The lake that holds its gas until it does not

The plume that stops below the surface followed a rising plume into stratified water, where it mixes as it goes, grows denser than its surroundings and stops at a level set by the stratification. That is the usual way for a stable column to behave. It treats a disturbance by absorbing it, and the layer a parcel cannot leave gave the local reason: a parcel moved up finds itself denser than the water around it and sinks back. That restoring tendency is the basis of nearly all stability in lakes, oceans and the atmosphere.

Lake Nyos, a crater lake in the Cameroonian highlands, is a column in which this reasoning is right at the place where the water sits and wrong a hundred metres higher. Its bottom water is heavier than the water above it and has stayed down for decades. Carbon dioxide seeps into it from a magmatic source below, in a place where no wind or winter is strong enough to overturn a tropical lake, and the gas accumulates. The mixture heavier than either water quotes this lake in passing, as an example of a stable density step that persists. The question is how something so stable could turn so suddenly. It did so on the evening of 21 August 1986, releasing perhaps a cubic kilometre of carbon dioxide, which flowed down the valleys and killed about 1,700 people and thousands of cattle up to 25 km away. Lake Monoun, 95 km to the south, had done the same on a smaller scale two years earlier.

The chain of events is a piece of ordinary physics, and it is rather simple. It has only two ingredients, Henry’s law and hydrostatic pressure, and the arithmetic they need is no harder than a tide table’s.

A lake a little under half full #

A liquid at a given temperature dissolves a gas in proportion to the pressure of that gas above it. For carbon dioxide in water at 23 °C the coefficient is about 0.036 mol per litre per atmosphere. A bottle of soda is the everyday demonstration, sealed at several atmospheres and saturated for that pressure. When its cap comes off, the pressure falls and the gas comes out.

Now think of a depth in a lake as a bottle sealed by the water above. Pressure rises by about an atmosphere per ten metres, so the deep water at 200 m is under 21 atmospheres, and it can hold about 0.75 mol/L before it is saturated.

The profile in the figure is representative of surveys made after 1986, with a surface layer holding little gas, above a gradient and a deep layer holding about a third of a mole per litre. Everywhere, the water holds less than it could. The lake is not bursting at the seams, and nothing inside it is on the point of forming a bubble. Bubbles cannot form spontaneously in a liquid that is below saturation at its local pressure, so the lake can stay in this state for a very long time, with gas slowly accumulating.

That safety is entirely due to staying put. A parcel of bottom water, moved upward with its gas intact, follows the vertical dashed line. Pressure falls, and the dissolved amount does not. It reaches the saturation line at the depth where hydrostatic pressure equals the gas’s partial pressure, near 88 m for this concentration. That depth is the crucial number, called the saturation depth. Above that, the parcel holds more gas than it can dissolve, and bubbles start to form. Bubbles need something to nucleate on, as the barrier a new phase has to climb explains, but a lake has plenty of suitable particles.

The numbers also show how much margin the state has. Bottom water at 200 m must be lifted by 110 m in order to reach this point, which at first seems a very large displacement to expect in a lake. Anything that can do this would have to carry quite a lot of energy. Yet it does not all have to be lifted at once. It requires only a small region, or a tube or streamer of water, which then drives the rest.

Heavier when dissolved, lighter when not #

Dissolved carbon dioxide does something a little surprising to water: it makes it heavier. A mole of the gas adds 44 g and only about 37 cm³, which increases density by about 7 kg/m³ per mole per litre. The deep water, with its dissolved carbon dioxide, is thus denser than the surface water by about 2.8 kg/m³, a few tenths of a per cent. This is what holds the column stable and means a tropical lake can keep a deep layer for decades. In fact, the bottom is slightly warmer than the water above it, fed by warm springs, which on its own would be unstable. The dissolved load overcomes this, as with the pond that is hottest at the bottom, which uses dissolved salt in the same way to allow a warm bottom layer to sit under a cooler one.

So the parcel starts out denser than its surroundings, and the ordinary reasoning applies: a modest lift is resisted. But the same gas, out of solution, has the opposite effect. Gas at atmospheric pressure occupies about 24 L per mole. Excess gas in a parcel at a depth where only part of it can stay dissolved, expanding to fill bubbles at that pressure, displaces a great deal of water. The bubble fraction of a parcel rises steeply with height. At 60 m it is about 26 per cent, and at 20 m about 66 per cent. The density of the parcel falls from about 1000 kg/m³ to a third of that. This is an extremely large buoyancy, which no temperature difference in any natural body of water could produce.

