Magnitude Frequency Analysis of Small Floods Using the Annual and Partial Series

David Keast,Joanna Ellison

doi:10.3390/w5041816

Abstract

Flood frequency analysis using partial series data has been shown to provide better estimates of small to medium magnitude flood events than the annual series, but the annual series is more often employed due to its simplicity. Where partial series average recurrence intervals are required, annual series values are often “converted” to partial series values using the Langbein equation, regardless of whether the statistical assumptions behind the equation are fulfilled. This study uses data from Northern Tasmanian stream-gauging stations to make empirical comparisons between annual series and partial flood frequency estimates and values provided by the Langbein equation. At T = 1.1 years annual series estimates were found to be one third the magnitude of partial series estimates, while Langbein adjusted estimates were three quarters the magnitude of partial series estimates. The three methods converged as average recurrence interval increased until there was no significant difference between the different methods at T = 5 years. These results suggest that while the Langbein equation reduces the differences between the quantile estimates of annual maxima derived from annual maxima series and partial duration series flood frequency estimates, it does not provide a suitable alternative method to using partial series data. These results have significance for the practical estimation of the magnitude-frequency of small floods.

Highlights

Estimates of the size and frequency of floods is important for infrastructure planning and design and in the management of water resources and riparian areas [1]
Data generally conformed well to statistical models, with both annual series and partial series flood frequency curves created from the probability distributions providing a fairly good fit (Figure 2) with the observed data from each of the thirteen stream gauging stations
This is demonstrated by results from the South Esk River above Macquarie River (Site 181) (Figure 2), with graphs of the fitted distributions against the observed data for both the annual and partial series for that site shown in Figure 2a and 2b respectively

Summary

Introduction

Estimates of the size and frequency of floods is important for infrastructure planning and design and in the management of water resources and riparian areas [1]. The Institution of Engineers Australia (IEA) recommends the use of the partial series for estimating the magnitude-frequency of frequent floods [4], as it has been shown to provide more accurate estimates of frequent flood events than the annual series [3,4]. The magnitude of frequent flood events is commonly determined by transforming annual series estimates using a formula known as the Langbein equation. Developed for use in specific statistical situations, the Langbein equation has subsequently been commonly used as a practical method to convert annual series intervals to partial series intervals, even when the statistical assumptions behind the equation are not met [5,9,10,11,12,13]

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