A new probabilistic rational method for design flood estimation in ungauged catchments for the state of New South Wales in Australia

Design flood estimates for ungauged catchments are needed in the planning and design of bridges, culverts and many other water infrastructure projects. The most commonly used methods of flood estimation in practice for the ungauged catchments include the Index Flood Method, quantile regression technique and Probabilistic Rational Method (PRM). In Australia, the regional flood frequency estimation (RFFE) methods recommended in Australian Rainfall and Runoff (ARR) 1987 include PRM for eastern New South Wales (NSW) and Victoria States. In the upcoming ARR 2016, the recommended RFFE method is based on regression and region-of-influence approaches for NSW, which is referred to as RFFE Model 2015. In this study, a new PRM is developed and tested for NSW. A total of 106 catchments are used to develop and test the new PRM. These data are obtained from ARR Project 5 Regional Flood Methods. The catchment areas for the selected catchments range from 1 to 1010 km2. The mean and median catchment areas are 273 km2 and 169 km2, respectively. The streamflow record lengths range from 20 to 82 years, with a mean of 38 years and median of 35 years. Twelve different forms of PRM are examined, which are formed based on different combinations of observed runoff coefficients (C10) and frequency factors (FFY). The C10 values at a test catchment site are estimated using inverse distance weighted method based on different combinations of the at-site C10 values i.e. (i) nearest one site; (ii) two nearest sites; (iii) three nearest sites; and (iv) five nearest sites. The FFY values are estimated using three different approaches. A leave-one-out (LOO) validation approach is adopted to compare various forms of the PRM. At-site flood frequency analysis (based on the log Pearson Type 3- Bayesian method) is used as the ‘benchmark’ for this LOO validation. It is found that the best PRM case is achieved when C10 value is estimated from the three nearest sites and FFY is taken as the median value over all the model catchments. The results of this study reveal that the new PRM can be used to accurately predict the peak flow rates for small-to-medium sized catchments in the NSW region. For the new PRM, the typical median relative error values based on the leave-one-out validation is 45% to 55% for 20% to 1% annual exceedance probabilities. However, for the 50% AEP flood, the median relative error value is 77%. These relative error values are comparable to ARR RFFE Model 2015. The main advantage of the new PRM against the ARR 1987 is that it does not need a contour map to estimate the runoff coefficient and it can be automated in an application tool like the ARR RFFE Model 2015. The new PRM is being extended for other states of Australia.