Regional analysis of PROQ transforms for flood frequency estimation based on GRADEX principles

ABSTRACT

The PROQ transform which converts rainfall P to runoff RO, then factored to produce peak discharge Q, can be used for regional design flood estimation. SPEED, a French method based on GRADEX principles is a PROQ transform. 1 in 100 annual exceedance probability discharges was estimated using SPEED for 40 Australian non-urban catchments. Inputs are catchment area and areal design rainfall depth. The SPEED transform involves three constant parameters: scaling factor a, non-linearity b and retention L. SPEED was found to be simple and effective (Nash-Sutcliffe E = 0.82). A local version of SPEED produced a similar performance (E = 0.74). A general form of PROQ was developed to explain similarities with other models such as the Probabilistic Rational Method and to develop the local SPEED transform. Gauge sites can be grouped based on a and L ‘bins’, using site-based mean values of these parameters. A PROQ model using two a bins and two L bins significantly enhanced predictive accuracy (E = 0.92).

KEYWORDS:

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

List of acronyms

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

E Nash-Sutcliffe efficiency

ENSO El Nino-Southern Oscillation

FFA 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

IFD Intensity-frequency-duration as applied to design rainfalls

IPO Interdecadal Pacific Oscillation

L Retention of rainfall within the catchment during flood event, expressed as a depth

LP3 Log Pearson 3 probability distribution

MRE Mean absolute relative error

P Rainfall depth

PRM Probabilistic Rational Method. An ARR 1987 method for ungauged, undeveloped Australian catchments superseded in 2016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)

RFFE Regional flood frequency estimation

RO Flood event runoff depth

SPEED Probabilistic System for Discrete Event-based Studies (French acronym) as described by Cayla (1993)

SR30 Strike rate of estimates within ±30% tolerance

Notes

1. For brevity, the PROQ transfer function and associated formula and variations will be referred to as PROQ.

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, Toowoomba. 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.