## A PhD Student’s Guide to EGU 2017

Science is a community effort, requiring collaboration and lots of different people providing different parts of the jigsaw to try to understand more and more of the full picture. Despite a lot of research being carried out individually in a lab, or at a desk, no one individual can do everything themselves, no matter how much of a genius they are. Sharing, discussing and debating are key to the progression of scientific ideas, and this ethos is something large scientific conferences like EGU cultivates.

Attending EGU for the first time as a PhD student was both an exciting and overwhelming experience due to its shear size and number of people. This year 14,496 people from 107 countries participated, giving 4,849 talks, 11,312 posters and 1,238 PICO presentations throughout the week!

With 649 scientific sessions running throughout the week, deciding how to spend your day was a significant challenge in itself! The EGU website and app allowed you to create a personal programme, cutting down the number of entire printed programmes being printed, aiming to try to make EGU slightly more environmentally friendly.

A ‘typical’ day at EGU consisted of something like…

7-8am: Wake up, shower and breakfast and then hop on the U-bahn to the conference centre. Pick up a EGU Today newsletter on the way into the centre, highlighting a few sessions happening that day that may be of general interest

8.30-10am: Division session of your choice consisting of six 15min talks. People also pick out specific talks in different sessions and hop between, especially if their work is more interdisciplinary and covers a few different sessions.

10-10.30am: Recharge with a much needed coffee break!

10.30am-12pm: Go to a debate on ‘Make Facts Great Again: how can scientists stand up for science?‘ There were a number of other topical debates throughout the week, including ‘Arctic environmental change: global opportunities and threats‘ and ‘Great Debate on Great Extinctions‘. This consisted of a short introduction from members of a panel, then questions from the floor.

12-1.30pm: Pick up something for lunch from one of the nearby bakeries or cafes around the conference centre, and sit in the nearby park and enjoy the sunshine (hopefully).

1.30-3pm: Explore the many information stands in the exhibition areas. These included publishing houses, geoscience companies, NGOs etc. Next go and vote in the EGU photograph competition: https://imaggeo.egu.eu/photo-contest/2017/, before stopping to listen to some PICO (Presenting Interactive COntent) presentations. These are very interactive sessions where speakers give a 2min overview of their work, after which people have the opportunity to go and question speakers further afterwards by a poster/couple of slides.

3-3.30pm: Tea/coffee break with cookies in the Early Career Scientists lounge.

3.30-5pm: Polar Science Career Session aimed at Early Career Scientists (there were also sessions for other divisions), consisting of an informal Q&A with a panel covering a variety of different career paths.

5-7pm: Poster sessions in the big halls with beer/juice and nibbles. These were a great opportunity for in depth discussion, and meeting other people in your field.

7-8.30pm: Early career scientist (ECS) reception with drinks and canapes, meet other ECS from all fields and chat with division leaders. This year 53% of EGU participants were ECSs, and there was a definite effort to cater for them throughout the week.

8.30-?: Dinner and drinks in Vienna town centre with peers, followed by an early night if you plan to make it to a 8.30am session tomorrow…

In addition to events highlighted, there were also a variety short courses running, for example ‘Tips and Tricks: How to Navigate EGU‘, ‘How to write a research grant‘ or ‘Rhyme your Research‘! EGU had its own official blog GeoLog, highlighting some of the events from each day: http://blogs.egu.eu/geolog/.

However, EGU is 5 days long, and despite the impressive offering of sessions being put on it would be a shame to go to Vienna and only see the conference centre… The odd extended lunch break to take the U-bahn (included as part of the entrance to the conference) to walk around the centre, or an afternoon off to explore a gallery or museum, or simply sit in one of the beautiful parks or cafes to enjoy some coffee and Sachertorte is definitely a must to recharge and finish off the week!

## The onset and end of wet seasons over Africa

For many Africans, the timing of the wet season is of crucial importance, especially for those reliant upon subsistence agriculture, who depend on the seasonal rains for crop irrigation. In addition, the wet season recharges lakes, rivers and water storage tanks which constitute the domestic water supply in some areas. The timing of the wet season also affects the availability of energy from hydroelectric schemes, and has impacts upon the prevalence of certain disease carrying vectors, such as mosquitoes.

