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John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
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Hans Dolezalek, Hannes Tammet, John Latham, and Martin A. Uman


Hans Dolezalek

The science of atmospheric electricity originated in 1752 by an experimental proof of a related earlier hypothesis (that lightning is an electrical event). In spite of a large effort, in part by such eminent physicists as Coulomb, Lord Kelvin, and many others, an overall, proven theory able to generate models with sufficient resolution is not yet available. Generally accepted and encompassing textbooks are now more than 20 years old. The voluminous proceedings of the, so far, nine international atmospheric electricity conferences (1954 to 1992) give much valuable detail and demonstrate impressive progress, as do a number of less comprehensive textbooks published in the last 20 years, but a general theory as indicated above is not yet created. Only now, are certain related measuring techniques and mathematical possibilities emerging.

Applications to practical purposes do exist in the field of lightning research (including the electromagnetic radiation emanating from lightning) by the establishment of lightning-location networks and by the now developing possibility of detecting electrified clouds that pose hazards to aircraft. Application of atmospheric electricity to other parts of meteorology seems to be promising but so far has seldom been instituted. Because some atmospheric electric signals propagate around the Earth and because of the existence of a global circuit, applications for the monitoring of global change processes and conditions are now being proposed. Significant secular changes in the global circuit would indicate a change in the global climate; the availability of many old data (about a span of 100 years) could help detect a long-term trend.

The concept of the “global circuit” is based on the theory of the global spherical capacitor: both the solid (and liquid) Earth as one electrode, and the high atmospheric layers (about the ionosphere) as the other, are by orders of magnitude more electrically conductive than the atmosphere between them. According to the “classical picture of atmospheric electricity,” this capacitor is continuously charged by the common action of all thunderstorms to a d.c. voltage difference of several hundred kilovolts, the Earth being negative. The much smaller but still existing conductivity of the atmosphere allows a current flowing from the ionosphere to the ground, integrated for all sink areas of the whole Earth, of the order of 1.5 kA. In this way, a global circuit is created with many generators and sink-areas both interspaced and distributed over the whole globe, all connected to two nodes: ionosphere and ground. Within the scope of the global circuit, for each location, the current density (order of several pA/m2) is determined by the voltage difference between ionosphere and ground (which is the same for all locations but varying in time) and the columnar resistance reaching from the ground up to the ionosphere (in the order of 1017 Ω m2).

Natural processes, especially meteorological processes and some human activity, which produce or move electric charges (“space charges”) or affect the ion distribution, constitute local generators and thereby “local circuits,” horziontally and/or in parallel or antiparallel to the local part of the global circuit. In many cases, the local currents are much stronger than the global ones, making the measurement of the global current at a given location and/or during a period of time very difficult or, often, impossible. The strongest local circuits usually occur with certain weather conditions (precipitation, fog, high wind, blown-up dust or snow, heavy cloudiness) that make measurement of the global circuit impossible everywhere; but even in their absence local generators exist in varying magnitudes and of different characters. The separation of the local and global shares in the measured values of current density is a central problem of the science of atmospheric electricity. Aerological measurements are of high value in this regard.

The above description is within the “classical picture” of atmospheric electricity, a group of hypotheses to explain the electrification of the atmosphere. It is probably fundamentally correct but certainly not complete; it has not yet been confirmed by systems of measurements resulting in no inner contradictions. In particular, extraterrestrial influences must be permitted; their general significance is still under debate.

Within this “classical picture” a kind of electric standard atmosphere may be constructed as shown in Table 1.

Values with a star, *, are rough average values from measurement. A star in parentheses, (*), points to a typical value from one or a few measurements. All other values have been calculated from starred values, under the assumption that at 2 km 50% and at 12 km 90% of the columnar resistance is reached. Voltage drop along one of the partial columns can be calculated by subtracting the value for the lower column from that of the upper one. Columnar resistances, conductances, and capacitances are valid for that particular part of the column which is indicated at the left. Capacitances are calculated with the formula for plate capacitors, and this fact must be considered also for the time constants for columns.

