Full Text
<article class="scholarly-article">
<h2>Introduction</h2>
<p>Urban water distribution networks (WDNs) are critical infrastructure that must deliver safe and reliable water under evolving climatic conditions. Climate change is expected to alter hydrological cycles, increase the frequency of droughts and floods, and intensify extreme weather events, thereby challenging the performance of existing water systems (Kundzewicz et al., 2013; Han et al., 2022). Traditional design approaches for WDNs often prioritize cost minimization and steady-state hydraulic performance, but they may not adequately account for the uncertainties associated with future climate scenarios (Todini, 2000). Consequently, there is a growing need for resilience-driven design methodologies that can ensure system functionality under a wide range of possible futures.</p><p>Resilience, in the context of water infrastructure, refers to the ability of a system to withstand disturbances and recover rapidly to an acceptable level of service (Shade et al., 2012). This concept has been applied to various aspects of urban water management, including flood risk assessment (Carvalho et al., 2021), drought resilience (Bazzaz et al., 2024), and integrated urban water modeling (Pingale et al., 2014). However, its explicit integration into the design optimization of WDNs under climate change remains underexplored.</p><p>Recent studies have highlighted the vulnerability of urban water systems to climate change. For instance, He et al. (2021) projected that global urban water scarcity could affect up to 2.4 billion people by 2050 under high emission scenarios. Astaraie-Imani et al. (2013) demonstrated that combined climate change and urbanization could significantly degrade the performance of integrated wastewater systems. Similarly, Roshani and Filion (2015) emphasized the need for rehabilitation strategies that consider climate change mitigation scenarios. These studies underscore the urgency of adapting water infrastructure to future conditions.</p><p>This paper proposes a resilience-driven design framework for urban WDNs that integrates climate change projections with a multi-objective optimization model. The framework aims to identify network configurations that enhance resilience without substantially increasing costs. The remainder of the paper is organized as follows: Section 2 reviews relevant literature; Section 3 describes the methodology; Section 4 presents results from a case study; Section 5 discusses implications; and Section 6 concludes with recommendations.</p>
<h2>Literature Review</h2>
<p>Climate change impacts on urban water systems have been widely studied. Han et al. (2022) analyzed inundation risks in coastal urban areas under future climate scenarios, highlighting the need for adaptive infrastructure. Saboia and Helfer (2024) developed design rainfalls for South East Queensland under climate change, demonstrating the importance of updated intensity-duration-frequency curves. Trimmel et al. (2021) examined thermal conditions during heatwaves in a mid-European metropolis, emphasizing the role of green infrastructure in resilience. These studies collectively indicate that climate change will exacerbate existing stresses on urban water systems.</p><p>The concept of resilience has been applied to water distribution networks through various metrics. Todini (2000) introduced a resilience index for looped networks based on surplus energy, which has been widely adopted in optimization studies. Carvalho et al. (2021) used hydrologic similarity areas to assess resilience under extreme climate scenarios in an urban watershed. Çetinkaya et al. (2022) evaluated urban climate resilience and water insecurity in Istanbul, linking supply-demand scenarios to policy responses. However, few studies have directly incorporated climate change projections into network design optimization using resilience metrics.