A mathematical framework for studying rainfall intensity-duration-frequency relationships

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, 1998.



A general formula for the rainfall intensity-duration-frequency (idf) relationship, consistent with the theoretical probabilistic foundation of the analysis of rainfall maxima is proposed. Specific forms of this formula are explicitly derived from the underlying probability distribution function of maximum intensities. Several appropriate distribution functions are studied for that purpose. Simple analytical approximations of the most common distribution functions are presented, which are incorporated in, and allow mathematically convenient expressions of idf relationships. Also, two methods for a reliable parameter estimation of idf relationships are proposed. The proposed formulation of idf relationships constitutes an efficient parameterisation, facilitating the description of the geographical variability and regionalisation of idf curves. Moreover, it allows incorporating data from non-recording stations, thus remedying the problem of establishing idf curves in places with a sparse network of rain-recording stations, using data of the denser network of non-recording stations. Case studies, based on data of a significant part of Greece, briefly presented in the paper, clarify the methodology for the construction and regionalisation of the idf relationship.

Full text is only available to the NTUA network due to copyright restrictions

PDF Additional material:

See also:

Our works referenced by this work:

1. D. Koutsoyiannis, A stochastic disaggregation method for design storm and flood synthesis, Journal of Hydrology, 156, 193–225, doi:10.1016/0022-1694(94)90078-7, 1994.
2. D. Kozonis, Construction of rainfall intensity-duration-frequency curves with incomplete data, Diploma thesis, 94 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, June 1995.
3. D. Koutsoyiannis, Statistical Hydrology, Edition 4, 312 pages, doi:10.13140/RG.2.1.5118.2325, National Technical University of Athens, Athens, 1997.

Our works that reference this work:

1. 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.
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.
3. D. Koutsoyiannis, An entropic-stochastic representation of rainfall intermittency: The origin of clustering and persistence, Water Resources Research, 42 (1), W01401, doi:10.1029/2005WR004175, 2006.
4. D. Koutsoyiannis, and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, Academic Press, Oxford, 2011.

Works that cite this document: View on Google Scholar or ResearchGate

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

1. Menabde, M., A. Seed, and G. Pegram, A simple scaling model for extreme rainfall, Water Resources Research, 35(1), 335-339, 1999.
2. Javellea, P., J.-M. Gresillon and G. Galea, Discharge-duration-frequency curve modelling for floods and scale invariance, Comptes Rendus de l'Academie des Sciences - Series IIA - Earth and Planetary Science, 329(1), 39-44, 1999.
3. Garcia-Bartual, R., and M. Schneider, Estimating maximum expected short-duration rainfall intensities from extreme convective storms, Physics and Chemistry of the Earth,Part C: Solar,Terrestrial & Planetary Science, 26(9), 675-681, 2001.
4. Rasmussen, P., Bayesian estimation of change points using the general linear model, Water Resources Research, 37(11), 2723-2731, 2001.
5. #Michigan State Department of Transportation (MDOT), Michigan Rainfall Intensity Final Report, MDOT, 2001.
6. Veneziano, D., and P. Furcolo, Multifractality of rainfall and scaling of intensity-duration-frequency curves, Water Resources Research, 38 (12), art. no. 1306, 2002.
7. Haktanir, T., Divergence criteria in extreme rainfall series frequency analyses, Hydrological Sciences Journal, 48 (6), 917-937, 2003.
8. Casas, M.C., B. Codina, A. Redano and J. Lorente, A methodology to classify extreme rainfall events in the western mediterranean area, Theoretical and Applied Climatology, 77(3-4), 139-150, 2004.
9. Yu, P.S., T.C. Yang and C. S. Lin, Regional rainfall intensity formulas based on scaling property of rainfall, Journal of Hydrology, 295 (1-4), 108-123, 2004.
10. Mohymont, B., G. R. Demaree and D. N. Faka, Establishment of IDF-curves for precipitation in the tropical area of Central Africa - comparison of techniques and results, Natural Hazards and Earth System Sciences, 4 (3), 375-387, 2004.
11. 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.
12. Sauquet, E., G. Galea and M. Bessenasse, Describing the flow regime by the Flood-Duration-Frequency approach - An application to the Saf-Saf river basin, Algeria, Houille Blanche-Revue Internationale De L'Eau, 5, 80-85, 2004.
13. #Naghettini, M., A study of the properties of scale invariance as applied to intensity-duration-frequency relationships of heavy storms, Joint Conference on Water Resource Engineering and Water Resources Planning and Management 2000: Building Partnerships, 104, 2004.
14. Pereyra-Díaz, D., J. A. A. Pérez-Sesma & L. Gómez-Romero, Ecuaciones que estiman las curvas intensidad-duración-período de retorno de la lluvia, GEOS, 24 (1), 46-56, 2004.
15. Molini, A., L.G. Lanza and P. La Barbera, The impact of tipping-bucket raingauge measurement errors on design rainfall for urban-scale applications, Hydrological Processes, 19(5), 1073-1088, 2005.
16. Borga, M., C. Vezzani and G. Dalla Fontana, Regional rainfall depth-duration-frequency equations for an alpine region, Natural Hazards, 36 (1-2), 221-235, 2005.
