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

7th Japanese Data Assimilation Workshop

By Joanne A. Waller

For decades data assimilation (DA) has played a crucial role in numerical weather prediction (NWP) where it is used to provide initial conditions for weather forecasts. These ‘initial conditions’ describe the current atmospheric state and are estimated using data assimilation by blending previous forecasts with atmospheric observations, weighted by their respected uncertainties. However data assimilation is not only applicable to NWP and in recent years it has been applied widely to different applications where numerical simulations and observations are available.

At the end of February 2017 over 100 scientists from around the globe arrived at the Japanese RIKEN Advanced Institute for Computational Science (AICS)  for the 7th Japanese Data Assimilation Workshop. The aim of the symposium was to bring together scientist from from numerous different disciplines, such as neuroscience, cardiology, molecular dynamics, cosmology, nanoscale materials science, terrestrial magnetism, paleoclimate, oceanography, atmospheric chemistry and of course NWP, to discuss the data assimilation issues shared  across these broad applications.

Presentations and posters covered a wide variety of topics including: how data assimilation combined with advanced intelligence can help improve numerical models; how high performance computing can be used to deal with the new era of ‘Big Data’; how non-Gaussianity and non-linearity can be handled in data assimilation; ideas on how assimilate data into multi component models (i.e. systems that connect multiple models such as atmospheric, land and ocean models) and many more.

The conference provided a perfect platform for many cross-disciplinary discussions and this highlighted that much can be learnt in general about data assimilation by considering the issues that arise across different scientific areas.

(Photo from