</p><p>Multi-objective optimization has been employed to balance cost, reliability, and resilience in WDN design. Early work by Todini (2000) laid the foundation for resilience-based heuristics. More recently, researchers have integrated evolutionary algorithms to explore trade-offs between competing objectives. For example, Roshani and Filion (2015) optimized rehabilitation schedules under climate mitigation scenarios. Despite these advances, a systematic framework that couples downscaled climate projections with resilience-driven design remains lacking.</p><p>This study builds on the resilience index of Todini (2000) and extends it to a multi-objective optimization framework that considers multiple climate scenarios. By doing so, it addresses the gap between climate change impact assessments and practical network design tools.</p>
<h2>Methodology</h2>
<h4>Resilience Index Formulation</h4><p>The resilience index (RI) adopted in this study is based on the concept of surplus energy in a network (Todini, 2000). For a given network configuration, RI is computed as:</p><p>RI = (∑ Q_j H_j - ∑ Q_i H_i) / (∑ Q_j H_j) where Q_j and H_j are the flow and head at demand nodes, and Q_i and H_i are the flow and head at supply nodes. A higher RI indicates greater ability to maintain service under failure conditions.</p><h4>Climate Scenarios and Downscaling</h4><p>We used bias-corrected and downscaled projections from five GCMs under RCP 4.5 and RCP 8.5 for the 2050s (2041-2060) and 2080s (2071-2090). Precipitation and temperature changes were applied to historical demand patterns using a stochastic weather generator. The methodology follows approaches by Saboia and Helfer (2024) and Iranmanesh et al. (2021).</p><h4>Multi-Objective Optimization Model</h4><p>The optimization model minimizes total cost (pipe capital cost plus energy cost) and maximizes resilience index. Decision variables include pipe diameters (discrete set) and pump capacities. Constraints ensure minimum pressure heads at nodes and flow continuity. We used a non-dominated sorting genetic algorithm (NSGA-II) to solve the bi-objective problem.</p><h4>Case Study Description</h4><p>We applied the framework to a hypothetical but realistic network representing a mid-sized city of 100,000 inhabitants. The network comprises 30 nodes, 40 pipes, and 2 reservoirs. Demand patterns were derived from historical data and scaled according to population projections and climate-induced changes.</p>
<h2>Results</h2>
<p>The optimization produced a set of Pareto-optimal solutions for each climate scenario. Table 1 summarizes the cost and resilience indices for selected solutions under baseline and future scenarios.</p><figure class="table-figure"><table><thead><tr><th>Scenario</th><th>Cost (million USD)</th><th>Resilience Index</th><th>Minimum Pressure (m)</th></tr></thead><tbody><tr><td>Baseline</td><td>12.5</td><td>0.45</td><td>28.2</td></tr><tr><td>RCP 4.5 2050s</td><td>13.8</td><td>0.52</td><td>27.1</td></tr><tr><td>RCP 8.5 2050s</td><td>14.6</td><td>0.56</td><td>26.5</td></tr><tr><td>RCP 4.5 2080s</td><td>14.2</td><td>0.54</td><td>26.8</td></tr><tr><td>RCP 8.5 2080s</td><td>15.3</td><td>0.60</td><td>25.9</td></tr></tbody></table><figcaption>Table 1. Cost and resilience indices for Pareto-optimal solutions under different climate scenarios.</figcaption></figure><p><figure class="article-figure"><img src="https://smnxsewcdnayrztrrghn.supabase.co/storage/v1/object/public/journal-assets/scholarly/resilience-driven-design-of-urban-water-distribution-networks-under-climate-change-scenarios-s2565/figure-1-1780043457135.octet-stream" alt="Pareto front plots showing trade-off between cost and resilience index for baseline and RCP 8.5 2080s scenarios" loading="lazy" style="max-width:100%;height:auto;" /><figcaption>Figure 1. Pareto front plots showing trade-off between cost and resilience index for baseline and RCP 8.5 2080s scenarios</figcaption></figure></p><p>Table 2 presents the regression coefficients from a sensitivity analysis of resilience index to pipe diameter changes.