According to measurements, U, the potential difference between 0 m and 65 km may vary by a factor of approximately 2. The total columnar resistance, Rc, is estimated to vary up to a factor of 3, the variation being due to either reduction of conductivity in the exchange layer (about lowest 2 km of this table) or to the presence of high mountains; in both cases the variation is caused in the troposphere. Smaller variations in the stratosphere and mesosphere are being discussed because of aerosols there. The air–Earth current density in fair weather varies by a factor of 3 to 6 accordingly. Conductivity near the ground varies by a factor of about 3 but only decreasing; increase of conductivity due to extraordinary radioactivity is a singular event. The field strength near the ground varies as a consequence of variations of air–Earth current density and conductivity from about ⅓ to about 10 times of the value quoted in the table. Conductivity near the ground shows a diurnal and an annual variation which depends strongly on the locality: air–Earth current density shows a diurnal and annual variation because the Earth–ionosphere potential difference undergoes such variations, and also because the columnar resistance is supposed to have a diurnal and probably an annual variation.

Conductivities and air–earth current densities on high mountains are greater than at sea level by factors of up to 10. Conductivity decreases when atmospheric humidity increases. Values for space charges are not quoted because measurements are too few to allow calculation of average values. Values of parameters over the oceans are still rather uncertain.

Theoretically, in fair weather conditions, Ohm’s law must be fulfilled for the electric field, the conduction current density, and the electrical conductivity of the atmosphere. Deviations point to shortcomings in the applied measuring techniques. Data which are representative for a large area (in the extreme, “globally representative data,” i.e., data on the global circuit), can be obtained on the ground only by stations on an open plane and only if local generators are either small or constant or are independently measured. Certain measurements with instrumented aircraft provide globally representative information valid for the period of the actual measurement.

TABLE 1. Electrical Parameters of the Clear (Fair Weather) Atmosphere, Pertinent to the Classical Picture of Atm. Electricity (Electric Standard Atmosphere)

Part of atmosphere for which the values are calculated (elements are in free, cloudless atmosphere)Currents, I, in A; and current densities, i, in A/m2Potential differences, U, in V; field strength E in V/m; U = 0 at sea levelResistances, R, in Ω; columnar resistances, Rc, in Ω m2 and resistivities, ρ, in Ω mConductances, G, in Ω-1; columnar conductances Gc, in Ω-1 m-2; total conductivities, γ, in Ω-1 m-1Capacitances, C, in F; columnar capacitances, Cc, in F m-2 and capacitivities, ε, in F m-1Time constants τ, in seconds
Volume element at about sea level, 1 m3i = 3 × 10-12*E0 = 1.2 × 102*ρ0 = 4 × 1013γ0 = 2.5 × 10-14ε0 = 8.9 × 10-12*τ0 = 3.6× 102
Lower column of 1 m2 cross section from sea level to 2 km heighti = 3 × 10-12At upper end: U1 = 1.8 × 105Rc1 = 6 × 1016Gc1 = 1.7 × 10-17Ccl = 4.4 × 10-15τc1 = 2.6 × 102
Volume element at about 2 km height, 1 m3i = 3 × 10-12E2 = 6.6 × 101ρ2 = 2.2 × 1013(*)γ2 = 4.5 × 10-14ε2 = 8.9 × 10-12*τ2 = 2 × 102
Center column of 1 m2 cross section from 2 to 12 kmi = 3 × 10-12At upper end: Um = 3.15 × 105Rcm = 4.5 × 1016Gcm = 5 × 10-17Ccm = 8.8 × 10-16τcm = 1.8 × 101
Volume element at about 12 km height, 1 m3i = 3 × 10-12E12 = 3.9 × 100ρ12 = 1.3 × 1012(*)γ12 = 7.7 × 10-13ε12 = 8.9 × 10-12τ12 = 1.2 × 101
Upper column of 1 m2 cross section from 12 to 65 km heighti = 3 × 10-12At upper end: Uu = 3.5 × 105Rcu = 1.5 × 1016Gcu = 2.5 × 10-17Ccu = 1.67 × 10-16τcm = 6.7 × 100
Whole column of 1 m2 cross section from 0 to 65 km heighti = 3 × 10-12At upper end: U = 3.5 × 105Rc = 1.2 × 1017Gc = 8.3 × 10-18Cc = 1.36 × 10-16τc = 1.64 × 101
Total spherical capacitor area: 5 ×1014m2i = 1.5 × 103U = 3.5 × 105*R = 2.4 × 102G = 4.2 × 10-3C = 6.8 × 10-2τ = 1.64 × 101
  • Note: All currents and fields listed are part of the global circuit, i.e., circuits of local generators are not included. Values are subject to variations due to latitude and altitude of the point of observation above sea level, locality with respect to sources of disturbances, meteorological and climatological factors, and man-made changes. For more explanations, see text.


