Importance of Copula-Based Bivariate Rainfall Intensity-Duration-Frequency Curves for an Urbanized Catchment Incorporating Climate Change
Publication: Journal of Hydrologic Engineering
Volume 28, Issue 7
Abstract
The intensity-duration-frequency (IDF) curve is a critical input for designing hydraulic infrastructure such as stormwater drainage systems. The last few decades have witnessed drastic changes in rainfall patterns and changes in their extremes, mostly associated with the impact of climate change. Therefore, it is important to study the possible drift in the IDF curve associated with the changing trends in historical rainfall data and future climatic conditions. Based on the understanding of the negative correlation between rainfall intensity and duration, this study used a bivariate copula-based approach for IDF curve development (considering historical rainfall data) and compared it with the conventional empirical models and univariate frequency analysis. The study identified the Frank copula (from 24 candidate copulas) with its parameters estimated by Bayesian inference and a hybrid-evolution Monte Carlo Markov Chain. In addition, the IDF curve was developed for four future climate scenarios corresponding to three different time periods. The proposed methodology was demonstrated for an urban catchment in Northeast India, for which the future climate scenarios were not considered for previous IDF curve development. The rainfall intensity from one of the empirical models and univariate analysis compared well with the corresponding values obtained using the IDF developed using bivariate analysis for short durations (). Both the time periods and different climate scenarios had a significant influence on the rainfall intensities compared to the historical bivariate IDF data. The recommendation from this study for this area is that to account for the influence of near future climate change on infrastructure with a design life of 50 years and , the representative concentration pathway (RCP) 6.0 scenario would yield the critical IDF curve. For long-term planning with a design life , it is desirable to consider the IDF curve based on the RCP 8.5 scenario. For the intermittent period P2 (2048–2074), both RCP 6.0 and RCP 8.5 exhibited a similar trend in terms of rainfall intensity. The results from this study and the literature recommend comprehensive studies on specific urban catchments to incorporate the impact of climate change on the IDF curve for assessing the adequacy of hydraulic structures from a future perspective.
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Data Availability Statement
Some data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions. Rainfall data used in this study is collected from the India Meteorological Department (IMD), Guwahati, Assam, India. Sharing this data with a third party needs permission from the IMD.
References
Agilan, V., and N. Umamahesh. 2016. “Is the covariate based non-stationary rainfall IDF curve capable of encompassing future rainfall changes?” J. Hydrol. 541 (Part B): 1441–1455. https://doi.org/10.1016/j.jhydrol.2016.08.052.
Agilan, V., and N. V. Umamahesh. 2017. “Non-stationary rainfall intensity-duration-frequency relationship: A comparison between annual maximum and partial duration series.” Water Resour. Manage. 31 (6): 1825–1841. https://doi.org/10.1007/s11269-017-1614-9.
Akaike, H. 1974. “A new look at the statistical model identification.” IEEE Trans. Autom. Control 19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.
Andimuthu, R., P. Kandasamy, B. V. Mudgal, A. Jeganathan, A. Balu, and G. Sankar. 2019. “Performance of urban storm drainage network under changing climate scenarios: Flood mitigation in Indian coastal city.” Sci. Rep. 9 (1): 7783. https://doi.org/10.1038/s41598-019-43859-3.
Ariff, N., A. Jemain, K. Ibrahim, and W. W. Zin. 2012. “IDF relationships using bivariate copula for storm events in peninsular Malaysia.” J. Hydrol. 470–471 (Nov): 158–171. https://doi.org/10.1016/j.jhydrol.2012.08.045.
Babu, R., K. Tejwani, M. Agarwal, and L. Bhushan. 1979. Rainfall intensity-duration-return period equations and nomographs of India. Bulletin No. 3. Dehradun, India: Central Soil and Water Conservation Research and Training Institute, ICAR.
Bairwa, A. K., R. Khosa, and R. Maheswaran. 2016. “Developing intensity duration frequency curves based on scaling theory using linear probability weighted moments: A case study from India.” J. Hydrol. 542 (Nov): 850–859. https://doi.org/10.1016/j.jhydrol.2016.09.056.
Bernard, M. M. 1932. “Formulas for rainfall intensities of long duration.” Trans. Am. Soc. Civ. Eng. 96 (1): 592–606. https://doi.org/10.1061/TACEAT.0004323.
