The field that keeps Greenwich time

A ship crossing an ocean in fair weather, under a clear sky and far from any land, can measure an electric field in the air above its deck. It points downward, it is around a hundred volts per metre at the water’s surface, and it is not constant: it drifts up and down by some fifteen per cent over a day. That much would be unremarkable. Temperature does the same, and so does humidity, and so does almost everything the sun touches.

What is remarkable is when it does it. A second ship on the far side of the world, measuring the same thing with the same instrument, sees its maximum at the same instant as the first — not at the same local time, but at the same moment by the clock at Greenwich. On a ship in the Pacific the field is highest before lunch; in the Atlantic it is highest in the evening; in the Indian Ocean it is highest in the small hours. Each ship’s curve, drawn against its own clock, looks like a different phenomenon. Drawn against Universal Time they lie on top of each other.

A local cause cannot synchronise the world. The field over each ship is reading something global, and the something turns out to be the potential of one enormous conductor wrapped round the entire planet — a conductor whose potential is maintained, from minute to minute, by every thunderstorm on Earth at once. The fair-weather field is the far end of an electric circuit whose batteries are storms thousands of kilometres away, and its daily cycle is the daily cycle of the world’s thunder, added up.

The argument that turns that into a quantitative statement is the most basic fact about potential there is: a conductor is an equipotential. Everything else is detail about where, between the two conductors, the potential difference sits.

Two conductors and a poor one between them #

The ground conducts, and so does the sea, far better than air does. So does the upper atmosphere, above about sixty kilometres, where sunlight and cosmic rays keep a large fraction of the gas ionised. Between those two lies a layer of air that conducts, but only barely. The Earth’s electrical structure is two good conductors separated by a leaky insulator: a spherical capacitor with a resistor in parallel with it.

The air conducts at all because it contains ions. At sea level over the ocean they are made almost entirely by cosmic rays — high-energy particles from outside the solar system and the showers of secondaries they trigger when they strike the upper atmosphere — at a rate of a few pairs per cubic centimetre per second. Over land, radon seeping from the soil adds to that. The ions recombine or stick to aerosol particles, and the balance leaves a few hundred to a thousand small ions per cubic centimetre, each drifting in a field with a mobility of roughly one or two square centimetres per volt-second. Multiply the number, the charge and the mobility, and the conductivity of air near the ground comes out at around $10^{-14}$ siemens per metre. Copper conducts some twenty-one orders of magnitude better.

Going up, the air gets thinner and the ions get two advantages at once. Cosmic-ray ionisation increases with height through the lower atmosphere, because fewer of the incoming showers have been absorbed, and the ions that are made travel further between collisions, so their mobility rises too. The two combine into a conductivity that increases roughly exponentially with height. The figure below uses that model: a conductivity of $2 \times 10^{-14}$ S/m at the surface, rising by a factor of $e$ every three kilometres.

The real profile is not a perfect exponential — the scale height lengthens above the cosmic-ray ionisation maximum at around fifteen kilometres, and the conductivity at sixty kilometres is closer to $10^{-9}$ than to the $10^{-5}$ the straight line on the left reaches — but the only part of the profile that matters for what follows is the bottom ten kilometres, and there the exponential is a fair description. What the left panel shows in one line is that the air’s ability to carry current spans many orders of magnitude between the ground and the top of the stratosphere, and that it is by far the worst near the surface, where people live and measure.

The right-hand panel is the consequence, and it is the first thing to understand about the whole system. The potential of the upper conductor — measured by balloon soundings since the 1950s, and found to be around 250 kilovolts positive with respect to the ground, varying between about 200 and 300 — is not spread evenly across the sixty kilometres of air. It is almost all used up in the first few.

Where a steady current puts the voltage #

The reason is a rule that holds for any steady current in any conductor. If nothing is piling up anywhere, the current through each horizontal layer of a column of air must be the same as through every other: charge arriving from above has to leave below, because charge is conserved and a steady state accumulates none. So the current density $J$ is one number all the way up the column. The field that drives it through any layer is Ohm’s law in local form, $E = J/\sigma$, and since $J$ is fixed and $\sigma$ rises with height, the field must fall with height in exact proportion:

$$E(z) = \frac{J}{\sigma(z)} = E_0\, e^{-z/H}.$$

The potential is the field integrated upward, and an exponentially falling field integrates to a potential that approaches its final value exponentially:

$$V(z) = V_\infty\left(1 - e^{-z/H}\right), \qquad E_0 = \frac{V_\infty}{H}.$$

With $V_\infty = 250$ kV and $H = 3$ km, the field at the ground is 83 volts per metre — close to the 100 to 130 measured over the oceans, which is all a two-parameter model should be asked to do. And the field at ten kilometres, just below the aircraft cruising height, is only three per cent of it.

