{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T17:56:08Z","timestamp":1775152568444,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UID\/297\/2025"],"award-info":[{"award-number":["UID\/297\/2025"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UID\/PRR\/297\/2025"],"award-info":[{"award-number":["UID\/PRR\/297\/2025"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["CTS\/00066"],"award-info":[{"award-number":["CTS\/00066"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UIDB\/06107\/2023-CREATE"],"award-info":[{"award-number":["UIDB\/06107\/2023-CREATE"]}]},{"award":["UID\/297\/2025"],"award-info":[{"award-number":["UID\/297\/2025"]}],"id":[{"id":"https:\/\/ror.org\/00snfqn58","id-type":"ROR","asserted-by":"publisher"}]},{"award":["UID\/PRR\/297\/2025"],"award-info":[{"award-number":["UID\/PRR\/297\/2025"]}],"id":[{"id":"https:\/\/ror.org\/00snfqn58","id-type":"ROR","asserted-by":"publisher"}]},{"award":["CTS\/00066"],"award-info":[{"award-number":["CTS\/00066"]}],"id":[{"id":"https:\/\/ror.org\/00snfqn58","id-type":"ROR","asserted-by":"publisher"}]},{"award":["UIDB\/06107\/2023-CREATE"],"award-info":[{"award-number":["UIDB\/06107\/2023-CREATE"]}],"id":[{"id":"https:\/\/ror.org\/00snfqn58","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Risks"],"abstract":"<jats:p>This paper presents a physics-based hazard model for catastrophe (CAT) modelling of urban flood risk\u2014a first step toward a complete CAT modelling framework. We introduce a linear second-order ordinary differential equation (ODE) system to simulate the underlying mechanisms of water accumulation, absorption, routing, and drainage across interconnected surfaces in densely built urban areas. The model treats an urban zone as a multivariate network of surfaces, each with unique hydrological properties, linked by directed water flows. For risk analysis, the external meteorological forcing (representing the precipitation input) is randomised. Our risk-analysis protocol relies on a Monte Carlo simulation of stochastic forcing. Its reliability is founded on rigorous mathematical properties proven for the ODE system (existence, uniqueness, positivity, monotonicity, and a priori bounds), ensuring that the probabilistic outputs are well-defined and physically plausible. A three-surface example illustrates the framework and a complete risk analysis is performed, yielding concrete risk metrics that inform mitigation strategies. Computational efficiency is shown to be optimal for linear ODE systems, outperforming generic methods. This work provides a foundational, physics-informed hazard model for next-generation CAT models, directly supporting the insurance industry\u2019s adaptation to climate change.<\/jats:p>","DOI":"10.3390\/risks14040083","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T16:51:02Z","timestamp":1775148662000},"page":"83","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A First Step Toward a CAT Model Framework: An ODE-Based Risk Analysis of Urban Floods Triggered by Meteorological Events"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-1664-9236","authenticated-orcid":false,"given":"Beatriz A.","family":"Curioso","sequence":"first","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4991-7568","authenticated-orcid":false,"given":"Manuel L.","family":"Esqu\u00edvel","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"},{"name":"Department of Mathematics, NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4805-2638","authenticated-orcid":false,"given":"Gracinda R.","family":"Guerreiro","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"},{"name":"Department of Mathematics, NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4226-1658","authenticated-orcid":false,"given":"Nadezhda P.","family":"Krasii","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"},{"name":"Department of Higher Mathematics, Don State Technical University, Gagarin Square 1, Rostov-on-Don 344000, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3814-6331","authenticated-orcid":false,"given":"Pedro A. C.","family":"Sousa","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, NOVA School of Science and Technology (NOVA FCT), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"},{"name":"Center for Technology and Systems (CTS), NOVA School of Science and Technology, Universidade Nova de Lisboa, Campus de Caparica, 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s11069-008-9277-8","article-title":"Flood risk analyses\u2014How detailed do we need to be?","volume":"49","author":"Apel","year":"2009","journal-title":"Natural Hazards"},{"key":"ref_2","unstructured":"Banerjee, Chandan, Bevere, Lucia, Garbers, Hendre, Grollimund, Balz, Lechner, Roman, and Weigel, Andreas (2020, January 21). Natural Catastrophes in 2023: Gearing Up for Today\u2019s and Tomorrow\u2019s Weather Risks. 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