Estimation of extreme quantiles at ungaged sites based on region-of-influence and weighting approaches to regional frequency analysis of maximum 24-h rainfall

  • Farshad Fathian
  • Zohreh DehghanEmail author
  • Seyed Saeid Eslamian
Original Paper


Lack of adequate and reliable data for estimating the extreme values of hydrological variables at ungaged sites has always been one of the issues facing hydrologists in designing and planning water resource projects. Regionalizing the considered hydrological variable, finding an acceptable relationship for estimating its extreme values at ungaged sites using given data of other stations, and applying their available attributes are the solutions for the mentioned issue. In this study, historical data of maximum 24-h rainfall (M24-hR) covering the statistical period of 30 years (1979–2008) were collected and used from 63 rainfall gaging stations situated at Lake Urmia basin, northwestern Iran. Afterwards, using the method of region-of-influence (ROI) regionalization, the study area was regionalized through the geographic attributes of the stations (including latitude, longitude, elevation above mean sea level, and distance to the center of Lake Urmia). Then, all possible situations were considered for providing an appropriate regression relationship to estimate the extreme quantiles of M24-hR at ungaged sites by defining various scenarios of weighting to the geographic attributes and rainfall quantiles. The results showed that among different defined weighting scenarios, weighting to both stations and attributes in the at-site situation had an effective impact on forming an appropriate regression relationship for the estimation of extreme quantiles at ungaged sites. However, in the regional situation, a scenario considering no weight for both stations and attributes resulted in the most acceptable estimation of the quantiles with the lowest error (MSE = 1.29 mm). Further, the study showed that in most scenarios, the extreme quantiles estimated by means of regional regression relationships at ungaged sites (MSE = 1.29~1.75 mm) resulted in lower errors than the at-site ones (MSE = 1.35~7.64 mm).


Regionalization Extreme quantiles Ungaged sites Regression relationship Weighting procedure Lake Urmia basin 



The authors acknowledge the Water Resources Management Company of Iran, the Meteorological Organization of Iran, and Isfahan University of Technology for providing data. The authors also appreciate the two anonymous reviewers for their helpful comments, which improved the quality of the paper.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Farshad Fathian
    • 1
  • Zohreh Dehghan
    • 2
    Email author
  • Seyed Saeid Eslamian
    • 2
  1. 1.Department of Water Science and Engineering, Faculty of AgricultureVali-e-Asr University of RafsanjanRafsanjanIran
  2. 2.Department of Water Engineering, Faculty of AgricultureIsfahan University of TechnologyIsfahanIran

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