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

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.

Evaluating Annual Maximum and Partial Duration Series for Estimating Frequency of Small Magnitude Floods

“…While previous studies (e.g., [14,16,20,21]) as well this study clearly indicate that the POT series better estimates small magnitude floods compared to the AM series, the POT method is not error free. As the selection of a POT discharge is an iterative process, it can produce fewer or greater numbers …”

“…To construct a flood series dataset, previous studies used both the daily mean (e.g., [14,17,19]) and daily instantaneous maximum (e.g., [18,31]) discharge data. None of the studies identified any particular difference in magnitude-frequency relationship based on whether daily mean or daily instantaneous maximum flow was used to generate a flood series.…”

“…Previous studies used both the annual maximum (AM) and peak over threshold (POT) series (commonly known as partial series) to estimate flood frequency in Australia (e.g., [13][14][15]) and elsewhere (e.g., [16][17][18]). The advantage of the AM series is that flood events can be considered independent, flood data can be extracted easily and frequency distributions generally conform to theoretical distributions.…”

Sensitivity of flood frequency analysis to data record, statistical model, and parameter estimation methods: An evaluation over the contiguous United States

“…However, in the case of limited data records (usually 10 to 20 years), only few data points are available for the estimation of the model parameters, causing important uncertainties in the parameters estimation (Keast & Ellison, 2013). To overcome this limitation and extend the available information, the partial duration series (PDS) approach, also known as peaks over threshold (PoT) can be adopted (Cunnane, 1973;Madsen, Rasmussen, & Rosbjerg, 1997).…”

A Novel Approach for Estimating the Recurrence Intervals of Channel-Forming Discharges

“…Using a partial duration series, also called peaks over threshold approach, to determine the RI has also seen much application [33][34][35][36][37][38][39]. For frequent floods, it is the recommended method as it provides better estimates than the annual series of peaks approach [38].…”