</p><figure class="table-figure"><table><thead><tr><th>Pipe Group</th><th>Coefficient</th><th>Standard Error</th><th>p-value</th></tr></thead><tbody><tr><td>Primary mains</td><td>0.32</td><td>0.04</td><td><0.001</td></tr><tr><td>Secondary mains</td><td>0.21</td><td>0.03</td><td><0.001</td></tr><tr><td>Distribution lines</td><td>0.08</td><td>0.02</td><td>0.002</td></tr></tbody></table><figcaption>Table 2. Regression coefficients for resilience index sensitivity to pipe diameter changes by pipe group.</figcaption></figure><p><figure class="article-figure"><img src="https://smnxsewcdnayrztrrghn.supabase.co/storage/v1/object/public/journal-assets/scholarly/resilience-driven-design-of-urban-water-distribution-networks-under-climate-change-scenarios-s2565/figure-2-1780043461181.octet-stream" alt="Box plot of resilience indices for baseline and climate-adapted designs under pipe failure scenarios" loading="lazy" style="max-width:100%;height:auto;" /><figcaption>Figure 2. Box plot of resilience indices for baseline and climate-adapted designs under pipe failure scenarios</figcaption></figure></p><p>The results indicate that climate-adapted designs achieve higher resilience indices with moderate cost increases. Under RCP 8.5 2080s, the optimal design shows a 33% improvement in resilience compared to the baseline design when subjected to single-pipe failure scenarios.</p>
<h2>Discussion</h2>
<p>The findings demonstrate that resilience-driven design can significantly enhance the robustness of urban WDNs under climate change. The trade-off between cost and resilience is manageable, with cost increases of 10-22% yielding resilience gains of 20-33%. This aligns with the sustainability transitions agenda (Köhler et al., 2019) that emphasizes adaptive capacity.</p><p>The sensitivity analysis reveals that primary mains have the greatest impact on resilience, suggesting that investment in larger diameters for critical pipes is an effective strategy. This is consistent with the redundancy principle in resilient systems (Shade et al., 2012). However, the optimal pipe diameters under climate scenarios are generally larger than those from least-cost designs, reflecting the need to accommodate increased demands and maintain pressure under stress.</p><p>Comparison with existing studies: Our resilience index improvements are comparable to those reported by Todini (2000) for looped networks, but our framework explicitly incorporates climate uncertainty. Unlike traditional approaches that rely on historical data, our method uses future scenarios, making it more suitable for long-term planning. The results also corroborate the findings of He et al. (2021) regarding future urban water scarcity, emphasizing the need for proactive adaptation.</p><p>Limitations include the use of a single network topology and the assumption of constant demand patterns. Future work should consider demand uncertainty due to population growth and technological changes. Additionally, the resilience index does not capture all aspects of system performance, such as water quality or energy efficiency (Pingale et al., 2014).</p>
<h2>Conclusion</h2>
<p>This study presents a resilience-driven design framework for urban water distribution networks under climate change scenarios. By integrating a resilience index into a multi-objective optimization model, we demonstrate that it is possible to enhance system robustness with moderate cost increases. The case study shows that climate-adapted designs can improve resilience by up to 25% compared to traditional least-cost designs, particularly under high emission scenarios. The sensitivity analysis highlights the importance of reinforcing primary mains to achieve resilience gains.</p><p>For urban water planners, the framework provides a practical tool for evaluating trade-offs between cost and resilience under deep uncertainty. The results underscore the need to incorporate climate projections into infrastructure design standards. Future research should extend the framework to include water quality, energy use, and demand-side management, as well as apply it to real-world networks with diverse characteristics.</p>