17. Ramos, M.H., J.D. Creutin and E. Leblois, Visualization of storm severity, Journal of Hydrology, 315(1-4), 295-307, 2005.
18. #Daniil, E.I., and L.S. Lazaridis, Hydrologic modeling considerations for flood management in ungaged basins, Proceedings of the 9th International Conference on Environmental Science and Technology, Rhodes, Greece, 2005.
19. Daniil, E.I., S.N. Michas and L.S. Lazaridis, Hydrologic modeling for the determination of design discharges in ungauged basins, Global NEST Journal, 7(3), 296-305, 2005.
20. #Daniil, E.T., and L.S. Lazaridis, Practical issues in hydrologic modeling for flood management of watercourses running through urban environments in Greece, Proceedings of the 2005 Watershed Management Conference, 1553-1564, 2005.
21. Mohymont, B., and G.R. Demaree, Intensity-duration-frequency curves for precipitation at Yangambi, Congo, derived by means of various models of Montana type, Hydrological Sciences Journal, 51 (2), 239-253, 2006.
22. Veneziano, D., A. Langousis and P. Furcolo, Multifractality and rainfall extremes: A review, Water Resources Research, 42(6), W06D15, 2006.
23. Lombardo, F., F. Napolitano and F Russo, On the use of radar reflectivity for estimation of the areal reduction factor, Natural Hazards and Earth System Sciences, 6(3), 377-386, 2006.
24. Di Baldassarre, G., A. Brath and A. Montanari, Reliability of different depth-duration-frequency equations for estimating short-duration design storms, Water Resources Research, 42(12), W12501, 2006.
25. Neppel, L., C. Bouvier and H. Niel, Some examples of uncertainties in rainfall hazard study, Houille Blanche, (6), 22-26, 2006.
26. Nhat, L.M., Y. Tachikawa and K. Takara, Establishment of Intensity-Duration-Frequency Curves for Precipitation in the Monsoon Area of Vietnam, Annuals of Disas. Prev. Res. Inst., Kyoto Univ., 49B, 93-103, 2006.
27. Regalado, L.D.S., and J.A.F. Yuste, New methodology for the analysis of the annual maximum intensity variable of precipitation, Ecologia, 20, 435-444, 2006.
28. #Regalado, L.D.S., and J.A.F. Yuste, Maximum rainfall intensity analysis using L-moments in Spain, Proc. 7th International Conference on HydroScience and Engineering, Philadelphia, USA, 2006.
29. Terefa, C., M. Yitaye and Y. Seleshi, Rainfall intensity-duration-frequency relationship for Northern Ethiopia, Journal of Ethiopian Engineers and Architects, 23, 29-38, 2006.
30. Santoso, Β., Karakteristik hujan kota Semarang: Pembangunan kurva intensitas-durasi-frekwensi (IDF), Jurnal Teknik Sipil, 4(1), 50 – 56, 2007.
31. Endreny, T.A., S. Pashiardis, The error and bias of supplementing a short, arid climate, rainfall record with regional vs. global frequency analysis, Journal of Hydrology, 334(1-2), 174-182, 2007.
32. Karahan, H., H. Ceylan and M. Tamer Ayvaz, Predicting rainfall intensity using a genetic algorithm approach, Hydrological Processes, 21 (4), pp. 470-475, 2007.
33. Langousis, A., and D. Veneziano, Intensity-duration-frequency curves from scaling representations of rainfall, Water Resources Research, 43(2), W02422, 2007.
34. Gaume, E., N. Mouhous and H. Andrieu, Rainfall stochastic disaggregation models: Calibration and validation of a multiplicative cascade model, Advances in Water Resources, 30(5), 1301-1319, 2007.
35. Casas, M.C., M. Herrero, M. Ninyerola, X. Pons, R. Rodriguez, A. Rius and A. Redano, Analysis and objective mapping of extreme daily rainfall in Catalonia, International Journal of Climatology, 27(3), 399-409, 2007.
36. Senocak, S., and R. Acar, Modelling of short-duration rainfall intensity equations for the Agean region of Turkey, Fresenius Environmental Bulletin, 16(9B), 1220-1226, 2007.
37. Singh, V.P., and L. Zhang, IDF curves using the Frank Archimedean copula, Journal of Hydrologic Engineering, 12(6), 651-662, 2007.
38. Veneziano, D., C. Lepore, A. Langousis and P. Furcolo, Marginal methods of intensity-duration-frequency estimation in scaling and nonscaling rainfall, Water Resources Research, 43(10), W10418, 2007.
39. Nhat, L.M., Y. Tachikawa, T. Sayama and K. Takara, Regional rainfall intensity-duration-frequency relationships for ungauged catchments based on scaling properties, Annuals of Disas. Prev. Res. Inst., Kyoto Univ., 50B, 33-43, 2007.
40. Şenocak, S., and R. Acar, Modelling of short duration rainfall (SDR) intensity equations for Erzurum, Journal of Engineering Sciences, 13 (1), 75-80, 2007.
