How much energy is available in a moist atmosphere?

Email: b.l.harris@pgr.reading.ac.uk

It is often useful to know how much energy is available to generate motion in the atmosphere, for example in storm tracks or tropical cyclones. To this end, Lorenz (1955) developed the theory of Available Potential Energy (APE), which defines the part of the potential energy in the atmosphere that could be converted into kinetic energy.

To calculate the APE of the atmosphere, we first find the minimum total potential energy that could be obtained by adiabatic motion (no heat exchange between parcels of air). The atmospheric setup that gives this minimum is called the reference state. This is illustrated in Figure 1: in the atmosphere on the left, the denser air will move horizontally into the less dense air, but in the reference state on the right, the atmosphere is stable and no motion would occur. No further kinetic energy is expected to be generated once we reach the reference state, and so the APE of the atmosphere is its total potential energy minus the total potential energy of the reference state.

Figure 1: Construction of the APE reference state for a 2D atmosphere. The purple shading indicates the density of the air; darker colours mean denser air. In the actual state, the density stratification is not completely horizontal, which leads to the air motion shown by the orange arrows. The reference state has a stable, horizontal density stratification, so the air will not move without some disturbance.

If we think about an atmosphere that only varies in the vertical direction, it is easy to find the reference state if the atmosphere is dry. We assume that the atmosphere consists of a number of air parcels, and then all we have to do is place the parcels in order of increasing potential temperature with height. This ensures that density decreases upwards, so we have a stable atmosphere.

However, if we introduce water vapour into the atmosphere, the situation becomes more complicated. When water vapour condenses, latent heat is released, which increases the temperature of the air, decreasing its density. One moist air parcel can be denser than another at a certain height, but then less dense if they are lifted to a height where the first parcel condenses but the second one does not. The moist reference state therefore depends on the exact method used to sort the parcels by their density.

It is possible to find the rearrangement of the moist air parcels that gives the minimum possible total potential energy, using the Munkres (1957) sorting algorithm, but this takes a very long time for a large number of parcels. Lots of different sorting algorithms have therefore been developed that try to find an approximate moist reference state more quickly (the different types of algorithms are explained by Stansifer (2017) and Harris and Tailleux (2018)). However, these sorting algorithms do not try to analyse whether the parcel movements they are simulating could actually happen in the real atmosphere—for example, many work by lifting all parcels to a fixed level in the atmosphere, without considering whether the parcels could feasibly move there—and there has been little understanding of whether the reference states they find are accurate.

As part of my PhD, I have performed the first assessment of these sorting algorithms across a wide range of atmospheric data, using over 3000 soundings from both tropical island and mid-latitude continental locations (Harris and Tailleux, 2018). This showed that whilst some of the sorting algorithms can provide a good estimate of the minimum potential energy reference state, others are prone to computing a rearrangement that actually has a higher potential energy than the original atmosphere.

We also showed that a new algorithm, which does not rely on sorting procedures, can calculate APE with comparable accuracy to the sorting algorithms. This method finds a layer of near-surface buoyant parcels, and performs the rearrangement by lifting the layer upwards until it is no longer buoyant. The success of this method suggests that we do not need to rely on possibly unphysical sorting algorithms to calculate moist APE, but that we can move towards approaches that consider the physical processes generating motion in a moist atmosphere.

References

Harris, B. L. and R. Tailleux, 2018: Assessment of algorithms for computing moist available potential energy. Q. J. R. Meteorol. Soc., 144, 1501–1510, https://doi.org/10.1002/qj.3297

Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157–167, https://doi.org/10.3402/tellusa.v7i2.8796

Munkres, J., 1957: Algorithms for the Assignment and Transportation Problems. J. Soc. Ind. Appl. Math., 5, 32–38, https://doi.org/10.1137/0105003

Stansifer, E. M., P. A. O’Gorman, and J. I. Holt, 2017: Accurate computation of moist available potential energy with the Munkres algorithm. Q. J. R. Meteorol. Soc., 143, 288–292, https://doi.org/10.1002/qj.2921

EGU 2019

From 7th-12th April, I had the exciting opportunity to attend the European Geosciences Union (EGU) General Assembly in Vienna. This was a much larger conference than any I had attended previously, with 16,273 scientists in attendance and 683 scientific sessions, which made for a whirlwind experience. I was staying with other PhD students from the department, so many evenings were spent comparing schedules and pointing out interesting courses to make sure none of us missed anything useful!

As part of the Tropical Meteorology and Tropical Cyclones session, I gave an oral presentation about my PhD work, which investigates the use of Available Potential Energy theory to study the processes involved in tropical cyclone intensification. The session included many excellent talks on different aspects of tropical meteorology, and it was great to speak with scientists whose interests are similar to mine about possible avenues for combining our work.

PhD students from the department present their research at EGU

One of the major advantages of attending such a large conference was the opportunity to learn more about areas of geoscience research that I wouldn’t normally encounter. I made a specific effort to attend a few sessions on topics that I am not familiar with, including wildfires (#FIREMIP), landslides and exoplanets. It was fascinating to see the work that goes on in different fields and I hope that being exposed to different methods and perspectives will help me to become a more creative researcher.

EGU is such a huge event that the scientific sessions are only part of the story. There were Great Debates on topics ranging from science in policy to the prioritisation of mental wellbeing for Early Career Scientists, two artists-in-residence creating pieces inspired by the science of the conference, and an extremely entertaining Poetry Slam event, which two of the Reading Meteorology PhD students were brave enough to participate in (or possibly just desperate enough for a ticket to the conveners’ party).

poetry

So now it’s the end of EGU
I caught the train – and I flew
We both did a talk
Learnt the German for fork
“Eine Gabel bitte” – thank you

– Sally Woodhouse & Kaja Milczewska

EGU was a great experience and after the conference I was able to take some time to explore Vienna, see some historic landmarks, and unwind from an enjoyably exhausting week of science. Although to begin my break from geoscience I did go straight to the Globe Museum, so perhaps I need to work on my relaxation techniques.


#traintoEGU – Sally Woodhouse

Aviation currently contributes over 2% of the annual global CO2 emissions which, if classed as a country, would make it one of the top ten emitters. A return flight to Vienna from London adds about 0.2 metric tonnes of CO2 to your carbon footprint (the UK annual mean per person is 6.5 metric tonnes).

An important part of science is sharing our research and one of the best ways to do that is at conferences, so we can’t just stop going! But there is another way … the train (0.04 metric tonnes CO2)! And if I’m spending all that time why not have a little adventure.

With the help of the man in seat 61 (check it out if you’re getting the train anywhere it’s so helpful!) we decided to go via Zurich. We had a night’s stop in Zurich, a morning there exploring and then an afternoon train through the stunning Arlberg Pass and beautiful views of Alpine Austria. Honestly the views made the 5am start the day before and sprint for the Eurostar all worth it. It was breath-taking for the whole 8 hour journey.

 

traintoEGU_Paris_Zurich

For the return trip we took the speedy route through Germany and Belgium – this is actually doable in a day but I decided to have an overnight in Brussels. I spent a lovely day wandering around the main sites and even managed a visit to the European Parliament!

It might take a bit longer but it was a wonderful adventure and I’d definitely recommend it to everyone traveling to EGU in future – maybe I’ll see you on the train.

traintoEGU_Brussels