Analysis of hourly rainfall data for the development of IDF relationships using the order statistics approach of probability distributions

Abstract

Rainfall intensities of various frequencies and durations are important parameters for the hydrologic design of storm sewers, culverts and other hydraulic structures. This can be achieved by the rainfall Intensity–Duration–Frequency (IDF) relationship, which is determined through rainfall frequency analysis. This paper exemplifies the use of the Gumbel and Fréchet distributions for modeling annual n-hourly maximum rainfall over different durations ‘n’ such as 1, 2, 3, 6, 12, 18, 24, 48, and 72 h (hr) recorded at Kanyakumari and Mandla rain-gauge stations. The order statistics approach is applied for the determination of distributional parameters in order to estimate rainfall and develop IDF relationships for different return periods. Goodness-of-Fit (GoF) tests such as the Anderson–Darling and Kolmogorov–Smirnov tests are employed for checking the adequacy of fitting the distributions to the recorded data. A diagnostic test involving the D-index is applied in order to select whether the Gumbel or the Fréchet is the most suitable distribution for the rainfall estimation. Model Performance Indicators (MPIs) such as the root mean square error and the correlation coefficient are used to analyse the performance of IDF relationships given by the Gumbel and Fréchet distributions. Based on the GoF and diagnostic test results, and MPI values, the study suggests that the IDF relationships developed using the Gumbel distribution are better suited for the estimation of rainfall intensity for Kanyakumari and Mandla.

Keywords:

• correlation
• Fréchet
• Gumbel
• mean square error
• order statistics
• rainfall

Keywords:

• C13
• C16 under C1
• C88 under C8

Acknowledgements

The author is grateful to the Director, Central Water and Power Research Station, Pune, for providing the research facilities to carry out the study. The author thanks the India Meteorological Department, Pune, for the supply of rainfall data.