An evaluation of a multi-day rainfall – runoff volume – peak discharge transform for flood frequency estimation

ABSTRACT

A new method to estimate design discharge quantiles is described based on converting multi-day rainfall P to flood event runoff RO, factored to generate discharge Q. The so-called PROQ transfer function is founded on simple flood volume-peak and GRADEX rainfall-runoff tanh relationships. Performance testing of PROQ, in both at-site and regional design flood contexts up to 1 in 100 annual exceedance probability, was made using south east Queensland streamgauge data. A statistical comparison against proven methods showed that the PROQ transform has significant potential as an alternative for design flood estimation. An example of how PROQ can be used within a design flood framework and recommendations for further enhancement are provided.

Abbreviations: AEP: Annual exceedance probability; AMS: Annual maximum series, extracted from the flood record at a gauge site; ANOVA: Analysis of variance; ARR: Australian Rainfall and Runoff guidelines; A-S: At-site. Describes a set of methods to estimate design flood quantiles by statistical analysis of the flood record at an individual gauge site; E: Nash–Sutcliffe efficiency; FFA: Flood frequency analysis; G-B: Multiple Grubbs-Beck test recommended by ARR 2019 for low flow censoring. Used for at-site flood frequency analysis; GEV: General extreme value probability distribution; GRADEX: Gradient of extreme values. Design flood probability concept originating in France based on parallelism of rainfall and runoff quantile curves; L: Retention of rainfall within the catchment during flood event, expressed as a depth; LP3: Log Pearson 3 probability distribution; P: Rainfall depth; PRM: Probabilistic Rational Method. An ARR method for ungauged, undeveloped Australian catchments superseded in 2016; PROQ: Transfer function based on converting P to RO and then factoring RO to estimate Q; PW: Palmen and Weeks. Regional method for ungauged, undeveloped Queensland catchments developed by Palmen and Weeks (2011); R: Retention curve number. Used in probabilistic charting of design floods based on PROQ; RE: Absolute relative error; REG: Regional. Describes a set of methods to estimate design flood quantiles using information obtained from at-site analyses of several representative catchments within a region; RO: Flood event runoff depth; SR30: Strike rate of estimates within ±30% tolerance.

KEYWORDS:

• Flood frequency
• design flood
• annual maximum series
• rainfall-runoff
• GRADEX, PROQ

Acknowledgments

The author appreciates the detailed and valuable comments provided by the editor and four anonymous reviewers which have led to considerable improvements to this paper.

Notes

1. With reference to his paper, equation 1 can be obtained by setting the weighting parameter r to zero.

Additional information

Notes on contributors

Ian Brodie

Ian Brodie is a water engineer who has worked as a consultant with major Australian firms and as an academic at the University of Southern Queensland, Australia. Ian has completed a Masters in Engineering Science at the University of New South Wales and a PhD on the topic of urban stormwater pollution at USQ. His technical interests are urban stormwater management and flood hydrology.