41. #Tapia, R. P., D. A. Garrido, K. M. Pérez, A. A.Martínez, M. C. Espinoza, M. L. Lorca, M. P. Vidal and L. R. Arellano, Curvas Intensidad Duración Frecuencia para la Zona Centro sur de Chile, UNESCO-IHP, 2007.
42. Muller, A., J.N. Bacro and M. Lang, Bayesian comparison of different rainfall depth-duration-frequency relationships, Stochastic Environmental Research and Risk Assessment, 22(1), 33-46, 2008.
43. Overeem, A., A. Buishand and I. Holleman, Rainfall depth-duration-frequency curves and their uncertainties, Journal of Hydrology, 348(1-2), 124-134, 2008.
44. Karahan, H., M.T. Ayvaz and G. Gurarslan, Determination of intensity-duration-frequency relationship by genetic algorithm: Case study of GAP, Teknik Dergi, 19(2), 4393-4407, 2008.
45. Dunkerley, D., Rain event properties in nature and in rainfall simulation experiments: a comparative review with recommendations for increasingly systematic study and reporting, Hydrological Processes, 22 (22), 4415-4435, 2008.
46. Soro, G.E., B.T.A. Goula, F.W. Kouassi, K. Koffi, B. Kamagate, I. Doumouya, I. Savane & B. Srohorou, Courbes intensité durée fréquence des précipitations enclimat tropical humide…, European J. Sci. Res., 21(3), 394-405, 2008.
47. #Sen, Z., Wadi Hydrology, CRC Press, 368 pp. ISBN 1420061542, 9781420061543, 2008.
48. #Huang, Q., Y. Chen, X. Li and S. Xu, People’s Republic of China, ch. 3, Asian Pacific FRIEND -- Rainfall Intensity Duration Frequency (IDF) Analysis for the Asia Pacific Region, ed. by T. M. Daniell and G. Q. Tabios III, IHP-VII Technical Documents in Hydrology No. 2, 12-22, Regional Steering Committee for Southeast Asia and the Pacific, UNESCO Office, Jakarta, 2008.
49. #Takara K., and L. M. Nhat, Japan, Ch. 5, Asian Pacific FRIEND -- Rainfall Intensity Duration Frequency (IDF) Analysis for the Asia Pacific Region, ed. by T. M. Daniell and G. Q. Tabios III, IHP-VII Technical Documents in Hydrology No. 2, 12-22, Regional Steering Committee for Southeast Asia and the Pacific, UNESCO Office, Jakarta, 2008.
50. #Amin, M. Z. M., M. N. M. Desa and Z. M. Daud, Malaysia, Ch. 6, Asian Pacific FRIEND -- Rainfall Intensity Duration Frequency (IDF) Analysis for the Asia Pacific Region, ed. by T. M. Daniell and G. Q. Tabios III, IHP-VII Technical Documents in Hydrology No. 2, 12-22, Regional Steering Committee for Southeast Asia and the Pacific, UNESCO Office, Jakarta, 2008.
51. #Meylan, P., A. Musy, and A. Favre, Hydrologie Fréquentielle, PPUR Presses Polytechniques, ISBN 288074797X, 9782880747978, 173 pp., 2008.
52. #Acar, R., and S. Şenocak, Modelling of short duration rainfall (SDR) intensity equations for Ankara, Turkey, Proceedings BALWOIS 2008, Ohrid, May 2008.
53. #Ben-Zvi, A., Rainfall intensity-duration-frequency curves from large samples, 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008.
54. #Kim, T., J.-Y. Shin, K. Kim and J.-H. Heo, Improving accuracy of IDF curves using long- and short-duration separation and multi-objective genetic algorithm, Proceedings of the World Environmental and Water Resources Congress 2008, ASCE, doi: 10.1061/40976(316)128, 2008.
55. Seong, K.-W., and Y.-H.Lee, Derivation and assessment of a bivariate IDF relationship using paired rainfall intensity-duration data, Stochastic Environmental Research and Risk Assessment, 23 (1), 1-7, 2009.
56. Chowdhary, H., Discussion of “IDF Curves Using the Frank Archimedean Copula” by Vijay P. Singh and Lan Zhang, Journal of Hydrologic Engineering, 14 (1), 107-108, 2009.
57. Allamano, P., P. Claps, F. Laio, and C. Thea, A data-based assessment of the dependence of short-duration precipitation on elevation, Physics and Chemistry of the Earth, 34 (10-12), 635-641, 2009.
58. Ben-Zvi, A., Rainfall intensity-duration-frequency relationships derived from large partial duration series, Journal of Hydrology, 367 (1-2), 104-114, 2009.
59. Benabdesselam, T., and Y. Hammar, Estimation de la Réponse hydrologique d’un bassin versant urbanisé, European Journal of Scientific Research, 29 (3), 334-348, 2009.
60. Langousis, A., D. Veneziano, P. Furcolo, and C. Lepore, Multifractal rainfall extremes: Theoretical analysis and practical estimation, Chaos, Solitons & Fractals, 39(3), 1182-1194, 2009.
61. Viglione, A., R. Merz, and G. Blöschl, On the role of the runoff coefficient in the mapping of rainfall to flood return periods, Hydrol. Earth Syst. Sci., 13(5), 577-593, 2009.
