Chapter 7: Atmospheric Electricity
7.1 The Atmospheric Electric Field
We will focus on the so-called ‘fair weather’ electric field, where fair weather implies no
precipitation; less than 4/10 of the sky is cloudy; and there are no other extreme conditions
(e.g. visibility problems). Near the ground, the electric field is quite variable, but on average
it is vertical, and downward, with a field strength of
E0  -120 V m-1
That implies that the ground surface is negatively charged. From Electrostatics we may
determine the corresponding surface charge density, :
E0 

0
(since the field is ‘one sided’), so that
 = 0 E0
= -8.85 x 10-12 x 120
 -1 nC m-2
At higher altitudes, E decreases, so that there must be a net positive “space charge” in the air.
The connection between this space charge and the electric field is given from Poisson’s
equation
dE 

dz  0
where  is the space charge density.  decreases rapidly with altitude, and hence so does
dE/dz. At large enough altitudes, E  0, so the net space just balances the surface charge –
the planet as a whole is electrically neutral. Mathematically this is given by

dE
dz
dz
0
E  E0  
   
1
0
1
0

  dz  0
0

     dz
0
The other important electrical parameter is the potential, which is given by
z
V  z     E dz
0
If we take the Earth’s surface as the reference (V(0) = 0), then V will increase rapidly at first,
where E is large, before leveling off at a final value, which is around 3 x 105 V at an altitude
around 20 km.
What is the nature of the space charge? Natural ionization is produced by
radioactive gases (mainly radon) – largest source
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radioactive substances in the ground
cosmic rays.
The production rate is roughly 10 ion pairs / cm3 / s. These ions rapidly attract a number of
neutral atoms, to form “small ions”. If they attach to an aerosol particle, they are “large ions”.
Oppositely charged ions may recombine, so that an equilibrium situation is established, with
around 600 +ve ions / cm3 and 500 –ve ions / cm3.
It has recently been suggested that these ions may play a key role in the formation of new
aerosol particles in the atmosphere. The formation of new particles from precursor gases
(such as sulphate aerosols from sulphuric acid and related gases) suffers from the same
difficulty as the formation of new cloud droplets from water vapour – it is so much easier if
there is a ‘seed’ there to begin with. Because a positive or negative ion may electrically
attract a significant number of molecules to stick to it, we have an object part way between a
molecule and a (tiny) particle. If two oppositely charged small ions meet, the resulting object
will be the sum of both.
7.2 The Atmospheric Electric Circuit
Under the influence of the fair weather electric field, the charged ions are free to move,
giving the air a conductivity, and hence a current flow:
j=E
where j is the current density (amps/m2)
 is the conductivity (-1 m-1)
and
E is the electric field.
 is quite small: around 10-12 or 10-13, compared with 108 for copper, 10-1 for germanium, and
10-11 for glass. Conservation of charge dictates that the current density, j, should be the same
at all heights, or else charge would build up somewhere. Hence, since we know that E
decreases with height,  must increase with height. This makes some sense: as the air density
decreases, charged particles should be able to move more freely, and so conductivity should
increase.
We may now imagine the following electric circuit, which corresponds to a so-called leaky
(spherical) capacitor:
potential difference
surface charge density
total surface area
V  3 x 105 V;
  1 x 10-9 Cm-2;
A  5 x 1014 m2.

total surface charge
Q=A
 5 x 105 C.

capacitance
C = Q/V
 5 x 105/3 x 105  1.7 F.
This capacitor is ‘leaky’, because of the current flowing. Measurements of E and  suggest a
value of
j  2.7 x 10-12 A m-2.

