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

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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 […]

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. Download 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. In the video below you can see the surface flooding affecting the slip road going North.

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

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!