Utilizing the Scale Invariance Principle for Deriving a Regional Intensity-Duration-Frequency Relationship in the Metropolitan Region of Belo Horizonte, Brazil
Publication: Journal of Hydrologic Engineering
Volume 28, Issue 7
Abstract
Intensity-duration-frequency (IDF) relationships are frequently required for hydraulic design and risk assessment in small catchments. Nonetheless, the usual scarcity of subdaily rainfall data may render the derivation of such models unfeasible in the locations of interest. For addressing this problem, in this study, we discuss a regional IDF relationship based on the principle of scale invariance, and apply this model to gauged sites in the metropolitan region of Belo Horizonte, Brazil. Our results indicated that a single regional-scale exponent, as derived from the average of estimates at training sites, is accurate enough (mean absolute error of 15%) for describing the probabilistic behavior of extreme rainfall across a large set of subdaily durations in the study area. In addition, the quantile estimates derived from our model are similar to those obtained with more complex regionalization methods, which suggests that the scale invariance principle may be an effective and parsimonious tool for extreme rainfall frequency analysis in poorly gauged areas.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors acknowledge the support to this research from CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).
References
Aguilar, M. G., and V. A. F. Costa. 2020. “A regional similarity-based approach for sub-daily rainfall nonparametric generation.” Rev. Bras. de Recursos Hídricos 25 (e5): 1–16. https://doi.org/10.1590/2318-0331.252020190054.
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.
Blanchet, J., D. Ceresetti, G. Molinié, and J. D. Creutin. 2016. “A regional GEV scale-invariant framework for Intensity–Duration–Frequency analysis.” J. Hydrol. 540 (Sep): 82–95. https://doi.org/10.1016/j.jhydrol.2016.06.007.
Boukhelifa, M., M. Meddi, and E. Gaume. 2018. “Integrated Bayesian estimation of intensity-duration-frequency curves: Consolidation and extensive testing of a method.” Water Resour. Res. 54 (10): 7459–7477. https://doi.org/10.1029/2018wr023366.
Cândido, M., and M. Naghettini. 2008. “SEAF—A prototype of an expert system for at side frequency analysis of hydrological annual maxima.” Av. en Recursos Hidráulicos 18 (Oct): 37–56.
Casas-Castillo, M. C., R. Rodríguez-Solà, X. Navarro, B. Russo, A. Lastra, P. González, and A. Redaño. 2018. “On the consideration of scaling properties of extreme rainfall in Madrid (Spain) for developing a generalized intensity-duration-frequency equation and assessing probable maximum precipitation estimates.” Theor. Appl. Climatol. 131 (1–2): 573–580. https://doi.org/10.1007/s00704-016-1998-0.
Ghanmi, H., Z. Bargaoui, and C. Mallet. 2016. “Estimation of intensity-duration-frequency relationships according to the property of scale invariance and regionalization analysis in a Mediterranean coastal area.” J. Hydrol. 541 (Oct): 38–49. https://doi.org/10.1016/j.jhydrol.2016.07.002.
Hosking, J. R. M., and J. R. Wallis. 1997. Regional frequency analysis an approach based on L-moments. Cambridge, UK: Cambridge University Press.
Innocenti, S., A. Mailhot, and A. Frigon. 2017. “Simple scaling of extreme precipitation in North America.” Hydrol. Earth Syst. Sci. 21 (11): 5823–5846. https://doi.org/10.5194/hess-21-5823-2017.
Koutsoyiannis, D. 2021. Stochastics of hydroclimatic extremes—A cool look at risk. Athens, Greece: Open Academic.
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.
Koutsoyiannis, D., and C. Onof. 2001. “Rainfall disaggregation using adjusting procedures on a Poisson cluster model.” J. Hydrol. 246 (1–4): 109–122. https://doi.org/10.1016/S0022-1694(01)00363-8.
Lima, C., H. Kwon, and J. Kim. 2016. “A Bayesian beta distribution model for estimating rainfall IDF curves in a changing climate.” J. Hydrol. 540 (Sep): 744–756. https://doi.org/10.1016/j.jhydrol.2016.06.062.
Lima, C. H. R., H. Kwonb, and Y. Kimb. 2018. “A local-regional scaling-invariant Bayesian GEV model for estimating rainfall IDF curves in a future climate.” J. Hydrol. 566 (Nov): 73–88. https://doi.org/10.1016/j.jhydrol.2018.08.075.
Marra, F., and E. Morin. 2015. “Use of radar QPE for the derivation of Intensity–Duration–Frequency curves in a range of climatic regimes.” J. Hydrol. 531 (Dec): 427–440. https://doi.org/10.1016/j.jhydrol.2015.08.064.