Bevacqua, E., D. Maraun, I. H. Haff, M. Widmann, and M. Vrac. 2017. “Multivariate statistical modelling of compound events via pair-copula constructions: Analysis of floods in Ravenna (Italy).” Hydrol. Earth Syst. Sci. 21 (6): 2701–2723. https://doi.org/10.5194/hess-21-2701-2017.
Bezak, N., M. Šraj, and M. Mikoš. 2016. “Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides.” J. Hydrol. 541 (Part A): 272–284. https://doi.org/10.1016/j.jhydrol.2016.02.058.
Cancelliere, A. 2017. “Non stationary analysis of extreme events.” Water Resour. Manage. 31 (10): 3097–3110. https://doi.org/10.1007/s11269-017-1724-4.
Cannon, A. J., S. R. Sobie, and T. Q. Murdock. 2015. “Bias correction of GCM precipitation by quantile mapping: How well do methods preserve changes in quantiles and extremes?” J. Clim. 28 (17): 6938–6959. https://doi.org/10.1175/JCLI-D-14-00754.1.
Chandra, R., U. Saha, and P. Mujumdar. 2015. “Model and parameter uncertainty in IDF relationships under climate change.” Adv. Water Resour. 79 (May): 127–139. https://doi.org/10.1016/j.advwatres.2015.02.011.
Chaudhuri, R. R., and P. Sharma. 2020. “Addressing uncertainty in extreme rainfall intensity for semi-arid urban regions: Case study of Delhi, India.” Nat. Hazards 104 (3): 2307–2324. https://doi.org/10.1007/s11069-020-04273-5.
Cheng, L., and A. AghaKouchak. 2014. “Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate.” Sci. Rep. 4 (1): 7093. https://doi.org/10.1038/srep07093.
Cheng, L., A. AghaKouchak, E. Gilleland, and R. W. Katz. 2014. “Non-stationary extreme value analysis in a changing climate.” Clim. Change 127 (2): 353–369. https://doi.org/10.1007/s10584-014-1254-5.
Cook, L. M., S. McGinnis, and C. Samaras. 2020. “The effect of modeling choices on updating intensity-duration-frequency curves and stormwater infrastructure designs for climate change.” Clim. Change 159 (2): 289–308. https://doi.org/10.1007/s10584-019-02649-6.
Deng, Z., X. Qiu, J. Liu, N. Madras, X. Wang, and H. Zhu. 2015. “Trend in frequency of extreme precipitation events over ontario from ensembles of multiple GCMs.” Clim. Dyn. 46 (9–10): 2909–2921. https://doi.org/10.1007%2Fs00382-015-2740-9.
de Souza Costa, C. E. A., C. J. C. Blanco, and J. F. de Oliveira-Júnior. 2019. “IDF curves for future climate scenarios in a locality of the Tapajós Basin, Amazon, Brazil.” J. Water Clim. Change 11 (3): 760–770. https://doi.org/10.2166/wcc.2019.202.
Douglas, E. M., and C. A. Fairbank. 2011. “Is precipitation in Northern New England becoming more extreme? Statistical analysis of extreme rainfall in Massachusetts, New Hampshire, and Maine and updated estimates of the 100-year storm.” J. Hydrol. Eng. 16 (3): 203–217. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000303.
Dourte, D., S. Shukla, P. Singh, and D. Haman. 2013. “Rainfall intensity-duration-frequency relationships for Andhra Pradesh, India: Changing rainfall patterns and implications for runoff and groundwater recharge.” J. Hydrol. Eng. 18 (3): 324–330. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000625.
Ganguli, P., and P. Coulibaly. 2019. “Assessment of future changes in intensity-duration-frequency curves for southern Ontario using north American (NA)-CORDEX models with nonstationary methods.” J. Hydrol.: Reg. Stud. 22 (Apr): 100587. https://doi.org/10.1016/j.ejrh.2018.12.007.
Gebru, T. A. 2020. “Rainfall intensity-duration-frequency relations under changing climate for selected stations in the Tigray region, Ethiopia.” J. Hydrol. Eng. 25 (11): 05020041. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001999.
Genest, C., and J. MacKay. 1986. “The joy of copulas: Bivariate distributions with uniform marginal.” Am. Stat. 40 (4): 280. https://doi.org/10.2307/2684602.