The same statement can be made about resistance, which is how an electrical engineer would make it. A thin layer of air of thickness $dz$ and unit area has a resistance $dz/\sigma(z)$, and the resistance of a column is the sum of those, in series. Most of that sum comes from the bottom, where $\sigma$ is smallest:

Half the resistance of the entire atmospheric column is in its lowest 2.1 kilometres, and nine tenths of it in the lowest seven. A column one metre square has a resistance of $H/\sigma_0 = 1.5 \times 10^{17}$ ohms. The atmosphere is five hundred million million of those columns side by side, all in parallel between the same two conductors, so the resistance of the whole thing is that figure divided by the Earth’s surface area — about 300 ohms in the model. Measured estimates are between 200 and 250.

Three hundred ohms and a quarter of a million volts make a current of some 850 amperes, running downward through the fair-weather sky at every moment, over the whole planet: a little under two picoamperes through each square metre of the surface, which is the value measured. It is a very small current density and a very respectable total. Something has to be supplying it, continuously, or the upper conductor would discharge.

Before looking at what, it is worth noticing what has been established without it. The fair-weather field at any one place is $J$ divided by the local conductivity. $J$ is set by the global voltage and the global resistance; the conductivity near the ground is set by the local air. So the field measured anywhere is a product of a global factor and a local one, and it can change for either reason. Fog, haze and smoke remove small ions by attaching them to droplets and particles, lower the local conductivity, and raise the local field — which is why the fair-weather field over industrial cities in the nineteenth and early twentieth centuries was two or three times its value over the ocean, and why old records of it are now read as records of air pollution. The ships had the advantage of air too clean for that to matter, which left only the global factor to vary.

A conductor has one potential #

The upper conductor is the key to the whole problem, and the way to see why is to ask how fast each layer of the atmosphere can rearrange its charge.

When a charge is put inside a conductor, the field it creates drives a current that carries it away to the surface, and the time this takes is the ratio of permittivity to conductivity, $\tau = \varepsilon_0/\sigma$. For copper that is around $10^{-19}$ seconds, which is why the inside of a metal is always field-free. For air it depends enormously on height:

Near the ground a charge placed in still air lingers for seven or eight minutes before the air’s own conduction cancels it. At forty kilometres it lasts under a millisecond; at seventy, a fraction of a microsecond. The upper atmosphere, on every timescale relevant to weather, is a conductor, and a conductor is an equipotential: any difference of potential between two parts of it drives a current that removes the difference, faster than anything could establish it.

That is the step that makes the circuit global. It means there is not a separate upper plate over each thunderstorm, charged by that storm and leaking through the local sky. There is one upper plate, round the whole planet, at one potential, and every storm charges it and every fair-weather patch of sky discharges it. A storm over the Congo raises the potential above a ship in the South Pacific by exactly as much as it raises the potential above the Congo. The fair-weather current everywhere is fed by all the storms everywhere, and the field at any one place is a reading of the world total.

The bottom of the column has the opposite property, and it is equally essential. Because the air near the ground takes minutes to relax, a field can be sustained in it — a steady field in a conductor is only possible because a steady current keeps replacing the charge that the conduction removes. And the charge that the field implies can be read off with Gauss’s law. A downward field of 100 volts per metre at the surface means a negative surface charge of $\varepsilon_0 E_0$, about 0.9 nanocoulombs on every square metre of the Earth — some 450,000 coulombs over the whole planet. The field falls with height, so the air between the ground and a few kilometres up must hold a matching positive space charge, and it does: the lower atmosphere in fair weather is very slightly positive, with most of the balancing charge in the lowest few kilometres, not at the ionosphere sixty kilometres up. The capacitor is not two plates sixty kilometres apart. It is a charged ground and a diffuse cloud of positive charge above it, whose effective separation is about one scale height.

Seven minutes of memory #

This has a consequence for how long the circuit could run on its own. The time to discharge a capacitor through a resistor is $RC$. The resistance of the column is $H/\sigma_0$ per unit area; the capacitance of a layer whose charge is separated by about $H$ is $\varepsilon_0/H$ per unit area; their product is

$$RC = \frac{H}{\sigma_0}\cdot\frac{\varepsilon_0}{H} = \frac{\varepsilon_0}{\sigma_0},$$

the relaxation time of the air at the ground. The scale height cancels. Were every thunderstorm on Earth switched off at once, the potential difference between the ground and the upper atmosphere would decay with a time constant of about seven minutes in the model; estimates from the measured profiles give somewhere between five and fifteen. The half-million coulombs on the ground would be gone within the hour.

