Khaled Haddad

A study on selection of probability distributions for at-site flood frequency analysis in Australia

The most direct method of design flood estimation is at-site flood frequency analysis, which relies on a relatively long period of recorded streamflow data at a given site. Selection of an appropriate probability distribution and associated parameter estimation procedure is of prime importance in at-site flood frequency analysis. The choice of the probability distribution for a given application is generally made arbitrarily as there is no sound physical basis to justify the selection. In this study, an attempt is made to investigate the suitability of as many as fifteen different probability distributions and three parameter estimation methods based on a large Australian annual maximum flood data set. A total of four goodness-of-fit tests are adopted, i.e., the Akaike information criterion, the Bayesian information criterion, Anderson–Darling test, and Kolmogorov–Smirnov test, to identify the best-fit probability distributions. Furthermore, the L-moments ratio diagram is used to make a visual assessment of the alternative distributions. It has been found that a single distribution cannot be specified as the best-fit distribution for all the Australian states as it was recommended in the Australian rainfall and runoff 1987. The log-Pearson 3, generalized extreme value, and generalized Pareto distributions have been identified as the top three best-fit distributions. It is thus recommended that these three distributions should be compared as a minimum in practical applications when making the final selection of the best-fit probability distribution in a given application in Australia.

Design flood estimation in ungauged catchments: a comparison between the probabilistic rational method and quantile regression technique for NSW

Abstract Design flood estimation for ungauged catchments is often required in hydrologie design. The most commonly adopted regional flood frequency analysis methods used for this purpose include the index flood method, regression based techniques and various forms of the rational method. This paper first examines the similarities and differences between the probabilistic rational method (PRM) (the currently recommended method for Victoria and eastern NSW in Australian Rainfall and Runoff) and the generalised least squares (GLS) based quantile regression technique (QRT). It then uses data from 107 catchments in NSW to compare the performance of these two methods. To make a valid comparison, the same predictor variables and data set have been used for both methods. Based on one-at-a-time and split sample validation tests and a range of evaluation statistics, it has been found that the GLS-based QRT performs better than the PRM. The particular advantage of the QRT is that it does not require a contour map of the runoff coefficient as with the PRM. The QRT also offers potential for improvement through inclusion of additional predictor variables. The QRT can also be integrated with the region of influence approach, where a region can be formed around an ungauged catchment by selecting an “appropriate number” of neighbouring gauged catchments. Overall, the QRT offers much greater flexibility and potential in terms of error analysis and further development as compared to the PRM.

Streamflow Data Preparation for Regional Flood Frequency Analysis: Lessons from Southeast Australia

Abstract This paper presents a case study on streamflow data preparation for a regional flood frequency analysis (RFFA) project for the states of Victoria and NSW, in connection with the forthcoming edition of Australian Rainfall and Runoff. The study gathered annual maximum flood series data for a large number of stations from Victoria and NSW, and applied various statistical techniques to prepare the final data set. It was found that a large primary data set, even if selected using a fairly stringent set of criteria, cannot guarantee a similarly large final data set, as streamflow data are affected by many sources of uncertainty. The trade-offs between quality and quantity are discussed and illustrated. The maximum rating ratio, defined as the ratio of the largest estimated flow and the maximum measured flow at a gauging station, is used to identify stations whose quantiles may be seriously affected by rating curve errors. In a case study involving Victorian stations, the importance of maintaining a high spatial coverage of stations was demonstrated. It was shown that a 50% reduction in the number of stations used in a RFFA resulted in an increase of the standard error of prediction of flood quantiles up to 90%.

Regional flood frequency analysis method for Tasmania, Australia: a case study on the comparison of fixed region and region-of-influence approaches

Abstract A new regional flood frequency analysis method for Tasmania is developed using data from 53 gauged catchments. The Bayesian generalized least squares regression (BGLSR) approach is used to developing prediction equations for selected flood quantiles using a quantile regression technique (QRT) and the first three moments of the log Pearson Type 3 distribution by means of a parameter regression technique (PRT). Regions are formed in three ways: (a) a fixed-region approach is examined in which all the sites in Tasmania are assumed to form one region; (b) a region of influence (ROI) approach is investigated in which a region is formed around each of the sites based on the criterion of minimum model error variance; and (c) the state of Tasmania is divided into two fixed regions (east Tasmania and west Tasmania) based on their distinct rainfall regimes. Independent testing showed that the BGLSR-ROI approach can deal quite well with the uncertainty in the regional estimation, as shown by the various regression diagnostics. Furthermore, the PRT-ROI approach was found to provide quantile estimates that are generally more accurate and consistent than the QRT. Generally, the ROI approach outperformed the fixed-region approach for Tasmania.