Hannes Tammet

The term “air ions” signifies all airborne particles that are the carriers of the electrical current in the air and have drift velocities determined by the electric field.

The probability of electrical dissociation of molecules in the atmospheric air under thermodynamic equilibrium is near to zero. The average ionization at ground level over the ocean is 2·106 ion pairs m-3 s-1. This ionization is produced mainly by cosmic rays. Over the continents, the ionizing radiation from soil and radioactive substances in the air each add about 4·106 m-3 s-1. The total average ionization rate of 107 m3 s-1 is equivalent to 17 μR/h, which is a customary expression of the background level of the ionizing radiations. The ionization rate over the ground varies in space due to the radioactivity of soil, and in time depending on the exchange of air between the atmosphere and radon-containing soil. Radioactive pollution increases the ionization rate. A temporary increase of about 10 times was registered in Sweden after the Chernobyl accident in 1986. The emission of 85Kr from nuclear power plants can noticeably increase the global ionization rate in the 21st century. The ionization rate decreases with altitude near the ground and increases at higher altitudes up to 15 km, where it has a maximum of about 5·107 m-3 s-1. Solar X-ray and extreme UV radiation cause a new increase at altitudes over 60 km.

Local sources of air ions are point discharges in strong electric fields, fluidization of charged drops from waves, etc.

The enhanced chemical activity of an ion results in a chain of ion-molecule reactions with the colliding neutrals, and, in the first microsecond of the life of an air ion, a charged molecular cluster called the cluster ion is formed. According to theoretical calculations in air free from exotic trace gases, the following cluster ions should be dominant:

NO3•(HNO3)•H2O, NO2•(H2O)2, NO3•H2O, O2•(H2O)4, O2•(H2O)5,

H3O+•(H2O)6, NH4+•(H2O)2, NH4+•(H2O), H3O+•(H2O)5, NH4+•NH3

A measurable parameter of air ions is the electrical mobility k, characterizing the drift velocity in the unit electric field. The mobility is inversely proportional to the density of air, and the results of measurements are as a rule reduced to normal conditions. According to their mobility, air ions are called fast (or small or light) ions with mobility k > 5·10-5 m2 V-1 s1 , intermediate ions, and slow (or large or heavy) ions with mobility k > 10-6 m2 V-1 s1. The boundary between intermediate and slow ions is conventional.

Cluster ions are fast ions. The mass of cluster ions can be measured with mass spectrometers, but possible ion-molecule reactions during the passage of the air through nozzles to the vacuum chamber complicate the measurement. Mass and mobility of cluster ions are highly correlated. The experimental results (Ref. 5) can be expressed by the empirical formula


where u is the unified atomic mass unit.

The value of the transport cross-section of a cluster ion is needed to calculate its mobility according to the kinetic theory of Chapman and Enskog. The theoretical estimation of transport cross-sections is rough and cannot be used to identify the chemical structures of cluster ions. Mass spectrometry is the main technique of identification of cluster ions.2

Märk and Castleman Ref. 4) presented an overview of over 1000 publications on the experimental studies of cluster ions. Most of them present information about ions of millisecond age range. The low concentration makes it difficult to get detailed information about masses and mobilities of the natural atmospheric ions at ground level. The results of a 1-year continuous measurement (Ref. 6) are given in Table 2.

