A probabilistic view of Hershfield's method for estimating probable maximum precipitation

D. Koutsoyiannis, A probabilistic view of Hershfield's method for estimating probable maximum precipitation, Water Resources Research, 35 (4), 1313–1322, doi:10.1029/1999WR900002, 1999.



A simple alternative formulation of Hershfield's statistical method for estimating probable maximum precipitation (PMP) is proposed. Specifically, it is shown that the published Hershfield data do not support the hypothesis that there exists a PMP as a physical upper limit, and therefore a purely probabilistic treatment of the data is more consistent. In addition, using the same data set, it is shown that Hershfield's estimate of PMP may be obtained using the generalized extreme value (GEV) distribution with shape parameter given as a specified linear function of the average value of annual maximum precipitation series and for return period of about 60,000 years. This formulation substitutes completely the standard empirical nomograph that is used for the application of the method. The application of the method can be improved when long series of local rainfall data are available that support an accurate estimation of the shape parameter of the GEV distribution.

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See also: http://dx.doi.org/10.1029/1999WR900002

Our works referenced by this work:

1. D. Koutsoyiannis, D. Kozonis, and A. Manetas, A mathematical framework for studying rainfall intensity-duration-frequency relationships, Journal of Hydrology, 206 (1-2), 118–135, doi:10.1016/S0022-1694(98)00097-3, 1998.
2. D. Koutsoyiannis, and G. Baloutsos, Analysis of a long record of annual maximum rainfall in Athens, Greece, and design rainfall inferences, Natural Hazards, 22 (1), 29–48, doi:10.1023/A:1008001312219, 2000.

Our works that reference this work:

1. D. Koutsoyiannis, Statistics of extremes and estimation of extreme rainfall, 1, Theoretical investigation, Hydrological Sciences Journal, 49 (4), 575–590, doi:10.1623/hysj.49.4.575.54430, 2004.
2. D. Koutsoyiannis, Statistics of extremes and estimation of extreme rainfall, 2, Empirical investigation of long rainfall records, Hydrological Sciences Journal, 49 (4), 591–610, doi:10.1623/hysj.49.4.591.54424, 2004.
3. S.M. Papalexiou, and D. Koutsoyiannis, A probabilistic approach to the concept of probable maximum precipitation, Advances in Geosciences, 7, 51-54, doi:10.5194/adgeo-7-51-2006, 2006.
4. D. Koutsoyiannis, Older and modern considerations in the design and management of reservoirs, dams and hydropower plants (Solicited), 1st Hellenic Conference on Large Dams, Larisa, doi:10.13140/RG.2.1.3213.5922, Hellenic Commission on Large Dams, Technical Chamber of Greece, 2008.
5. D. Koutsoyiannis, C. Makropoulos, A. Langousis, S. Baki, A. Efstratiadis, A. Christofides, G. Karavokiros, and N. Mamassis, Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability, Hydrology and Earth System Sciences, 13, 247–257, doi:10.5194/hess-13-247-2009, 2009.
6. D. Koutsoyiannis, and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, doi:10.1016/B978-0-444-53199-5.00027-0, Academic Press, Oxford, 2011.
7. S.M. Papalexiou, D. Koutsoyiannis, and C. Makropoulos, How extreme is extreme? An assessment of daily rainfall distribution tails, Hydrology and Earth System Sciences, 17, 851–862, doi:10.5194/hess-17-851-2013, 2013.
8. D. Koutsoyiannis, and S.M. Papalexiou, Extreme rainfall: Global perspective, Handbook of Applied Hydrology, Second Edition, edited by V.P. Singh, 74.1–74.16, McGraw-Hill, New York, 2017.
9. A. Koskinas, A. Tegos, P. Tsira, P. Dimitriadis, T. Iliopoulou, P. Papanicolaou, D. Koutsoyiannis, and Τ. Williamson, Insights into the Oroville Dam 2017 spillway incident, Geosciences, 9 (37), doi:10.3390/geosciences9010037, 2019.
10. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023.

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Other works that reference this work (this list might be obsolete):

