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 The recommended form of citation is: John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL. If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.

# ATMOSPHERIC ELECTRICITY

Hans Dolezalek, Hannes Tammet, John Latham, and Martin A. Uman

# I. SURVEY AND GLOBAL CIRCUIT

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/m2 Potential differences, U, in V; field strength E in V/m; U = 0 at sea level Resistances, R, in Ω; columnar resistances, Rc, in Ω m2 and resistivities, ρ, in Ω m Conductances, G, in Ω-1; columnar conductances Gc, in Ω-1 m-2; total conductivities, γ, in Ω-1 m-1 Capacitances, C, in F; columnar capacitances, Cc, in F m-2 and capacitivities, ε, in F m-1 Time constants τ, in seconds Volume element at about sea level, 1 m3 i = 3 × 10-12* E0 = 1.2 × 102* ρ0 = 4 × 1013 γ0 = 2.5 × 10-14 ε0 = 8.9 × 10-12* τ0 = 3.6× 102 Lower column of 1 m2 cross section from sea level to 2 km height i = 3 × 10-12 At upper end: U1 = 1.8 × 105 Rc1 = 6 × 1016 Gc1 = 1.7 × 10-17 Ccl = 4.4 × 10-15 τc1 = 2.6 × 102 Volume element at about 2 km height, 1 m3 i = 3 × 10-12 E2 = 6.6 × 101 ρ2 = 2.2 × 1013(*) γ2 = 4.5 × 10-14 ε2 = 8.9 × 10-12* τ2 = 2 × 102 Center column of 1 m2 cross section from 2 to 12 km i = 3 × 10-12 At upper end: Um = 3.15 × 105 Rcm = 4.5 × 1016 Gcm = 5 × 10-17 Ccm = 8.8 × 10-16 τcm = 1.8 × 101 Volume element at about 12 km height, 1 m3 i = 3 × 10-12 E12 = 3.9 × 100 ρ12 = 1.3 × 1012(*) γ12 = 7.7 × 10-13 ε12 = 8.9 × 10-12 τ12 = 1.2 × 101 Upper column of 1 m2 cross section from 12 to 65 km height i = 3 × 10-12 At upper end: Uu = 3.5 × 105 Rcu = 1.5 × 1016 Gcu = 2.5 × 10-17 Ccu = 1.67 × 10-16 τcm = 6.7 × 100 Whole column of 1 m2 cross section from 0 to 65 km height i = 3 × 10-12 At upper end: U = 3.5 × 105 Rc = 1.2 × 1017 Gc = 8.3 × 10-18 Cc = 1.36 × 10-16 τc = 1.64 × 101 Total spherical capacitor area: 5 ×1014m2 i = 1.5 × 103 U = 3.5 × 105* R = 2.4 × 102 G = 4.2 × 10-3 C = 6.8 × 10-2 τ = 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.

# II. AIR IONS

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.

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

$m\approx \frac{850\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{u}}{{\left[0.3+k/\left({10}^{-4}{\text{m}}^{\text{2}}{\text{V}}^{\text{-1}}{\text{s}}^{-1}\right)\right]}^{3}}$

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 – ions unit Average mobility 1.36 1.56 10-4 m2 V-1 s1 The corresponding mass 190 130 u The corresponding diameter 0.69 0.61 nm The average concentration 400 360 106 m-3 The corresponding conductivity 8.7 9.0 fS

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:

${p}_{q}\left(d\right)={\left(2\pi d\text{/}{d}_{0}\right)}^{1/2}\mathrm{exp}\left(-{q}^{2}{d}_{0}\text{/}2d\right)$

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/nm P0/% p-1+p1/% p-2+p2/% Pq>2/% k1/10-9 m2 V-1 s-1 3 98 2 0 0 15000 10 90 10 0 0 1900 30 70 30 0 0 250 100 42 48 10 0 28 300 24 41 23 12 5.1 1000 14 25 21 40 1.11 3000 8 15 14 63 0.33

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. 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.

## References

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. [https://doi.org/10.1029/JD091iD07p07897]
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. [https://doi.org/10.1080/02786829008959363]
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. [https://doi.org/10.1016/S0065-2199(08)60266-3]
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. [https://doi.org/10.1029/JA085iA03p01273]
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.

# III. THUNDERSTORM ELECTRICITY

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.

# IV. LIGHTNING

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.

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

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

 Minimuma Representative values Maximuma Continued on next page... Stepped leader Length of step, m 3 50 200 Time interval between steps, µs 30 50 125 Average speed of propagation of stepped leader, m/sb 1.0 × 105 2.0 × 105 3.0 × 106 Charged deposited on stepped-leader channel, coulombs 3 5 20 Dart leader Speed of propagation, m/sb 1.0 × 106 1.0 × 107 2.4 × 107 Charged deposited on dart-leader channel, coulombs 0.2 1 6 Return strokec Speed of propagation, m/sb 2.0 × 107 1.0 × 108 2.0 × 108 Maximum current rate of increase, kA/µs <1 100 400 Time to peak current, µs <1 2 30 Peak current, kA 2 30 200 Time to half of peak current, µs 10 50 250 Charge transferred excluding continuing current, coulombs 0.02 3 20 Channel length, km 2 5 15 Lightning flash Number of strokes per flash 1 4 26 Time interval between strokes in absence of continuing current, ms 3 60 100
 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.

• Adapted from Uman, M.A., Lightning, Dover Paperbook, New York, 1986, and Uman, M.A., The Lightning Discharge, Academic Press, San Diego, 1987.

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You always have a choice over whether or not to accept Cookies. When you first visit the Website and we notify you about our use of Cookies, you can choose not to consent to such use. If you continue to use the Website, you are consenting to our use of Cookies for the time being. However, you can choose not to continue accepting Cookies at any later time. In this section, we describe ways to manage Cookies, including how to disable them.

You can manage Cookies through the settings of your internet browser. You can choose to block or restrict Cookies from being placed on your computer or device. You can also review periodically review the Cookies that have been placed there and disable some or all of them.

Please be aware that if you choose not to accept certain Cookies, it may mean we are unable to provide you with some services or features of the Website.

In order to keep up with changing legislation and best practice, we may revise this Cookie Policy at any time without notice by posting a revised version on this Website. Please check back periodically so that you are aware of any changes.

## Questions or Concerns

You can also contact the Privacy Officer for the Informa PLC group at [email protected].

Here is a list of cookies we have defined as 'Strictly Necessary':

### Taylor and Francis 'First Party' Cookies

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Here is a list of the cookies we have defined as 'Performance'.

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Accessibility

The Voluntary Product Accessibility Template (VPAT) is a self-assessment document which discloses how accessible Information and Communication Technology products are in accordance with global standards.

The VPAT disclosure templates do not guarantee product accessibility but provide transparency around the product(s) and enables direction when accessing accessibility requirements.

Taylor & Francis has chosen to complete the International version of VPAT which encompasses Section 508 (US), EN 301 549 (EU) and WCAG2.1 (Web Content Accessibility Guidelines) for its products.