Climate change is already threatening many vulnerable populations, and changes in the timing or intensity of the wet season, or increasing uncertainty in the timing of the onset, may lead to significant socio-economic impacts. But before we consider future projections or past changes in the seasonality, we need to go back a few steps.

The first step is to find a method for determining when the wet season starts and ends (its ‘onset’ and ‘cessation’). In order to look at large-scale shifts in the timing of the wet season and relate this to wider-scale drivers, this method needs to be applicable across the entirety of continental Africa. Most previous methods for determining the onset focus on the national to regional scale, and are dependent on the exceedance of a certain threshold e.g. the ﬁrst week with at least 20mm of rainfall, with one rainfall event of more than 10mm, and no dry spell of more than 10 days after the rain event for the next month. While such definitions work well at a national scale they are not applicable at a continental scale where rainfall amounts vary substantially. A threshold suitable for the dry countries at the fringes of the Sahara would not be suitable in the wetter East African highlands.

In addition to a vast range of rainfall amounts, the African continent also spans multiple climatic regimes. The seasonal cycle of precipitation over continental Africa is largely driven by the seasonal progression of the ITCZ and associated rain belts, which follows the maximum incoming solar radiation. In the boreal summer, when the thermal equator sits between the equator and the Tropic of Cancer, the ITCZ sits north of the equator and West Africa and the Sahel experience a wet season. During the boreal autumn the ITCZ moves south, and southern Africa experiences a wet season during the austral summer, followed by the northward return of the ITCZ during the boreal spring. As a consequence of this, central African regions and the Horn of Africa experience two wet seasons per year – one as the ITCZ travels north, and a second as the ITCZ travels south. A method for determining the onset and cessation at the continental scale thus needs to account for regions with multiple wet seasons per year.

In our paper (available here) we propose such a method, based on the method of Liebmann et al (2012). The method has three steps:

• Firstly, determine the number of seasons experienced per year at the location (or grid point) of interest. This is achieved using harmonic analysis – the amplitude of the first and second harmonic were computed, using the entire timeseries and their ratio compared. If the ratio was greater than 1.0, i.e. the amplitude of the second harmonic was greater than the amplitude of the first harmonic then the grid point was defined as having two wet seasons per year (biannual), if the ratio was less than one then it was defined as having an annual regime. Figure 1 shows the ratio for one African rainfall dataset (TARCATv2). Three regions are identified as biannual regions; the Horn of Africa, an equatorial strip extending from Gabon to Uganda and a small region on the southern West African coastline.

• Secondly the period of the year when the wet season occurs was determined. This was achieved by looking for minima and maxima in the climatological cumulative daily rainfall anomaly to identify one or two seasons.
• The third and final stage is to calculate the onset and cessation dates for each year. This is done by looking for the minima and maxima in the cumulative daily rainfall anomaly, calculated for each season.

Figure 2 shows the seasonal progression of the onset and cessation, with the patterns observed in agreement with those expected from the driving physical mechanisms, and continuous progression across the annual/biannual boundaries. Over West Africa and the Sahel, Figure 2a-b shows zonally-contiguous progression patterns with onset following the onset of the long rains and moving north, and cessation moving southward, preceding the end of the short rains. Over southern Africa Figure 2c-d shows the onset over southern Africa starting in the north-west and south-east, following the onset of the short rains, reaching the East African coast last, and cessation starting at the Zimbabwe, Mozambique, South Africa border and spreading out radially into the cessation of the long rains.

As well as testing the method for compatibility with known physical drivers of African rainfall, agreement across multiple satellite-based rainfall estimates was also examined. In general, good agreement was found across the datasets, particularly for regions with an annual regime and over the biannual region of East Africa.

The advantage of having a method that works at the continental scale is the ability to look at the impact of large-scale oscillations on wider-scale variability. One application of this method was to investigate the impact of El Niño upon both the annual rains and short rains (Figure 3). In Figure 3 we see the well-documented dipole in rainfall anomaly, with higher rainfall totals over 0–15°S and the Horn of Africa in El Niño years and the opposite between 15°S and 30°S.  This anomaly is stronger when we use this method compared with using standard meteorological seasons. We can also see that while the lower rainfall to the south is colocated with later onset dates and a consequentially shorter season, the higher rainfall over the Horn of Africa is associated with later cessation of the short rains, with only small differences in onset date.

