Regional flood frequency analysis using Bayesian generalized least squares: a comparison between quantile and parameter regression techniques

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.

This paper presents the development and validation of an artificial intelligence based regional flood frequency analysis (RFFA) model for application in ungauged catchments of eastern Australia. The artificial intelligence based techniques with a flexible model structure and non-linear approach can overcome the limitations of the conventional RFFA models, which are generally based on linear relationship between flood statistics and catchment characteristics. Till now, there have been limited applications of artificial intelligence based techniques to RFFA problems in Australia. This study has developed four artificial intelligence based RFFA models for eastern Australia, using a comprehensive flood database available as a part of Australian Rainfall and Runoff (ARR) revision 'Project 5 Regional flood methods'. These four RFFA models are based on artificial neural network (ANN), genetic algorithm based artificial neural network (GAANN), gene-expression programing (GEP) and co-active neuron fuzzy inference system (CANFIS). A total of 452 catchments from the states of New South Wales, Victoria, Queensland and Tasmania have been considered by this study. These dataset is divided into training and validation sets. Data of 362 catchments (training data set) have been used to train the model and the data from the remaining 90 catchments (validation data set) used to validate the model. The models have been trained/calibrated using the training data set that involved minimisation of the mean squared error between the observed and predicted flood quantiles by the model (being trained) for a given ARI for the training data set. Six average recurrence intervals (ARI) flood quantiles (2, 5, 10, 20, 50 and 100 years) were considered in this study. Four evaluation statistics are adopted to assess the model accuracy: median ratio of the predicted flood quantile (Qpred) and observed flood quantile (Qobs), denoted by Qpred/Qobs ratio, plots of Qobs and Qpred, median relative error and coefficient of efficiency. This is initially done for the training data set and then repeated for the validation data set. The artificial intelligence based RFFA models have been ranked based on their relative performances in relation to the above criteria to identify the best trained/calibrated model. It has been found that none of the four models is superior across all the six ARIs against the adopted criteria. The ANN based RFFA model has a better ranking score in terms of training/calibration; therefore, it is suggested that the ANN-based RFFA model is the best calibrated model among the four artificial intelligence based RFFA models for eastern Australia.

This paper examines the applicability of principal component analysis (PCA) and cluster analysis in regional flood frequency analysis. A total of 88 sites in New South Wales, Australia are adopted. Quantile regression technique (QRT) is integrated with the PCA to estimate the flood quantiles. A total of eight catchment characteristics are selected as predictor variables. A leave-one-out validation is applied to determine the efficiency of the developed statistical models using an ensemble of evaluation diagnostics. It is found that the PCA with QRT model does not perform well, whereas cluster/group formed with smaller sized catchments performs better (with a median relative error values ranging from 22% to 37%) than other clusters/groups. No linkage is found between the degree of heterogeneity in the clusters/groups and precision of flood quantile prediction by the multiple linear regression technique.

In this paper, a new index is proposed for the selection of the best regional frequency analysis method. First, based on the theory of reliability, the new selective index is developed. The variances of three regional T‐year event estimators are then derived. The proposed methodology is applied to an actual watershed. For each regional method, the reliability of various T‐year regional estimates is computed. Finally, the reliability‐based selective index graph is constructed from which the best regional method can be determined. In addition, the selection result is compared with that based on the traditional index, root mean square error. The proposed new index is recommended as an alternative to the existing indices such as root mean square error, because the influence of uncertainty and the accuracy of estimates are considered. Copyright © 2003 John Wiley & Sons, Ltd.

Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin, China

Flood frequency analysis estimates reliable design flood, which is critical for the safety of any hydraulic, hydrologic construction and management. The overall objective of this study is to perform flood frequency analysis for Seonath and Hasdeo river basins of Chhattisgarh state, India. In this study, homogeneous regions are delineated by Ward cluster analysis. Cluster variables are L-moment ratios of annual maximum events and catchment characters. Index flood is performed for parametric quantile estimation of flood events. L-moments are employed in regionalization, frequency distribution selection, and distribution parameter estimation. Locally weighted polynomial model (Locfit) is performed for at-site frequency analysis. Flood quantiles are estimated for regions and at sites. In regional flood frequency analysis, regionalisation based on annual maximum flood series shows better flood quantiles than regionalisation based on site characteristics. It reveals that geophysical homogeneity does not mean hydrologic homogeneity. Regional formulae for annual mean discharge are formulated based on catchment character for estimation of flood quantiles for ungauged catchments.KeywordsFlood frequency analysisCluster analysisL-momentsIndex floodLocfit

Estimation of design floods in ungauged catchments using a regional index flood method. A case study of Lake Victoria Basin in Kenya

