From Germany to Brazil: on climate risk communication

by Javier García-Pintado

Last week, on 22-23 October 2018, around 230 scientists from the three ocean and climate related clusters of excellence in northern Germany met in Berlin in the joint conference on Ocean – Climate – Sustainability Research Frontiers. The participants brought in lively discussions within the context of scientific and societal action towards ocean and climate research. Apart from the discussions more oriented toward the basic climate science and technical aspects, from a personal standpoint (perhaps because of its distance from my own work), I found a number of presentations from “The Future Ocean” cluster in Kiel, which include scholars from politics, social science, philosophy and international law most interesting. Some of these presentations offered a window on the connection between climate change and global and local politics in countries (e.g.; as tropical islands in the Indian ocean, who generally rely on external aid) most affected by increasing sea levels and coastal erosion. In common, this class of talks indicated a need for improving the communication of climate and natural risk science to society. Actually, a huge component of the unpredictability in future climate projections comes from the societal component.

However, as analyzed in one talk in the conference, it seems that, ultimately, public opinion is mostly driven by what is shown on TV, and TV, public offer is in turn mostly driven by the economic powers. Thus, as described the writer Jose Luis Sampedro more than 6 years ago, “public opinion” (defined in Wikipedia as consisting of the “desires, wants, and thinking of the majority of the people”), is in reality the “opinion of the media” or the “opinion of the economic powers”. This clearly connects to the results of Brazil elections just yesterday and the new presidency, and so to the derived very uncertain future of the Amazon management. Apart from the risks to biodiversity, a further deforestation of the Amazon rainforest would make it impossible to cut carbon pollution and the aspirational target of no more than 1.5ºC global warming above pre-industrial temperatures set in the Paris climate agreement. Brazilian people (and they are not alone) seem either oblivious to the problem or convinced that they are not affected by it (even, as from a friend’s personal communication last week, it appears that some people in Brazil sadly believe climate change is an European hoax to take control over their rainforest). Generally rising sea levels and increased storm surge risks, as well as the extra energy accumulated in the Earth system in general (and ocean in particular, boosting atmospheric convection and associated flood risks), will surely lead to a further demand of online, continuously updated, risk information to face emergency situations in the future city. One can wish the best for Brazil and the Amazon, which is the best for the world. In any case, let’s hope that Copacabana is not swallowed in the sea before Rio is transformed into a resilient city.

Machine learning and data assimilation

Machine learning and data assimilation

by Rossella Arcucci

Imagine a world where it is possible to accurately predict the weather, climate, storms, tsunami and other computational intensive problems in real time from your laptop or even mobile phone – if one has access to a supercomputer then to be able to predict at unprecedented scales/detail. This is the long term aim of our work on Data Assimilation with Machine Learning at the Data Science Institute (Imperial College London, UK) and as such, we believe, it will be a key component of future Numerical Forecasting systems.

We proved that the integration of machine learning with Data assimilation can increase the reliability of prediction, reducing errors by including information with an actual physical meaning from observed data. The resulting cohesion of machine learning and data assimilation is then blended in a future generation of fast and more accurate predictive models. This integration is based on the idea of using machine learning to learn the past experiences of an  assimilation process. This follows the principle of Bayesian approach.

Edward Norton Lorenz stated “small causes can have larger effects”, the so called butterfly effect. Imagine a world where it is possible to catch “small causes” in real time and predict effects in real time as well. To know to act! A world where science works with continuously learning from observation.

Figure 1. Comparison of the Lorenz system trajectories obtained by the use of Data Assimilation (DA) and by the integration of machine learning with Data assimilation (DA+NN)

DARE first field trip to Tewkesbury

DARE first field trip to Tewkesbury

The Dare team went on a field trip last month! It was a well planned and executed trip – as you would expect from a group of mathematicians. It was also a very interesting trip for us since most of us have only ever used data (e.g. for improving forecasts) not collected it. Even better Tewkesbury area has become a sort of benchmark for testing new data assimilation methods, ideas, tools, observations, etc, and so many of us have worked with LisFlood numerical model (developed by a team led by Prof. Paul Bates at the University of Bristol) over the Tewkesbury domain. We have seen the river runs in the model outputs, watched the rivers Avon and Severn go out of banks in our plots, and investigated various SAR images of the area but we have never been to the area. We generally do not need to visit the area when working with the models, however, now that there was a chance to do so, it was no surprise that many of us were keen to go. And we did go like ‘d’ A-team:

Figure 1. ‘d’A-team have arrived!

