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THE GLOBAL ATMOSPHERIC-ELECTRICAL CIRCUIT 207 the diurnal maximum of the fair-weather potential gradient at the Earth's surface occurred at the same universal time (about 1900 UT). Furthermore, radio measurements of atmospherics showed that global thunderstorm activity also peaked near 1900 UT, with the main thunderstorm centers being in Africa and South America. Scientists studying meteorological statistics of thunderstorm activity found similar diurnal variations. The diurnal UT variation of potential gradient over the oceans was similar to the diurnal UT variation of thunderstorm occurrence frequency with no phase delay. These experimental facts all contributed to the concept of the Earth's global electrical circuit and furthermore suggested that thunderstorms were the generators within the circuit. This concept of the global electrical circuit persists today, although there are still basic problems and details that need to be resolved (Dolezalek, 1971, 1972; Kasemir, 1979). THUNDERSTORMS AS GENERATORS IN THE GLOBAL CIRCUIT The vast majority of clouds in the atmosphere form and dissipate without ever producing precipitation or lightning. A cloud, however, interacts with atmospheric ions and becomes electrified to a certain degree. The small, fast ions in the atmosphere almost exclusively provide the electrical conductivity. The intermediate and large ions do not greatly contribute because of their lower mobility. The fast ions within clouds become attached to more massive cloud particles and thereby decrease the electrical conductivity within the cloud relative to the surrounding clear air. As a result of this electrical conductivity change alone, clouds act as an electrical obstacle; space charge develops on the surface of the cloud, and the distribution of fair-weather conduction currents and fields flowing in the vicinity of the cloud are altered. As convective activity intensifies, electrification increases. Strong electrification generally begins with the rapid vertical and horizontal development of a fair-weather cumulus cloud into a cumulonimbus type. Most of the lightning on Earth is produced by strongly convective cumulonimbus clouds with a vigorous system of updrafts and downdrafts. The updrafts and downdrafts associated with convection and the interactions between cloud and precipitation particles (Tzur and Levin, 1981; Rawlins, 1982) act in some manner that eventually separates charges within the thundercloud. Charge-separation processes usually fill the upper portion of the thundercloud with the main positive charge and the lower portion with the main negative charge. The measured charge structure within individual clouds is complex (Krehbiel et al., 1979), and a simplifying assumption that is usually made for modeling purposes considers the charge to be distributed in a spherical fashion within some finite volume. A finite spherical distribution of charge has the same distant electric-field structure in space as an equivalent point charge. Therefore, for simplicity in studies of the electrical interaction of a thunderstorm with its immediate environment, the lightning charges, which are lowered to ground during a lightning stroke, and the main thunderstorm charges are usually represented as a series of point charges. The main negative charge in the lower part of a thunderstorm (Krehbiel et al., 1979) occurs at a height where the atmospheric temperature is between â10Â°C and â20Â°C. This temperature range is typically between 6 and 8 km for summer thunderstorms and around 2 km for winter thunderstorms. The positive charge at the top of the storm does not have so clear a relationship with temperature as the negative charge but can typically occur between â25Â°C and â60Â°C depending on the size of the storm. This temperature range usually lies between 8 and 16 km in altitude. The ensemble of thunderstorms occurring over the globe at any given time will have positive and negative charge centers located over a large altitude range depending on the atmospheric structure, the size of the thunderstorm, its type (e.g., air mass, frontal), its location (e.g., ocean, plains, or mountains), its latitude, its stage of development, and other factors. There is no generally accepted model of thunderstorm electrification that can be used to calculate the current that storms release into the global electrical circuit. Measurements by Gish and Wait (1950), Stergis et al. (1957a), Vonnegut et al. (1966, 1973), and Kasemir (1979) showed that the total current flowing upward from thunderstorms areas ranges from 0.1 to 6 A with an average of about 0.7 A per thunderstorm cell. It is, thus, possible to use this value in a theoretical model without referring to the details of the charge-separation mechanisms. The simplest model used to investigate the electrical interactions of a thunderstorm with its immediate environment assumes a quasi-static dipolar charge distribution embedded within the thundercloud, which is immersed in a conducting atmosphere whose electrical conductivity increases exponentially from the surface of the Earth to a highly conducting region somewhere within the ionosphere above about 60 km. In the quasi-static state these charges are maintained in equilibrium against discharge currents by assuming that a steady convection current acts between the two charge centers in the updraft and downdraft regions of the storm. In earlier studies only conduction currents were assumed to flow in the environment, and although
THE GLOBAL ATMOSPHERIC-ELECTRICAL CIRCUIT 208 this assumption is probably valid in the highly conducting region above a storm it is not valid within and below the storm, where corona, lightning, precipitation, convection, and displacement currents all contribute to the charge exchange between charge centers and between the storm and the surface of the Earth. Holzer and Saxon (1952) and Kasemir (1959) presented analytic solutions for the potential distribution around thunderstorms whose charge distributions are represented as point dipole current sources. A calculated normalized potential distribution around a quasi-static dipolar charge structure within the atmosphere (Kasemir, 1959) is shown in Figure 15.1(a). The lines represent streamlines of current flow between the two charge centers and between the charge centers and the ionosphere and the ground. The highly conducting Earth's surface is considered by including image point sources within the Earth for the solution of the electrostatic potential distribution around the thunderstorm. The currents flow upward from the positive charge center toward the ionosphere and from the ground toward the negative charge. There is also a current flow between the charges. All currents are calculated as conduction currents in this simple model and have considerably more complexity in actual storms. Figure 15.1 (a) Schematic giving the current streamlines of dipolar point current sources embedded within an atmosphere with exponentially increasing conductivity over a perfectly conducting Earth, (b) schematic of a lumped parameter representation of the global atmospheric electrical circuit where the thunderstorm is represented as a current generator with internal