Probability distributions for explaining hydrological losses in South Australian catchments

S H P W Gamage,S Beecham,G A Hewa

doi:10.5194/hess-17-4541-2013

S H P W Gamage, S Beecham + Show 1 more

Open Access

https://doi.org/10.5194/hess-17-4541-2013

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Abstract

Abstract. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall–runoff models. The use of representative single values of hydrological losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. The probability distribution method is potentially a better technique to describe losses. However, a lack of understanding of how losses are distributed can limit the use of this technique. This paper aims to identify a probability distribution function that can successfully describe hydrological losses of a catchment of interest. The paper explains the systematic process of identifying probability distribution functions, the problems faced during the distribution fitting process and a new generalised method to test the adequacy of fitted distributions. The goodness-of-fit of the fitted distributions are examined using the Anderson–Darling test and the Q–Q plot method and the errors associated with quantile estimation are quantified by estimating the bias and mean square error (MSE). A two-parameter gamma distribution was identified as one that successfully describes initial loss (IL) data for the selected catchments. Further, non-parametric standardised distributions that describe both IL and continuing loss data are also identified. This paper will provide a significant contribution to the Australian Rainfall and Runoff (ARR) guidelines that are currently being updated, by improving understanding of hydrological losses in South Australian catchments. More importantly, this study provides new knowledge on how IL in a catchment is characterised.

Highlights

Hydrological losses have wide temporal and spatial variability, but are important inputs to rainfall–runoff (RR) models
The A–D test was carried out to investigate whether the initial loss (IL) and continuing loss (CL) data follow the normal, exponential or Weibull distributions
The two–parameter gamma distribution was successfully fitted for observed IL data

Summary

Introduction

Hydrological losses have wide temporal and spatial variability, but are important inputs to rainfall–runoff (RR) models. Considering the random nature of hydrological losses, probabilistic modelling has been suggested as a better approach to overcome the problems associated with models that use single representative values of input parameters (Rahman et al, 2000; Loveridge et al, 2012; Hill et al, 2012; Rahman et al, 2002a; Nathan et al, 2003; Kuczera et al, 2006b). A joint probability approach (JPA) that incorporates probabilistic behaviours of the input variables can improve RR simulations (Golian et al, 2012), and improve estimation of major flood flows that are required for the design and operation of large water infrastructure (Haddad et al, 2010a; Rahman et al, 2000, 2002b; Nathan et al, 2003; Kuczera et al, 2006a). The most common parameters included in JPAs include initial soil moisture

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