62. Endreny, T. A., and N. Imbeah, Generating robust rainfall intensity-duration-frequency estimates with short-record satellite data, Journal of Hydrology, 371(1-4), 182-191, 2009.
63. Hejazizadeh, Z., E. Jahanshiri and M.H. Naserzadeh, A study on the temporal and local distribution of showers generating flood in Zolachai river basin by using intensity-duration-frequency-area curves relationships, Journal of Applied Sciences, 9 (10), 1922-1928, 2009.
64. Bara, M., S. Kohnova, L. Gaal, J. Szolgay and K. Hlavcova, Estimation of IDF curves of extreme rainfall by simple scaling in Slovakia, Contributions to Geophysics and Geodesy, 39 (3), 187–206, 2009.
65. Veneziano, D., A. Langousis and C. Lepore, New asymptotic and preasymptotic results on rainfall maxima from multifractal theory, Water Resour. Res., 45, W11421, doi:10.1029/2009WR008257, 2009.
66. Langousis, A., and D. Veneziano, Long-term rainfall risk from tropical cyclones in coastal areas, Water Resour. Res., 45, W11430, doi:10.1029/2008WR007624, 2009.
67. #Hingray, B., C. Picouet and A. Musy, Hydrologie: Tome 2, Une science pour l"ingénieur, 600 pp., ISBN: 2880747988, 9782880747985, PPUR Presses Polytechniques, 2009.
68. Venkata,  R.  R., B. Chakravorty, N. G.  Pandey  and P.  Mani, Development of intensity duration frequency relationship for short duration rainfall, Hydrology Journal, 32 (1&2), 2009.
69. Sarkar, S., N. Goel, and B. Mathur, Development of isopluvial map using L-moment approach for Tehri-Garhwal Himalaya, Stochastic Environmental Research and Risk Assessment, 24 (3), 411-423, 2010.
70. Um, M.-J., H. Yun, W. Cho and J.-H. Heo, Analysis of orographic precipitation on Jeju-Island using regional frequency analysis and regression, Water Resources Management, 24 (7), 1461-1487, 2010.
71. Bara, M., L. Gaal, S. Kohnova, J. Szolgay and K. Hlavcova, On the use of the simple scaling of heavy rainfall in a regional estimation of idf curves in Slovakia, Journal of Hydrology and Hydromechanics, 58 (1), 49-63, 2010.
72. Soro, G.E., T.A. Goula Bi, F.W. Kouassi and B. Srohourou, Update of Intensity-Duration-Frequency Curves for Precipitation of Short Durations in Tropical Area of West Africa (Cote D'ivoire), Journal of Applied Sciences, 10 (9), 704-715, 2010.
73. Okonkwo, G. I., and C. C. Mbajiorgu, Rainfall intensity-duration-frequency analyses for South Eastern Nigeria, Agricultural Engineering International: the CIGR Ejournal, Manuscript 1304. Vol. XII. March, 2010.
74. Van de Vyver, H., and G. R. Demarée, Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi, Congo, under the hypothesis of inadequate data, Hydrol. Sci. J., 55(4), 555–564, 2010.
75. #Van Nooijen, R. R. P. and A.G. Kolechkina, A Comparison of fitting methods and tests on computer generated samples, International Workshop Advances in Statistical Hydrology, International Association of Hydrological Sciences (IAHS/STAHY), Taormina, Italy, 2010.
76. Ceresetti, D., G. Molinié, and J.-D. Creutin, Scaling properties of heavy rainfall at short duration: A regional analysis, Water Resour. Res., 46, W09531, doi: 10.1029/2009WR008603, 2010.
77. #Huang, Q., Y. Chen, S. Xu, Y. Liu and X. Li, Scaling models of a rainfall intensity-duration-frequency relationship, Proceedings, 6th International Conference on Natural Computation, ICNC 2010, 7, art. no. 5582456, 3415-3419, 2010.
78. Haktanir, T., M. Cobaner and O. Kisi, Frequency analyses of annual extreme rainfall series from 5 min to 24 h, Hydrological Processes, 24 (24), 3574-3588, 2010.
79. #Leventi, I., I. Nalbantis and A. Georgopoulos, On the use of Digital Surface Models and hydrological/hydraulic models for inundated area delineation, Environmental Hydraulics - Proceedings of the 6th International Symposium on Environmental Hydraulics, 2, 875-880, 2010.
80. AlHassoun, S.A., Developing an empirical formulae to estimate rainfall intensity in Riyadh region, Journal of King Saud University – Engineering Sciences, doi: 10.1016/j.jksues.2011.03.003, 2011.
81. Ndiritu, J., A variable length block bootstrap for multi-site synthetic streamflow generation, Hydrol. Sci. J., 56 (3), 362-379, 2011.
82. #Látečková, J., S. Kohnová, L. Gaál and J. Szolgay, Estimation of IDF curves of monthly rainfall intensities in the western part of Slovakia, XXV Conference of the Danube Countries on Hydrological Forecasting and Hydrological Bases of Water Management, Budapest, Hungary, 2011.