resistance W i , W0 represents the resistance between cloud top and the ionosphere, Wa represents the fairweather load resistance, and Wu represents the resistance between the thunderstorm and the ground (Kasemir, 1959). Holzer and Saxon (1952) showed that the current output from such a thunderstorm model is sensitive to the charge-separation distance, with a greater current output from larger storms having intense vertical velocities and charge-separation capability. They also showed that storms with frequent cloud-to-ground lightning strokes move negative charge to the Earth's surface and leave the cloud with a net positive charge that has a greater current output than a dipole. Thus, according to their calculations, even a weak storm with charge separation could supply a current to the ionosphere and the global circuit. Kasemir (1959) showed that the exponential conductivity increase with altitude in the atmosphere is important for the current flow from thunderstorms toward the ionosphere. He pointed out that if the atmosphere had a constant conductivity at all altitudes the primary thunderstorm source current would flow downward to the image source, with no current flow toward the ionosphere and into the global circuit. Anderson and Freier (1969) considered both the limiting fast and slow time variations within thunderstorms. Their dipole quasi-static solutions for slow time variation show that the potential distribution about thunderstorms is affected by both the conductivity and the charge-separation distance within storms. Their calculations also suggest that the thunderstorm, in a quasi-static sense, may be electrically closed and only the pumping action of lightning discharges can provide the current necessary to maintain the ionospheric potential. Park and Dejnakarintra (1973, 1977a) considered a dipolar thunderstorm model and analytically solved for the current output and the mapping of thundercloud electric fields into the ionosphere. This model considered the anisotropy of the electrical conductivity above about 60 km and assumed that the Earth's geomagnetic-field lines were vertical. The largest ionospheric fields were calculated to occur at night over giant thunderstorms with values on the order of 10-4 V/m at 100 km. During the day the calculated dc electric fields are 1 to 2 orders of magnitude smaller because of the increased ionospheric electrical conductivity caused by solar extreme ultraviolet (EUV) radiation ionization. Dejnakarintra and Park (1974) examined the penetration of lightning-induced ac fields into the ionosphere and found that the lightning electric-field signal recovery time decreases rapidly with increasing altitude until at 100 km the electric-field wave form appears as a sharp pulse. The ac fields are also larger at night than during the day, when ionospheric conductivities are larger. Wait (1960) pointed out that there is a constant radial
THE GLOBAL ATMOSPHERIC-ELECTRICAL CIRCUIT 209 potential associated with the lower-order (n = 0) mode in a concentric spherical cavity excited by a radial current- moment element. He estimated that the potential across the earth-ionosphere gap caused by a single 3-km-length lightning discharge of 1000 A would be on the order of 1 V, and he suggested that the omnipresent constant voltage during fair weather might result from the accumulated action of a number of lightning strokes. Hill (1971) further examined the resonant hypothesis and showed that the atmospheric field is generated through electrostatic induction by equivalent charge dipoles from thunderclouds. Using parameters of lightning frequency and the magnitude of the current moment within storms available at that time, he found an ionospheric potential only about one third of the observed intensity. Schumann resonances in the earth-ionosphere cavity are also excited by worldwide lightning activity, and this subject has been reviewed by Polk (1982). Willett (1979) pointed out that the total current supplied to the global electric circuit from a thunderstorm differs depending on whether the storm is considered to be a current or a voltage generator. For a current thunderstorm generator, where the current supplied to the global circuit is independent of the load, his results showed that current output is proportional to the assumed source current strength and to a proportionality factor that depends on the ratio of the height of the ionosphere to the electrical conductivity scale height. For a voltage-source thunderstorm generator, where the charging current increases with time until limited by some voltage-sensitive dissipative mechanism such as lightning or corona, the current output may be somewhat smaller depending on assumptions made concerning the storm's internal resistance. Not enough is known about the thunderstorm generator to distinguish be tween the current and voltage source models. Freier (1979) presented a thunderstorm model with more details than point-charge sources and conduction currents. He considered the atmosphere between the Earth and the ionosphere divided into three separate regions as shown in Figure 15.2. In region 1, below the negative layer of charge in a thunderstorm, he considered conduction, displacement, and precipitation current densities, allowing all to vary with altitude. In region 2, between the bottom and top of the thunderstorm cloud, he considered charging, conduction, displacement, and precipitation current densities that also vary in space and time. In region 3, above the storm, only conduction and displacement are considered. All lightning currents are considered to be discontinuous charge transfers, and in the fair-weather regions far to the side of the thunderstorm only conduction currents flow. Figure 15.2 Schematic illustrating the various currents that flow within and in the vicinity of thunderstorms: J E is the conduction current, J c is a convection current, J L is the lightning current, J p is the precipitation current, âD/ât is the displacement current, and J M is the total Maxwell current. This model is an improvement over previous thunderstorm models, which considered lumped circuit parameters of columnar resistance as shown in Figure 15.1 (b) for the dipolar conduction current generator. Freier (1979) used it to describe a charge-transfer mechanism that may occur during large severe storms when precipitation is heavy and when the storms are, in certain instances, accompanied by tornadoes. The precipitation current during such storms may be so large that it removes much of the negative charge in the lower portion of the storm and allows the generator to operate between the positive charge and the ground. During such storms much more electrical energy is produced, with a possibly greater current output that must be considered in any global electric model. Krider and Musser (1982) pointed out that the time variations in thunderstorm electric fields, both aloft and at the ground, can be interpreted as a total Maxwell current density that varies slowly in intervals between lightning discharges. The total Maxwell current, J M , consists of field-dependent currents, both linear and nonlinear (corona), J E ; convection currents, J C ; lightning currents, J L ; and the displacement current density, âD/2ât.