Coalitional Game Theory for Stormwater Management and Green Infrastructure Practices
Publication: Journal of Water Resources Planning and Management
Volume 150, Issue 1
Abstract
As global warming and climate variability bring about more frequent and intense rainstorms and accelerate sea level rise, our social and built environments are at heightened risk of flood-induced damages and costs. All levels of governance stand to benefit from deepened understanding of possible outcomes resulting from decentralized human behavior in the realm of water resources engineering and management, particularly in coastal areas. Game theory allows scientists to predict preferred strategies and interactions of rational self-interested actors in coalitional games, wherein players increase their individual payoffs through formation of strategic subsets. When applied to infrastructure planning, this practice can be used to identify which coalitions should form to benefit their overall hydrologic system. This research aims to inform green infrastructure decisions in Charleston, South Carolina’s Market Street watershed using a coalitional game theory solution concept, the Shapley value, in combination with rainfall-runoff simulation in storm water management model (SWMM). Results offer insights into stormwater services and flood managers concerning suggested areas of focus for green infrastructure spending and advocacy to reduce flooding and resulting property damage.
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Data Availability Statement
The authors confirm that the derived data supporting the findings of this study are available in the article and the Supplemental Materials. Other required data, such as model and model parameters, are available from the corresponding author upon reasonable request.
Acknowledgments
This work was partially based on a project supported by the National Science Foundation (NSF) under Grant No. 2238639.
References
Abebe, Y. A., A. Ghorbani, I. Nikolic, N. Manojlovic, A. Gruhn, and Z. Vojinovic. 2020. “The role of household adaptation measures to reduce vulnerability to flooding: A coupled agent-based and flood modelling approach.” Hydrol. Earth Syst. Sci. Discuss. 2020 (Jul): 1–40. https://doi.org/10.5194/hess-2020-272.
Abebe, Y. A., A. Ghorbani, I. Nikolic, Z. Vojinovic, and A. Sanchez. 2019a. “A coupled flood-agent-institution modelling (CLAIM) framework for urban flood risk management.” Environ. Modell. Software 111 (Jan): 483–492. https://doi.org/10.1016/j.envsoft.2018.10.015.
Abebe, Y. A., A. Ghorbani, I. Nikolic, Z. Vojinovic, and A. Sanchez. 2019b. “Flood risk management in Sint Maarten–A coupled agent-based and flood modelling method.” J. Environ. Manage. 248 (Oct): 109317. https://doi.org/10.1016/j.jenvman.2019.109317.
Ahern, J. 2011. “From fail-safe to safe-to-fail: Sustainability and resilience in the new urban world.” Landscape Urban Plann. 100 (4): 341–343. https://doi.org/10.1016/j.landurbplan.2011.02.021.
Ahiablame, L., and R. Shakya. 2016. “Modeling flood reduction effects of low impact development at a watershed scale.” J. Environ. Manage. 171 (Apr): 81–91. https://doi.org/10.1016/j.jenvman.2016.01.036.
Ahiablame, L. M., B. A. Engel, and I. Chaubey. 2013. “Effectiveness of low impact development practices in two urbanized watersheds: Retrofitting with rain barrel/cistern and porous pavement.” J. Environ. Manage. 119 (Apr): 151–161. https://doi.org/10.1016/j.jenvman.2013.01.019.
An, L., M. Linderman, J. Qi, A. Shortridge, and J. Liu. 2005. “Exploring complexity in a human-environment system: An agent-based spatial model for multidisciplinary and multiscale integration.” Ann. Assoc. Am. Geogr. 95 (1): 54–79. https://doi.org/10.1111/j.1467-8306.2005.00450.x.
Bai, Y., N. Zhao, R. Zhang, and X. Zeng. 2018. “Storm water management of low impact development in urban areas based on SWMM.” Water 11 (1), https://doi.org/10.3390/w11010033.
Bandini, S., S. Manzoni, and G. Vizzari. 2009. “Agent based modeling and simulation: An informatics perspective.” J. Artif. Soc. Social Simul. 12 (4): 4.
Baptiste, A. K., C. Foley, and R. Smardon. 2015. “Understanding urban neighborhood differences in willingness to implement green infrastructure measures: A case study of Syracuse, NY.” Landscape Urban Plann. 136 (Apr): 1–12. https://doi.org/10.1016/j.landurbplan.2014.11.012.