In addition to using this method for research purposes, its application within an operational setting is also being explored. Hopefully, the method will be included within the Rainwatch platform, which will be able to provide users with a probabilistic estimate of whether or not the season has started, based on the rainfall experienced so far that year, and historical rainfall data.

For more details, please see the paper detailing this work:

Dunning, C.M., E Black, and R.P. Allan (2016) The onset and cessation of seasonal rainfall over Africa, Journal of Geophysical Research: Atmospheres, 121 11,405-11,424, doi: 10.1002/2016JD025428

References:

Liebmann, B., I. Bladé, G. N. Kiladis, L. M. Carvalho, G. B. Senay, D. Allured, S. Leroux, and C. Funk (2012), Seasonality of African precipitation from 1996 to 2009, J. Clim.25(12), 4304–4322.

When it comes to doctoral funding, the current method means project funds can come from a variety of sources, such as research councils, charities, industry partners or a mixture of these. In this blog post I will talk about my experience of being jointly funded by a research council and industrial partner.

To start with, I am not actually a PhD student like most people in the Meteorology department here at the University of Reading, but an EngD student. An EngD is a more industrial focused PhD, based on collaboration between industry and academia. There is a taught element to an EngD in the first year, during which a range of modules are covered, on everything from business analysis to sustainability. Additionally, a portion of time is dedicated to work for the industrial sponsor during the course of the project. An EngD still has the same end goal of a PhD, of an intellectual contribution to knowledge.

EngDs were started by the Engineering and Physical Sciences Research Council (EPSRC) back in 1992 and after initial success, the program was expanded in 2009. Out of this expansion came the Technologies for Sustainable Built Environments (TSBE) Centre at the University of Reading. The TSBE Centre has produced 40 EngDs over 8 years, covering a wide variety of disciplines, from modelling energy usage in the home to the effect of different roofing materials on bats. Each student is based within multiple academic departments and the industrial partner organisation with the aim of answering real world research questions.

My project is in collaboration with the BT Group and looks at weather impacts on the UK telecommunications network. I have found that being in an industrial sponsored project is of great benefit. It has been useful to get experience of how industry works, as it can be very different to the academic life in which most doctoral students find themselves. There have also been a lot of opportunities for training in specialist subjects including industrial project management and help to get chartership from professional bodies for those who want it. Being linked with an industrial partner can also offer strong networking and knowledge transfer opportunities, as was the case when I attended a recent interdisciplinary conference of the newly formed Tommy Flowers Institute. This institute has been formed by BT, along with other partner organisations, to further support collaboration between industry and academia.

It can be a challenge at times to balance the approaches of academia and industry. They do not always pull you in the same direction but this is often the same with any lengthy piece of work produced under the guidance of different advisors from different disciplines. The strength with the EngD partnership comes from the different perspectives offered from those different fields to ultimately solve the problem in question.

For me working on a heavily applied problem in the setting of a real organisation has been of greater benefit to me than working on a purely theoretical problem would have been. I have enjoyed seeing my preliminary output being tested within the organisation and look forward to being able to test a more advanced version in the final stages of my project.

Alan Halford is funded by the EPSRC and BT and supported by the TSBE centre.

## Innovating for Sustainable Development

In 2016 the United Nations (UN) Sustainable Development Goals (SDGs) officially came into force to tackle key global challenges under a sustainable framework.

The SDGs comprise 17 global goals and 169 targets to be achieved across the next 15 years. As part of the ‘2030 Agenda’ for sustainable development, these goals aim to address a range of important global environmental, social and economic issues such as climate change, poverty, hunger and inequality. Adopted by leaders across the world, these goals are a ‘call for action’ to ensure that no one is left behind. However, the SDGs are not legally binding. The success of goals will rely solely on the efforts of individual countries to establish and implement a national framework for achieving sustainable development.

As part of the NERC funded ‘Innovating for Sustainable Development’ programme, students here in the Department of Meteorology were given the opportunity to explore and find solutions to key environmental challenges as outlined in the UN’s SDGs.

Run by the SCENARIO and SSCP doctoral training partnerships, the programme challenged students from a variety of disciplines and institutions to re-frame the SDGs from a multi-disciplinary perspective and to develop tangible, innovative solutions for sustainable development.