TABLE 2. Properties of Ions in Air

+ ions– ionsunit
Average mobility1.361.5610-4 m2 V-1 s1
The corresponding mass190130u
The corresponding diameter0.690.61nm
The average concentration400360106 m-3
The corresponding conductivity8.79.0fS

The distribution of tropospheric cluster ions according to the mobility and estimated mass is depicted in Figure 1.

The problems and results of direct mass spectrometry of natural cluster ions have been analyzed by Eisele (Ref. 2) for ground level and by Meyerott, Reagan and Joiner (Ref. 5) for stratospheric measurements. Air ions in the high atmosphere are a subject of ionospheric physics.

During its lifetime (about 1 min), a cluster ion at ground level collides with nearly 1012 molecules. Thus cluster ions are able to concentrate trace gases of very low concentration if they have an extra high electron or proton affinity. For example, Eisele (Ref. 2) demonstrated that a considerable fraction of positive atmospheric cluster ions in the unpolluted atmosphere at ground level probably consists of a molecule derived from pyridine. The concentration of these constituents is estimated to be about 10-12. Therefore, air-ion mass and mobility spectrometry is considered as a promising technique for trace analysis in the air. Mass and mobility spectrometry of millisecond-age air ions has been developed as a technique of chemical analysis known as “plasma chromatography.” (Ref. 1) The sensitivity of the detection grows with the age of the cluster ions measured.

The mechanisms of annihilation of cluster ions are ion-ion recombination (on the average 3%) and sedimentation on aerosol particles (on the average 97% of cluster ions at ground level). The result of the combination of a cluster ion and neutral particle is a charged particle called an aerosol ion. In conditions of detailed thermodynamic equilibrium, the probability that a spherical particle of diameter d carries q elementary charges is calculated from the Boltzmann distribution:


where d0 = 115 nm (at 18 °C). The supposition about the detailed equilibrium is an approximation, and the formula is not valid for particles less than d0. On the basis of numerical calculations by Hoppel and Frick (Ref. 3) the following charge probabilities and electrical mobility can be derived, as shown in Table 3. Column definitions for Table 3 are as follows.

Column heading Definition
d Diameter of cluster ion, in nm
P0 Probablity that a neutral (charge = 0) cluster ion is produced, in %
P+1-P-1 Probability that a cluster ion with ions of charge +1 and -1 is produced, in %
P+2-P-2 Probability that a cluster ion with ions of charge +2 and -2 is produced, in %
Pq>2 Probability that a cluster ion with ions of charge greater than ± 2 is produced, in %
k Electricalmobility of cluster ion, in units of 10-9 m2 V-1 s-1

TABLE 3. Probabilities of Creating Paired Air Ions as a Function of Cluster Size

d/nmP0/%p-1+p1/%p-2+p2/%Pq>2/%k1/10-9 mV-1 s-1

figure 1 showing positive ions      figure 1 showing negative ions

FIGURE 1. Average mobility and mass spectra of natural tropospheric cluster ions. Concentrations of the mobility fractions were measured in a rural site every 5 min over 1 year.6 Ion mass is estimated according to the above empirical formula.


figure 2 described below

FIGURE 2. Mobility and size spectra of tropospheric aerosol ions.6 The wide bars mark the fraction concentrations theoretically estimated on the basis of the standard size distribution of tropospheric aerosol. The pin bars with head + and − mark average values of positive and negative aerosol ion fraction concentrations measured in a rural site every 5 min during 4 months.

The last line of the table presents the mobility of a particle carrying one elementary charge. The distribution of the atmospheric aerosol ions over mobility is demonstrated in Figure 2.

Although the concentration of aerosol in continental air at ground level is an order of magnitude higher than the concentration of cluster ions, the mobilities of aerosol ions are so small that their percentage in air conductivity is less than 1%.