Bates, B. C., S. W. Kundzewicz, and J. P. Palutikof. 2008. “Climate change and water: IPCC technical paper VI.” Accessed September 1, 2023. https://www.ipcc.ch/site/assets/uploads/2018/03/climate-change-water-en.pdf.
Berglund, E. Z. 2015. “Using agent-based modeling for water resources planning and management.” J. Water Resour. Plann. 141 (11): 04015025. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000544.
Bliss, D. J., R. D. Neufeld, and R. J. Ries. 2009. “Storm water runoff mitigation using a Green roof.” Environ. Eng. Sci. 26 (2): 407–418. https://doi.org/10.1089/ees.2007.0186.
Braden, J., J. Eheart, and R. Saleth. 1991. “Bargaining rules for a thin spot water market.” Land Econ. 67 (3): 326–339. https://doi.org/10.2307/3146428.
Carter, T., and L. Fowler. 2008. “Establishing green roof infrastructure through environmental policy instruments.” Environ. Manage. 42 (Jul): 151–164. https://doi.org/10.1007/s00267-008-9095-5.
CEMHS (Center for Emergency Management and Homeland Security). 2020. “The Spatial Hazard Events and Losses Database for the United States, V. 17.0.” ASU Center for Emergency Management and Homeland Security. Accessed September 1, 2022. http://www.sheldus.org.
Chaffin, B. C., W. D. Shuster, A. S. Garmestani, B. Furio, S. L. Albro, M. Gardiner, M. Spring, and O. O. Green. 2016. “A tale of two rain gardens: Barriers and bridges to adaptive management of urban stormwater in Cleveland, Ohio.” J. Environ. Manage. 183 (Dec): 431–441. https://doi.org/10.1016/j.jenvman.2016.06.025.
Charleston County. 2010. “History.” Charleston, SC Official Website. Accessed September 1, 2023. https://www.charleston-sc.gov/2010/History.
City of Charleston. 2015. Sea level rise strategy: Charleston, South Carolina. Charleston, SC: City of Charleston.
City of Charleston. 2023. “Charleston rainproof.” Accessed September 1, 2023. https://www.charleston-sc.gov/rainproof.
City of Charleston Information and Technology GIS Division. 2021a. “Buildings.” City of Charleston GIS. Accessed September 1, 2023. https://gis.charleston-sc.gov/.
City of Charleston Information and Technology GIS Division. 2021b. “Edge of pavement.” City of Charleston GIS. Accessed September 1, 2023. https://gis.charleston-sc.gov/.
City of Charleston Information and Technology GIS Division. 2021c. “Zoning map.” City of Charleston GIS. Accessed September 1, 2023. https://gis.charleston-sc.gov/.
Climate Engine. 2021. “ASCE grass reference evapotranspiration dataset.” Accessed September 1, 2023. https://app.climateengine.com/climateEngine.
Coleman, S., S. Hurley, D. Rizzo, C. Koliba, and A. Zia. 2018. “From the household to watershed: A cross-scale analysis of residential intention to adopt green stormwater infrastructure.” Landscape Urban Plann. 180 (Dec): 195–206. https://doi.org/10.1016/j.landurbplan.2018.09.005.
Davis, A. P. 2008. “Field performance of bioretention: Hydrology impacts.” J. Hydrol. Eng. 13 (2): 90–95. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:2(90).
Dawson, R. J., R. Peppe, and M. Wang. 2011. “An agent-based model for risk-based flood incident management.” Nat. Hazards 59 (Oct): 167–189. https://doi.org/10.1007/s11069-011-9745-4.
Eckart, K., Z. McPhee, and T. Bolisetti. 2018. “Multiobjective optimization of low impact development stormwater controls.” J. Hydrol. 562 (Jul): 564–576. https://doi.org/10.1016/j.jhydrol.2018.04.068.
Ellis, K., S. Whiteside, E. Smith, C. Berg, D. Caraco, S. Drescher, G. Hoffmann, B. Keppler, M. LaRocco, and A. Turner. 2014. “Low impact development in coastal South Carolina: A Planning and design guide.” Accessed September 1, 2023. http://www.northinlet.sc.edu/LID.