Two things follow. The first is that the generators must be running constantly. Somewhere on Earth, at every moment of every day, enough storms are active to supply several hundred amperes into the upper plate — and the counts bear that out: at any instant between one and two thousand thunderstorms are in progress, each driving an average of roughly half an ampere to an ampere upward from its cloud top through the conducting air above it. The second is that the circuit has a short memory. It cannot average the storms over a day, because it forgets them in minutes. So its potential follows the instantaneous world total of thunderstorm activity almost exactly, and any daily rhythm in that total appears in the field without being smoothed away.

That rhythm exists because thunderstorms are overwhelmingly a land phenomenon and an afternoon one. Sunlight heats the ground, the ground heats the air in contact with it, and by mid-afternoon the lower atmosphere has been made unstable enough to overturn in towering convective cells. The oceans, with their enormous heat capacity, barely have an afternoon at all, and their storms are fewer and weaker in the electrical sense. So the world’s thunder comes mostly from three places — the Americas, Africa with Europe, and the band from South-East Asia to northern Australia — each producing most of it in its own local afternoon, which is a different time in Greenwich for each.

The world’s thunder, added by the hour #

A model of the total is simple to build. Give each continental region a daily cycle of activity that rises to a peak in the mid-afternoon of its own longitude and falls away overnight, weight each by how much of the world’s thunderstorm activity it carries, and add them up in Universal Time.

Asia and Australasia’s afternoon arrives first in Universal Time, around eight in the morning at Greenwich; Africa and Europe’s follows around two in the afternoon; the Americas’ comes last, around eight in the evening. Because the Americas carry the largest share — the Amazon basin and the Central American isthmus are among the most thunder-rich places on Earth — their peak dominates the sum, and the total reaches its maximum near 19 UT and its minimum near 3 UT, when the dark side of the planet sits over the Pacific and almost nowhere with land is in its afternoon.

The measured curve, first assembled from the survey ship Carnegie’s cruises between 1915 and 1929 and since reproduced by every fair-weather campaign clean enough to see it, has the same shape: a single maximum near 19 UT, a minimum near 3 UT, and a range of about fifteen to twenty per cent either side of the mean. It is called the Carnegie curve, after the ship. The first analysts of those records, at the Carnegie Institution’s Department of Terrestrial Magnetism in the early 1920s, noticed that the ocean measurements varied in step with Greenwich time before anybody had a satisfactory explanation of why they should, and it was the comparison of that curve with thunderstorm statistics by continent, published at the end of the decade, that closed the argument C. T. R. Wilson had proposed in 1920: the storms are the batteries.

The model in the figure is not fitted to the curve. Its peak times and weights are round numbers chosen to represent where the world’s storms are, and its only purpose is to show that three afternoon peaks at three longitudes, weighted unequally, must add up to a single world peak in Universal Time — and that its position is decided by which continent carries most. That the model and the Carnegie curve agree to within an hour and a few per cent is a statement about the storms, not about the fitting.

Three ships and one clock #

The last figure is the observation the essay opened with, drawn from the model. Each ship multiplies the global thunderstorm factor by its own local conductivity, which over clean ocean is the same everywhere, and plots the product against its own local solar time.

The three curves are the same curve, shifted by eight hours each, because eight hours is 120 degrees of longitude. A daily cycle driven by the local sun would put all three peaks at the same point on this axis — mid-afternoon, like a temperature record. Instead they sit at three widely separated local hours that correspond to one Universal Time, and the Pacific ship’s field is highest before noon because the Americas are in their afternoon then.

This is the cleanest evidence available that the upper atmosphere is a single equipotential. If each region’s storms charged only the sky above them, the far side of the planet would see no daily cycle at all, or a shifted and diluted one. What is seen is one cycle, everywhere, at one moment. The planet’s potential moves up and down as a unit, and the ships are merely voltmeters at different places on the same conductor.

What the generator actually is #

The circuit so far has been described from the fair-weather side, where the physics is linear and the model is easy. The generator side is not. A thunderstorm separates charge by collisions between soft hail, known as graupel, and small ice crystals in the cloud’s mixed-phase region, where both coexist with supercooled water; which way the charge goes depends on temperature and liquid water content in ways laboratory experiments still dispute in detail. The usual result is a positive charge near the cloud top and a negative one lower down, separated by several kilometres and by potential differences of tens to hundreds of megavolts.