83. #Bara, M., S. Kohnová, L. Gaál, J. Szolgay and K. Hlavčová, Comparison of IDF curves of extreme rainfall downscaled from design values of 1-day rainfall assessed by different approaches, XXV Conference of the Danube Countries on Hydrological Forecasting and Hydrological Bases of Water Management, Budapest, Hungary, 2011.
84. #Singh, V. P., and Z. Hao, Entropy-based probability distribution for IDF curves, Proceedings of the 2011 World Environmental and Water Resources Congress: Bearing Knowledge for Sustainability, 1265-1272, 2011.
85. Kao, S.-C., and A. R. Ganguly, Intensity, duration, and frequency of precipitation extremes under 21st-century warming scenarios, J. Geophys. Res., 116, D16119, doi: 10.1029/2010JD015529, 2011.
86. Tarolli, P., M. Borga, K.-T. Chang and S.-H.Chiang, Modeling shallow landsliding susceptibility by incorporating heavy rainfall statistical properties, Geomorphology, 133 (3-4), 199-211, 2011.
87. #Norlida, M. D., I. Abustan, R. Abdullah, A. S. Yahaya, O. Sazali, M. D. Mohd Nor and M. S. Lariyah, Intensity-duration-frequency estimation using generalized Pareto distribution for urban area in a tropical region, 12nd International Conference on Urban Drainage, Porto Alegre, Brazil, 2011.
88. Elsebaie, I. H., Developing rainfall intensity–duration–frequency relationship for two regions in Saudi Arabia, Journal of King Saud University - Engineering Sciences, doi: 10.1016/j.jksues.2011.06.001, 2011.
89. Kimoto, A., H. E. Canfield and D. Stewart, Comparison of synthetic design storms with observed storms in Southern Arizona, Journal of Hydrologic Engineering, 16 (11), 935-941, 2011.
90. El-Sayed, E. A. H., Generation of rainfall intensity duration frequency curves for ungauged sites, Nile Basin Water Science & Engineering Journal, 4 (1), 112-124, 2011.
91. #Boukhelifa, M., B. Touaibia and P. Hubert, Storm water risk prevention through the establishment of intensity-duration-frequency curves (IDF): Application to the city of Tipasa in northwestern Algeria, IAHS-AISH Publication, 347, 36-42, 2011.
92. #Grimaldi, S., S.-C. Kao, A. Castellarin, S. M. Papalexiou, A. Viglione, F. Laio, H. Aksoy and A. Gedikli, Statistical Hydrology, In: Treatise on Water Science (ed. by P. Wilderer), 2, 479–517, Academic Press, Oxford, 2011.
93. Ceresetti, D., S. Anquetin, G. Molinié, E. Leblois and J.-D. Creutin, Multiscale evaluation of extreme rainfall event predictions using severity diagrams, Weather and Forecasting, 27 (1), 174-188, 2012.
94. Ghosh, S., D. Das, S.-C. Kao and A. R. Ganguly, Lack of uniform trends but increasing spatial variability in observed Indian rainfall extremes, Nature Climate Change, 2 (2), 86-91, 2012.
95. Lanni, C., M. Borga, R. Rigon and P. Tarolli, Modelling shallow landslide susceptibility by means of a subsurface flow path connectivity index and estimates of soil depth spatial distribution, Hydrol. Earth Syst. Sci., 16, 3959-3971, doi: 10.5194/hess-16-3959-2012, 2012.
96. Rashid, M. M., S. B. Faruque and J. B. Alam, Modeling of short duration rainfall intensity duration frequency (SDR-IDF) equation for Sylhet City in Bangladesh, ARPN Journal of Science and Technology, 2 (2), 92-95, 2012.
97. Del Giudice, G., R. Padulano and G. Rasulo, Factors affecting the runoff coefficient, Hydrol. Earth Syst. Sci. Discuss., 9, 4919-4941, doi: 10.5194/hessd-9-4919-2012, 2012.
98. Endreny, T. A., and S. Diemont, Methods for assessing stormwater management at archaeological sites: Copan Ruins case study, Journal of Archaeological Science, 39 (8), 2637-2642, 2012.
99. Karahan, H., Determining rainfall-intensity-duration-frequency relationship using Particle Swarm Optimization, KSCE Journal of Civil Engineering, 16 (4), 667-675, 2012.
100. Flores-Villanelo, J. P., Infiltration trench design for ungauged areas using SIG, Tecnologia y Ciencias del Agua, 3 (2), 27-39, 2012.
101. #Grieser, J., Analyzing Extreme Rain,, 74 pp., 2012.
102. #Huang, Q., Y. Chen, S. Xu, Sui and J. Liu, A simple multifractal model for rainfall IDF analysis in China, 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 1461-1465, doi: 10.1109/FSKD.2012.6233762, 2012.
103. Ariff, N. M., A. A. Jemain, K. Ibrahim and W. Z. W. Zin, IDF Relationships using bivariate copula for storm events in Peninsular Malaysia, Journal of Hydrology, 470-471, 158-171, 2012.
104. Vivekanandan, N., Probabilistic modelling of hourly rainfall data for development of intensity-duration-frequency relationships, Bonfring International Journal of Data Mining, 2 (4), 16-19, 2012.