The essential feature is a reversal of the usual stabilising mechanism. In the salt that sinks through a stable sea, a difference between two diffusing properties gives a slow, modest instability. Here the instability is much more direct: a parcel below its saturation depth is pushed back, and a parcel above it is flung upward. There is a threshold, and the same fluid is on both sides of it. No energy has to be added in order to release this, for it is stored in the gas’s dissolved state. The lake is in a metastable state with enormous free energy, and the height of the barrier is about 110 m of lifting.

That is also why a limnic eruption is not a boiling event. The column that boils from the middle deals with a geyser, whose release is a change of phase of the water itself, driven by heat. Here, the water does not change phase, and the temperature hardly changes at all; a soda bottle is the fairer comparison, and so is a shaken champagne bottle when it is opened.

How much speed the bubbles can buy #

Once a parcel passes its saturation depth, its buoyancy accelerates it upward. Ignoring friction, mixing and the slip of the gas past the water, energy conservation gives the rise speed, by integrating the buoyancy force, $g\alpha$ per unit mass, where $\alpha$ is the bubble fraction:

$$w^2 = 2g\int \alpha\,dz.$$

This gives about 27 m/s at the surface for the surveyed water, with its concentration from after the event. Deep water before 1986 must have held substantially more than what was left, so the true value was probably higher, as the second curve suggests. That is a ceiling for each concentration: a real plume loses a good deal to friction with its surroundings. On the other hand, a rising bubbly plume entrains and carries deep water along with it, which feeds more gas into the rising column, so that the column does not need to run out for some time. Once a pathway exists, it is self-sustaining until the gas above the saturation level is exhausted. An observer on the shore would see something like a fountain or a very large eruption from the middle of the lake.

Evidence around the lake is consistent with this kind of speed. Vegetation was flattened on a headland, water surged about 25 m up the shore on one side and a brown stain from the iron-rich deep water, which oxidised on contact with air, spread across the surface afterward. About a metre of water level was missing from the lake when it was first surveyed, because that amount had been carried away as spray. The fountain must also have cooled the lake surface: the expansion of a gas and evaporation of water remove heat from the plume, and this was observed as an unusually cold surface temperature days later.

What set it off #

Nobody saw the start of the event, and the cause of the initial lift has never been settled. There are several candidates. Landslides from the cliff on the lake’s western side might have pushed cold, surface water down into the deep. Rain falling on a cool windy evening in August, when thermal stratification is weakest, might have sent a sinking current down the edge of the lake, which would displace the deep water upward. A small volcanic discharge at the bottom is another possibility, though the geochemistry suggests the release was of stored gas and not a magmatic pulse. Slow accumulation could have raised a saturation layer near a certain depth by itself, with no external trigger at all.

Part of what makes the event hard to reconstruct is that those candidates are not mutually exclusive. All they have to do is provide one modest displacement, somewhere, of a tube of water, for about a minute, and the rest happens by itself. The question is therefore not what could deliver enough energy; it is how large a trigger the lake had grown sensitive to, by the end of August 1986. A slope that is steep enough will fail to any trigger, and one reasonable view is that the question of which trigger was at work is secondary.

The event was also self-limiting. Having released a large part of the gas above the saturation level and mixed the column, the plume stops when the remaining deep layer is too poor in gas for the lift to work. Measurements from a few years after 1986 found that the lake still held most of its gas in the deepest layer, and that it had started to recharge. This makes the danger a repeating one, on a time scale of decades.

A pipe that pumps itself #

The obvious remedy, once the mechanism had been understood, is to do the same thing slowly and in a controlled way. A vertical pipe is lowered to the deep layer with its top near the surface. Something has to start the flow, and a pump will do this: raise deep water up the pipe until it reaches its saturation depth, and bubbles begin to form within the pipe.

After that no pump is required. The column in the pipe is lighter than the lake water outside at every level above the saturation depth, by exactly the buoyancy just discussed. So the pressure at the pipe’s mouth is lower than the pressure outside, and water keeps flowing in. The available drive, as the figure shows, is about 37 metres of water with the surveyed gas load, an upper bound since no friction is included. At Nyos a pilot pipe in 1995 demonstrated this, and the first permanent pipe, 203 m deep, began operating in January 2001 with a fountain tens of metres high that became something of a local landmark. Two more were added in 2011. Lake Monoun was treated in the same way.

