Earth Electricity
The Fair Weather Electric Field
The Fair Weather Electric Field
At about the time when Ben Franklin was teaching about the electrical nature of lightning (Chapter 1), Le Monnier (1752) first demonstrated that the atmosphere was electrified, even in fair weather.
As it became understood that a conducting fluid existed in the air, Linss (1887) first realized that this conducting fluid would soon cancel out the field produced by any bound charge.
Long before Elster and Geitel (1899a,b) and Wilson (1900) discovered small ions in the air, Coulomb (1795) found that the air itself was conducting and that charge on a conductor would leak away in the air.
Thus, two unsolved mysteries, known since the late 1700s, remain about fair weather electricity:
(1) What was the source of the large-scale electric field and why was it not quickly reduced to zero by charges in the conducting fluid?
(2) What was the source of the conducting fluid or, in other words, why didn’t the large-scale electric field sweep away all the free charge in the atmosphere?
Another critical discovery came in 1911 when Victor Hess was conducting an atmospheric electricity experiment to study radioactive ions in the air.
Using a balloon experiment, he found that the conductivity increased with altitude rather than the expected decrease, thus leading to the discovery of cosmic radiation (Hess, 1911).
Putting these ideas together, Wilson (1920) first proposed that the earth was a conductor and that thunderstorms over the globe must act to put negative charge on the ground and positive charge in the upper atmosphere, functioning like a leaky capacitor. Thus, the concept of a global electric circuit was born (see Fig. 2.1).
Fig. 2.1. Schematic of the global electrical circuit.
After Roble and Tzur (1986).
Reproduced with permission of the National Academy of Sciences.
The idea of a global circuit was quickly accepted by the scientific community after Mauchly (1923) used electric field data from the Carnegie research vessel to show that the fair weather electric field seemed to have a peak at around 19:00 h UT, independent of where the measurements were taken over the globe.
Then, Whipple and Scrase (1936) connected these global field variations with the fact that thunderstorms occur most frequently over land in the afternoon (local time) and proposed that the global circuit daily variation in fair weather was simply caused by variation of the global land mass as the earth rotates (see Fig. 2.2).
At 19:00 UT, there is more land mass in the late afternoon than during other times of the day, such as 04:00 UT when the Pacific Ocean is in late afternoon (local time) and the global circuit has a minimum.
Fig. 2.2. Percent variation from the mean of the vertical electric field magnitude over the ocean as a function of local time, along with the diurnal variations of land mass in local-time afternoons.
After Roble and Tzur (1986). Reproduced with permission of the National Academy of Sciences.
Thus, for more than a century, atmospheric electrodynamics has been known to be intimately connected to global phenomena in the upper atmosphere and space (Chalmers, 1967).
A simple model of the global electric current system is as follows. Consider the earth and the ionosphere to be charged and functioning like capacitor “plates” enclosing a conducting medium.
If a source was not charging the earth, the capacitor would simply discharge due to the conducting medium like a leaky capacitor.
On the other hand, if no method existed to create new ions between the plates, the potential difference would soon sweep out the charge between the plates, shutting off the global current.
The source of the ions is dominated by galactic cosmic rays with energies typically 100 GeV or more, each of which slams into the atmosphere, leaving a trail of highly ionized gas in its wake.
These energetic charged tracks left by the cosmic rays cause extensive air showers (EAS) of relativistic secondaries at the earth’s surface, and most of the millions of electron-ion pairs produced in the process immediately recombine.
However, a small percentage of the free charge of the EAS attaches to air molecules, becoming much less mobile, and therefore remains in the air and disperses after most of the EAS charge has recombined.
These residual ions form the basis of the atmospheric conductivity at all altitudes above about 1 km over solid ground (below that, atmospheric ions are mostly produced by the radioactive decay of natural outgassing from the earth, such as 222Rn).
The ion pair production rate as a function of altitude is shown in Fig. 2.3, where we see that the peak production rate occurs between 10 and 30 km.
The rate decreases above this layer because the lower density air in the upper atmosphere presents less of a target for cosmic rays.