EPA. 2014. “Climate change indicators in the United States, 2014 3rd Edition.” Accessed September 1, 2023. www.epa.gov/climatechange/indicators.
EPA. 2018. “Urban runoff: Low impact development.” Accessed September 1, 2023. https://www.epa.gov/nps/urban-runoff-low-impact-development.
EPA and L. A. Rossman. 2015. “Storm water management model user’s manual version 5.1.” Accessed September 1, 2023. https://nepis.epa.gov/Exe/ZyPDF.cgi?Dockey=P100N3J6.TXT.
Farooqui, A. D., and M. A. Niazi. 2016. “Game theory models for communication between agents: A review.” Complex Adapt. Syst. Model. 4 (13): 1–31. https://doi.org/10.1186/s40294-016-0026-7.
FEMA. 2021. “HAZUS.” Accessed September 1, 2023. https://msc.fema.gov/portal/resources/hazus.
Gately, D. 1974. “Sharing the gains from regional cooperation: A game theoretic application to planning investment in electric power.” Int. Econ. Rev. 15 (1): 195–208.
Ghodsi, S. H., Z. Zahmatkesh, E. Goharian, R. Kerachian, and Z. Zhu. 2020. “Optimal design of low impact development practices in response to climate change.” J. Hydrol. 580 (Jan): 124266. https://doi.org/10.1016/j.jhydrol.2019.124266.
Goharian, E., and S. J. Burian. 2018. “Developing an integrated framework to build a decision support tool for urban water management.” J. Hydroinf. 20 (3): 708–727. https://doi.org/10.2166/hydro.2018.088.
Goharian, E., S. J. Burian, T. Bardsley, and C. Strong. 2016. “Incorporating potential severity into vulnerability assessment of water supply systems under climate change conditions.” J. Water Resour. Plann. Manage. 142 (2): 04015051. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000579.
Hart, S. 2008. “Shapley value.” In The new Palgrave dictionary of economics. London: Palgrave Macmillan.
Homer, C., J. Dewitz, L. Yang, S. Jin, P. Danielson, G. Xian, J. Coulston, N. Herold, J. Wickham, and K. Megown. 2015. “Completion of the 2011 national land cover database for the conterminous United States—Representing a decade of land cover change information.” Photogramm. Eng. Remote Sens. 81 (5): 345–354.
Howe, G. M. 1950. “Map of drainage system Charleston S.C.” Accessed September 1, 2023. https://www.charleston-sc.gov/DocumentCenter/View/5558/drainage1950?bidId=.
Hyun, J. Y., S. Y. Huang, Y. C. E. Yang, V. Tidwell, and J. Macknick. 2019. “Using a coupled agent-based modeling approach to analyze the role of risk perception in water management decisions.” Hydrol. Earth Syst. Sci. 23 (5): 2261–2278. https://doi.org/10.5194/HESS-23-2261-2019.
Ichihara, K., and J. P. Cohen. 2010. “New York City property values: What is the impact of green roofs on rental pricing?” Lett. Spatial Resour. Sci. 4 (1): 21–30. https://doi.org/10.1007/S12076-010-0046-4.
IPCC (Intergovernmental Panel on Climate Change). 2014. “Climate change 2014: Synthesis report: Contribution of working groups I, II and III to the fifth assessment report of the intergovernmental panel on climate change.” Accessed September 1, 2023. http://www.ipcc.ch.
Jones, M. P., and W. F. Hunt. 2010. “Performance of rainwater harvesting systems in the southeastern United States.” Resour. Conserv. Recycl. 54 (Aug): 623–629. https://doi.org/10.1016/j.resconrec.2009.11.002.
Just, R. E., and S. Netanyahu. 2004. “Implications of ‘Victim Pays’ infeasibilities for interconnected games with an illustration for aquifer sharing under unequal access costs.” Water Resour. Res. 40 (5). https://doi.org/10.1029/2003WR002528.
Kilgour, D. M., A. Nishikori, and N. Okada. 1988. “Control regulation of water pollution: An analysis using game theory.” J. Environ. Manage. 27 (2): 179–194.
