Water Smart Cities: a Modular Modelling Framework for Nature-Based Stormwater Management in Urban Areas

The design of urban neighbourhoods involves addressing a multitude of interrelated factors, which makes decision-making increasingly challenging. This complex task is further exacerbated by the steady expansion of urban areas, the increasing frequency and intensity of meteorological extremes, and the growing interest in sustainable urban drainage systems and the Nature-based Solutions (NBS). Within this context, and as part of the Water Smart Cities (WSC) European project funded by the European Regional Development Fund (ERDF), a modular software tool has been developed to rapidly assess the performance of NBS and conventional grey infrastructure for stormwater management in relatively small urban catchments. The tool is intended to support urban planners, decision-makers, and civil engineering consultancies by offering an intermediate level of modelling complexity that bridges the gap between simple spreadsheet-based approaches and highly detailed hydraulic-hydrological simulation platforms.

The software architecture is based on nodal modelling and organised into interconnected modules that address various aspects of urban water management. Hydraulic and hydrological components provide quantitative assessments, while ecosystem services and water quality aspects are represented by a combination of quantitative outputs and qualitative indicators. This modular structure enables the flexible testing and comparison of alternative urban drainage strategies, including both NBS and grey solutions, within a consistent modelling framework.

This contribution focuses on the hydraulic-hydrological solver and its applications. The solver is implemented in Python using the JAX library, and is based on an implicit numerical formulation. JAX enables just-in-time compilation, automatic differentiation for efficient Jacobian evaluation, and parallel computation on CPU and GPU architectures provided one adopts a pure functional programming paradigm using continuously differentiable model formulations. The implicit formulation improves numerical stability and ensures synchronous coupling between interacting system components, thereby avoiding artificial numerical delays.

Unlike spreadsheet-based tools, which are generally limited to volume-based evaluations, the proposed solver explicitly represents the dynamic interactions between structures and their spatial organisation. It allows the assessment of outlet regulations, pipe characteristics, spillway geometries, soil properties and . This provides design-relevant information to communicate modelling uncertainties and support planning and decision-making. Several applied case studies will be presented to showcase the implications of modelling choices and the range of design possibilities in the context of water-sensitive urban development.

Acknowledgments: The project Water Smart Cities is part of the projects portfolio SWaM@Sc, cofunded by the European Union and by the Walloon Region (ERDF)