Volcanoes

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Will the Icelandic volcano cool us off?

Big Ideas: 
  • The ash cloud changes the Earth's albedo and therefore changes the balance between incoming and outgoing radiation, which may change the Earth's temperature.

Will the Eyjafjallajökull eruption change the climate1?

Volcanoes do a number of things that can affect the climate:

1. They belch greenhouse gases that can potentially warm the earth.

2. They emit clouds of ash and sulphur dioxide, which reflect away incoming sunlight.

3. The ash can darken snow cover and glaciers, which absorbs more sunlight than clean snow and ice.

4. They stop jet flights, thus preventing a load of greenhouse gas from entering the atmosphere.

We can dispose of the first easily. Humans add almost 30 gigatonnes of carbon dioxide to the atmosphere annually. Mount Pinatubo's eruption in 1991, the biggest in recent years, added only about 40 megatonnes. So humans are the equivalent of several hundred Mount Pinatubos, each year. If volcanoes did add significant quantities to the atmosphere, we would see big spikes in global carbon dioxide concentration measurements. We don't2.

But the second is more serious (and much bigger than (3) and (4), which we won't consider here). It is also amenable to some straightforward physics, which is what this C21 website is all about. The earth is heated by incoming sunlight, and cooled by outgoing thermal radiation. The hotter the earth gets, the more it radiates. This is the primary negative feedback mechanism that keep the earth's temperature (sort-of) stable. This we discuss in some detail on another page.

Volcanoes emit enormous quantities of ash and sulphur dioxide, both of which reflect sunlight, increasing our albedo A, currently measured to be about 0.3. The intensity of sunlight measured at the top of our atmosphere is called the solar constant, S, and its value is about 1.367 kW/m2. The mean incident solar intensity, Iin, is simply this divided over the entire surface area of Earth. In other words, it is the power per area that the Earth's surface would receive if the Sun was shining equally on every surface of the Earth.

$ I_{in} = \dfrac{S}{4}(1-A) $

Eqn. 1

(The factor of 4 comes from the fact that the Sun "sees" the Earth as a disk of area πr2, whereas the total surface area of the earth is 4πr2.)

This incoming intensity is matched by the outgoing thermal radiation, which is simply a function of surface temperature, according to the Stefan-Boltzmann law:

$ I_{out} = \sigma T_{e}^{4} $

Eqn. 2

Here σ is a universal constant. For a rigorous analysis Te should be the radiation temperature of the upper atmosphere, but for the simple proportional treatment we adopt here, we can use it to approximate the change in the Earth's surface temperature. To reach a stable temperature after a change in A, the earth's temperature changes until Iin = Iout. Because we assume nothing else is changing, we can say that Te4 is proportional to (1-A), i.e.Te ∝ (1-A)1/4. Or, by rewriting Eqns. 1 and 2 in terms of a new albedo A' and a new temperature Te' and dividing the two to get rid of terms we don't care about:

$ \dfrac{T'_{e}}{T_{e}} = \left( \dfrac{1-A'}{1-A}\right )^{1/4} $

Eqn. 3

Figure 1.  The area affected by the Eyjafjallajökull eruption as shown in the media3

So how much is A changed by the Eyjafjallajökull eruption? Let's take a worst-case scenario and assume the plume from the volcano reflects all sunlight. The area, judging from Figure 1, appears to be about twice that of Scandinavia, or 2 million km2. Viewed from the Sun, this plume always appears at an angle. Its mean latitude is about 60 deg, so we divide this area by 2 (because the cosine of 60deg is 0.5), and the resulting 1 million km2 is only 0.2% of the earth's surface (510 million km2). If the albedo of the plume rises from 0.3 to a maximum possible of 1.0 that means the total albedo of earth becomes 0.3 + 1.0×0.7×0.2/100 = 0.3014. Putting this in equation 3 (don't round off and throw out the baby with the bath water!) and assuming that Te is the present value of 287.5K, yields Te' = 287.36K, or a drop of 0.14K (or Celsius). This is comparable to typical year-to-year variations in the mean surface temperature of the Earth4. However, the change is unlikely to be anything like this big, because the time-constant for the earth to respond to such changes is about 5 years5, so to achieve this change in temperature, the ash plume would have to stay in the atmosphere for about a decade.

The much larger Mount Pinatubo did cool the Earth by about 0.5C in the early 90s.

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