What matters to the circuit is how that separated charge reaches the two plates. Above the cloud, the conductivity is already higher than near the ground, and the positive upper charge drives a steady conduction current upward to the ionosphere — the current that charges the global upper plate, typically around an ampere per storm. Below the cloud, negative charge reaches the ground by lightning, by rain carrying charge down, and by point discharge from trees, grass and structures in the strong field under the cloud. The circuit closes through the fair-weather sky everywhere else, from the ionosphere back down to the ground.

A thunderstorm, in this picture, is a battery with its positive terminal pointing up. It needs to be tall and vigorous enough to separate charge faster than its own leaky surroundings recombine it, and that is a threshold condition, which is why continental afternoon convection dominates. It has emerged more recently that electrified shower clouds which never produce lightning at all — especially over the oceans — supply a substantial share of the current, perhaps a third, which is one of several reasons why the global circuit’s generator is known only in outline despite a century of measurement.

How far the model reaches #

The exponential conductivity profile has been used here for its arithmetic, not its accuracy. Above about fifteen kilometres the ionisation stops increasing and the conductivity grows more slowly; at mountain sites the lower boundary is higher and the column resistance smaller; over land, aerosol makes the lowest kilometre far less conducting than the model’s surface value. None of those changes the three conclusions: that the voltage sits where the resistance is, near the ground; that the top of the column is a conductor on the timescales of weather; and that the circuit’s discharge time is short, set by the ground-level conductivity.

The equipotential is not perfect either. At high latitudes the solar wind drives electric fields across the polar caps of tens of kilovolts, which are superimposed on the global potential there, and during geomagnetic storms the ionosphere itself becomes structured. Those effects are why the cleanest measurements of the Carnegie curve come from low and middle latitudes over the ocean. The approximation that the upper atmosphere is one conductor at one potential is still good to several per cent of 250 kilovolts over most of the world, and it is the approximation that the whole observation depends on.

There is also a limit to how far the random walkers of the essay on harmonic averages can be taken here. In the charge-free region between conductors, a potential is the average of its boundary values, and a walker’s wanderings compute it. The atmosphere is not charge-free and not static: it carries a steady current and a space charge that the current maintains. Its potential satisfies Poisson’s equation with a source that is itself decided by the conductivity, which is why the profile is exponential rather than linear and why the harmonic-averaging picture needs extending before it applies. The boundary argument survives, though. The ionosphere’s potential is one number because it is a conductor, and every point below it sees that number through a column of air whose resistance decides how the drop is shared out, exactly as no static arrangement of charge can hold a charge still because the potential in empty space has nowhere to hide an extremum.

A climate thermometer made of voltage #

Because the ionospheric potential integrates every electrically active storm on Earth, it has been proposed more than once as a single-number index of global convection — a thermometer for the planet’s thunder, readable from one balloon sounding or one clean ocean site. Global thunderstorm activity is expected to rise with temperature, since warmer surfaces drive stronger convection, and some analyses of long records have found the fair-weather field varying with the El Niño cycle and with tropical temperature on timescales of years. Others have found the long records dominated by changes in local pollution, which alter the local factor rather than the global one and are hard to separate from it.

The difficulty is the one the model makes explicit. What any ground station measures is the global potential divided by the local resistance of the air above it, and a century of changes in coal smoke, diesel exhaust and aerosol at a land observatory is a century of changes in that resistance. Only clean sites — the open ocean, Antarctic plateaux, high mountains — measure something close to the global factor alone, and they are few, far between, and not continuously staffed.

The capacitor analogy is worth a last look in that light. The capacitance between two conductors is decided by their geometry alone, and here the relevant geometry is not the sixty-kilometre gap to the ionosphere but the three-kilometre scale of the space charge near the ground — which depends on the conductivity profile, and therefore on cosmic rays, aerosol and the height of the boundary layer. The Earth is a capacitor whose effective plate separation is set by the weather.

Still open: whether the circuit’s current changes clouds. The fair-weather current passes through every cloud on the planet, and at the edges of layer clouds, where the conductivity changes abruptly, it deposits charge on droplets and aerosol particles. Charged particles are collected by droplets more efficiently than neutral ones, so in principle the global circuit can alter how clouds form and precipitate. Measurements over Antarctica have found small but statistically significant changes in surface pressure following changes in the ionospheric potential driven by the solar wind, and some cloud records respond to sudden drops in cosmic-ray intensity. Whether the effect is large enough to matter to weather or climate, and whether the global circuit’s hourly Carnegie cycle leaves any trace in the world’s clouds, has not been settled. The field that keeps Greenwich time is measured and explained; whether it does anything besides keep it is an open question.