The programme began with an ‘Interdisciplinary Challenges Workshop’ where students participated in activities and exercises to review the importance of the SDGs and to consider their multi-disciplinary nature. Students were encouraged to think creatively and discuss issues related to each of the goals, such as: ‘Is this SDG achievable?’, ‘Are the goals contradictory?’ and ‘How could I apply my research to help achieve the SDGs?’

Following this, three ‘Case Study’ days explored a handful of the SDGs in greater detail, with representatives from industry, start-ups and NGOs explaining how they are working to achieve a particular SDG, their current challenges and possible opportunities for further innovation.

The first Case Study day focused on both SDG 7 – Affordable and Clean Energy and SDG 12 – Responsible Consumption and Production. For SDG 7, insightful talks were given by the Moving Energy Initiative on the issue of delivering energy solutions to millions of displaced people, and BBOXX, on their work to produce and distribute off-grid solar power systems to rural communities in places such as Kenya and Rwanda. In the afternoon, presentations given by Climate-KIC start up NER and Waitrose showcased the efforts currently being taken to reduce wasteful food production and packaging, while Forum for the Future emphasised the importance of addressing sustainable nutrition.

The second Case Study day focused on SDG 6 – Clean Water and Sanitation. Experts from WaterAid, De-Solenator, Bear Valley Ventures, UKWIR and the International Institute for Environmental Development outlined the importance of confronting global sanitation and water challenges in both developing and developed nations. Alarmingly, it was highlighted that an estimated 40% of the global population are affected by water scarcity and 2.4 billion people still lack access to basic sanitation services, with more than 80% of human activity wastewater discharged into rivers without going through any stage of pollution removal (UN, 2016).

The last Case Study day explored SDG 9 – Industry, Innovation and Infrastructure and SDG 11 – Sustainable Cities and Communities. A range of talks on building technologies, carbon neutral buildings and sustainable solar technologies were given, along with a presentation by OPDC on the UK’s largest regeneration project. The day finished off with an overview from the Greater London Authority about the London Infrastructure Map and their new approach to sustainable planning and development across the city.

The programme finished off with a second workshop. Here students teamed up to develop innovative business ideas aimed at solving the SDG challenges presented throughout the Case Study events. Business coaches and experts were on hand to offer advice to help the teams develop ideas that could become commercially viable.

On the 16th March the teams presented their business ideas at the ‘Meet the Cleantech Pioneers’ networking event at Imperial’s new Translation and Innovation Hub (I-HUB). An overview of the projects can be found here. This event, partnered with the Climate-KIC accelerator programme, provided an excellent platform for participants to showcase and discuss their ideas with a mix of investors, entrepreneurs, NGOs and academics all interested in achieving sustainable development.

Overall the programme provided a great opportunity to examine the importance of the SDGs and to work closely with PhD students from a range of backgrounds. Fundamentally the process emphasised the point that, in order for the world to meet the 2030 Agenda, many sustainable development challenges still need to be better understood and many solutions still need to be provided – and here scientific research can play a key role. Furthermore, it was made clear that a high level of interdisciplinary thinking, research and innovation is needed to achieve sustainable development.

References:

UN, 2016: Clean Water and Sanitation – Why it matters, United Nations, Accessed 05 March 2017. [Available online at http://www.un.org/sustainabledevelopment/wp-content/uploads/2016/08/6_Why-it-Matters_Sanitation_2p.pdf]

## Can we really use El Niño to predict flooding?

R. Emerton, H. Cloke, E. Stephens, E. Zsoter, S. Woolnough, F. Pappenberger (2017). Complex picture for likelihood of ENSO-driven flood hazard. Nature Communications. doi: 10.1038/NCOMMS14796

When an El Niño is declared, or even forecast, we think back to memorable past El Niños (such as 1997/98), and begin to ask whether we will see the same impacts. Will California receive a lot of rainfall? Will we see droughts in tropical Asia and Australia? Will Peru experience the same devastating floods as in 1997/98, and 1982/83?

El Niño and La Niña, which see changes in the ocean temperatures in the tropical Pacific, are well known to affect weather, and indeed river flow and flooding, around the globe. But how well can we estimate the potential impacts of El Niño and La Niña, and how likely flooding is to occur?