 

However we had a more important reason for visiting too – we were going to the Tewkesbury area to collect metadata from a number of river cameras located near Tewkesbury town. These river cameras are high definition webcams owned and serviced by Farson Digital Ltd in various location over the UK. We had recently discovered that six of such cameras are within the LisFlood model domain and have captured the November 2012 floods in the area. With the permission from the Farson Digital Ltd, we have obtained hourly daylight images of the floods from 21st November 2012 to 5th of December 2012. Hence, the aim our trip was to obtain accurate (with errors of no more than few centimeters) positional information (i.e. latitude, longitude, height) of the cameras themselves as well as the positional information of a number of markers in the images for each of the cameras. We need this information to extract as accurately as possible water extents and water depth from these images using image processing tools (which we are currently working on).

Figure 2. Rivers Avon and Severn domain map in the LisFlood model with the six river cameras located where the red/white circles are positioned.

 

To take these measurements we had borrowed some tools from the Department of Geography at the University of Reading. We used a differential GPS tool (GNSS) to very accurately (on order of few centimeters) measured the position of a given point in 3D space, that is its latitude, longitude, and height above the sea level, however, it had to be used on the ground (e.g. could not measure remote or high points such as building corners where some cameras were mounted) and not be too close to buildings or large trees. To measure remote and high points we used Total Station, which allowed us to shoot a laser beam to the desired point to measure its 3D position in space.

Figure 3. Steve Edgar from the Environmental Agency showing masterclass with TotalStation.

 

We had planned to visit all six cameras within the space of the two days 16th and17th of April, however, despite our best plans and fantastic organisation skills we were too ambitious with our time and we had to drop the camera furthest from our base – the Bewdley camera (see map with camera positions in figure 2). Thus, on our first day, we took measurements from Wyre Piddle, Evesham, and Digglis Lock cameras, spotting ourselves live on the Farson Digital Ltd site.

Figure 4. Dare team spotted at the Evesham site live on Farson Digital Ltd river cameras on 16th of April.

 

We returned to our base – the Tewkesbury Park Hotel, to be joined by the Ensemble team from the Lancaster University. Ensemble Project is lead by Prof. Gordon Blair, and as Dare is funded by the EPSRC Senior Fellowship in Digital Technology for Living with Environmental Change. It was very interesting to meet the Ensemble project team and learn more in-depth about their work, future interests, and scope for the collaboration.

Figure 5. Prof. Gordon Blair (University of Lancaster) giving an overview of the Ensemble project and introducing his team.

 

On our second day, the Dare team visited the Tewkesbury camera while the Ensemble team learned more about the purpouse of the data collection and the Novermber 2012 floods in the area. Then we all jointly measured a large number of points at the Strensham Lock. In 2012 we all would have been totally sumberged in water in this picture since the flood waters completely swallowed the island on which the house is standing flooding the building along with it.

Figure 6. Dare and Ensemble project teams at the Strensham Lock.

 

Our grand finale was the meeting with the director of the Farson Digital Ltd Glyn Howells as well as a number of stakeholders who have commissioned the cameras we visited. It was very interesting for us to learn how the network of the river cameras was born from the need to know and understand the current state of the river for a variety of river users – fishermen, campers, boaters, etc. Also, how these cameras have become invaluable assets to many stakeholders for various reasons – greatly reducing the number of river condition related phone enquiries, monitoring river bank and bridge conditions, and so on.

Now a month later we have downloaded and processed the data we collected from these stations. In figure 7 we have plotted the data points we took at the Tewkesbury site, owned both by the Environmental Agency and Tewkesbury Marina (both of which we greatly thank for their support and assistance before and during our trip, especially to Steve Edgar from EA and Simon Amos and Bruno from Tewkesbury Marina). In the figure, the red dots are the camera positions – pre-2016 and current camera positions, and the black dots are all the other measurements we took using both the TotalStation and GNSS tools, which are plotted against the Environmental Agency lidar data with 1m horizontal resolution.