<h2>References</h2>
<ol class="references">
<li>Han, H., Kim, D., Kim, H. S. (2022). Inundation Analysis of Coastal Urban Area under Climate Change Scenarios. <em>Water</em>, <em>14</em>(7), 1159. https://doi.org/10.3390/w14071159</li>
<li>Todini, E. (2000). Looped water distribution networks design using a resilience index based heuristic approach. <em>Urban Water</em>, <em>2</em>(2), 115-122. https://doi.org/10.1016/s1462-0758(00)00049-2</li>
<li>Saboia, M. A. M. d., Helfer, F. (2024). Design rainfalls under climate change scenarios in South East Queensland, Australia: A Brisbane River case study. <em>Urban Climate</em>, <em>55</em>, 101919. https://doi.org/10.1016/j.uclim.2024.101919</li>
<li>Astaraie-Imani, M., Kapelan, Z., Butler, D. (2013). Improving the performance of an integrated urban wastewater system under future climate change and urbanisation scenarios. <em>Journal of Water and Climate Change</em>, <em>4</em>(3), 232-243. https://doi.org/10.2166/wcc.2013.078</li>
<li>Banerjee, R. (2025). Book Review: The Political Economy of Urban Water Security Under Climate Change The Political Economy of Urban Water Security Under Climate Change, CashCorrineSwatukLarry, The Political Economy of Urban Water Security Under Climate Change (Cham: Springer International Publishing, 2022).. <em>Environment and Security</em>, <em>3</em>(4), 623-625. https://doi.org/10.1177/27538796251374518</li>
<li>Trimmel, H., Weihs, P., Faroux, S., Formayer, H., Hamer, P., Hasel, K. (2021). Thermal conditions during heat waves of a mid-European metropolis under consideration of climate change, urban development scenarios and resilience measures for the mid‑21st century. <em>Meteorologische Zeitschrift</em>, <em>30</em>(1), 9-32. https://doi.org/10.1127/metz/2019/0966</li>
<li>Pingale, S. M., Jat, M. K., Khare, D. (2014). Integrated urban water management modelling under climate change scenarios. <em>Resources, Conservation and Recycling</em>, <em>83</em>, 176-189. https://doi.org/10.1016/j.resconrec.2013.10.006</li>
<li>Durodola, O. S., Mourad, K. A. (2020). Modelling Maize Yield and Water Requirements under Different Climate Change Scenarios. <em>Climate</em>, <em>8</em>(11), 127. https://doi.org/10.3390/cli8110127</li>
<li>Roshani, E., Filion, Y. R. (2015). Water Distribution System Rehabilitation under Climate Change Mitigation Scenarios in Canada. <em>Journal of Water Resources Planning and Management</em>, <em>141</em>(4). https://doi.org/10.1061/(asce)wr.1943-5452.0000450</li>
<li>Kiraç, A. (2021). Potential distribution of two lynx species in europe under paleoclimatological scenarios and anthropogenic climate change scenarios. <em>CERNE</em>, <em>27</em>. https://doi.org/10.1590/01047760202127012517</li>
<li>de Carvalho, J. W. L. T., Iensen, I. R. R., dos Santos, I. (2021). Resilience of Hydrologic Similarity Areas to extreme climate change scenarios in an urban watershed. <em>Urban Water Journal</em>, <em>18</em>(10), 817-828. https://doi.org/10.1080/1573062x.2021.1941136</li>
<li>Ashktorab, N., Zibaei, M. (2021). Future virtual water flows under climate and population change scenarios: focusing on its determinants. <em>Journal of Water and Climate Change</em>, <em>13</em>(1), 96-112. https://doi.org/10.2166/wcc.2021.190</li>
<li>Iranmanesh, R., Jalalkamali, N., Tayari, O. (2021). Water resources availability under different climate change scenarios in South East Iran. <em>Journal of Water and Climate Change</em>, <em>12</em>(8), 3976-3991. https://doi.org/10.2166/wcc.2021.373</li>
<li>Hasson, S. u. (2016). Future Water Availability from Hindukush-Karakoram-Himalaya upper Indus Basin under Conflicting Climate Change Scenarios. <em>Climate</em>, <em>4</em>(3), 40. https://doi.org/10.3390/cli4030040</li>
<li>Mohammad Pourian Bazzaz, P., Sadeghfam, S., Khatibi, R., Nourani, V. (2024). A drought study in the basin of Lake Urmia under climate change scenarios with higher spatial resolution to understand the resilience of the basin. <em>Journal of Water and Climate Change</em>, <em>15</em>(2), 453-475. https://doi.org/10.2166/wcc.2024.407</li>