A specific class of aerosol ions is condensed aerosol ions produced as a result of the condensation of gaseous matter on the cluster ions. In aerosol physics the process is called ion-induced nucleation; it is considered as one of the processes of gas-to-particle conversion. The condensed aerosol ions have an inherent charge. Their sizes and mobilities are between the sizes and mobilities of cluster ions and of ordinary aerosol ions. Water and standard constituents of atmospheric air are not able to condense on the cluster ions in the real atmosphere. Thus the concentration of condensed aerosol ions depends on the trace constituents in the air and is very low in unpolluted air. Knowledge about condensed aerosol ions is poor because of measurement difficulties.


  1. Carr, T. W., Ed., Plasma Chromatography, Plenum Press, New York and London, XII + 259 pp., 1984.
  2. Eisele, F. L., Identification of Tropospheric Ions, J. Geophys. Res., vol. 91, no. D7, pp. 7897–7906, 1986. []
  3. Hoppel, W. A., and Frick, G. M., The Nonequilibrium Character of the Aerosol Charge Distributions Produced by Neutralizers, Aerosol Sci. Technol., vol. 12, no. 3, pp. 471–496, 1990. []
  4. Mark, T. D., and Castleman, A. W., Experimental Studies on Cluster Ions, in Advances in Atomic and Molecular Physics, vol. 20, pp. 65–172, Academic Press, 1985. []
  5. Meyerott, R. E., Reagan, J. B., and Joiner, R. G., The Mobility and Concentration of Ions and the Ionic Conductivity in the Lower Stratosphere, J. Geophys. Res., vol. 85, no. A3, pp. 1273–1278, 1980. []
  6. Salm, J., Tammet, H., Iher, H., and Hörrak, U., Atmospheric Electrical Measurements in Tahkuse, Estonia (in Russian), in Voprosy Atmosfernogo Elektrichestva, pp. 168–175, Gidrometeoizdat, Leningrad, 1990.


John Latham

The development of improved radar techniques and instruments for in-cloud electrical and physical measurements, coupled with a much clearer recognition by the research community that establishment of the mechanism or mechanisms responsible for electric field development in thunderclouds, culminating in lightning, is inextricably linked to the concomitant dynamical and microphysical evolution of the clouds, has led to significant progress over the past decade.

Field studies indicate that in most thunderclouds the electrical development is associated with the process of glaciation, which can occur in a variety of incompletely understood ways. In the absence of ice, field growth is slow, individual hydrometeor charges are low, and lightning is produced only rarely. Precipitation — in the solid form, as graupel — also appears to be a necessary ingredient for significant electrification, as does significant convective activity and mixing between the clouds and their environments, via entrainment.

Increasingly, the view is being accepted that charge transfer leading to field-growth is largely a consequence of rebounding collisions between graupel pellets and smaller vapor-grown ice crystals, followed by the separation under gravity of these two types of hydrometeor. These collisions occur predominantly within the temperature range −15 to −30 °C, and for significant charge transfer need to occur in the presence of supercooled cloud droplets.

The field evidence is inconsistent with an inductive mechanism, and extensive laboratory studies indicate that the principal charging mechanism is non-inductive and associated — in ways yet to be identified — with differences in surface characteristics of the interacting hydrometeors.

Laboratory studies indicate that the two most favored sites for corona emission leading to the lightning discharge are the tips of ephemeral liquid filaments, produced during the glancing collisions of supercooled raindrops, and protuberances on large ice crystals or graupel pellets. The relative importance of these alternatives will depend on the hydrometeor characteristics and the temperature in the regions of strongest fields; these features are themselves dependent on air-mass characteristics and climatological considerations.

A recently identified but unresolved question is why, in continental Northern Hemisphere thunderclouds at least, the sign of the charge brought to ground by lightning is predominantly negative in summer but more evenly balanced in winter.