Figure 7. Locations of the point measurements from both Total Station and GNSS we took at the Tewkesbury town. Red dots are camera locations (pre-2016 and current positions), black dots are measurements of various reference points that can be seen from the camera. To make this image we used the Environmental Agency 1m horizontal resolution lidar data and LandSerf open source GIS software.

 

We are currently working on extracting the water extent from these images which we then will use to produce water depth observations. Our final aim is to see how much forecast improvement such rich source of observations offer, in particular, before the rising limb of the flood.

We are very thankful to Glyn Howells and the various stakeholders for permitting us to use of the images, allowing us to take the necessary measurements, assisting us on the sites, and joining at the workshop!

Our first DARE workshop

Our first DARE workshop

by Sarah Dance

Workshop participants

The DARE team organised a workshop on data science for high impact weather and flood prediction, held by the river at the lovely University of Reading Greenlands Campus in Henley-on-Thames, 20-22 Nov 2017. The workshop objectives were to enable discussion and exchange of expertise at the boundary between digital technology, data science and environmental hazard modelling, including

  • Data assimilation and data science for flood forecasting and risk planning
  • Data assimilation and data science for high impact weather forecasting
  • Smart decision making using environmental data

The meeting was attended by over 30 participants from  5 different countries. We had some great presentations ( to be made available on this webpage) and discussion. We came up with some recommendations to help promote and deliver research and business applications in the digital technology-environmental hazard area. We plan to write a meeting report detailing these recommendations that we hope will be published in a peer-reviewed international journal.  Watch this space!

 

Serving society with better weather and climate information.

Serving society with better weather and climate information.

by Sarah Dance

I have just come back from the European Meteorological Society 2017 conference in Dublin, where I was co-convenor for a session on Data Assimilation. It’s theme was Serving Society with better Weather and Climate Information. A key challenge for the meteorological communities is how best to harness the wealth of data now available – both observational and modelled – to generate and communicate effectively relevant, tailored and timely information ensuring the highest quality support to users’ decision-making.  The conference produced some highlight videos that sum up the activities better than I could!

Wetropolis flood demonstrator

Wetropolis flood demonstrator

By Onno Bokhove, School of Mathematics, University of Leeds, Leeds.

  1. What is Wetropolis?

The Wetropolis flood demonstrator is a conceptual, life installation showcasing what an extreme rainfall event is and how such an event can lead to extreme flooding of a city, see below in Fig. 1. A Wetropolis day is chosen to be 10s and it rains on average every 5.5min for 90% of the time during a Wetropolis day, i.e., 9s in two locations both in an upstream reservoir and in a porous moor in the middle of the catchment. This is extreme rainfall and it causes extreme flooding in the city. It can rain either 10%, 20%, 40% or 90% in a day; and, either nowhere, only in the reservoir, only on the porous moor or in both locations. Rainfall amount and rainfall location are randomly drawn via two skew-symmetric Galton boards, each with four outcomes, see Fig. 2. Each Wetropolis day, so every 10s, a steel ball falls down the Galton board and determines the outcome, which outcome we can follow visually: at the first split there is a 50% chance of the ball going to the left and of 50% to the right, and the next two splits one route can only go right with a 100% chance and the other one splits even with 50%-50% again; subsequent splits are even again. An extreme event occurs with probability 7/256, so about 3% of the time. In 100 wd’s, or 1000s, this amounts to about every 5.5min on average. When a steel ball rolls through one of the four channels of the Galton board it optically triggers a switch and via Arduino electronics each Galton board steers pump actions of (1,2,4,9)s causing it to rain in the reservoir and/or the porous moor.

Fig. 1. Overview of the Wetropolis flood demonstrator with its winding river channel of circa 5.2m and the slanted flood plains on one side, a reservoir, the porous moor, the (constant) upstream inflow of water, the canal with weirs, the higher city plain, and the outflow in the water tank/bucket with its three pumps. Two of these pumps switch on randomly for (1,2,4,9)s of the 10s `Wetropolis Day’ (SI-unit: wd). Photo compilation: Luke Barber.