This question is what some of us in the Water@Reading research group at the University of Reading have been looking to answer in our recent publication in Nature Communications. As part of our multi- and inter-disciplinary research, we work closely with the Red Cross / Red Crescent Climate Centre (RCCC), who are working on an initiative called Forecast-based Financing (FbF, Coughlan de Perez et al.). FbF aims to distribute aid (for example providing water purification tablets to prevent spread of disease, or digging trenches to divert flood water) ahead of a flood, based on forecasts. This approach helps to reduce the impact of the flood in the first place, rather than working to undo the damage once the flood has already occurred.

Photo credit: Red Cross / Red Crescent Climate Centre

In Peru, previous strong El Niños in 1982/83 and 1997/98 had resulted in devastating floods in several regions. As such, when forecasts in early 2015 began to indicate a very strong El Niño was developing, the RCCC and forecasters at the Peruvian national hydrological and meteorology agency (SENAMHI) began to look into the likelihood of flooding, and what FbF actions might need to be taken.

Typically, statistical products indicating the historical probability (likelihood [%] based on what happened during past El Niños) of extreme precipitation are used as a proxy for whether a region will experience flooding during an El Niño (or La Niña), such as these maps produced by the IRI (International Research Institute for Climate and Society). You may also have seen maps which circle regions of the globe that will be drier / warmer / wetter / cooler – we’ll come back to these shortly.

These rainfall maps show that Peru, alongside several other regions of the world, is likely to see more rainfall than usual during an El Niño. But does this necessarily mean there will be floods? And what products are out there indicating the effect of El Niño on rivers across the globe?

For organisations working at the global scale, such as the RCCC and other humanitarian aid agencies, global overviews of potential impacts are key in taking decisions on where to focus resources during an El Niño or La Niña. While these maps are useful for looking at the likely changes in precipitation, it has been shown that the link between precipitation and flood magnitude is nonlinear (Stephens et al.),  – more rain does not necessarily equal floods – so how does this transfer to the potential for flooding?

The motivation behind this work was to provide similar information, but taking into account the hydrology as well as the meteorology. We wanted to answer the question “what is the probability of flooding during El Niño?” not only for Peru, but for the global river network.

To do this, we have taken the new ECMWF ERA-20CM ensemble model reconstruction of the atmosphere, and run this through a hydrological model to produce the first 20th century global hydrological reconstruction of river flow. Using this new dataset, we have for the first time estimated the historical probability of increased or decreased flood hazard (defined as abnormally high or low river flow) during an El Niño (or La Niña), for the global river network.

The question – “what is the probability of flooding during El Niño?”, however, remains difficult to answer. We now have maps of the probability of abnormally high or low river flow (see Figure 1), and we see clear differences between the hydrological analysis and precipitation. It is also evident that the probabilities themselves are often lower, and much more uncertain, than might be useful – how do you make a decision on whether to provide aid to an area worried about flooding, when the probability of that flooding is 50%?

The likely impacts are much more complex than is often perceived and reported – going back to the afore-mentioned maps that circle regions of the globe and what their impact will be (warmer, drier, wetter?) – these maps portray these impacts as a certainty, not a probability, with the same impacts occurring across huge areas. For example, in Figure 2, we take one of the maps from our results, which indicates the probability of increased or decreased flood hazard in one month during an El Niño, and draw over this these oft-seen circles of potential impacts. In doing this, we remove all information on how likely (or unlikely) the impacts are, smaller scale changes within these circles (in some cases our flood hazard map even indicates a different impact), and a lot of the potential impacts outside of these circles – not to mention the likely impacts can change dramatically from one month to the next. For those organisations that take actions based on such information, it is important to be aware of the uncertainties surrounding the likely impacts of El Niño and La Niña.

“We conclude that while it may seem possible to use historical probabilities to evaluate regions across the globe that are more likely to be at risk of flooding during an El Niño / La Niña, and indeed circle large areas of the globe under one banner of wetter or drier, the reality is much more complex.”

PS. During the winter of 2015/16, our results estimated an ~80% likelihood of increased flood hazard in northern coastal Peru, with only ~10% uncertainty surrounding this. The RCCC took FbF actions to protect thousands of families from potentially devastating floods driven by one of the strongest El Niños on records. While flooding did occur, this was not as severe as expected based on the strength of the El Niño. More recently, during the past few months (January – March 2017), anomalously high sea surface temperatures (SSTs) in the far eastern Pacific (known as a “coastal El Niño” in Peru but not widely acknowledged as an El Niño because central Pacific SSTs are not anomalously warm) have led to devastating flooding in several regions and significant loss of life. And Peru wasn’t the only place that didn’t see the impacts it expected in 2015/16; other regions of the world, such as the US, also saw more rainfall than normal in places that were expected to be drier, and California didn’t receive the deluge they were perhaps hoping for. It’s important to remember that no two El Niños are the same, and El Niño will not be the only influence on the weather around the globe. While El Niño and La Niña can provide some added predictability to the atmosphere, the impacts are far from certain.