Kim, J., J. Lee, Y. Song, H. Han, and J. Joo. 2018. “Modeling the runoff reduction effect of low impact development installations in an industrial area, South Korea.” Water 10 (8): 968. https://doi.org/10.3390/w10080967.
Lawyer, C. 2022. Coalitional game theory for stormwater management and Green infrastructure practices. Columbia, SC: Univ. of South Carolina.
Loucks, D. P., and E. van Beek. 2017. “Water resources planning and management: An overview.” In Water resource systems planning and management. Cham, Switzerland: Springer.
Macal, C. M., and M. J. North. 2010. “Tutorial on agent-based modelling and simulation.” J. Simul. 4 (3): 151–162. https://doi.org/10.1057/jos.2010.3.
Macro, K., L. S. Matott, A. Rabideau, H. Ghodsi, and Z. Zhu. 2019. “OSTRICH-SWMM: A new multi-objective optimization tool for green infrastructure planning with SWMM.” Environ. Modell. Software 113 (Mar): 42–47. https://doi.org/10.1016/j.envsoft.2018.12.004.
Madani, K. 2010. “Game theory and water resources.” J. Hydrol. 381 (3–4): 225–238. https://doi.org/10.1016/j.jhydrol.2009.11.045.
Manson, S. M. 2001. “Calibration, verification, and validation.” In Proc., Meeting the Challenge of Complexity: Proc. of a Special Workshop on Land-Use/Land-Cover Change, 42–46. Santa Barbara, CA: Center for Spatially Integrated Social Science at Univ. of California at Santa Barbara.
Michaelis, T., L. Brandimarte, M. Mazzoleni, S. Archfield, and S. Pande. 2020. “Capturing flood-risk dynamics with a coupled agent-based and hydraulic modelling framework.” Hydrol. Sci. J. 65 (9): 1458–1473. https://doi.org/10.1080/02626667.2020.1750617.
Milly, P. C. D., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. Kundzewicz, D. P. Lettenmaier, and R. J. Stouffer. 2008. “Stationarity is dead: Whither water management?” Science 319 (5863): 573–574. https://doi.org/10.1126/science.1151915.
Miquel, S., B. van Velzen, H. Hamers, and H. Norde. 2006. “Fixed tree games with multilocated players.” Netw. Int. J. 47 (2): 93–101.
Molnar, C. 2022. “Shapley values.” In Interpretable machine learning: A guide for making black box models explainable. 2nd ed. La Jolla, CA: International Machine Learning Society.
Montalto, F. A., T. A. Bartrand, A. M. Waldman, K. A. Travaline, C. H. Loomis, C. McAfee, J. M. Geldi, G. J. Riggall, and L. M. Boles. 2013. “Decentralised Green infrastructure: The importance of stakeholder behaviour in determining spatial and temporal outcomes.” Struct. Infrastruct. Eng. 9 (12): 1187–1205. https://doi.org/10.1080/15732479.2012.671834.
Morris, J. T., and K. A. Renken. 2020. “Past, present, and future nuisance flooding on the Charleston peninsula.” PLoS One 15 (9), https://doi.org/10.1371/journal.pone.0238770.
Multi-Resolution Land Characteristics Consortium. 2011. “National Land Cover Database 2011.” Accessed September 1, 2023. https://www.mrlc.gov/data/legends/national-land-cover-database-2011-nlcd2011-legend.
Myerson, R. B. 1991. Game theory: Analysis of conflict. Cambridge, MA: Harvard University Press.
Niazi, M. A., and A. Hussain. 2012. Cognitive agent-based computing–I: A unified framework for modeling complex adaptive systems using agent-based & complex network-based methods. New York: Springer.
NOAA (National Oceanic and Atmospheric Administration). 2015. “Observed water levels at 8665530, Charleston, Cooper River Entrance SC.” Tides & Currents. Accessed September 1, 2023. https://tidesandcurrents.noaa.gov/waterlevels.html?id=8665530.
NOAA (National Oceanic and Atmospheric Administration). 2016. “The historic South Carolina Floods of October 1-5, 2015.” Accessed September 1, 2023. https://www.weather.gov/media/publications/assessments/SCFlooding_072216_Signed_Final.pdf.
