<p>Wetropolis is a transportable <q>table-top</q> demonstration model with extreme rainfall and flooding events. It is a conceptual model with random rainfall, river flow, a flood plain, an upland reservoir, a porous moor, representing the upper catchment and visualising groundwater flow, and a city which can flood following extreme rainfall. Its aim is to let the viewer experience extreme rainfall and flood events in a physical model on reduced spatial and temporal scales. In addition, it conveys concepts of flood storage and control, via manual intervention. To guide the building of an operational Wetropolis, we have explored its spatial and temporal dimensions first in a simplified mathematical design. We explain this mathematical model in detail since it was a crucial step in Wetropolis' design and it is of scientific interest from a hydrodynamic modelling perspective. The key novelty is the supply of rainfall every Wetropolis day (unit wd), varied temporally and spatially in terms of both the amount of rain and the rainfall location. The joint probabilities (rain amount times rain location) are determined daily as one 10 of 16 possible outcomes from two asymmetric Galton boards, in which steel balls fall down every wd, with the most extreme rainfall event involving 90 % rainfall on both moor and reservoir. This occurs with a probability of circa 3 % and – by design – can cause severe floods in the city. This randomised rainfall has a Wetropolis' return period of 6:06min, short enough to wait for but sufficiently <q>extreme</q> or long to get slightly irritated as a viewer. While Wetropolis should be experienced live, here we provide a photographic overview. To date, Wetropolis has been showcased to over 200 flood victims at workshops and 15 exhibitions on recent UK floods, as well as to flood practitioners and scientists at various workshops. To enhance Wetropolis' reach, we analyse and report here how both the general public and professionals interacted with Wetropolis. We conclude with a discussion on some ongoing design changes, including how people can experience natural flood management in a revised Wetropolis design, before highlighting how the <q>Wetropolis experience</q> can stimulate new approaches in hydrological modelling, flood mitigation and control in science, education and water management.</p>