Marra, F., E. Morin, N. Peleg, Y. Mei, and E. Anagnostou. 2017. “Intensity–duration–frequency curves from remote sensing rainfall estimates: Comparing satellite and weather radar over the eastern Mediterranean.” Hydrol. Earth Syst. Sci. 21 (5): 2389–2404. https://doi.org/10.5194/hess-21-2389-2017.
McClymont, K., D. Morrison, L. Beevers, and E. Carmen. 2020. “Flood resilience: A systematic review.” J. Environ. Plann. Manage. 63 (7): 1151–1176. https://doi.org/10.1080/09640568.2019.1641474.
Menabde, M., A. Seed, and G. Pegram. 1999. “A simple scaling model for extreme rainfall.” Water Resour. Res. 35 (1): 335–339. https://doi.org/10.1029/1998WR900012.
Naghettini, M. 2017. Fundamentals of statistical hydrology. Cham, Switzerland: Springer.
Noor, M., T. Ismail, S. Shahid, M. Asaduzzaman, and A. Dewan. 2021. “Evaluating intensity-duration-frequency (IDF) curves of satellite-based precipitation datasets in Peninsular Malaysia.” Atmos. Res. 248 (Jan): 105203. https://doi.org/10.1016/j.atmosres.2020.105203.
Pinheiro, M. M. G., and M. Naghettini. 1998. “Análise Regional de Freqüência e Distribuição Temporal das Tempestades na Região Metropolitana de Belo Horizonte–RMBH.” Rev. Bras. de Recursos Hídricos 3 (4): 73–88. https://doi.org/10.21168/rbrh.v3n4.p73-88.
Renard, B. 2011. “A Bayesian hierarchical approach to regional frequency analysis.” Water Resour. Res. 47 (11): 1–21. https://doi.org/10.1029/2010wr010089.
Rodríguez-Solà, R., M. C. Casas-Castillo, X. Navarro, and A. Redaño. 2017. “A study of the scaling properties of rainfall in Spain and its appropriateness to generate intensity-duration-frequency curves from daily records.” Int. J. Climatol. 37 (2): 770–780. https://doi.org/10.1002/joc.4738.
Sampaio, J., and V. Costa. 2021. “Bayesian regional flood frequency analysis with GEV hierarchical models under spatial dependency structures.” Hydrol. Sci. J. 66 (3): 422–433. https://doi.org/10.1080/02626667.2021.1873997.
Sane, Y., et al. 2018. “Intensity–duration–frequency (IDF) rainfall curves in Senegal.” Nat. Hazards Earth Syst. Sci. 18 (7): 1849–1866. https://doi.org/10.5194/nhess-18-1849-2018.
Soltani, S., R. Helfi, P. Almasi, and R. Modarres. 2017. “Regionalization of rainfall intensity–duration–frequency using a simple scaling model.” Water Resour. Manage. 31 (13): 4253–4273. https://doi.org/10.1007/s11269-017-1744-0.
Stephenson, A., E. Lehmann, and A. Phatak. 2016. “A max-stable process model for rainfall extremes at different accumulation durations.” Weather Clim. Extremes 13 (Sep): 44–53. https://doi.org/10.1016/j.wace.2016.07.002.
Van de Vyver, H. 2018. “A multiscaling-based intensity–duration–frequency model.” Hydrol. Processes 32 (11): 1635–1647. https://doi.org/10.1002/hyp.11516.
Venkatesh, K., R. Maheswaran, and J. Devacharan. 2021. “Framework for developing IDF curves using satellite precipitation: A case study using GPM-IMERG V6 data.” Earth Sci. Inf. 15 (1): 671–687. https://doi.org/10.1007/s12145-021-00708-0.
Westra, S., R. Mehrotra, A. Sharma, and R. Srikanthan. 2012. “Continuous rainfall simulation: 1. A regionalized subdaily disaggregation approach.” Water Resour. Res. 48 (1): W01535. https://doi.org/10.1029/2011WR010489.
Yeo, M., V. Nguyen, and T. A. Kpodonu. 2021. “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.
Yusop, Z., H. Nasir, and F. Yusof. 2014. “Disaggregation of daily rainfall data using Bartlett Lewis Rectangular Pulse Model: A case study in central Peninsular Malaysia.” Environ. Earth Sci. 71 (8): 3627–3640. https://doi.org/10.1007/s12665-013-2755-7.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 28 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Oct 17, 2022
Accepted: Jan 31, 2023
Published online: Apr 19, 2023
Published in print: Jul 1, 2023
Discussion open until: Sep 19, 2023
ASCE Technical Topics:
- Business management
- Climates
- Design (by type)
- Developing countries
- Disaster risk management
- Engineering fundamentals
- Environmental engineering
- Hydraulic design
- Infrastructure
- Meteorology
- Models (by type)
- Practice and Profession
- Precipitation
- Rainfall
- Rainfall duration
- Rainfall frequency
- Rainfall intensity
- Risk management
- Scale models
- Urban and regional development
- Urban areas
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