Table 1.

The proposed participatory modelling approach. The activities with their objectives, the tools/methods adopted, and the expected results are shown. The five steps of the qualitative modelling phase are in grey, while the three steps of the quantitative modelling phase are in white. This work focuses on the quantitative phase. For more details on the qualitative one, please refer to Coletta et al. (2024).

#	TASKS	AIMS	TOOLS/METHODS	OUTCOMES
1	Literature review and baseline analysis for preliminary Causal Loop Diagram (CLD) building	To build a preliminary CLD, based on the scientific knowledge and background information on the study area	–Literature review on urban flooding –Gathering information about the study area, e.g., from reports, existing models, etc.	A preliminary CLD on the study area, based on the scientific knowledge, focused on urban flood risk
2	Interviews with stakeholders for preliminary CLD improvement	To collect and structure stakeholder knowledge for improving the key cause-effect chains of the preliminary CLD	–Semi-structured interviews with stakeholders and email exchange –Analysis of semi-structured interviews –Integration of scientific and stakeholder knowledge	A CLD on urban flood risk which integrates scientific and stakeholder knowledge
3	CLD causal structure validation	To validate the general structure and key CLD connections	Collective model testing and participatory exercises	Final structure of CLD
4	Behaviour Over Time (BOT) graphs construction with stakeholders	To collect stakeholder perception on the dynamic evolution of some key variables of the system	BOT graphs construction	Graphs on the dynamic evolution of the system based on stakeholder perception
5	CLD integration based on stakeholder-built BOT graphs	–To analyse the main dynamics and impacts of flood in the CLD –To integrate BOT graphs results into the final CLD	BOT graphs and key CLD feedback loops analysis	Formulation of hypotheses on urban system dynamics and flood risk management policies
1	Building a Stock and Flow (SF) model related to the current system condition	–Identifying stock, flow, auxiliary and input variables –Determining equations and parameters using literature, existing models, reports, databases, and stakeholder input –Developing sub-models and calculating indices that provide aggregated information on system dynamics	–Literature review and data collection for model input, e. g., from reports, existing models, etc. –Interviews with stakeholders and email exchange –Behaviour Over Time (BOT) graphs	A SF model on urban flood risk combining scientific and stakeholder knowledge
2	Validating the SF model	Validating the model through analysis of key variables/indices over time	–Comparing stakeholder-built BOT graphs with model-simulated trends for the same variables –Collective model testing and participatory exercises to validate other variables	Final SF model on urban flood risk
3	Building and analysing future scenarios	–Developing future scenarios for stakeholder discussion –Co-designing alternative scenarios with stakeholders –Comparing future scenarios –Selecting the most effective scenario and performing a sensitivity analysis to identify key monitoring variables	–Reviewing literature and engaging stakeholders in scenario exploration –Comparative analysis of urban system dynamics under different flood scenarios –Sensitivity analysis of the most effective scenario	Recommendations for implementing an effective strategy (bundle of actions) and monitoring key variables to enhance urban flood resilience