 

Wetropolis’ construction is based on my mathematical design with a simplified one-dimensional kinematic model representing the winding river, a one-dimensional nonlinear advection diffusion equation for the rainfall dynamics in the porous moor, and simple time-dependent box models for the canal sections and the reservoir, all coupled together with weir relations. The resulting numerical calculations were approximate but led to the design by providing estimates of the strength of the pumps (1-2l in total for the three aquarium pumps), the length and hence the size of the design with the river water residence time typically being 15-20s, and the size of the porous moor. The moor visually shows the dynamics of the ground water level during no or weak rainfall as well as strong rainfall, and how it can delay the through flow when the conditions are dry prior to the rainfall by circa 2-3wd (20-30s). When the rainfall is strong, e.g., for two consecutive days of extreme Boxing Day rainfall (see movie in [2]), the moor displays surface water overflow and thus drains nearly instantly in the river channel.

Fig. 2 Asymmetric Galton board. Every Wetropolis day, 10s, a steel ball is released at the top (mechanism not shown here). The 4×4 possible outcomes in two of such boards, registered in each by 4 electronic eyes (not shown here either), determine the rainfall and location in Wetropolis, repectively. Photo: Wout Zweers.

Wetropolis’ development and design was funded as an outreach project in the Maths Foresees’ EPSRC Living with Environmental Change network [1].

  1. What are its purposes?

Wetropolis was first designed to be a flood demonstrator in outreach purposes for the general public. It can fit in the back half of a car and can be transported. Comments from everyone, including the public, are positive. Remarks from scientists and flood practitioners such as people from the Environment Agency, however, made us realise that Wetropolis can also be used and extended to test models and explore concepts in the science of flooding.

 

  1. Where has Wetropolis been showcased hitherto?

The mathematical design and modelling was done and presented early June 2016 at a seminar for the Imperial College/University of Reading Mathematics of Planet Earth Doctoral Training Centre. Designer Wout Zweers and I started Wetropolis’ construction a week later. One attempt failed (see June 2016 posts in [2]) because I made an error in using the Manning coefficient in the calculations, necessitating an increase of the channel length to 5m to have sufficient residence time of water in the 1:100 sloped river channel. Over the summer progress was made with a strong finish late August 2016 so we could showcase it at the Maths Foresees’ General Assembly in Edinburgh [1]. It was subsequently shown at the Leeds Armley Museum public Boxing Day exhibit December 8th, 2016 and also in March 2017. I gave a presentation for 140 flood victims for the Churchtown Flood Action Group Workshop, late January 2017 in Churchtown, on the science of flood including Wetropolis. We showcased it further at: Be Curious public science festival, University of Leeds; the Studygroup Maths Foresees (see Fig. 3), at the Turing Gateway to Mathematics, Cambridge; and, a workshop of the River and Canal Trust in Liverpool.


Fig. 3. Wetropolis at the Turing Gateway to Mathematics. Photo TGM. Duncan Livesey and Robert Long (Fluid Dynamics’ CDT, Leeds) are explaining matters.

  1. What are its strengths and weaknesses?

The strength of Wetropolis is that it is a life visualisation of probability for rainfall and flooding in extreme events combined, river hydraulics, groundwater flow, and flow control, since the reservoir has valves such that we can store and release water interactively). It is a conceptual model of flooding rather than a literal scale model. This is both a weakness and a strength because one needs to explain the translation of a 1:200 return period extreme flooding and rainfall event to one with a 1:5.5min return period, explain that the moor and reservoir are conceptual valleys where all the rain falls, since rain cannot fall everywhere. This scaling and translation is part of the conceptualisation, which the audience, whether public or scientific, needs to grasp. The visualisations of flooding in the city and the ground water level changes will be improved.