1. Arnaud, P., and J. Lavabre, A stochastic model of hourly rainfall with rainfall-runoff transformation for predicting flood frequency, Revue des Sciences de l'Eau, 13(4), 441-462, 2000.
2. Arnaud, P., and J. Lavabre, Coupled rainfall model and discharge model for flood frequency estimation, Water Resources Research, 38 (6), art. no. 1075, 2002.
3. Douglas, E.M., and A.P. Barros, Probable maximum precipitation estimation using multifractals: Application in the eastern United States, Journal of Hydrometeorology, 4 (6), 1012-1024, 2003.
4. Lazaridou, P.L., E.I. Daniil, S.N. Michas, P.N. Papanicolaou and L.S. Lazarides, Integrated environmental and hydraulic design of Xerias river, Corinthos, Greece, Training Works, Water, Air and Soil Pollution: Focus, 4, 319-330,2004.
5. #Daniil, E.I., S. Michas, G. Bouklis, P.L. Lazaridou and L.S. Lazarides L.S., Flood management and control in an urban environment: Diakoniaris case study, River Flow 2004, Vol. 2, 1411-1420, ed. by M. Greco et al., Balkema (ISBN 9058096882), 2004.
6. Arnaud, P., J. Lavabre, B. Sol and C. Desouches, Rainfall risk of France, Houille Blanche, (5) 102-111, 2006.
7. #Daniil, E.I., G.D. Bouclis, S.N. Michas, P.L. Lazaridou & L.S. Lazarides, Hydrologic issues in flood management and control in an urban environment in Greece, Proceedings of Protection & Restoration of the Environment VIII, Mykonos, Greece, 2006.
8. Deshpande, N.R., B.D. Kulkarni, A.K. Verma and B.N. Mandal, Extreme rainfall analysis and estimation of Probable Maximum Precipitation (PMP) by statistical methods over the Indus river basin in India, Journal of Spatial Hydrology, 8(1), 22-36, 2008
9. Casas, M.C., R. Rodríguez, R. Nieto and A. Redaño, The estimation of probable maximum precipitation: The case of Catalonia, Annals of the New York Academy of Sciences, 1146, 291-302, 2008.
10. #Noorian, A.M., and E. Fattahi, Comparison between physical and statistical methods for estimation of PMP in southwest basins of Iran, Proceedings BALWOIS 2008, Ohrid, May 2008.
11. Xu Y.-P., and Y.-K. Tung, Constrained scaling approach for design rainfall estimation, Stochastic Environmental Research and Risk Assessment, 23(6), 697-705, 2009.
12. #Xu, Y. P., Y. K. Tung, F. Cao and Y. Tong, Constrained scaling approach for design rainfall estimation, Advances in Water Resources and Hydraulic Engineering - Proceedings of 16th IAHR-APD Congress and 3rd Symposium of IAHR-ISHS, 35-39, 2009.
13. Castellarin, A., R. Merz and G. Blöschl, Probabilistic envelope curves for extreme rainfall events, Journal of Hydrology, 378 (3-4), 263-271, 2009.
14. Fernandes, W., M. Naghettini and R. Loschi, A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions, Stochastic Environmental Research and Risk Assessment, 24, 1127–1143, DOI: 10.1007/s00477-010-0365-4, 2010.
15. Poon, H. C., and H. H. Hwee, Probable maximum precipitation derivation in Malaysia: Review and comparison, International Journal of HydroClimatic Engineering, 1 (1), 37-72, 2010.
16. #Lavabre, J., and P. Arnaud, Estimation de l'aléa pluvial en France métropolitaine, Editions Quae, Paris, 2010.
17. Fernando, W. C. D. K., and S. S. Wickramasuriya, The hydro-meteorological estimation of probable maximum precipitation under varying scenarios in Sri Lanka, International Journal of Climatology, 31 (5), 668-676, 2011.
18. Casas, M. C., R. Rodríguez, M. Prohom, A. Gázquez and A. Redaño, Estimation of the probable maximum precipitation in Barcelona (Spain), International Journal of Climatology, 31 (9), 1322-1327, 2011.
19. Gheidari, M. H. N., A. Telvari, H. Babazadeh and M. Manshouri, Estimating design probable maximum precipitation using multifractal methods and comparison with statistical and synoptically methods - Case study: Basin of Bakhtiari Dam, Water Resources, 38 (4), 484-493, 2011.
20. #Lee, P. S., and G. J.-Y. You, The risk analysis of long term impact to reservoir under extreme hydrologic events - Shihmen reservoir, a case study, Proceedings of the 2011 World Environmental and Water Resources Congress: Bearing Knowledge for Sustainability, 1237-1246, 2011.
21. Heng, H. H., and C. P. Hii, A review on probable maximum precipitation (PMP) estimation in Malaysia, International Journal of Hydrology Science and Technology, 1 (1-2), 63-87, 2011.
22. Shamir, E., K. P. Georgakakos and M. J. Murphy Jr., Frequency analysis of the 7–8 December 2010 extreme precipitation in the Panama Canal Watershed, Journal of Hydrology, 480, 136-148, 2013.
23. Alias, N. E., and K. Takara, Estimating the probable maximum precipitation of Kuala Lumpur, Malaysia and Yodo River basin, Japan using statistical methods, Journal of Disaster Research, 8 (1), 197-198, 2013.