Genest, C., and L.-P. Rivest. 1993. “Statistical inference procedures for bivariate archimedean copulas.” J. Am. Stat. Assoc. 88 (423): 1034–1043. https://doi.org/10.1080/01621459.1993.10476372.
Hassanzadeh, E., A. Nazemi, and A. Elshorbagy. 2014. “Quantile-based downscaling of precipitation using genetic programming: Application to IDF curves in Saskatoon.” J. Hydrol. Eng. 19 (5): 943–955. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000854.
Herath, S. M., P. R. Sarukkalige, and V. T. V. Nguyen. 2016. “A spatial temporal downscaling approach to development of IDF relations for Perth airport region in the context of climate change.” Hydrol. Sci. J. 61 (11): 2061–2070. https://doi.org/10.1080/02626667.2015.1083103.
Hosseinzadehtalaei, P., H. Tabari, and P. Willems. 2020. “Climate change impact on short-duration extreme precipitation and intensity–duration–frequency curves over Europe.” J. Hydrol. 590 (Nov): 125249. https://doi.org/10.1016/j.jhydrol.2020.125249.
IPCC (Intergovernmental Panel on Climate Change). 2007. Contribution of working groups I, II and III to the fourth assessment report of the intergovernmental panel on climate change., edited by R. K. Pachauri and L. A. Meyer. Geneva: IPCC.
IPCC (Intergovernmental Panel on 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, 151(10.1017)., edited by R. K. Pachauri and L. A. Meyer. Geneva: IPCC.
Jane, R., L. Cadavid, J. Obeysekera, and T. Wahl. 2020. “Multivariate statistical modelling of the drivers of compound flood events in South Florida.” Nat. Hazards Earth Syst. Sci. 20 (10): 2681–2699. https://doi.org/10.5194/nhess-20-2681-2020.
Kao, S.-C., and R. S. Govindaraju. 2007. “A bivariate frequency analysis of extreme rainfall with implications for design.” J. Geophys. Res.: Atmos. 112 (D13). https://doi.org/10.1029/2007JD008522.
Kao, S.-C., and R. S. Govindaraju. 2008. “Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas.” Water Resour. Res. 44 (2). https://doi.org/10.1029/2007WR006261.
Khazaei, M. R. 2021. “A robust method to develop future rainfall IDF curves under climate change condition in two major basins of Iran.” Theor. Appl. Climatol. 144 (1–2): 179–190. https://doi.org/10.1007/s00704-021-03540-0.
Kothyari, U. C., and R. J. Garde. 1992. “Rainfall intensity-duration-frequency formula for India.” J. Hydraul. Eng. 118 (2): 323–336. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:2(323).
Kourtis, I. M., I. Nalbantis, G. Tsakiris, B. E. Psiloglou, and V. A. Tsihrintzis. 2022. “Updating IDF curves under climate change: Impact on rainfall-induced runoff in urban basins.” Water Resour. Manage. 1–26. https://doi.org/10.1007/s11269-022-03252-8.
Koutsoyiannis, D., D. Kozonis, and A. Manetas. 1998. “A mathematical framework for studying rainfall intensity-duration-frequency relationships.” J. Hydrol. 206 (1–2): 118–135. https://doi.org/10.1016/S0022-1694(98)00097-3.
Kuo, C.-C., T. Y. Gan, and M. Gizaw. 2015. “Potential impact of climate change on intensity duration frequency curves of central Alberta.” Clim. Change 130 (2): 115–129. https://doi.org/10.1007/s10584-015-1347-9.
Kurowicka, D., and W. T. van Horssen. 2015. “On an interaction function for copulas.” J. Multivariate Anal. 138 (Jun): 127–142. https://doi.org/10.1016/j.jmva.2014.12.012.
Lee, T., and C. Jeong. 2014. “Nonparametric statistical temporal downscaling of daily precipitation to hourly precipitation and implications for climate change scenarios.” J. Hydrol. 510 (Mar): 182–196. https://doi.org/10.1016/j.jhydrol.2013.12.027.
Lee, T., C. Son, M. Kim, S. Lee, and S. Yoon. 2020. “Climate change adaptation to extreme rainfall events on a local scale in Namyangju, South Korea.” J. Hydrol. Eng. 25 (5): 05020005. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001906.
Mailhot, A., I. Beauregard, G. Talbot, D. Caya, and S. Biner. 2011. “Future changes in intense precipitation over Canada assessed from multi-model NARCCAP ensemble simulations.” Int. J. Climatol. 32 (8): 1151–1163. https://doi.org/10.1002/joc.2343.