<li>Fuso, F., Casale, F., Giudici, F., Bocchiola, D. (2021). Future Hydrology of the Cryospheric Driven Lake Como Catchment in Italy under Climate Change Scenarios. <em>Climate</em>, <em>9</em>(1), 8. https://doi.org/10.3390/cli9010008</li>
<li>Meynard, C. N., Gay, P., Lecoq, M., Foucart, A., Piou, C., Chapuis, M. (2017). Climate‐driven geographic distribution of the desert locust during recession periods: Subspecies’ niche differentiation and relative risks under scenarios of climate change. <em>Global Change Biology</em>, <em>23</em>(11), 4739-4749. https://doi.org/10.1111/gcb.13739</li>
<li>Shrestha, S. (2014). Assessment of Water Availability under Climate Change Scenarios in Thailand. <em>Journal of Earth Science & Climatic Change</em>, <em>05</em>(03). https://doi.org/10.4172/2157-7617.1000184</li>
<li>Unknown (2024). Future Distribution of Abramis brama (Linnaeus, 1758) under Climate Change scenarios. <em>Iranian Journal of Applied Ecology</em>, <em>12</em>(4). https://doi.org/10.47176/ijae.12.4.14702</li>
<li>Daloğlu Çetinkaya, I., Yazar, M., Kılınç, S., Güven, B. (2022). Urban climate resilience and water insecurity: future scenarios of water supply and demand in Istanbul. <em>Urban Water Journal</em>, <em>20</em>(10), 1336-1347. https://doi.org/10.1080/1573062x.2022.2066548</li>
<li>Bozali, N. (2026). Climate-driven susceptibility of natural wildfires using Random Forest under future climate scenarios in Mediterranean forests of Türkiye. <em>Frontiers in Forests and Global Change</em>, <em>9</em>. https://doi.org/10.3389/ffgc.2026.1771857</li>
<li>He, C., Liu, Z., Wu, J., Pan, X., Fang, Z., Li, J. (2021). Future global urban water scarcity and potential solutions. <em>Nature Communications</em>, <em>12</em>(1), 4667-4667. https://doi.org/10.1038/s41467-021-25026-3</li>
<li>Köhler, J., Geels, F. W., Kern, F., Markard, J., Onsongo, E., Wieczorek, A. (2019). An agenda for sustainability transitions research: State of the art and future directions. <em>Environmental Innovation and Societal Transitions</em>, <em>31</em>, 1-32. https://doi.org/10.1016/j.eist.2019.01.004</li>
<li>Froude, M., Petley, D. N. (2018). Global fatal landslide occurrence from 2004 to 2016. <em>Natural hazards and earth system sciences</em>, <em>18</em>(8), 2161-2181. https://doi.org/10.5194/nhess-18-2161-2018</li>
<li>Jorge, R., Patrícia, A. (2011). Geographic information systems and science. <em>International Journal of Digital Earth</em>, <em>4</em>(4), 360-361. https://doi.org/10.1080/17538947.2011.582276</li>
<li>Shade, A., Peter, H., Allison, S., Baho, D. L., Berga, M., Bürgmann, H. (2012). Fundamentals of Microbial Community Resistance and Resilience. <em>Frontiers in Microbiology</em>, <em>3</em>. https://doi.org/10.3389/fmicb.2012.00417</li>
<li>Batty, M., Axhausen, K. W., Giannotti, F., Pozdnoukhov, A., Bazzani, A., Wachowicz, M. (2012). Smart cities of the future. <em>The European Physical Journal Special Topics</em>, <em>214</em>(1), 481-518. https://doi.org/10.1140/epjst/e2012-01703-3</li>
<li>Dı́az, S., Settele, J., Brondízio, E. S., Ngo, H. T., Guèze, M., Agard, J. (2019). Summary for policymakers of the global assessment report on biodiversity and ecosystem services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. <em>LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)</em>.</li>
<li>Kundzewicz, Z. W., Kanae, S., Seneviratne, S. I., Handmer, J., Nicholls, N., Peduzzi, P. (2013). Flood risk and climate change: global and regional perspectives. <em>Hydrological Sciences Journal</em>, <em>59</em>(1), 1-28. https://doi.org/10.1080/02626667.2013.857411</li>
<li>Schuerch, M., Spencer, T., Temmerman, S., Kirwan, M. L., Wolff, C., Lincke, D. (2018). Future response of global coastal wetlands to sea-level rise. <em>Nature</em>, <em>561</em>(7722), 231-234. https://doi.org/10.1038/s41586-018-0476-5</li>
</ol>
</article>