24. Bossé, B., B. Bussière, R. Hakkou, A. Maqsoud and M. Benzaazoua, Assessment of phosphate limestone wastes as a component of a store-and-release cover in a semiarid climate, Mine Water and the Environment, 10.1007/s10230-013-0225-9, 2013.
25. Lee, B.-S., and G. J.-Y. You, An assessment of long-term overtopping risk and optimal termination time of dam under climate change, Journal of Environmental Management, 121, 57-71, 2013.
26. Beauchamp, J., R. Leconte, M. Trudel and F. Brissette, Estimation of the summer-fall PMP and PMF of a northern watershed under a changed climate, Water Resources Research, 10.1002/wrcr.20336, 2013.
27. #Sidek, L. M., M. D. Mohd Nor, P. R. Rakhecha, H. Basri, W. Jayothisa, R. S. Muda, M. N. Ahmad and A. Z. Abdul Razad, Probable Maximum Precipitation (PMP) over mountainous region of Cameron Highlands- Batang Padang Catchment of Malaysia, 4th International Conference on Energy and Environment 2013 (ICEE 2013), IOP Conf. Series: Earth and Environmental Science 16, 10.1088/1755-1315/16/1/012049, 2013.
28. #Tomlinson, E., B. Kappel, G. Muhlestein, D. Hultstrand and T. Parzybok, Probable Maximum Precipitation Study for Arizona, Arizona Department of Water Resources, Arizona, USA, 2013.
29. #Kappel, B., G. Muhlestein, E. Tomlinson, D. Hultstrand and M. Johnson, Calculating Arizona basin-specific PMP using the PMP evaluation tool, Association of State Dam Safety Officials Annual Conference 2013, Dam Safety 2013, 2, 904-969, 2013.
30. #Lorente Castelló, J., M.C. Casas Castillo, R.Rodríguez Solà and A. Redaño Xipell, Extreme rainfall rates and probable maximum precipitation, Adverse Weather in Spain, 135-148, 2013.
31. Lagos, M. A. Z., and X. M. Vargas, PMP and PMF estimations in sparsely-gauged Andean basins and climate change projections, Hydrological Sciences Journal, 10.1080/02626667.2013.877588, 2014.
32. De Paola, F., M. Giugni, M. E. Topa and E. Bucchignani, Intensity-Duration-Frequency (IDF) rainfall curves, for data series and climate projection in African cities, SpringerPlus, 10.1186/2193-1801-3-133, 2014.
33. Costa, V., W. Fernandes and M. Naghettini, A Bayesian model for stochastic generation of daily precipitation using an upper-bounded distribution function, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-014-0880-9, 2014.
34. Soltani, M., F. Khoshakhlagh, P. Zawar-Reza, S. T. K. Miller, M. Molanejad and A. R. SaadatAbadi, Probable maximum precipitation estimation using statistical and physical methods over Esfahan Province of Iran, Research Journal of Forest and Environmental Protection, 1 (1), 38-55, 2014.
35. Ishida, K., M. Kavvas, S. Jang, Z. Chen, N. Ohara and M. Anderson, Physically based estimation of maximum precipitation over three watersheds in Northern California: Atmospheric boundary condition shifting, J. Hydrol. Eng., 10.1061/(ASCE)HE.1943-5584.0001026, 2014.
36. #Salas, J. D., G. Gavilán, F. R. Salas, P. Y. Julien and J. Abdullah, Uncertainty of the PMP and PMF, Handbook of Engineering Hydrology - Modeling, Climate Change and Variability (ed. by S. Eslamian), Taylor & Francis, Boca Raton, FL, USA, 575-603, 2014.
37. Griffiths, G.A., A. I. McKerchar and C. P. Pearson, Towards prediction of extreme rainfalls in New Zealand, Journal of Hydrology (New Zealand), 53 (1), 41-52, 2014.
38. Walega, A., and B. Michalec, Characteristics of extreme heavy precipitation events occurring in the area of Cracow (Poland), Soil and Water Research, 9 (4), 182-191, 2014.
39. Micovic, Z., M.G. Schaefer and G.H. Taylor, Uncertainty analysis for Probable Maximum Precipitation estimates, Journal of Hydrology, 521, 360-373, 2015.
40. Pérez-Zanón, N., M.C. Casas-Castillo, R. Rodríguez-Solà, J.C. Peña, A. Rius, J.G. Solé and A. Redaño, Analysis of extreme rainfall in the Ebre Observatory (Spain), Theoretical and Applied Climatology, 10.1007/s00704-015-1476-0, 2015.
41. Chavan, S.R., and V.V. Srinivas, Probable maximum precipitation estimation for catchments in Mahanadi river basin, Aquatic Procedia, 4, 892-899, 2015.
42. #Donnelly, C.R., ICOLD 2015 - Question 97, Spillways [Évacuateurs de Crues], DOI: 10.13140/RG.2.1.4513.9041, 2015.
43. #Haddad, K., and A. Rahman, Estimation of large to extreme floods using a regionalization model, Landscape Dynamics, Soils and Hydrological Processes in Varied Climates (ed. by A.M. Melesse and W. Abtew, 279-292, 10.1007/978-3-319-18787-7_14, 2016.

Tagged under: Course bibliography: Hydrometeorology, Determinism vs. stochasticity, Extremes, Rainfall models