Below 10 km, most cosmic rays and their secondary particles have already spent their energy, leaving fewer total ion pairs at the lowest levels.
Fig. 2.3. Pair production rate plot. Profiles of the ionization rate at different latitudes in years of the minimum (1965) and maximum (1958) of the 11-year solar sunspot cycle (Neher, 1961, 1967).
After Gringel et al. (1986). Reproduced with permission of the National Academy of Sciences.
The average conductivity created by these ions is plotted versus altitude in Fig. 2.4 and is nearly exponential below 80 km (Hale, 1984).
We see in this figure that the conductivity still increases above the pair production rate peak shown in Fig. 2.3 because the ion-neutral collision frequency drops dramatically with increasing altitude, thus increasing the conductivity (see Eq. 1.8). Volland (1984) represents the atmospheric resistivity ρ (equal to the inverse conductivity σ) below 60 km altitude with the function of z (km):
Fig. 2.4. Electrical conductivity of the atmosphere as a function of altitude. The variability is remarkable, both in time and space, depending on the particle flux of various types. From the ground to the edge of space, σ varies by 10 orders of magnitude.
After Hale (1984). Reproduced with permission of the American Geophysical Union.
ρz=1σz=ρ1exp−4.527z+ρ2exp0.375z+ρ3exp0.121z
where ρ11012Ωm=46.9,ρ21012Ωm=22.2,ρ31012Ωm=5.9.
At the earth’s surface, the conductivity σ(0) = 1/ρ(0) is about 10− 14 S/m, which is still finite but extremely low. Integrating the column resistivity from the ground to the ionosphere gives 1.2 × 1017 Ωm2.
However, if you divide this number by the earth’s surface area, you find that the total resistance from the ground to the ionosphere is only about 230 Ω.
In our simple model, the capacity of a spherical capacitor can be calculated as follows. We first calculate the potential between two concentric spheres for which the outer sphere of radius b is grounded and the inner plate has charge Q. The electric field is then E=Q4πɛr3r where r is the radial vector.
For air, ɛ ≈ ɛo, the permittivity of free space. Using E = − ∇ V where V is the voltage and converting this to an integral, V=−∫abE⋅dr=−∫baQ4πɛor2dr.
Performing this integral, V=Q4πɛob−aab. Since Q = CV, (2.1)C=4πɛoabb−a.
For our case, the distance b − a is equal to the atmospheric scale height, H, since the conductivity increases so rapidly that the effective height of the outer plate is approximately at the 1/e point for resistivity or H = 7.9 km.
We obtain a capacity of about 0.6 F. Using the value of 230 Ω to approximate the resistance between the plates, we estimate that the time constant for the global circuit should be on the order of 138 s.
Estimates of this time constant by others vary from a few minutes to 40 min.
The total voltage between the earth and the ionosphere is difficult to measure instantaneously, but many groups have estimated the voltage to be 250-350 kV using a variety of techniques.
Experimentally, we know that the earth carries a net negative charge compared to the upper atmosphere/ionosphere.
Direct voltage drops on the order of 200 kV have been measured between sea level and 1.5 km (20% of the 7.9 km exponential scale height discussed above) (Woosley and Holzworth, 1987), representing a charge of Q = CV ~ 2 × 105 C.
Discharging this amount of charge in an RC time constant results in a current estimate for the global circuit of I ~ 1500 A.
Thus, ~ 103 A is the order of magnitude for the sum of all the global thunderstorms in series to drive the global circuit. If all of these storms turned off suddenly, the earth would completely discharge within 10-30 min.
Bering et al. (1998) discussed estimates for the global circuit elements, noting that the most common type of lightning stroke to ground puts negative charge on the earth. However, there remains a controversy as to whether the dominant charging mechanism results from the net lightning charge to ground or is more related to the quasi-dc current from the whole thunderstorm.
Many measurements over thunderstorms suggest that each storm produces between 0.1 and 10 A of continuous, upward vertical current (positive charge moving upward). Thus, the ~ 103 A in the global circuit could be produced by the ~ 103 thunderstorms estimated to be active simultaneously.
Telluric Currents
