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

Mathematics of Planet Earth Jamboree

 by Jemima Tabeart

On 20th-22nd March the Mathematics of Planet Earth Centre for Doctoral Training (MPE CDT) held its third annual Jamboree event. This is a celebration of the work of the staff and students of the CDT and includes seminars from industrial and academic speakers, as well as the opportunity for students to present their research. For the first time this year, the first two days of the Jamboree were used to host an Industrial study group. Representatives from EDF Energy and AIR Worldwide (catastrophe modelling for the insurance and re-insurance industry) posed real-world problems to cross-cohort groups of students, who then attempted to provide some new mathematical insight into possible solutions.

 

Our group was given a task by EDF Energy to investigate the interaction of extreme wind and rain events in the UK. EDF Energy’s assets in the UK include nuclear and other types of power plants, so understanding of extreme events is important in order to they can take appropriate safety measures. Currently extreme rain and wind events are considered separately, and we were asked to consider ways of determining how to define and deal with extreme wind-rain events. We were given hourly reanalysis data from the last 40 years, on a coarse 1 degree grid over the UK. The group split into two parts: one looking at more conceptual ideas about how extreme events can be caused by an interaction of factors, and the other considering the data provided.

 

Our part of the group identified some known extreme weather events, and focused on the data for these time periods. We looked at which events had both extreme wind and extreme rain, and mapped these to geographical locations to see where extreme wind-rain occurs most frequently. We also tried to see if there was a time lag between rain and wind events in the same location. Initial plots indicated that the most likely lag time was 0 hours, although this might be due to the relatively coarse resolutions. Other members of the group also suggested a method for combining the threshold values for extreme wind and rain to create a combined parameter. As well as a presentation of the main ideas that took place on the day to industry representatives, written reports will be sent to the respective companies so that they can take the suggestions further.

 

The study group was a great opportunity for cross-cohort work that brought together students with contrasting research interests. The challenge of producing something in a short amount of time is very different to what we normally expect as PhD students, and the ideas of getting stuck in straight away and not spending hours agonising over every decision is something that will be useful going forward. I really enjoyed working with real-world data and on problems outside my usual subject area – applying techniques I’ve learned during my PhD to other applications is very satisfying, and gives me the confidence that I am developing my transferable skills through my research!