The system has one lovely safety feature. Its drive disappears exactly when the danger does, since the flow stops when the water at the mouth can no longer reach saturation before the top of the pipe. That happens near 0.036 mol/L, the concentration that is saturated at one atmosphere. Between the dangerous level and this one, the pipe runs without any supervision or electricity, in a remote place, with no moving parts. A physical process that once killed 1,700 people is now maintained, in a tamed form, as a method for making them safe.

The cure carries a risk of its own, because the water being removed from the deep layer is heavy and stabilises the column. Removing it from below while returning it to the top reduces the density contrast with depth. So the question of how quickly degassing can safely proceed had to be studied. Calculations indicated that it could weaken the top of the deep layer and that recharging from the vent might also matter. Monitoring of gas content and of stratification has continued since then, and at Nyos it has found that gas has fallen substantially.

A river of air #

The other half of this disaster was in the air. Carbon dioxide is about one and a half times as dense as air at the same temperature and pressure. A cloud of it released at ground level does not rise and disperse as a hot plume would. It flows downhill as a heavy current, keeping its concentration until it is mixed away.

A gravity current moves at about $\sqrt{g'h}$ times a coefficient, where $g'$ is gravity reduced by the fractional density excess. For a layer 50 m thick with 30 per cent carbon dioxide, this is about 9 m/s or 32 km/h: faster than anyone can run, and somewhat slower than a road vehicle. The building that breathes through its doors drew the same kind of exchange flow in a far gentler setting, as cold air moves through a doorway. Survivors in Nyos described a smell like rotten eggs or gunpowder and a sudden loss of consciousness, and they woke up hours later to find everyone around them dead. Concentrations above about ten per cent cause unconsciousness in a very short time, since they act directly on breathing and on the blood’s acidity, not merely by displacing oxygen. There was no warning for those downhill from the lake, at night, in the valleys.

Hillsides proved to be a line of survival in some places. Those who happened to be higher up at the time often lived, while lower villages were devastated. The event’s human geography matches a heavy fluid’s behaviour exactly. Maps of the casualties look like a flood’s.

What these estimates leave out #

The profile is representative, not a measurement of any particular date. The state of the lake in 1986 was not measured. Henry’s coefficient is taken at a single temperature and its slight dependence on pressure and dissolved salts is ignored. The parcel argument treats a lifted parcel as closed, with no mixing, and a real rising plume entrains water from outside. The speed integration ignores all friction and the slip of bubbles through the water, and it is meant only as a bound. The gas fraction formula assumes the gas comes out of solution as soon as it can, ignoring any lag from the need to nucleate and grow bubbles. All of this is a one-dimensional sketch.

The figure for the heavy gas front is a simple estimate that ignores mixing, heating by the ground and all the terrain. Nothing in it tells where such a flow goes. To say where a real cloud would have gone needs a three-dimensional calculation for that terrain, with its release rate, and the reconstructions done have had to assume the rate. The pipe’s drive is an upper bound that ignores friction in the pipe and the slip of gas bubbles past the water, both significant, as well as any lag in bubbles appearing.

Still open: what Lake Kivu will do #

Far larger than Nyos, Lake Kivu between Rwanda and the Democratic Republic of the Congo holds about 300 km³ of carbon dioxide and about 60 km³ of methane dissolved in its deep water, and has some two million people living on its shores. Its gas concentration has been rising, at least for methane, according to surveys several decades apart, and how close it is to any threshold is the subject of ongoing study. Sediment layers on its bottom suggest that large release events have occurred, roughly every thousand years in the distant past. Unlike at Nyos, its bottom water is stabilised by dissolved salts too, which provides a larger margin.

Since 2015, methane has been extracted there as a fuel, by raising deep water through a pipe, degassing it and returning the water at a chosen depth. Returning that water at the wrong depth, or too rapidly, could itself alter the stratification. A large volcanic eruption from nearby Nyiragongo sent lava toward the lake in 2021 and raised fears of an overturn, which did not occur; whether a lava flow reaching the deep layer could trigger one is not known. The physics of a single parcel is simple, and how a basin of that size, with its own volcanic system, might actually fail is not.

Deep water in a lake is held stable by the very gas it stores, since dissolved carbon dioxide adds weight. Lift it past the depth where the pressure no longer keeps that gas dissolved, and the same gas makes it a mostly gaseous, far lighter column, driving itself upward. Nothing has to be heated or added. The instability that killed 1,700 people in 1986, run slowly in a 200 m pipe, now drains the lake until the danger is gone.