Mailhot, A., S. Duchesne, D. Caya, and G. Talbot. 2007. “Assessment of future change in intensity–duration–frequency (IDF) curves for Southern Quebec using the Canadian regional climate model (CRCM).” J. Hydrol. 347 (1–2): 197–210. https://doi.org/10.1016/j.jhydrol.2007.09.019.
Mamo, T. G. 2015. “Evaluation of the potential impact of rainfall intensity variation due to climate change on existing drainage infrastructure.” J. Irrig. Drain. Eng. 141 (10): 05015002. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000887.
Maraun, D. 2013. “Bias correction, quantile mapping, and downscaling: Revisiting the inflation issue.” J. Clim. 26 (6): 2137–2143. https://doi.org/10.1175/JCLI-D-12-00821.1.
Mirhosseini, G., P. Srivastava, and X. Fang. 2014. “Developing rainfall intensity-duration-frequency curves for Alabama under future climate scenarios using artificial neural networks.” J. Hydrol. Eng. 19 (11): 04014022. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000962.
Moftakhari, H., J. E. Schubert, A. AghaKouchak, R. A. Matthew, and B. F. Sanders. 2019. “Linking statistical and hydrodynamic modeling for compound flood hazard assessment in tidal channels and estuaries.” Adv. Water Resour. 128 (Jun): 28–38. https://doi.org/10.1016/j.advwatres.2019.04.009.
Mohebbi, A., S. Akbariyeh, M. Maruf, Z. Wu, J. C. Acuna, and K. R. Adams. 2021. “Development of rainfall intensity-duration-frequency curves based on dynamically downscaled climate data: Arizona case study.” J. Hydrol. Eng. 26 (5): 05021005. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002068.
Nelsen, R. B. 1999. “Archimedean copulas.” In An introduction to copulas, 89–124. New York: Springer.
Nguyen, T.-H., and V.-T.-V. Nguyen. 2020. “Linking climate change to urban storm drainage system design: An innovative approach to modeling of extreme rainfall processes over different spatial and temporal scales.” J. Hydro-environ. Res. 29 (Mar): 80–95. https://doi.org/10.1016/j.jher.2020.01.006.
Nguyen, V.-T.-V., T.-D. Nguyen, and A. Cung. 2007. “A statistical approach to downscaling of sub-daily extreme rainfall processes for climate-related impact studies in urban areas.” Water Sci. Technol. Water Supply 7 (2): 183–192. https://doi.org/10.2166/ws.2007.053.
Noor, M., T. Ismail, E.-S. Chung, S. Shahid, and J. Sung. 2018. “Uncertainty in rainfall intensity duration frequency curves of peninsular Malaysia under changing climate scenarios.” Water 10 (12): 1750. https://doi.org/10.3390/w10121750.
Paola, F. D., M. Giugni, M. Topa, and E. Bucchignani. 2014. “Intensity-duration-frequency (IDF) rainfall curves, for data series and climate projection in African cities.” Springerplus 3 (1): 133. https://doi.org/10.1186/2193-1801-3-133.
Pereira, M. J. M. G., L. F. S. Fernandes, E. M. B. Macário, S. M. Gaspar, and J. G. Pinto. 2015. “Climate change impacts in the design of drainage systems: Case study of Portugal.” J. Irrig. Drain. Eng. 141 (2): 05014009. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000788.
Rahmani, M. A., and M. Zarghami. 2013. “A new approach to combine climate change projections by ordered weighting averaging operator: Applications to northwestern provinces of Iran.” Global Planet. Change 102 (Mar): 41–50. https://doi.org/10.1016/j.gloplacha.2013.01.007.
Rajeevan, M., J. Bhate, and A. K. Jaswal. 2008. “Analysis of variability and trends of extreme rainfall events over India using 104 years of gridded daily rainfall data.” Geophys. Res. Lett. 35 (18). https://doi.org/10.1029/2008GL035143.
Requena, A. I., D. H. Burn, and P. Coulibaly. 2019. “Pooled frequency analysis for intensity–duration–frequency curve estimation.” Hydrol. Processes 33 (15): 2080–2094. https://doi.org/10.1002/hyp.13456.
