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## What is the scale height of water vapour in the Earth’s atmosphere?

Someone recently asked me what was the scale height of water vapour in the Earth’s atmosphere, so I decided to see if I could find out. The scale height of water vapour is particularly important for infrared, sub-millimetre, millimetre and microwave astronomy, as it is the water vapour in the Earth’s atmosphere which prevents large fractions of these parts of the electromagnetic spectrum from reaching the ground. This is why we can, for example, only study the Cosmic Microwave Background from space or from a few particularly dry places on Earth such as Antarctica and the Atacama desert in Chile.

## What does the term ‘scale height’ mean?

First of all, let me explain what the term “scale height” means. It is the altitude by which one needs to go up for the quantity of something (water, nitrogen, oxygen, carbon dioxide) to go down by a factor of $1/e$, where $e$ is the base of natural logarithms, and $e=2.71828.....$. The scale height, usually written as $H$, is dependent upon the temperature of the gas, the mass of the molecules, and the gravity of the planet. We can write that

$H = \frac{ kT }{ Mg } \text{ (1)}$

where $k$ is Boltzmann’s constant, $T$ is the temperature (in Kelvin), $M$ is the  mass of the molecule and $g$ is the value of the acceleration due to gravity. If we were to plot the atmospheric pressure as a function of altitude we find that it follows an exponential, this is because of the differential equation which produces Equation (1) above (I will go into the mathematics of how Equation (1) is derived in a separate blog).

In the case of air, which is some 80% nitrogen molecules and 20% oxygen molecules, the scale height has been well determined and is $7.64 \text{ kilometres}$ (or, to put it another way, it drops by a half every $5.6 \text{ km}$). So, if one were at an altitude of $5.6 \text{ km}$, half of the atmosphere would be below you. Go up another $5.6 \text{ km}$ and it drops by a half again, so at $11.2 \text{ km}$ 75% of the atmosphere is below you.

## What is the scale height of water vapour in the Earth’s atmosphere?

Determining the scale height of water vapour in the Earth’s atmosphere is, I have discovered, essentially impossible. Or, to put it better, it is a meaningless figure. This is because it varies too much. It depends on temperature, so even in a given place it can vary quite a bit. So, instead, we talk of precipitable water vapour (PWV) at a particular place (both location and altitude). PWV is the equivalent height of a column of water if we were to take all the water vapour in the atmosphere above a particular location and it were to precipitate as rain.

The Mount Abu Infrared Observatory in India, for example, is at an altitude of 1,680 metres, and quotes a PWV of 1-2mm in winter. The PWV would be higher in summer, as water sinks in the atmosphere when it is cold. For Kitt Peak in Arizona, which is at an altitude of 2,090 metres, the PWV varies between about 15mm and 25mm. This is why very little infrared astronomy is done at Kitt Peak. For Mauna Kea in Hawaii, which is at an altitude of just over 4,000 metres, it varies between 0.5mm and 2mm. This is why there are a number of infrared, sub-mm and millimetre wave telescopes there.

At the South Pole, which is at an altitude of 2,835 metres, the PWV is measured to be between 0.25 and 0.4 in the middle of the Austral winter (June/July/August). Why is this so much lower than Mauna Kea, even though it it is at a lower altitude? It is because it is so much colder.

The average Precipitable Water Vapour at the South Pole averaged over a 50-year period from 1961 to 2010. Even in the Austral summer it is low, but in the Austral winter (June/July/August) it drops to as low as 0.25 to 0.35mm, one of the lowest values found anywhere on Earth.

High in the Atacama desert, on the Llano de Chajnantor (the Chajnantor plateau), which is at an altitude of 5,000 metres and where ALMA and other millimetre and microwave telescopes are being located, the PWV is typically about 1mm, and drops to as low as 0.25mm some 25% of the time (see e.g. this website). This is why Antarctica and the Atacama desert (in particular the Chajnantor plateau) have become places to study the Cosmic Microwave Background from the Earth’s surface; we need exceptionally dry air for the microwaves to reach the ground.

## Summary

To summarise, it is meaningless to talk about a scale height for water vapour in the Earth’s atmosphere, as the vertical distribution of water vapour not only varies from location to location, but varies at a given location. So, instead, we talk about Precipitable Water Vapour (PWV); the lower this number the drier the air is above our location. To be able to do infrared, sub-millimetre, millimetre and microwave astronomy we need the PWV to be as low as possible, the best sites (Antarctica and the Atacama) get as low as 0.25mm and are usually below 1mm. The exceptionally dry air above Antarctica and the Atacama desert enable us to study the Cosmic Microwave Background from the ground, something we usually have to do from space.

## Robert Falcon Scott in Cardiff

When Robert Falcon Scott’s ship the “Terra Nova” left the British Isles to head to Antarctica in his attempt to be the first person to get to the South Pole, it was from the port of Cardiff that the ship sailed. Thankfully there are numerous memorials to this important connection between Cardiff and Scott in the city.

