Design flood estimation in ungauged catchments: Quantile regression technique and probabilistic rational method compared

Estimation of design floods in ungauged catchments is frequently required in hydrological practice and is of great economic significance. The most commonly adopted methods for this task include the Probabilistic Rational Method, the U.S. Soil Conservation Service Method, the Index Flood Method and the U. S. Geological Survey Quantile Regression Technique. The Probabilistic Rational Method has been recommended in the Australian Rainfall and Runoff for general use in south-east Australia (I. E. Aust., 1997). The central component of this technique is a dimensionless runoff coefficient which in the ARR is assumed to vary smoothly over geographical space, an assumption that may not be satisfied in many cases because two nearby catchments though are likely to share similar climatic characteristics but may exhibit quite different physical characteristics. There has been limited study on the assessment of the Probabilistic Rational Method on independent test catchments. Recently, a Quantile Regression Technique has been proposed for south-east Australia (Rahman, 2005). This paper compares the performances of the Probabilistic Rational Method and Quantile Regression Technique for south-east Australian catchments. The study uses streamflow and catchment characteristics data from 98 catchments in southeast Australia. A total of 20 catchments were selected randomly from the 98 catchments and put aside for independent testing of the Quantile Regression Technique and the Probabilistic Rational Method. The 20 test catchments and the 78 catchments used for the model development were found to have very similar catchment characteristics. It has been found that the Quantile Regression Technique in general provides more accurate design flood estimates than the Probabilistic Rational Method. The 75^th percentile values of the relative errors in design flood estimates for the average recurrence intervals of 2, 5, 10, 20, 50 and 100 years were in the range of 45 to 62% for the Quantile Regression Technique as compared to 61% to 80% for the Probabilistic Rational Method. It has also been found that there is a chance of about 10% that the error in design flood estimates will exceed 100% with both the Quantile Regression Technique and the Probabilistic Rational Method. Hence, the users of these techniques should be aware of this large error and provision should be made accordingly.