Sadegh, M., E. Ragno, and A. AghaKouchak. 2017. “Multivariate copula analysis toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework.” Water Resour. Res. 53 (6): 5166–5183. https://doi.org/10.1002/2016WR020242.
Salas, J. D., and J. Obeysekera. 2014. “Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events.” J. Hydrol. Eng. 19 (3): 554–568. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000820.
Salvadori, G., and C. D. Michele. 2004. “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res. 40 (12): W12511. https://doi.org/10.1029/2004WR003133.
Sarhadi, A., D. H. Burn, M. C. Ausín, and M. P. Wiper. 2016. “Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula.” Water Resour. Res. 52 (3): 2327–2349. https://doi.org/10.1002/2015WR018525.
Schwarz, G. 1978. “Estimating the dimension of a model.” Ann. Stat. 6 (2): 461–464. https://doi.org/10.1214/aos/1176344136.
Sharma, D., A. D. Gupta, and M. S. Babel. 2007. “Spatial disaggregation of bias-corrected GCM precipitation for improved hydrologic simulation: Ping river basin, Thailand.” Hydrol. Earth Syst. Sci. 11 (4): 1373–1390. https://doi.org/10.5194/hess-11-1373-2007.
Sherman, C. W. 1931. “Frequency and intensity of excessive rainfalls at Boston, Massachusetts.” Trans. Am. Soc. Civ. Eng. 95 (1): 951–960. https://doi.org/10.1061/TACEAT.0004286.
Shrestha, A., M. Babel, S. Weesakul, and Z. Vojinovic. 2017. “Developing intensity–duration–frequency (IDF) curves under climate change uncertainty: The case of Bangkok, Thailand.” Water 9 (2): 145. https://doi.org/10.3390/w9020145.
Simonovic, S. P., A. Schardong, and D. Sandink. 2017. “Mapping extreme rainfall statistics for Canada under climate change using updated intensity-duration-frequency curves.” J. Water Resour. Plann. Manage. 143 (3): 04016078. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000725.
Singh, R., D. S. Arya, A. K. Taxak, and Z. Vojinovic. 2016. “Potential impact of climate change on rainfall intensity-duration-frequency curves in Roorkee, India.” Water Resour. Manage. 30 (13): 4603–4616. https://doi.org/10.1007/s11269-016-1441-4.
Singh, V. P., and L. Zhang. 2007. “IDF curves using the Frank Archimedean copula.” J. Hydrol. Eng. 12 (6): 651–662. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:6(651).
Sklar, M. 1959. “Fonctions de repartition an dimensions et leurs marges.” Publ. Inst. Stat. Univ. Paris 8: 229–231.
Soltani, S., P. Almasi, R. Helfi, R. Modarres, P. M. Esfahani, and M. G. Dehno. 2020. “A new approach to explore climate change impact on rainfall intensity–duration–frequency curves.” Theor. Appl. Climatol. 142 (Aug): 911–928. https://doi.org/10.1007/s00704-020-03309-x.
Srivastav, R. K., A. Schardong, and S. P. Simonovic. 2014. “Equidistance quantile matching method for updating IDFCurves under climate change.” Water Resour. Manage. 28 (9): 2539–2562. https://doi.org/10.1007/s11269-014-0626-y.
Switzman, H., T. Razavi, S. Traore, P. Coulibaly, D. H. Burn, J. Henderson, E. Fausto, and R. Ness. 2017. “Variability of future extreme rainfall statistics: Comparison of multiple IDF projections.” J. Hydrol. Eng. 22 (10): 04017046. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001561.
Uraba, M. B., L. N. Gunawardhana, G. A. Al-Rawas, and M. S. Baawain. 2019. “A downscaling-disaggregation approach for developing IDF curves in arid regions.” Environ. Monit. Assess. 191 (4): 1–17. https://doi.org/10.1007/s10661-019-7385-4.
Uttarwar, S. B., S. D. Barma, and A. Mahesha. 2020. “Bivariate modeling of hydroclimatic variables in humid tropical coastal region using Archimedean copulas.” J. Hydrol. Eng. 25 (9): 05020026. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001981.
Vinnarasi, R., and C. Dhanya. 2019. “Bringing realism into a dynamic copula-based non-stationary intensity-duration model.” Adv. Water Resour. 130 (Aug): 325–338. https://doi.org/10.1016/j.advwatres.2019.06.009.
