A critical review of probability of extreme rainfall: principles and models

D. Koutsoyiannis, A critical review of probability of extreme rainfall: principles and models, Advances in Urban Flood Management, edited by R. Ashley, S. Garvin, E. Pasche, A. Vassilopoulos, and C. Zevenbergen, 139–166, doi:10.1201/9780203945988.ch7, Taylor and Francis, London, 2007.



Probabilistic modelling of extreme rainfall has a crucial role in flood risk estimation and consequently in the design and management of flood protection works. This is particularly the case for urban floods, where the plethora of flow control sites and the scarcity of flow measurements make the use of rainfall data indispensable. For half a century, the Gumbel distribution has been the prevailing model of extreme rainfall. Several arguments including theoretical reasons and empirical evidence are supposed to support the appropriateness of the Gumbel distribution, which corresponds to an exponential parent distribution tail. Recently, the applicability of this distribution has been criticized both on theoretical and empirical grounds. Thus, new theoretical arguments based on comparisons of actual and asymptotic extreme value distributions as well as on the principle of maximum entropy indicate that the Extreme Value Type 2 distribution should replace the Gumbel distribution. In addition, several empirical analyses using long rainfall records agree with the new theoretical findings. Furthermore, the empirical analyses show that the Gumbel distribution may significantly underestimate the largest extreme rainfall amounts (albeit its predictions for small return periods of 5-10 years are satisfactory), whereas this distribution would seem as an appropriate model if fewer years of measurements were available (i.e., parts of the long records were used).

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

PDF Additional material:

See also: http://dx.doi.org/10.1201/9780203945988.ch7


In section 5 entitled "Empirical justification of the distribution type of extreme rainfall" the first appearance of the word "underestimates" should be corrected to "overestimates", so that the sentence reads:

"These observations demonstrate how important the correct choice of the theoretical model is and how much the EV1 distribution overestimates the return period of extreme rainfall."

Our works that reference this work:

1. 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.
2. 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.
3. 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.

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

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

1. Clark, C., Flash floods - the Boltby incident, International Water Power and Dam Construction, 2008.
2. Sadiq, S. M., and N. H. Safaa, Comparing of standard and recent extreme probable distributions corresponding to Iraqi streams flow, Journal of Engineering and Development, 14 (4), 93-108, 2010.
3. Gubareva, T. S., Spatial patterns of flood distribution on rivers in temperate zone of the North Hemisphere, Izvestiya Akademii Nauk, Seriya Geograficheskaya, (2), 65-77, 2011.
4. #Liew, S. C., S. V. Raghavan, S.-Y. Liong and R. Sanders, Development of intensity-duration-frequency curves: incorporating climate change projection, Proc. 10th International Conference on Hydroinformatics, 2012.
5. #Liew, S. L., S.-Y. Liong and S. V. Raghavan, A novel approach, using regional climate model, to derive present and future IDF curves for data scarce sites, Willis Research Network, 2012.
6. Shahzadi, A., A. S. Akhter and B. Saf, Regional frequency analysis of annual maximum rainfall in monsoon region of Pakistan using L-moments, Pakistan Journal of Statistics and Operation Research, 9 (1), 111-136, 2013.
7. 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.
8. 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, 10.1002/hyp.9839, 2013.

Tagged under: Course bibliography: Hydrometeorology, Extremes, Rainfall models