  1. Where does Wetropolis go from here?

Wetropolis’ revisited is under design to illustrate aspects of Natural Flood Management such as slowing-the-flow by inserting or taking our roughness features, leaky dams and the great number of such dams needed to create significant storage volume of flood waters, as well as the risk of their failure. Wetropolis will (likely) be shown alongside my presentation in the DARE international workshop on high impact weather and flood prediction in Reading, November 20-22, 2017. Finally, analysis of river levels gauges combined with the peak discharge of the Boxing Day 2015 floods of the Aire River leading to the extreme massive flooding in Kirkstall, Leeds reveals that the estimated flood excess volume is about a 1 mile by 1 mile by 1.8m deep (see [3] and Fig. 4). Storing of all this excess flood volume in 4 to 5 artificially induced and actively controlled flood plains upstream of Leeds seems possible. Moreover, it could possibly have prevented the floods. Active control of flood plains via moveable weirs is now considered, also in a research project with Wetropolis featuring as conceptual yet real test environment. (PhD and/or DARE postdoc posts are available soon.)

Fig. 4. Leeds’ flood levels at Armley Mills Museum: 1866: bottom, 2015: top, 5.21m. Photo O.B. with Craig Duguid (Fluid Dynamics’ CDT, Leeds) showcasing Wetropolis.

 References and links

[1] Maths Forsees UK EPSRC LWEC network [2] Resurging Flows, public page with movies of experiments, river flows and Boxing Day 2015 floods in Leeds and Bradford, photos and comments on fluid dynamics. Two movies on 31-08-2016 show Wetropolis in action. In one case two consecutive extreme rainfall events led to a Boxing Day 2105 type of flood. (What is the chance of this happening in Wetropolis?) Recall that record rainfall over 48hrs in Bingley and Bradford, Yorkshire, contributed for a large part to the Boxing Day floods in 2015. [3] ‘Inconvenient Truths’ about flooding . My introduction at the 2017 Study Group.

Coupled atmosphere-ocean data assimilation re-interpreted

Coupled atmosphere-ocean data assimilation re-interpreted

by Polly Smith

So my original plan for this blog was to write something about my research on coupled atmosphere-ocean data assimilation but then my PI Amos Lawless beat me to it with his recent post. I was pondering on how I might put a new spin on things when I remembered someone telling me about the Up-Goer Five challenge. The idea is to try to describe a complicated subject using only the thousand most common English words. A quick google search shows that as usual I am rather late to the party – plenty of people have already had a go and there are some brilliant descriptions out there.

This is what I came up with …

People want to know if it will be hot or cold, dry or raining today, tomorrow, next month, next year and further. People who work with large pretend worlds on big computers want to get better at telling everyone what might happen to help them plan ahead; to do this we need to look at what both the near-sky and big blue water are doing now and what they might do in time to come. To get the best guess going forward we have to start from the right point. My work is trying to help the big computer people move forward with this problem. This is hard because there are lots of things we do not know about how the real world near-sky and big blue water work and about the conversations they have together; they are joined to each other but not in an easy way. Seeing what the near-sky is doing can help us understand the big blue water and seeing what the big blue water is doing can help us understand the near-sky, but we can’t see everything all the time. Our approach is to use the things we already understand about how the near-sky and big blue water work together to make a small pretend world on a computer, and then add some numbers seen from the real world about what the near-sky and big blue water are doing close to now and what they were doing in the near past. We also give the computer a starting guess and tell it how good we think this first guess is and how good we think the seen world is – this is hard to know for sure but we are working on different ways to do this as best we can. The computer takes our directions and puts all this stuff together in an amazing way to give us an even better starting point from which we can build a picture of how things may look going forward. Things can change very quickly in the real world so finding exactly the right answer is not possible, but we can make a very good guess and we expect to get even better as we continue to work hard to learn more about the world.

This was far from easy, but a really useful exercise in describing science in a non-technical way; a great idea if you want to try and communicate your science to a wider audience. Why not give it a go?

“Weather” by Randall Munroe (https://xkcd.com/1324/)

 

 

Can observations of the ocean help predict the weather?

Can observations of the ocean help predict the weather?

by Dr Amos Lawless

It has long been recognized that there are strong interactions between the atmosphere and the ocean. For example, the sea surface temperature affects what happens in the lower boundary of the atmosphere, while heat, momentum and moisture fluxes from the atmosphere help determine the ocean state. Such two-way interactions are made use of in forecasting on seasonal or climate time scales, with computational simulations of the coupled atmosphere-ocean system being routinely used. More recently operational forecasting centres have started to move towards representing the coupled system on shorter time scales, with the idea that even for a weather forecast of a few hours or days ahead, knowledge of the ocean can provide useful information.