total current
I = j A  1350 A.
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
(total) resistance
R = V/I  220 .
Because of the current flowing, this capacitor should discharge itself in a typical time of
 = Q/I  370 s = 6 min.
(This calculation can also be done via the time constant of an RC circuit:  = RC = Q/I.)
Clearly there must be some mechanism re-charging the upper plate!
So far we have looked only at fair weather conditions: what about cloudy conditions, and
especially thunderstorms. We do know that a great deal of electrical activity goes on in
thunderstorms: lightning, for example! So this is the fundamental hypothesis made to “close”
the atmospheric circuit. Three processes are involved:
The thunderstorm itself provides the charge separation mechanism (to be discussed in more
detail in the next section), which produces positive charges at high altitudes and
negative charges lower down. This implies a (net) upward current.
Above the cloud, the field is the reverse of the fair weather field, as the top of the
thunderstorm is at a higher voltage than the ionosphere. This produces a net upward
current (which mainly results from the downward flow of electrons).
Below the cloud, the field is also reversed. An upward current flows, both by conduction and
convection.
Thus, each thunderstorm is responsible for an upward flowing electric current. Support for
this theory is found in measurements of the fair weather electric field which shows variations
which parallel thunderstorm activity, at least when averaged over large areas.
7.3 Thunderstorm Electrification
Measurements clearly show that charge separation does occur in clouds, especially in large
convective clouds and thunderstorms. The upper regions may be charged to around 24 C,
while the lower parts may contain –20 C. A further small positively charge layer, of around 4
C, occurs at the very bottom.
What physical processes lead to such charge separation? It is presumably a three-step
process: firstly an ice particle must become electrically polarized by some mechanism;
secondly, some of the charge must be transferred to another ice particle in a collision; and
finally, differently charged particles must be separated from one another by motions within
the cloud. We shall now examine these three steps in turn.
The first step is by far the most poorly understood, and a number of theories have been
proposed. The evidence for each is not convincing. Consider a large ice crystal, falling under
gravity. Because of the downward directed electric field, it will become slightly electrically
polarized – negative on the top, positive on the bottom. Alternative theories are based on the
thermoelectric effect, with temperature gradients producing voltages across the ice particle.
As a polarized ice pellet falls within the cloud, it will collide with smaller ice crystals, carried
upwards by the strong updrafts. These will collide with the underside of the polarized pellet,
which is positively charged, and some of this charge will be transferred to the smaller
crystals. Updrafts will continue to carry these ice crystals to the top of the cloud.
An alternative mechanism to explain the first step is based on the process of riming. When a
small, supercooled droplet collides with the underside of a large ice pellet, it may stick in its
entirety, or it may splatter, producing fragments which fly off, and continue upwards. These
fragments may acquire a positive charge in the process. If the ice particle was already
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polarized, as described above, positive charges may more easily be transferred to the
fragments.
As positive charge starts to accumulate at the top of the cloud, and negative charge near the
bottom, the downward-directed electric field will increase. This will enhance the polarization
of the large ice pellets, so speeding up the process of charge separation. The major unsolved
problem in cloud electrification is how the whole process gets started in the first place.
7.4 Lightning
The process just described can lead to the build up of large charge centres inside the cloud.
Eventually a situation is reached where the air cannot support such high voltages and
electrical breakdown occurs: flashing discharges, known as lightning. These discharges can
occur between cloud and ground, cloud and the surrounding air, within the cloud, and cloud
to ionosphere. When flashes do occur, the sudden heating and expansion of the air along the
discharge track produces sound waves – thunder.
High-speed photography has revealed that lightning is actually a multistage process. The first
stage of the cloud-to-ground flash is the stepped leader – steps of around 50 m, with pauses in
between of around 50 s. The flash is only visible for around 1 s during each step. Each
new step may involve one or more branches, as it tries to find the most conductive path to the
ground. The entire process takes about 20 ms, cloud to ground.
When the tip is within 10 – 20 m of the ground, a sharp point or object becomes sufficiently
charged that a ‘connecting discharge’ is initiated. This discharge rises to meet the stepped
leader, and then continues up the ionized channel it had created. This is much stronger, with
peak currents around 104 A, and reaches the cloud in around 0.1 ms. This is the return (main)
stroke, and is much more luminous than the stepped leader.
Most lightning discharges are multistroke, not single stroke flashes. A few hundredths of a
second later, a new cloud-to-ground discharge is initiated. This time it will propagate quickly
and continuously along the channel. This “dart leader” takes only about 2 ms to reach the
ground, and is again followed by a return stroke. This process – dart leader, return stroke –
may sometimes be repeated up to 20 times.
Lightning discharges involve large energies, mainly due to the very high potentials achieved
in the charging process: as high as 108 V. An entire flash may discharge a relatively modest
30 C through such a potential difference, giving a total energy of
30 C x 108 V = 3 x 109 J
enough to power a 100 W light globe for a year.
Electrical breakdown itself is actually the result of large electric fields (V/m), not large
potential differences as such. Electric fields are related to the gradient of the potential, which
becomes quite large around sharp points. This is the reason for using lightning rods. In fact,
such points may actually initiate the stepped leader, from ground to cloud.
The breakdown process involves the ionization of the air molecules, resulting in an electron
avalanche (although the positive ions will also make a contribution to the overall current).
The accelerated electrons will collide with other molecules, stripping further electrons – the
avalanche. Behind this flood of electrons will be a sea of positive ions, which will absorb
many of the electrons coming along behind. Thus the average electron may only travel
around 10 m downwards.
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