Martin A. Uman

From both ground-based weather-station data and satellite measurements, it has been estimated that there are about 100 lightning discharges, both cloud and ground flashes, over the whole Earth each second; representing an average global lightning flash density of about 6 km-2 yr-1. Most of this lightning occurs over the Earth’s land masses. For example, in central Florida, where thunderstorms occur about 90 days/yr, the flash density for discharges to earth is about 15 km-2 yr-1. Some tropical areas of the Earth have thunderstorms up to 300 days/yr.

Lightning can be defined as a transient, high-current electric discharge whose path length is measured in kilometers and whose most common source is the electric charge separated in the ordinary thunderstorm or cumulonimbus cloud. Well over half of all lightning discharges occur totally within individual thunderstorm clouds and are referred to as intracloud discharges. Cloud-to-ground lightning, however, has been studied more extensively than any other lightning form because of its visibility and its more practical interest. Cloud-to-cloud and cloud-to-air discharges are less common than intracloud or cloud-to-ground lightning.

Lightning between the cloud and Earth can be categorized in terms of the direction of motion, upward or downward, and the sign of the charge, positive or negative, of the developing discharge (called a leader) that initiates the overall event. Over 90% of the worldwide cloud-to-ground discharges is initiated in the thundercloud by downward-moving negatively charged leaders and subsequently results in the lowering of negative charge to Earth. Cloud-to-ground lightning can also be initiated by downward-moving positive leaders, less than 10% of the worldwide cloud-to-ground lightning being of this type although the exact percentage is a function of season and latitude. Lightning between cloud and ground can also be initiated by leaders that develop upward from the Earth. These upward-initiated discharges are relatively rare, may be of either polarity, and generally occur from mountaintops and tall man-made structures.

We discuss next the most common type of cloud-to-ground lightning. A negative cloud-to-ground discharge or flash has an overall duration of some tenths of a second and is made up of various components, among which are typically three or four high-current pulses called strokes. Each stroke lasts about a millisecond, the separation time between strokes being typically several tens of milliseconds. Such lightning often appears to “flicker” because the human eye can just resolve the individual light pulse associated with each stroke. A drawing of the components of a negative cloud-to-ground flash is found in Figure 3. Some values for salient parameters are found in Table 1. The negatively charged stepped leader initiates the first stroke in a flash by propagating from cloud to ground through virgin air in a series of discrete steps. Photographically observed leader steps in clear air are typically 1 μs in duration and tens of meters in length, with a pause time between steps of about 50 μs. A fully developed stepped leader lowers up to 10 or more coulombs of negative cloud charge toward ground in tens of milliseconds with an average downward speed of about 2 × 105 m/s. The average leader current is in the 100 to 1000 A range. The steps have pulse currents of at least 1 kA. Associated with these currents are electric- and magnetic-field pulses with widths of about 1 μs or less and risetimes of about 0.1 μs or less. The stepped leader, during its trip toward ground, branches in a downward direction, resulting in the characteristic downward-branched geometrical structure commonly observed. The electric potential of the bottom of the negatively charged leader channel with respect to ground has a magnitude in excess of 107 V. As the leader tip nears ground, the electric field at sharp objects on the ground or at irregularities of the ground itself exceeds the breakdown value of air, and one or more upward-moving discharges (often called upward leaders) are initiated from those points, thus beginning the attachment process. An understanding of the physics of the attachment process is central to an understanding of the operation of lightning protection of ground-based objects and the effects of lightning on humans and animals, since it is the attachment process that determines where the lightning connects to objects on the ground and the value of the early currents which flow. When one of the upward-moving discharges from the ground (or from a lightning rod or an individual) contacts the tip of the downward-moving stepped leader, typically some tens of meters above the ground, the leader tip is effectively connected to ground potential. The negatively charged leader channel is then discharged to earth when a ground potential wave, referred to as the first return stroke, propagates continuously up the leader path. The upward speed of a return stroke near the ground is typically near one third the speed of light, and the speed decreases with height. The first return stroke produces a peak current near ground of typically 30 kA, with a time from zero to peak of a few microseconds. Currents measured at the ground fall to half of the peak value in about 50 μs, and currents of the order of hundreds of amperes may flow for times of a few milliseconds up to several hundred milliseconds. The longer-lasting currents are known as continuing currents. The rapid release of return stroke energy heats the leader channel to a temperature near 30,000 K and creates a high-pressure channel which expands and generates the shock waves that eventually become thunder, as further discussed later. The return stroke effectively lowers to ground the charge originally deposited onto the stepped-leader channel and additionally initiates the lowering of other charges that may be available to the top of its channel. First return-stroke electric fields exhibit a micro second scale rise to peak with a typical peak value of 5 V/m, normalized to a distance of 100 km by an inverse distance relationship. Roughly half of the field rise to peak, the so-called “fast transition,” takes place in tenths of a microsecond, an observation that can only be made if the field propagation is over a highly conducting surface such as salt water.