NOAA (National Oceanic and Atmospheric Administration). 2021. “What percentage of the American population lives near the coast? Ocean facts.” Accessed September 1, 2023. http://oceanservice.noaa.gov/facts/population.htmlv.
NOAA (National Oceanic and Atmospheric Administration). 2022. “Accessed September 1, 2023. U.S. coastline to see up to a foot of sea level rise by 2050.” https://www.noaa.gov/news-release/us-coastline-to-see-up-to-foot-of-sea-level-rise-by-2050.
Parker, D. C., S. M. Manson, M. A. Janssen, M. J. Hoffmann, and P. Deadman. 2003. “Multi-agent systems for the simulation of land-use and land-cover change: A review.” Ann. Assoc. Am. Geogr. 93 (2): 314–337. https://doi.org/10.1111/1467-8306.9302004.
Parrachino, I., A. Dinar, and F. Patrone. 2006. “Cooperative game theory and its application to natural, environmental, and water resource issues: 3. Application to water resources.” In Application to water resources (november 2006). World bank policy research working paper, 4074. Amsterdam, Netherlands: Elsevier.
Patt, A., and B. Siebenhüner. 2005. “Agent based modeling and adaptation to climate change.” Q. J. Econ. 74 (2): 310–320. https://doi.org/10.3790/vjh.74.2.310.
Peterson, B., and M. Porter. 2020. Charleston and the South Carolina coast flooded record 89 times in 2019. Charleston, SC: Post and Courier.
Platt, S. E. 2020. “Urban dialectics, misrememberings, and memory-work: The Halsey map of Charleston, South Carolina.” Int. J. Hist. Archaeol. 24 (4): 989–1014. https://doi.org/10.1007/s10761-019-00533-8.
Qin, H. P., Z. Li, and G. Fu. 2013. “The effects of low impact development on urban flooding under different rainfall characteristics.” J. Environ. Manage. 129 (Nov): 577–585. https://doi.org/10.1016/j.jenvman.2013.08.026.
Raei, E., M. Reza Alizadeh, M. Reza Nikoo, and J. Adamowski. 2019. “Multi-objective decision-making for green infrastructure planning (LID-BMPs) in urban storm water management under uncertainty.” J. Hydrol. 579 (Dec): 124091. https://doi.org/10.1016/j.jhydrol.2019.124091.
Randall, M., J. Støvring, M. Henrichs, and M. B. Jensen. 2020. “Comparison of SWMM evaporation and discharge to in-field observations from lined permeable pavements.” Urban Water J. 17 (6): 491–502. https://doi.org/10.1080/1573062X.2020.1776737.
Shapley, L. S. 1953. “Stochastic games.” Proc. Natl. Acad. Sci. USA 39 (10): 1095–1100. https://doi.org/10.1073/pnas.39.10.1095.
Shoham, Y., and K. Leyton-Brown. 2008. Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge, UK: Cambridge University Press.
Simpson, M. G. 2010. Low impact development modeling to manage urban storm water runoff and restore predevelopment site hydrology. Fort Collins, CO: Colorado State Univ.
Støvring, J., T. Dam, and M. B. Jensen. 2018. “Hydraulic performance of lined permeable pavement systems in the built environment.” Water 10 (5): 587. https://doi.org/10.3390/w10050587.
Tanim, A. H., W. McKinnie, and E. Goharian. 2022. Enhanced simulation of coastal compound flooding through fully-coupled modeling framework. New York: Authorea Preprints.
Tank Depot. 2022a. “2000 Gallon plastic water storage tank.” Accessed September 1, 2023. https://www.tank-depot.com/water-tanks/water-tanks-by-gallon-capacity/2000-gallon-water-tanks/.
Tank Depot. 2022b. “5000 Gallon Norwesco plastic potable water storage tank.” Accessed September 1, 2023. https://www.tank-depot.com/water-tanks/water-tanks-by-gallon-capacity/5000-gallon-water-tanks/.
Tupper, J. A. 2012. A cost comparison of a low impact development to traditional residential development along the South Carolina Coast. Columbia, SC: Univ. of South Carolina.
Ureta, J., M. Motallebi, A. E. Scaroni, S. Lovelace, and J. C. Ureta. 2021. “Understanding the public’s behavior in adopting green stormwater infrastructure.” Sustainable Cities Soc. 69 (Jun): 102815. https://doi.org/10.1016/j.scs.2021.102815.