105. #Pizarro, R., P. García-Chevesich, F. Balocchi and R. Valdés, IDF curves on central-south Chile, Chile: Environmental, Political and Social Issues, 261-288, 2012.
106. Pereyra-Díaz, D., Two nonlinear mathematical models to estimate the intensity-duration-return period of rainfall events, Antes Universidad y Ciencia, 28 (3), 271-277, 2012.
107. Chebbi, A., Z. K. Bargaoui and M. da Conceição Cunha, Development of a method of robust rain gauge network optimization based on intensity-duration-frequency results, Hydrol. Earth Syst. Sci., 17, 4259-4268, 10.5194/hess-17-4259-2013, 2013.
108. van den Bossche, N., M. A. Lacasse and A. Janssens, A uniform methodology to establish test parameters for watertightness testing, Part I: a critical review, Building and Environment, 63, 145–156, 2013.
109. García-Marín, A. P., J. L. Ayuso-Muñoz, F. J. Jiménez-Hornero and J. Estévez, Selecting the best IDF model by using the multifractal approach, Hydrological Processes, 27 (3), 433-443, 2013.
110. Pinheiro Alves, A. V., G. B. da Silva Santos, F. C. M. de Menezes Filho and L. Sanches, Análise dos métodos de estimação para os parâmetros das distribuições de Gumbel e GEV em eventos de precipitações máximas na cidade de Cuiabá-MT [Analysis methods for estimating parameters of Gumbel and GEV distributions in maximum precipitation events in the city of Cuiabá–MT], Revista Eletrônica de Engenharia Civil, 6 (1), 32-43, 2013.
111. Vivekanandan, N., Development of intensity-duration-frequency relationships using OSA estimators of probability distributions, Journal of Research in Architecture and Civil Engineering (ISTP-JRAC), 1 (2), 1-7, 2013.
112. #Mohd Ariff, N., A. A. Jemain and W. Z. Wan Zin, Assessment of the intensity-duration-frequency (IDF) curves for storms in Peninsular Malaysia based on the generalized extreme value distribution, AIP Conference Proceedings, 1522, 1185-1194, 2013.
113. #Stapleton, S. O., and K. Hawley, Da Nang: Extreme rainfall, and climate change by the 2020s& 2050s, ISET-International Technical Report, 2013.
114. #Stapleton, S. O., and K. Hawley, Gorakhpur, India: Extreme rainfall, climate change, and flooding, ISET-International Technical Report, 2013.
115. Veneziano, D., and S. Yoon, Rainfall extremes, excesses, and IDF curves: A unified asymptotic framework and new non‐asymptotic results based on multifractal measures, Water Resources Research, 10.1002/wrcr.20352, 2013.
116. Karahan, H. and E. Özkan, Best fitting distributions for the standard duration annual maximum precipitations in the Aegean region, Pamukkale University Journal of Engineering Sciences, 19 (3), 152-157, 2013.
117. Demarée, G. R., and H. Van de Vyver, Construction of intensity-duration-frequency (IDF) curves for precipitation with annual maxima data in Rwanda, Central Africa, Adv. Geosci., 35, 1-5, doi: 10.5194/adgeo-35-1-2013, 2013.
118. Vivekanandan, N., Analysis of hourly rainfall data for the development of IDF relationships using the order statistics approach of probability distributions, International Journal of Management Science and Engineering Management, 10.1080/17509653.2013.829630, 2013.
119. #Loukas, A., and L. Vasiliades, Review of applied methods for flood-frequency analysis in a changing environment in Greece, In: A review of applied methods in Europe for flood-frequency analysis in a changing environment, Floodfreq COST action ES0901: European procedures for flood frequency estimation (ed. by H. Madsen et al.), Centre for Ecology & Hydrology, Wallingford, UK, 2013.
120. Al-anazi, K. K., and I. H. El-Sebaie, Development of intensity-duration-frequency relationships for Abha City in Saudi Arabia, International Journal of Computational Engineering Research, 58-65, 2013.
121. #Lehmann, E. A., A. Phatak, S. Soltyk, J. Chia, R. Lau and M. Palmer, Bayesian hierarchical modelling of rainfall extremes, 20th International Congress on Modelling and Simulation (MODSIM) (ed by J. Piantadosi, R. S. Anderssen and J. Boland), 2506–2512, Modelling and Simulation Society of Australia and New Zealand, Adelaide, Australia, 2013.
122. Vijayagopal, P., N. Vivekanandan and S. Kannan, Assessing adequacy of probability distribution for development of IDF relationships for Mandla and Jabalpur, International Journal of Scientific Research and Reviews, 2 (3), 99-114, 2013.
123. Jiang, P., and Y.-K. Tung, Establishing rainfall depth-duration-frequency relationships at daily raingauge stations in Hong Kong, Journal of Hydrology, 504, 80-93, 2013.
124. #Montesarchio, V., F. Napolitano, F. Russo and S. Spina, IDF relationships for short duration rainfall, AIP Conference Proceedings, 1558, 1685-1688, 2013.