A big challenge in performing coupled atmosphere-ocean simulations on short time scales is to determine the current state of both the atmosphere and ocean from which to make a forecast. In standard atmospheric or oceanic prediction the current state is determined by combining observations (for example, from satellites) with computational simulations, using techniques known as data assimilation. Data assimilation aims to produce the optimal combination of the available information, taking into account the statistics of the errors in the data and the physics of the problem. This is a well-established science in forecasting for the atmosphere or ocean separately, but determining the coupled atmospheric and oceanic states together is more difficult. In particular, the atmosphere and ocean evolve on very different space and time scales, which is not very well handled by current methods of data assimilation. Furthermore, it is important that the estimated atmospheric and oceanic states are consistent with each other, otherwise unrealistic features may appear in the forecast at the air-sea boundary (a phenomenon known as initialization shock).

However, testing new methods of data assimilation on simulations of the full atmosphere-ocean system is non-trivial, since each simulation uses a lot of computational resources. In recent projects sponsored by the European Space Agency and the Natural Environment Research Council we have developed an idealised system on which to develop new ideas. Our system consists of just one single column of the atmosphere (based on the system used at the European Centre for Medium-range Weather Forecasts, ECMWF) coupled to a single column of the ocean, as illustrated in Figure 1.  Using this system we have been able to compare current data assimilation methods with new, intermediate methods currently being developed at ECMWF and the Met Office, as well as with more advanced methods that are not yet technically possible to implement in the operational systems. Results indicate that even with the intermediate methods it is possible to gain useful information about the atmospheric state from observations of the ocean. However, there is potentially more benefit to be gained in moving towards advanced data assimilation methods over the coming years. We can certainly expect that in years to come observations of the ocean will provide valuable information for our daily weather forecasts.

Figure 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

Smith, P.J., Fowler, A.M. and Lawless, A.S. (2015), Exploring strategies for coupled 4D-Var data assimilation using an idealised atmosphere-ocean model. Tellus A, 67, 27025, http://dx.doi.org/10.3402/tellusa.v67.27025.

Fowler, A.M. and Lawless, A.S. (2016), An idealized study of coupled atmosphere-ocean 4D-Var in the presence of model error. Monthly Weather Review, 144, 4007-4030, https://doi.org/10.1175/MWR-D-15-0420.1

First recording of surface flooding in London using CCTV cameras

On Friday 2nd of June 2017 Met Office issued a yellow warning of heavy rain with possible hail and lightning over London. Also Environmental Agency issued a number of flood alerts for London for the same period of time. This allowed us to test our newly setup system for recording open data CCTV images from London Transport Cameras (aka JamCams).

Following the flood alerts we setup to record all Transport for London (TFL) cameras which where within the main flood alert areas, these were 4 areas in London.

Figure 1. Areas selected for recording TFL CCTV camera images on 2nd of June 2017 corresponding to flood alerts from Environmental Agency.

This resulted in downloading images from just over 110 CCTV cameras accross from  the marked areas in Figure 1. Dowload started on many cameras at 2:30pm on 2nd of June 2017 and continued for 24h with an image downloaded every 5min.

Many of these images showed heavy rain as it passed over London on the afternoon of the 2nd June 2017; some cameras even captured images of lightning which was seen over North London but we didn’t capture any images of flooding in the four coloured areas in Figure 1.

Figure 2. Image of heavy rain on A23 Brixton Rd/Vassell Rd as seen by one of the CCTV cameras in London on 2nd July 2017 at 5:19pm
Figure 3. Image of lightning on captured on London CCTV camera at A12 East Cross Route on 2nd of June 2017 at 4:17pm

However, following the flooding allert on London for Transport site allowed us to capture surface flooding that happened on the North Circular road between 4-7pm resulting in traffic jams in the area.

Figure 4. Map of the surface flooding on the North Circular on 2nd of June 2017

The surface flooding was very localised and only one camera captured it, the one just below the blue circle in the Figure 4. We recorded both still and video images from this camera.

