle describing the magnetic field. Thus the direction of the magnetic field gives the direction to the point of a lightning strike. Note also that for a given strike point the magnetic field at the point of observation has opposite polarities for negative and positive return strokes. This is so because the directions of positive current are opposite to each other in the two cases.

The electric potential of a point in space in the vicinity of Earth can be easily defined by assuming the potential of Earth to be zero. The potential can be calculated by evaluating the line integral of the electrostatic field from a point on the ground to a point where the electrical potential is needed. The path of the integration is immaterial because the result is independent of the path of integration. This is because electrostatic fields are conservative. The potential of a metal object in the vicinity of the ground can be defined in the same way. In finding this potential it is possible to integrate the electric field from the ground to any point of the metal object along any path. This is because any point on the metal object has the same potential because, by definition, a metal contains free electrons that move along the surface of the metal and redistribute themselves until the potential at any point of the metal object is the same. But how does one define the potential of a cloud? One problem with the concept of cloud potential is that a cloud is just a collection of charges located on a nonconducting medium, which means that there is no specific definition for the potential of a cloud. The potential of a cloud may vary from one point to another. It may be very high close to the charge centers low at points far from them. Thus, when we speak about cloud potential in connection with a stepped leader, we actually mean the potential of the cloud near the region where the stepped leader was initiated.

A lightning flash can interact with any object either electrically or mechanically or both. In this chapter, both direct and indirect effects of lightning flashes are described. Following a description of the basic physical phenomena associated with direct and indirect lightning strikes, these effects are illustrated here by considering the effects of lightning strikes on residential houses, wind turbines, trees, airplanes, and power lines.

Every year around three billion lightning flashes occur around the world. In tropical regions, approximately 10–20 % of lightning flashes strike the ground while the rest take place inside a cloud. In temperate regions, the corresponding figure is approximately 50 %. From time to time lightning flashes striking the ground interact with humans, causing injuries and sometimes death. Statistics concerning the number of deaths caused by lightning are available only for a few countries. Statistics from many countries in tropical regions are not available, but the number of deaths caused by lightning is likely to be higher in those countries as a result of the higher number of lightning strikes and the amount of time spent outside and in unprotected buildings. The global mortality rate from lightning could be around 1,000 per year. Table 16.1 tabulates the lightning-caused fatalities in several countries.

A lightning conductor is a device invented by Benjamin Franklin to protect buildings from lightning strikes. It provides a low-resistance path for the lightning current to flow to the ground, preventing any damage that would have resulted if the lightning current had passed through the building to the ground. Let us now consider how a lightning conductor acts during a lightning strike.

The attachment of a stepped leader to a grounded structure is mediated by a connecting leader issued by the grounded structure. In the case of short structures, the length of the connecting leader is usually small, but it could be several tens of meters long in the case of tall structures. However, in the electro-geometrical method (EGM), the presence of a connecting leader is neglected (Chap. 17). Thus, the conclusions based on EGM on the attachment of stepped leaders to tall grounded structures could be in error. This simplifying assumption in EGM motivated several scientists to create lightning attachment models that included the effect of connecting leaders. Four models are used by lightning researchers at present, and this chapter presents the basic ideas associated with these models. The four models were introduced by Eriksson [1], Dellera and Garbagnati [2], Rizk [3], and Becerra and Cooray [4, 5]. These models are referred to here as the Eriksson model, the Dellera and Garbagnati model, the Rizk model, and the Becerra and Cooray model.

Thunderstorms and lightning flashes are processes that take place in the Earth’s atmosphere and they can modify it over both the short term and the long term. Thus, understanding the effects of thunderstorms and lightning in the atmosphere is a must, and these effects must be used as inputs in any atmospheric model created to understand the effects of human-made greenhouse gases in the atmosphere. This chapter provides a brief description of the effects of lightning and thunderstorms in the atmosphere, which are of interest in climatology.

Based on various experiences and observations several phenomena associated with thunderstorms and lightning have become part of folklore. These are forked lightning, bead lightning, ribbon lightning, and ball lightning. As outlined subsequently, evidence for some of these are well documented in the literature based on experimental observations, whereas others are based on personal accounts of observations. A brief description of each of these phenomena is given in this chapter.