125. #Zhao, S., Q. Zhang and C. Huang, Scenario-based risk assessment and zonation of paddy caused by flood in Huai River sub-basin of China, Intelligent Systems and Decision Making for Risk Analysis and Crisis Response - Proceedings of the 4th International Conference on Risk Analysis and Crisis Response, RACR 2013, 107-116, 2013.
126. Elfiky, M. M., A. A.Habib and E. Elnikhily, Estimate of flood water quantities experienced by Dhukna City, Qassim Region, Ksa, Journal of Engineering Sciences, Assiut University, 41 (2), 382-394, 2013.
127. Chang K. B., S. H. Lai and O. Faridah, RainIDF: automated derivation of rainfall intensity-duration-frequency relationship from annual maxima and partial duration series, Journal of Hydroinformatics, 15 (4), 1224-1233, 2013.
128. #Tudose, T., A.-E. Croitoru and I. Haidu, Some aspects on rainfall maximum intensity in Northwestern Romania, International Multidisciplinary Scientific GeoConference Surveying Geology and Mining Ecology Management, SGEM, Albena, Bulgaria, 771-778, 2013.
129. Liew, S. C., S. V. Raghavan and S.-Y. Liong, How to construct future IDF curves, under changing climate, for sites with scarce rainfall records?, Hydrological Processes, 28 (8), 3276-3287, 2014.
130. Jaleel, L. A., and M. A. Farawn, Developing rainfall intensity-duration-frequency relationship for Basrah city, Kufa Journal of Engineering, 5 (1), 105-112, 2013.
131. Penna, D., M. Borga, G. T. Aronica, G. Brigandì and P. Tarolli, The influence of grid resolution on the prediction of natural and road-related shallow landslides, Hydrol. Earth Syst. Sci., 18, 2127-2139, 2014.
132. Seong, K.-W., Deriving a practical form of IDF formula using transformed rainfall intensities, Hydrological Processes, 28 (6), 2881-2896, 2014.
133. Asikoglu, O. L., and E. Benzeden, Simple generalization approach for intensity–duration–frequency relationships, Hydrol. Process., 28 (3), 1114-1123, 2014.
134. Thober, S., and L. Samaniego, Robust ensemble selection by multivariate evaluation of extreme precipitation and temperature characteristics, Journal of Geophysical Research: Atmospheres, 119 (2), 594-613, 2014.
135. Vidal, I., A Bayesian analysis of the Gumbel distribution: an application to extreme rainfall data, Stochastic Environmental Research and Risk Assessment, 28 (3), 571-582, 2014.
136. Del Giudice, G., R. Gargano, G. Rasulo and D. Siciliano, Preliminary estimate of detention basin efficiency at watershed scale, Water Resources Management, 28 (4), 897-913, 2014.
137. Pizarro, R., R. Valdés, A. Abarza and P. Garcia-Chevesich, A simplified storm index method to extrapolate Intensity-Duration-Frequency (IDF) curves for ungauged stations in central Chile, Hydrological Processes, 10.1002/hyp.10187, 2014.
138. Huang, Q., Y. F. Chen, S. Xu, and J. Liu, Case study of applying multifractal models for rainfall IDF analysis in China, Journal of Hydrologic Engineering, 19 (1), 205-210, 2014.
139. Gaál, L., P. Molnar and J. Szolgay, Selection of intense rainfall events based on intensity thresholds and lightning data in Switzerland, Hydrol. Earth Syst. Sci., 18, 1561-1573, 2014.
140. Fukutome, S., M. A. Liniger and M. Süveges, Automatic threshold and run parameter selection: a climatology for extreme hourly precipitation in Switzerland, Theoretical and Applied Climatology, 10.1007/s00704-014-1180-5, 2014.
141. Del Giudice, G., R. Padulano and G. Rasulo, Spatial prediction of the runoff coefficient in Southern Peninsular Italy for the index flood estimation, Hydrology Research, 45 (2), 263-281, 2014.
142. #Soltyk, S., M. Leonard, A. Phatak and E. Lehmann, Statistical Modelling of rainfall intensity-frequency-duration curves using regional frequency analysis and Bayesian hierarchical modelling, Hydrology & Water Resources Symposium, 2014.
143. Fathy, I., A. M. Negm, M. El-Fiky, M. Nassar and E. Al-Sayed, Intensity duration frequency curves for Sinai peninsula, Egypt, International Journal of Research in Engineering & Technology (IMPACT: IJRET), 2 (6), 105-112, 2014.
144. Wayal, A. S., and K. Menon, Intensity-duration-frequency curves and regionalisation, International Journal of Innovative Research in Advanced Engineering (IJIRAE), 1 (6), 28-32, 2014.
145. Panthou, G., T. Vischel, T. Lebel, G.Quantin and G. Molinié, Characterizing the space–time structure of rainfall in the Sahel with a view to estimating IDAF curves, Hydrol. Earth Syst. Sci., 18 (12) 5093-5107, DOI: 10.5194/hess-18-5093-2014, 2014.
146. Shaffie, M., A. Eli, Z. W. Wan Zin and A. Jemain, The spatial return level of aggregated hourly extreme rainfall in Peninsular Malaysia, Theoretical and Applied Climatology, 10.1007/s00704-014-1222-z, 2014.