Full reference:

R. Emerton, H. Cloke, E. Stephens, E. Zsoter, S. Woolnough, F. Pappenberger (2017). Complex picture for likelihood of ENSO-driven flood hazard. Nature Communications. doi: 10.1038/NCOMMS14796

Press Release:

## The Influence of the Weather on Bird Migration

As well as being a meteorologist, I am a bird watcher. This means I often combine meteorology and bird watching to see the impact of the weather on birds. Now that we are well into March my focus in bird watching turns to one thing – the migration.

March generally marks the time when the first summer migrants start arriving into the UK. Already this year we have had reports of Sand Martin, Wheatear, Garganey, Little Ringed Plover, White Wagtail, Osprey, Swallow, House Martin, Ring Ouzel and Whitethroat (up to 9 March), some of which are depicted below.

There are many people that consider the arrival dates of certain migratory species of birds and how this arrival date changes over many years. I do keep extensive records of the birds that I see (and thus arrival dates), but what interests me more are the odd days in the record, and the sightings of unusual birds and working out how they arrived at their destinations.

A good example of this can be found by looking at my first Swallow sighting of the year in Kent and East Sussex. Since I started bird watching in 2001 my first Swallow of the year has moved from around 10 April to between 26-March and 1 April. However in 2013 my first record was 15 April. Then in 2015 and 2016 I saw my first Swallow on 1 April and 27 March respectively (I was in Cheshire in 2014 in late March/early April).

So what happened; why were the Swallows late in Kent in 2013? Well, it all comes down to wind direction. The spring of 2013 was very chilly and along the east coast there were plenty of N/NE winds – this would have provided a head wind so the Swallows would preferentially not migrate up the east coast in those conditions but instead migrate up the west coast where there were southerlies.

So, the wind direction plays a key part in the migration of birds. If conditions are for a tailwind or very light winds the birds will migrate; otherwise they will stay put. However, headwinds can lead to some interesting phenomena associated with bird migration – ‘falls’.

A ‘fall’ occurs when there are a large number of migrants building up along the coastline at a departure point (so for the interest of UK bird watchers Northern France), as they cannot get to their destination. When the wind direction changes the birds will then migrate en masse and quite literally fall out of the sky.

It’s not all about the wind direction though; rain is also a key factor that bird watchers consider when looking at weather forecasts. Essentially, fronts and showers are great for bird watchers. On migration birds will often fly higher than they normally would. This means on a clear sunny day you could easily miss birds passing overhead as they are so high up. However, with the rain the birds will often fly lower, avoiding the in-cloud turbulence. For many of the summer migrants their food sources (insects) also fly lower in these conditions.

This means that a forecast of showers with a southerly wind is generally what I look for from mid-April onwards (particularly as an inland birder), as it means there is a good chance of migratory species turning up – also because then I can head out after work as the evenings are brighter. This is something that I did last year and ended up recording the first Sandwich Tern (photo below (not of the bird I saw)) of the year in Berkshire.

So in summary, it’s not as simple as just keeping an eye on the wind direction – there are other factors that can influence the birds’ migration and where they will end up. For more information about the impact of weather on bird sightings (considering both rare and common birds) check out my blog.

## The advection process: simulating wind on computers

Email: js102@zepler.net   Web: datumedge.co.uk   Twitter: @hertzsprrrung

If we know which way the wind is blowing then we can predict a lot about the weather. We can easily observe the wind moving clouds across the sky, but the wind also moves air pollution and greenhouse gases. This process is called transport or advection. Accurately simulating the advection process is important for forecasting the weather and predicting climate change.

I am interested in simulating the advection process on computers by dividing the world into boxes and calculating the same equation in every box. There are many existing advection methods but many rely on these boxes having the correct shape and size, otherwise these existing methods can produce inaccurate simulations.