figure 3 described below

FIGURE 3. Sequence of steps in cloud-to-ground lightning.

After the first return-stroke current has ceased to flow, the flash, including charge motion in the cloud, may end. The lightning is then called a single-stroke flash. On the other hand, if additional charge is made available to the top of the channel, a continuous or dart leader may propagate down the residual first-stroke channel at a typical speed of about 1 × 107 m/s. The dart leader lowers a charge of the order of 1 C by virtue of a current of about 1 kA. The dart leader then initiates the second (or any subsequent) return stroke. Subsequent return-stroke currents generally have faster zero-to-peak rise times than do first-stroke currents, but similar maximum rates of change, about 100 kA/μs. Some leaders begin as dart leaders, but toward the end of their trip toward ground become stepped leaders. These leaders are known as dart-stepped leaders and may have different ground termination points (and separate upward leaders) from the first stroke. Most often the dart-stepped leaders are associated with the second stroke of the flash. Nearly half of all flashes exhibit more than one termination point on ground with the distance between separate terminations being up to several kilometers. Subsequent return-stroke radiated electric and magnetic fields are similar to, but usually a factor of two or so smaller than first return-stroke fields. About one third of all multiple-stroke flashes has at least one subsequent stroke that is larger than the first stroke.

Cloud-to-ground flashes that lower positive charge, though not common, are of considerable practical interest because their peak currents and total charge transfer can be much larger than for the more common negative ground flash. The largest recorded peak currents, those in the 200- to 300-kA range, are due to the return strokes of positive lightning. Such positive flashes to ground are initiated by downward-moving leaders that do not exhibit the distinct steps of their negative counterparts. Rather, they show a luminosity that is more or less continuous but modulated in intensity. Positive flashes are generally composed of a single stroke followed by a period of continuing current. Positive flashes are probably initiated from the upper positive charge in the thundercloud charge dipole when that cloud charge is horizontally separated from the negative charge beneath it, the source of the usual negative cloud-to-ground lightning. Positive flashes are relatively common in winter thunderstorms (snow storms), which produce few flashes overall, and are relatively uncommon in summer thunderstorms. The fraction of positive lightning in summer thunderstorms apparently increases with increasing latitude and with increasing height of the ground above sea level.

Distant lightning return stroke fields are often referred to as sferics (called “atmospherics” in the older literature). The peak in the sferics frequency spectrum is near 5 kHz due to the bipolar or ringing nature of the distant return-stroke electromagnetic signal and to the effects of propagation.

Thunder, the acoustic radiation associated with lightning, is sometimes divided into the categories “audible,” sounds that one can hear, and “infrasonic,” below a few tens of hertz, a frequency range that is inaudible. This division is made because it is thought that the mechanisms that produce audible and infrasonic thunder are different. Audible thunder is thought to be due to the expansion of a rapidly heated return stroke channel, as noted earlier, whereas infrasonic thunder is thought to be associated with the conversion to sound of the energy stored in the electrostatic field of the thundercloud when lightning rapidly reduces that cloud field.