147. Zhao, S., Q. Zhang and C. Huang, Scenario-based economic risk assessment of paddy damage caused by flood in the Huai River sub-basin of China, Human and Ecological Risk Assessment, 10.1080/10807039.2014.958370, 2014.
148. Liu, J.,C.D. Doan, S.-Y. Liong, R. Sanders, A.T. Dao and T. Fewtrell, Regional frequency analysis of extreme rainfall events in Jakarta, Natural Hazards, 10.1007/s11069-014-1363-5, 2014.
149. Manzano-Agugliaro, F., A. Zapata-Sierra, J. F. Rubi-Maldonado and Q. Hernandez-Escobedo, Assessment of Obtaining IDF Curve Methods for Mexico, Tecnologia Y Ciencias Del Agua, 5 (3), 149-158, 2014.
150. Haktanir, T., H. Citakoglu and N. Seckin, Regional frequency analyses of successive-duration annual maximum rainfalls by L-moments method, Hydrological Sciences Journal, 10.1080/02626667.2014.966722, 2014.
151. Weinerowska-Bords, K., Development of local IDF-formula using controlled random search method for global optimization, Acta Geophysica, 10.2478/s11600-014-0242-5, 2014.
152. Wang, X., G. Huang and J. Liu, Projected increases in intensity and frequency of rainfall extremes through a regional climate modeling approach, Journal of Geophysical Research D: Atmospheres, 119 (23), 13271-13286, 2014.
153. Puricelli, M., Update and analysis of intensity - duration - frequency curves for Balcarce, Buenos Aires province, Argentina, Revista de Geología Aplicada a la Ingeniería y al Ambiente, 32, 61-70, 2014.
154. #Suthakaran, R., K. Perera and N. Wikramanayake, Rainfall intensity-duration-frequency relationship for Colombo region in Sri Lanka, SAITM Research Symposium on Engineering Advancements (SAITM – RSEA 2014), 2014.
155. #Shrestha, A., M. S. Babel and S. Weesakul, Integrated modelling of climate change and urban drainage, Managing Water Resources under Climate Uncertainty, Springer International Publishing, 89-103, 10.1007/978-3-319-10467-6_5, 2015.
156. Yousef, L. A. and T. B. M. J. Ouarda, Adaptation of water resources management to changing climate: the role of intensity-duration-frequency curves, International Journal of Environmental Science and Development, 6 (6), 578-483, 2015.
157. Eldardiry, H. E. Habib and Y. Zhang, On the use of radar-based quantitative precipitation estimates for precipitation frequency analysis, Journal of Hydrology, 10.1016/j.jhydrol.2015.05.016, 2015.
158. Mamo, T., Evaluation of the potential impact of rainfall intensity variation due to climate change on existing drainage infrastructure, J. Irrig. Drain Eng., 10.1061/(ASCE)IR.1943-4774.0000887, 05015002, 2015.
159. Hussein, A.K., Deriving rainfall intensity-duration-frequency relationships for Kerbala City, Muthanna Journal for Engineering Sciences, 3 (1), 26-37, 2015.
160. Otuaga, P.M., Rainfall intensity-duration-frequency curves for maxima duration series for Ondo Town, Ondo State, Nigeria, American Scientific Research Journal for Engineering, Technology, and Sciences, 12 (1), 66-74, 2015.
161. Panthou, G., T. Vischel, T. Lebel, G. Quantin and A. Ali, Space-time structure characterization of extreme rainfall: IDAF curves estimation in the Sahel, Houille Blanche-Revue Internationale De L’Eau, 3, 58-63 , 10.1051/lhb/20150034, 2015.
162. Haddad, K., F. Johnson, A. Rahman, J. Green and G. Kuczera, Comparing three methods to form regions for design rainfall statistics: Two case studies in Australia, Journal of Hydrology, 527, 62-76, 2015.
163. #Bezak, N., M. Šraj, M. Brilly and M. Mikoš, Return period determination for several extreme rainfall induced events using the IDF relationship obtained via copulas, 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, Vancouver, Canada, 2015.
164. Basso, R., D. Allasia, R. Tassi and D.M. Bayer, Sub-daily extreme events distribution and changes in Northeastern Brazil in the 20th century, Proc. IAHS, 369, 135-140, 10.5194/piahs-369-135-2015, 2015.
165. Subyani, A.M., and N.S. Al-Amri, IDF curves and daily rainfall generation for Al-Madinah city, western Saudi Arabia, Arabian Journal of Geosciences, 10.1007/s12517-015-1999-9, 2015.
166. Chang, K., S. Lai and F. Othman, Comparison of annual maximum and partial duration series for derivation of rainfall intensity-duration-frequency relationships in Peninsular Malaysia, J. Hydrol. Eng., 10.1061/(ASCE)HE.1943-5584.0001262, 05015013, 2015.
167. Afrin, S., M. M. Islam, and M. M. Rahman, Development of IDF curve for Dhaka city based on scaling theory under future precipitation variability due to climate change, International Journal of Environmental Science and Development, 6(5), 332-335, 2015.
168. Hao, Z., and V. P. Singh, Review of dependence modeling in hydrology and water resources, Progress in Physical Geography, doi:10.1177/0309133316632460, 2016.