Vinnarasi, R., and C. T. Dhanya. 2016. “Changing characteristics of extreme wet and dry spells of Indian monsoon rainfall.” J. Geophys. Res.: Atmos. 121 (5): 2146–2160. https://doi.org/10.1002/2015JD024310.
Vittal, H., S. Karmakar, and S. Ghosh. 2013. “Diametric changes in trends and patterns of extreme rainfall over India from pre-1950 to post-1950.” Geophys. Res. Lett. 40 (12): 3253–3258. https://doi.org/10.1002/grl.50631.
Vu, M. T., S. V. Raghavan, J. Liu, and S.-Y. Liong. 2018. “Constructing short-duration IDF curves using coupled dynamical-statistical approach to assess climate change impacts.” Int. J. Climatol. 38 (6): 2662–2671. https://doi.org/10.1002/joc.5451.
Wang, X., M. Gebremichael, and J. Yan. 2010. “Weighted likelihood copula modeling of extreme rainfall events in Connecticut.” J. Hydrol. 390 (1–2): 108–115. https://doi.org/10.1016/j.jhydrol.2010.06.039.
Westra, S., H. J. Fowler, J. P. Evans, L. V. Alexander, P. Berg, F. Johnson, E. J. Kendon, G. Lenderink, and N. M. Roberts. 2014. “Future changes to the intensity and frequency of short-duration extreme rainfall.” Rev. Geophys. 52 (3): 522–555. https://doi.org/10.1002/2014RG000464.
Willems, P., K. Arnbjerg-Nielsen, J. Olsson, and V. Nguyen. 2012. “Climate change impact assessment on urban rainfall extremes and urban drainage: Methods and shortcomings.” Atmos. Res. 103 (Jan): 106–118. https://doi.org/10.1016/j.atmosres.2011.04.003.
Xu, K., C. Ma, J. Lian, and L. Bin. 2014. “Joint probability analysis of extreme precipitation and storm tide in a coastal city under changing environment.” PLoS One 9 (10): e109341. https://doi.org/10.1371/journal.pone.0109341.
Yeo, M.-H., V.-T.-V. Nguyen, and T. A. Kpodonu. 2020. “Characterizing extreme rainfalls and constructing confidence intervals for IDF curves using scaling-GEV distribution model.” Int. J. Climatol. 41 (1): 456–468. https://doi.org/10.1002/joc.6631.
Yue, S., T. Ouarda, and B. Bobée. 2001. “A review of bivariate gamma distributions for hydrological application.” J. Hydrol. 246 (1–4): 1–18. https://doi.org/10.1016/S0022-1694(01)00374-2.
Zahmatkesh, Z., S. J. Burian, M. Karamouz, H. Tavakol-Davani, and E. Goharian. 2015a. “Low-impact development practices to mitigate climate change effects on urban stormwater runoff: Case study of New York City.” J. Irrig. Drain. Eng. 141 (1): 04014043. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000770.
Zahmatkesh, Z., M. Karamouz, E. Goharian, and S. J. Burian. 2015b. “Analysis of the effects of climate change on urban storm water runoff using statistically downscaled precipitation data and a change factor approach.” J. Hydrol. Eng. 20 (7): 05014022. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001064.
Zhang, L., and V. P. Singh. 2006. “Bivariate flood frequency analysis using the copula method.” J. Hydrol. Eng. 11 (2): 150–164. https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(150).
Zhao, L., N. Cui, J. Guan, P. Du, Y. Zhang, and S. Jiang. 2021. “Copula-based risk analysis of agricultural water shortage under natural precipitation conditions in the Guanzhong plain, a drought-prone region of China.” J. Hydrol. Eng. 26 (6): 04021016. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002084.
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Journal of Hydrologic Engineering
Volume 28 • Issue 7 • July 2023
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© 2023 American Society of Civil Engineers.
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Received: Jul 27, 2021
Accepted: Feb 24, 2023
Published online: Apr 26, 2023
Published in print: Jul 1, 2023
Discussion open until: Sep 26, 2023
ASCE Technical Topics:
- Bodies of water (by type)
- Catchments
- Climate change
- Climates
- Curvature
- Engineering fundamentals
- Environmental engineering
- Geometry
- Infrastructure
- Mathematics
- Meteorology
- Precipitation
- Rainfall
- Rainfall duration
- Rainfall frequency
- Rainfall intensity
- Urban and regional development
- Urban areas
- Water and water resources
- Water management
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