During my PhD, I’ve been developing a new advection method that produces accurate simulations regardless of cell shape or size. In this post I’ll explain how advection works and how we can simulate advection on computers. But, before I do, let’s talk about how we observe the weather from the ground.

In meteorology, we generally have an incomplete picture of the weather. For example, a weather station measures the local air temperature, but there are only a few hundred such stations dotted around the UK. The temperature at another location can be approximated by looking at the temperatures reported by nearby stations. In fact, we can approximate the temperature at any location by reconstructing a continuous temperature field using the weather station measurements.

So far we have only talked about temperatures varying geographically, but temperatures also vary over time. One reason that temperatures change over time is because the wind is blowing. For example, a wind blowing from the north transports, or advects, cold air from the arctic southwards over the UK. How fast the temperature changes depends on the wind speed, and the size of the temperature contrast between the arctic air and the air further south. We can write this as an equation. Let’s call the wind speed $v$ and assume that the wind speed and direction are always the same everywhere. We’ll label the temperature $T$, label time $t$, and label the south-to-north direction $y$, then we can write down the advection equation using partial derivative notation,

$\frac{\partial T}{\partial t} = - \frac{\partial T}{\partial y} \times v$

This equation tells us that the local temperature will vary over time ($\frac{\partial T}{\partial t}$), depending on the north-south temperature contrast ($- \frac{\partial T}{\partial y}$) multiplied by the wind speed $v$.

One way to solve the advection equation on a computer is to divide the world into boxes, called cells. The complete arrangement of cells is called a mesh. At a point at the centre of each cell we store meteorological information such as temperature, water vapour content or pollutant concentration. At the cell faces where two cells touch we store the wind speed and direction. The arrangement looks like this:

The above example of a mesh over the UK uses cube-shaped cells stacked in columns above the Earth, and arranged along latitude and longitude lines. But more recently, weather forecasting models are using different types of mesh. These models tesselate the globe with squares, hexagons or triangles.

Weather models must also rearrange cells in order to represent mountains, valleys, cliffs and other terrain. Once again, different models rearrange cells differently. One method, called the terrain-following method, shifts cells up or down to accommodate the terrain. Another method, called the cut-cell method, cuts cells where they intersect the terrain. Here’s what these methods look like when we use them to represent an idealised, wave-shaped mountain:

Once we’ve chosen a mesh and stored temperature at cell centres and the wind at cell faces, we can start calculating a solution to the advection equation which enables us to forecast how the temperature will vary over time. We can solve the advection equation for every cell separately by discretising the advection equation. Let’s consider a cell with a north face and a south face. We want to know how the temperature stored at the cell centre, $T_\mathrm{cell}$, will vary over time. We can calculate this by reconstructing a continuous temperature field and using this to approximate temperature values at the north and south faces of the cell, $T_\mathrm{north}$ and $T_\mathrm{south}$,

$\frac{\partial T_\mathrm{cell}}{\partial t} = - \frac{T_\mathrm{north} - T_\mathrm{south}}{\Delta y} \times v$

where $\Delta y$ is the distance between the north and south cell faces. This is the same reconstruction process that we described earlier, only, instead of approximating temperatures using nearby weather station measurements, we are approximating temperatures using nearby cell centre values.

There are many existing numerical methods for solving the advection equation but many do not cope well when meshes are distorted, such as terrain-following meshes, or when cells have very different sizes, such as those cells in cut-cell meshes. Inaccurate solutions to the advection equation lead to inaccuracies in the weather forecast. In extreme cases, very poor solutions can cause the model software to crash, and this is known as a numerical instability.

We can see a numerical instability growing in this idealised example. A blob is being advected from left to right over a range of steep, wave-shaped mountains. This example is using a simple advection method which cannot cope with the distorted cells in this mesh.

We’ve developed a new method for solving the advection equation with almost any type of mesh using cubes or hexagons, terrain-following or cut-cell methods. The advection method works by reconstructing a continuous field from data stored at cell centre points. A separate reconstruction is made for every face of every cell in the mesh using about twelve nearby cell centre values. Given that weather forecast models have millions of cells, this sounds like an awful lot of calculations. But it turns out that we can make most of these calculations just once, store them, and reuse them for all our simulations.

Here’s the same idealised simulation using our new advection method. The results are numerically stable and accurate.