Why did he set sail from Cardiff? It was partly because the coal used to power the Terra Nova was South Wales anthracite, which was generally recognised in the early 20th Century as the best coal in the World, and partly because per head of population the Welsh had raised more money for his expedition than any other region of Britain.

Scott dined at the Royal Hotel on the night of the 13th of June 1910, and on the morning of the 15th the Terra Nova set sail, but Scott went back to London to complete some last minute fund-raising and planning. He boarded a faster ship and caught up with the Terra Nova in South Africa, before leaving the ship again in Melbourne to do more fundraising. He joined the ship again in New Zealand, and then they sailed south to McMurdo Sound to begin their assault on the Pole.

Scott dined at the Royal Hotel in Cardiff before the Terra Nova sailed from Cardiff Port

## Cosmic neutrinos detected by IceCube

Several months ago, I blogged about the experiment being done by a neutrino detector called IceCube at the South Pole to try to determine the nature of cosmic rays. A couple of weeks ago it was announced by the IceCube team that they had detected, for only the second time ever, neutrinos coming from beyond our Solar System.

## What are neutrinos?

Neutrinos are amongst the most mysterious and elusive particles in nature. They were first proposed back in 1930 by Wolgang Pauli to solve a problem to do with radioactive beta decay. In radioactive beta decay, a neutron will turn into a proton, spitting out a high energy beta particle (which is actually an electron) from the nucleus. Experiments showed that the energy of these electrons varied, which seemed to violate the principle of the conservation of energy.

Pauli suggested that the energy was actually being shared between two particles, the electron and a new particle which he dubbed the neutrino, which means “little neutral one” in Italian. However, it was not until 1956 that they were first actually detected. The reason they took so long to detect is that they do not interact very much with matter. They have no electrical charge, so do not feel the electromagnetic force. They have next to no mass so do not feel the gravitational force, and they do not feel the strong nuclear force which keeps atomic nuclei together.

The only force they feel is the weak nuclear force. As a consequence of how little neutrinos interact with matter, they can pass through the Earth essentially unimpeded. Every seconds, billions pass through your body without interacting at all with any of the atoms in your body. However, very rarely, a neutrino will directly strike an atomic nucleus, and this collision enables us to detect them. IceCube uses huge columns of very pure water buried below the ice-sheet in Antarctica to shield the neutrino detectors from the background radiation and cosmic rays.

## Neutrinos from the Sun

The Sun converts Hydrogen to Helium in its core, in a process known as the proton-proton chain. During this process, in addition to large amounts of energy being produced, neutrinos are generated.

The proton-proton chain in the core of the Sun, which converts Hydrogen to Helium, producing energy and neutrinos in the process.

The Sun is the strongest source of neutrinos beyond our terrestrial laboratories, but when physicists first started detecting neutrinos from the Sun in the 1960s they discovered a problem. It seemed that the Sun was only producing one third of the neutrinos that calculations predicted, or at least we were only detecting one third. This became known as the solar neutrino problem, and was not solved until the last 15 years. As this is quite a fascinating and involved story, I will talk about the solar neutrino problem and its resolution in more detail in a future blog.

## Supernova 1987A

In February 1987 a star was seen to explode in the nearby Large Magellanic Cloud, a satellite galaxy of the Milky Way. It was seen independently by Ian Shelton and Oscar Duhalde on the same evening whilst both were observing at the Las Campanas Observatory in Chile.

This was the first naked-eye supernova since the early 17th Century, and of course allowed astronomers to study supernovae in detail for the first time. But, 3 hours before anyone had seen the supernova, a burst of neutrinos was detected by 3 separate neutrino detectors, the Kamiokande II detector in Japan, the Irive-Michigan-Brooklyn detector in the USA and the Baksan detector in Russia. These neutrinos (strictly speaking, anti-neutrinos) were produced when the core of the dying star collapsed to form a neutron star. In this process, protons and electrons combine to produce neutrons and anti-neutrinos, in a process known as reverse beta decay. The detection of this burst of anti-neutrinos from supernova 1987A was the first time neutrinos were detected from beyond our Solar System.

## The IceCube detections

In the announcement from the IceCube team, they have stated that IceCube has detected 28 cosmic neutrinos to date, but as of yet they do not know from which objects these neutrinos have come. This does, however, bring us a step closer to realising the promise of using neutrinos to better understand the nature of astrophysical objects. In particular, as I described in my previous blog, neutrinos hold the promise of enabling us to understand the origin of high energy cosmic rays. Because the rays themselves are bent by interstellar magnetic fields, tracing their origin is night-on impossible. But, neutrinos are not affected by the magnetic fields, and so should travel to us from their cosmic source in a straight line.

To date, IceCube is the only neutrino detector in the World which is capable of detecting cosmic neutrinos, but with other neutrino detectors being planned and built, we may indeed soon be entering a new era of astronomy.