Uncertainty analysis of pollutant build-up modelling based on a Bayesian weighted least squares approach

Reliable pollutant build-up prediction plays a critical role in the accuracy of urban stormwater quality modelling outcomes. However, water quality data collection is resource demanding compared to streamflow data monitoring, where a greater quantity of data is generally available. Consequently, available water quality datasets span only relatively short time scales unlike water quantity data. Therefore, the ability to take due consideration of the variability associated with pollutant processes and natural phenomena is constrained. This in turn gives rise to uncertainty in the modelling outcomes as research has shown that pollutant loadings on catchment surfaces and rainfall within an area can vary considerably over space and time scales. Therefore, the assessment of model uncertainty is an essential element of informed decision making in urban stormwater management. This paper presents the application of a range of regression approaches such as ordinary least squares regression, weighted least squares regression and Bayesian weighted least squares regression for the estimation of uncertainty associated with pollutant build-up prediction using limited datasets. The study outcomes confirmed that the use of ordinary least squares regression with fixed model inputs and limited observational data may not provide realistic estimates. The stochastic nature of the dependent and independent variables need to be taken into consideration in pollutant build-up prediction. It was found that the use of the Bayesian approach along with the Monte Carlo simulation technique provides a powerful tool, which attempts to make the best use of the available knowledge in prediction and thereby presents a practical solution to counteract the limitations which are otherwise imposed on water quality modelling.

Comparison of ordinary and generalised least squares regression models in regional flood frequency analysis: A case study for New South Wales

Abstract Regional flood frequency analysis (RFFA) techniques are commonly used to estimate design floods for ungauged catchments. In Australian Rainfall and Runoff (ARR), the probabilistic rational method (PRM) was recommended for eastern New South Wales (NSW). Recent studies in Australia have shown that regression-based RFFA methods can provide more accurate design flood estimates than the PRM. This paper compares ordinary least squares (OLS) and generalised least squares (GLS) based quantile regression techniques using data from 96 small-to medium-sized catchments across NSW for average recurrence intervals of 2 to 100 years. The advantages of the GLS regression are that this accounts for the inter-station correlation and varying record lengths from site to site. An independent test based on both the split-sample and one-at-a-time validation approaches employing a wide range of statistical diagnostics indicates that the GLS regression provides more accurate flood quantile estimates than the OLS one. The developed regression equations are relatively easy to apply, which require data for only two to three predictors, catchment area, design rainfall intensity and stream density. The findings from this study together with those from other RFFA studies being examined as a part of ARR upgrade projects will inform the development of RFFA techniques for inclusion in the revised edition of ARR.

Derivation of short-duration design rainfalls using daily rainfall statistics

Abstract Design rainfall intensity–frequency–duration data are a basic input to many water-related development projects. To derive design rainfalls, one needs long period of recorded rainfall data. Although daily rainfall data are generally widely available, short-duration rainfall data are scarce. For many urban applications, design rainfalls for much shorter durations are needed, which cannot be obtained directly from daily read rainfall data. This paper presents a simple approach that can be adopted to derive design rainfalls of short durations using daily rainfall data and other physio-climatic characteristics using a novel ‘index frequency combined with parameter regression technique’. This uses L moments to reduce the impacts of sampling variability in the analysis. Furthermore, this adopts generalised least squares regression to account for the inter-station correlation of the rainfall data in the analysis. The proposed method is applied to a pilot data set consisting of 203 rainfall stations across Australia. An independent Monte Carlo cross-validation test shows that the proposed method is capable of generating consistent and accurate design rainfall estimates from 6-min to 12-h duration. The developed technique can be adapted to other countries where there is a scarcity of short-duration rainfall data, but daily rainfall data are abundant.

Regional Flood Estimation in New South Wales Australia Using Generalized Least Squares Quantile Regression

This paper investigates the applicability of quantile regression technique (QRT) as a viable regional flood frequency analysis (RFFA) method for the state of New South Wales in Australia. The study uses data from 96 small to medium-sized unregulated basins across New South Wales to develop a generalized least squares (GLS)-based QRT. An independent test employing a wide range of statistical diagnostics indicates that the developed regression equations based on the GLS regression can provide quite accurate flood quantile estimates with median relative error values in the range of 13–42%. The developed regression equations are relatively easy to apply and require data for only three predictors—basin area, design rainfall intensity, and stream density.

A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling.

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

Design Flood Estimation for Ungauged Catchments: Application of Artificial Neural Networks for eastern Australia

Design flood estimation in small to medium sized ungauged catchments is frequently required in hydrological design of water infrastructure. In Australia, design flood estimation in smaller ungauged catchments is often estimated using the rational method. In recent years, there have been notable researches in Australia on the replacement of the rational method by other techniques which are hydrologically more meaningful and which can overcome the major limitations with the rational method. These methods include various forms of regression approaches and index flood methods. This paper focuses on the application of the artificial neural networks (ANN) to design flood estimation in ungauged catchments in the eastern part of Australia. This uses data from 399 stream gauging stations across eastern Australia to develop a regional flood estimation method based on the ANN. An independent test based on split-sample validation shows that the ANN can provide quite reasonable design flood estimates for small to medium sized ungauged catchments in eastern part of Australia. The best model was found to include two variables, catchment area and design rainfall intensity for the average recurrence intervals in the range of 10 to 100 years.