Investigating, understanding and visualising floods through the Wetropolis Flood Investigator

Motivation: engaging visualisation of floods

We will introduce the Wetropolis Flood Investigator: a mathematical model and physical set-up. Wetropolis consists of a random weather or rain machine driving rainfall in a down-scaled river-catchment landscape. When this randomly determined rainfall is extreme, in terms of location and duration, we will observe flooding in a conceptual city. Hence, we note that Wetropolis visualises the random nature of a return-period or an Annual Exceedance Probability (AEP) for extreme rainfall and flooding events. We will not let you wait for on average 100 years for a 1:100yr flood. Instead Wetropolis’ return-periods for 1-2-3-day(s) of extreme rainfall and flooding events are shorter, circa 50s, 5min and 28min on average, respectively. We don’t want you to turn to dust so a “Wetropolis Day” is only 10s!

Visualising return periods or Event probabilities

Corresponding Event Probabilities (EPs) are circa 1/5, 1/25 and 1/125. You may find these by taking the inverse and multiplying by 10s. As we noted these EPs are determined by the weather machine via modified Galton-boards through which a steel ball falls every 10s, giving 4×4=16 possible outcomes. One outcome is linked to an extreme rainfall event. We have now also included climate change and droughts  in the Wetropolis model after urgent requests by public and academics.

Come and see Wetropolis (e.g. on YouTube, below)! 1000s of members of the public and flood professionals have already seen Wetropolis in action. We have shown Wetropolis at exhibitions of the Mathematics of Planet Centre of Doctoral training at Imperial College (London, 2020/2022) and at the conference Flood & Coast (2023 Telford). Surprisingly given its outreach origin, intense interactions with flood professionals revealed that we should use Wetropolis as education, policy and scientific flood investigator. So that is what we will do.

Cutting-edge objectives

We therefore arrive at the following cutting-edge objectives on how to use Wetropolis:

• We will analyse the efficacy of importance sampling for (modelling) extreme flooding events of intermediate rareness and assess the computational gains; analyse changing points of extreme events and their (A)EP’s due to climate change; and, validate such analyses against Wetropolis as scientific laboratory experiment;
• We will create educational projects at secondary school and junior-college level on the arithmetic and statistics of extreme events and climate data for flooding inspired by Wetropolis, including on return periods or (A)EPs, and involve physical models; and,
• We will develop novel policy visualisation tools on flood-mitigation measures and associated uncertainty for decision-makers.

Hence, we arrive at our scientific, educational and/or policy considerations.

Questions on forecasting floods and climate-change effects

Our questions on the scientific research objectives are:

• What do you think is the computational gain of importance sampling for events of intermediate extremeness? Do you think that is worthwhile considering that flood-risk maps concern (intermediate) AEPs=(3.3,1,0.1)%, mimicked by Wetropolis’ EPs=(1/5,1/25,1/125)?
• How can we understand the effects of spatio-temporal rainfall patterns on flooding using advanced and variation-reducing Monte-Carlo simulations? Which permutations of landscape-elements in Wetropolis lead to the least and worst city flooding? How can we optimise and choose flood-mitigation measures using advanced and variation-reducing Monte-Carlo simulations?
• How well do you think can we discern and calculate non-stationarity in these various (A)EPs from data, including change-point analysis of data due to (sudden) climate change?
• Can we establish a real-time Wetropolis flood-forecasting and flood-control model, in-situ visualised as scientific test-bed, yet on reduced Wetropolis’ time scales?

Active developing and testing of tools

We will develop a set of modern modelling tools to perform our scientific research:

• We will employ the existing one-dimensional design model with kinematic river flow and diffusive ground-water dynamics, which lends itself for various simplified importance sampling models of the extreme flooding events.
• We will couple our existing one-dimensional shallow-water model to groundwater dynamics in a first realistic Wetropolis model with flood plains.
• We will further develop two-dimensional river-flow and (two or three-dimensional) ground-water models to add more reality.
• We will include real-time data acquisition for data assimilation (based on classical or particle filters) and parameter estimation. Thus we will constrain bottom friction and inflow uncertainty in order to bring the models back to Wetropolis’ reality.
• We will compare machine-learning techniques with “classical” data assimilation.
• We will make a real-time comparison and display between Wetropolis and model flood forecasting with flood control and flood mitigation.

We are excited to tell you that we have an integrated industrial and academic team. The company Jacobs in Leeds will actively support this Wetropolis research project as CASE partner. That includes hosting a 3 to 9 month series of placements. Everyone is particularly interested and excited about the joined activities proposed. Herein, we will promote engaging educational outreach and the use and analysis of Jacobs’ flood and groundwater modelling tools.