We are currently setting up similar systems to download live traffic CCTV images from Leeds, Bristol, Exeter, Newcastle, Glasgow, and Tewkesbury.

Sewer network challenge at MathsForesees study group 2017

by Sanita Vetra-Carvalho

The second Maths Foresees study group was held on 3rd-6th April 2017, hosted by the Turing Gateway to Mathematics at the Isaac Newton Institute, Cambridge. The Maths Foresees network was established in May 2015 under the EPSRC Living with Environmental Change (LWEC) umbrella to forge strong links between researchers in the applied mathematics and environmental science communities and end-users of environmental research. The Maths Foresees events take a collaborative approach to industry problem solving where over the course of four days, mathematical and environmental scientists explored real challenges posed by companies operating in the environmental sector.

In this second event, there were five industry challenges presented to the participants (around 50 in total) from three companies: JBA, Sweco and Environmental Agency. All of the challenges this year were linked to flooding issues:

I joined the group interested solving sewer modelling challenge proposed by Sweco and presented by James Franklin. The urban flood model InfoWorks ICM (Integrated Catchment Modeling) by Innovyze that is used by Sweco, comprises a subsurface sewer network and a street-level road surface model. The two are coupled via manholes but smaller drains/gullies are not included since the exact locations of gullies and drains are not known (it would be very costly in manpower to locate them) and more importantly it would be computationally unfeasible to directly model gullies in InfoWorks model. As a consequence, the model does not represent floodwater drainage correctly. In a typical simulation, floodwater stays on the road surface and does not drain away as it should. This results in an inaccurate flood extents, particularly in urban environments (see an image below of a typical simulation of a storm).

A typical simulation using InfoWorks ICM: floodwater stays on the road surface and pools indefinitely rather than charging the network during the recession of a storm.

The challenge for the group was to see how we could improve the model representation of the collection network; that is how to represent gullies in the model to simulate a more realistic exchange (sinks and sources) of surface water between the sewer network and surface model.

Our group had two and half days to propose a solution. Our initial idea to couple a 2D surface shallow water model to a 1D sewer network model (also shallow water model) to model realistic fluid exchange between the two models turned out to be too difficult to accomplish in the limited time period. Hence, we concentrated our efforts on the main problem at hand, how to represent realistic sinks in the model without directly resolving gullies in the model. To this end, our group produced two 2D surface models: 2D shallow water model and 2D diffusive wave model. The second model was developed in parallel as in a future it would be easier to couple to a 1D drainage network. Our group run both models on an idealised road setting: 100m straight road with 3 manholes every 30m and 20 gullies every 10m, where directly resolved (see image below).

Representation of an idealised 100m road with gullies and manholes

We compared runs where we resolved gullies directly on the mesh every 10m on both sides of the road (the case which is computationally unfeasible for Sweco to run but is the most realistic) to line sink runs where we averaged the effect of the number gullies on the road and removed the surface liquid from the model at each gridpoint that is adjacent to the pavement. Both of our 2D surface models showed that the line sink representation of the gullies removed approximately the same volume of surface water in the model as directly resolving each gully in the model thus making line sink solution a realistic and computationally affordable to represent the effect of gullies in the model. While our solution lacked the two-way flow exchange between the surface model and sewer network we proposed that if implemented in the InfoWorks model the volume of water sunk through line sinks would become a source in the sewer network through the nearest manhole in the model. Our findings and the proposed solution to the Sweco challenge was positively received by James Franklin. A full report of our solution will be published on Turing Gateway to Mathematics site over next two months.

I very much enjoyed being part of the Maths Foresees study group 2017 and am very thankful to all the organisers at MathsForesees network and Turing Gateway of Mathematics for organising this event as well as Isaac Newton Institute for hosting it. It was very refreshing to be ‘locked’ into the Isaac Newton Institute alongside other participants to solve these challenges in a mentally very rich and inspiring environment. The event naturally offered a very fruitful ground for networking too. I would encourage any mathematician interested in solving environmental problems to take a part in any future MathsForesees events!

Our boards of brainstorming @MathsForesees event