US Global Change Research Program. 2017. “Summary findings of the fourth national climate assessment.” Accessed September 1, 2023. https://nca2018.globalchange.gov/.
Van De Meene, S. J., R. R. Brown, and M. A. Farrelly. 2009. “Exploring sustainable urban water governance: A case study of institutional capacity.” Water Sci. Technol. 59 (10): 1921–1928. https://doi.org/10.2166/wst.2009.190.
Voicu, I., and V. Been. 2008. “The effect of community gardens on neighboring property values.” Real Estate Econ. 36 (2): 241–283. https://doi.org/10.1111/j.1540-6229.2008.00213.x.
Von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton, NJ: Princeton University Press.
Wagenaar, D. J. 2012. The significance of flood duration for flood damage assessment. Delft, Netherlands: Delft Univ. of Technology.
Wang, M., D. Zhang, S. Lou, Q. Hou, Y. Liu, Y. Cheng, J. Qi, and S. K. Tan. 2019. “Assessing hydrological effects of bioretention cells for urban stormwater runoff in response to climatic changes.” Water 11 (5): 1–20. https://doi.org/10.3390/w11050997.
Wayfair. 2022. “60 Gallons Gal: Weather resistant plastic drainable dual overflow planter rain barrel.” https://www.wayfair.com/storage-organization/pdp/60-gal-weather-resistan-plastic-drainable-rain-barrel-tgrb1002.html.
Weather Underground. 2015. “Charleston AFB, SC weather history.” Weather Underground. Accessed September 1, 2023. https://www.wunderground.com/history/daily/us/sc/charleston-air-force-base/KCHS/date/2015-10-1.
William, R., J. Garg, and A. S. Stillwell. 2017. “A game theory analysis of green infrastructure stormwater management policies.” Water Resour. Res. 53 (9): 8003–8019. https://doi.org/10.1002/2017WR021024.
William, R., A. Goodwell, M. Richardson, P. V. V. Le, P. Kumar, and A. S. Stillwell. 2016. “An environmental cost-benefit analysis of alternative green roofing strategies.” Ecol. Eng. 95 (Oct): 1–9. https://doi.org/10.1016/j.ecoleng.2016.06.091.
Williams, E., and T. Moore. 2020. “Rising tides take Charleston to the brim, threatening businesses.” The Post and Courier, October 19, 2020.
Xu, T., H. Jia, Z. Wang, X. Mao, and C. Xu. 2017. “SWMM-based methodology for block-scale LID-BMPs planning based on site-scale multi-objective optimization: A case study in Tianjin.” Front. Environ. Sci. Eng. 11 (Apr): 1–12. https://doi.org/10.1007/s11783-017-0934-6.
Yang, L. E., J. Scheffran, D. Süsser, R. Dawson, and Y. D. Chen. 2018. “Assessment of flood losses with household responses: Agent-based simulation in an urban catchment area.” Environ. Model. Assess. 23 (4): 369–388. https://doi.org/10.1007/s10666-018-9597-3.
York, C., E. Goharian, and S. J. Burian. 2015. “Impacts of large-scale stormwater green infrastructure implementation and climate variability on receiving water response in the Salt Lake City area.” Am. J. Environ. Sci. 11 (4): 278–292. https://doi.org/10.3844/ajessp.2015.278.292.
Zahmatkesh, Z., J. B. Steven, M. Karamouz, H. Tavakol-Davani, and E. Goharian. 2014. “Low-impact development practices to mitigate climate change effects on urban stormwater runoff: Case study of New York City.” J. Irrig. Drain. 14 (1): 04014043. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000770.
Zhang, S., and Y. Guo. 2014. “SWMM simulation of the storm water volume control performance of permeable pavement systems.” J. Hydraul. Eng. 20 (8): 06014010. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001092.
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Journal of Water Resources Planning and Management
Volume 150 • Issue 1 • January 2024
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© 2023 American Society of Civil Engineers.
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Received: Sep 12, 2022
Accepted: Aug 14, 2023
Published online: Oct 17, 2023
Published in print: Jan 1, 2024
Discussion open until: Mar 17, 2024
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