The technology of artificially initiating lightning by firing upward small rocket trailing grounded wire of a few hundred meters length has been well-developed during the past decade. Such “triggered” flashes are similar to natural upward-initiated discharges from tall structure. They often contain subsequent strokes which, when they occur, are similar to the subsequent strokes in natural lightning. These triggered subsequent strokes have been the subject of considerable recent research.

Also in the past 10 years or so sophisticated lightning locating equipment has been installed throughout the world. For example, all ground flashes in the U.S. are now centrally monitored for research, for better overall weather prediction, and for hazard warning for aviation, electric utilities and other lightning-sensitive facilities.

Information on lightning physics can be found in M. A. Uman, The Lightning Discharge, Academic Press, San Diego, 1987; on lightning death and injury in Medical Aspects of Lightning Injury, C. Andrews, M. A. Cooper, M. Darveniza, and D. Mackerras, Eds., CRC Press, Boca Raton, FL, 1992. Ground flash location information for the U.S., in real time or archived, is available from Geomet Data Service of Tucson, AZ, which is also a source of the names of providers of those data in other countries.

Table 4 has data for cloud-to-ground lightning discharges bringing negative charge to earth. The values listed are intended to convey a rough feeling for the various physical parameters of lightning. No great accuracy is claimed since the results of different investigators are often not in good agreement. These values may, in fact, depend on the particular environment in which the lightning discharge is generated. The choice of some of the entries in the table is arbitrary.

TABLE 4. Data for Cloud-to-Ground Lightning Discharges

MinimumaRepresentative valuesMaximuma
Continued on next page...
Stepped leader
Length of step, m350200
Time interval between steps, µs3050125
Average speed of propagation of stepped leader, m/sb1.0 × 1052.0 × 1053.0 × 106
Charged deposited on stepped-leader channel, coulombs3520
Dart leader
Speed of propagation, m/sb1.0 × 1061.0 × 1072.4 × 107
Charged deposited on dart-leader channel, coulombs0.216
Return strokec
Speed of propagation, m/sb2.0 × 1071.0 × 1082.0 × 108
Maximum current rate of increase, kA/µs<1100400
Time to peak current, µs<1230
Peak current, kA230200
Time to half of peak current, µs1050250
Charge transferred excluding continuing current, coulombs0.02320
Channel length, km2515
Lightning flash
Number of strokes per flash1426
Time interval between strokes in absence of continuing current, ms360100
  • a The words maximum and minimum are used in the sense that most measured values fall between these limits.
  • b Speeds of propagation are generally determined from photographic data and are “two-dimensional.” Since many lightning flashes are not vertical, values stated are probably slight underestimates of actual values.
  • c First return strokes have longer times to current peak and generally larger charge transfer than do subsequent return strokes.

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Searching for Chemicals and Properties

The CRC Handbook of Chemistry and Physics (HBCP) contains over 700 tables in over 450 documents which may be divided into several pages, all categorised into 17 major subject areas. The search on this page works by searching the content of each page individually, much like any web search. This provides a challenge if you want to search for multiple terms and those terms exist on different pages, or if you use a synonym/abbreviation that does not exist in the document.

We use metadata to avoid some of these issues by including certain keywords invisibly behind each table. Whilst this approach works well in many situations, like any web search it relies in the terms you have entered existing in the document with the same spelling, abbreviation etc.

Since chemical compounds and their properties are immutable, a single centralised database has been created from all chemical compounds throughout HBCP. This database contains every chemical compound and over 20 of the most common physical properties collated from each of the >700 tables. What's more, the properties can be searched numerically, including range searching, and you can even search by drawing a chemical structure. A complete list of every document table in which the compound occurs is listed, and are hyperlinked to the relevant document table.

The 'Search Chemicals' page can be found by clicking the flask icon in the navigation bar at the top of this page. For more detailed information on how to use the chemical search, including adding properties, saving searches, exporting search results and more, click the help icon in to top right of this page, next to the welcome login message.

Below is an example of a chemical entry, showing its structure, physical properties and document tables in which it appears.

image of an example chemical entry
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Cookie Policy

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