In semi-arid catchments, the contribution of floods to annual runoff is important. The High Atlas Mountain catchments (N’Fis, Rheraya, Ourika, Zat and R’dat) located in the south of Morocco, upstream of the city of Marrakech, are an example of those basins where floods provide the main contribution to surface water resources. The goal of this study is to evaluate whether a regional flood frequency analysis could improve the estimation of the magnitude and the occurrence of floods in these mountainous catchments. The database considered is long-term measurement of daily discharge at the outlets with record length varying from 35 to 45 years. The index flood method is considered to build a regional model based on the generalized extreme values distribution. The results showed a contrasted seasonal behavior, with floods caused by either rainfall during the autumn season or a mix of rainfall and snowmelt for spring events. As a consequence, two distinct regional models have been computed, one for autumn and one for spring events. No significant trends have been found for seasonal maximum discharge in all the catchments. The results of the regional frequency analysis show that the regional model provides better flood quantiles estimates than a standard at-site model. However, there is a much greater uncertainty for both local and regional estimates of floods occurring during the autumn than during spring events, which are estimated with a good level of accuracy. This research provides insights into how to improve the estimation of flood return levels useful for water resources management in these semi-arid mountainous catchments.

A basin -wide flood frequency analysis using Index flood and L-moment s approach offers an attractive solution to provide flood quant ile estimations at hundreds of ungauged sites within the Red River Basin of the North . L-moments diagrams and hierarchical clustering techniques were used initially to delineate hydrologic regions within the basin . Although the northern plain is relatively flat and almost monotonous, the analyses have show n that four homogeneous regions could be established for the basin . The whole basin as a region is also established for the purpose of flood estimations along the main stem . Appropriate probability distrib utions are fitted to t he pooled regional flood peak s in each region . Monte Carlo simulations are performed to decide the best distribution for each region , and the dominant distributions found are the Log -Pearson Type III and the generalized Pareto distrib utions . The regression of index flood with the physical factors of drainage area and basin slopes for two of the five regions are not very satisfactory . However, t he flood quantile estimates are sufficient for preliminary planning purposes. Basis for Reg ional Flood Frequency Analysis and L -moments The Red River of the North Basin has 91 gauged sites but that number was not sufficient for economic planning purposes as flood quantile estimations at hundreds of ungauged sites within the basin were required . Regional flood frequency analysis is a good alternative approach to flood quantile estimation using a single station approach. It is well accepted that using a regional approach in flood frequency analysis is effective in extending the flood information at a site to sites within a homogeneous region. Recent papers by Burn and Goel (2000), Cunderlik and Burn (2002), Pfister et al. (2002), and Lim and Lye (2003) are examples of such undertakings. The extension enables flood quantile estimates for any site i n a region to be expressed or inferred in terms of flood data recorded at all gauging sites in that region. Design flood estimations using a regional approach can often be carried out using methods such as the index -flood method and the direct regression o n quantiles method.

Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites

Regional flood frequency analysis by combining self-organizing feature map and fuzzy clustering

Region of influence is a common approach to estimate runoff information at ungauged locations. To estimate flood quantiles from annual maximum discharges, the Generalized Least Squares (GLS) framework has been recommended to account for unequal sampling variance and intersite correlation, which requires a proper evaluation of the sampling covariance structure. Since some jurisdictions do not have clear guidelines to perform this evaluation, a general procedure using copulas and a nonparametric intersite correlation model is investigated to estimate sampling covariance structure in situations where no common at-site distribution is imposed or when some paired sites do not have common periods of record. The investigated methodology is applied on 771 sites in Canada. The Normal copula is verified to be an adequate model that better fit paired observations than other types of extreme copulas. A sensitivity analysis is carried out to evaluate the impact of either ignoring, or considering a simpler form of, intersite correlation. Additionally, super regions are defined based on drainage area and mean annual precipitation to improve the calibration of pooling groups across large territories and a wide range of climate conditions. Performance criteria based on cross-validation revealed that using super regions and a combination of geographic distance and similarity between catchment descriptors improves the calibration of the pooling groups by providing more accurate estimates.

Water resource engineers extensively use regional flood frequency analysis to compute the discharge at ungauged sites with limited flow records in the river basins. Frequency and magnitude are the two important factors required to be analyzed for an effective assessment of flood disaster risk management. Globally, many linear clustering techniques are employed to categorize the watershed which are ineffective when dealing with noise and outliers. The present study overcomes this by proposing a relatively new nonlinear clustering algorithm based on hierarchical estimation of densities (NLCAHD) for the Cauvery basin, where the Homogeneity test (H) is enforced to identify the group of stations with same populations. Discordancy measure is carried out for screening the data in order to eliminate the conflicting sites from the group. The whole basin is classified into six homogeneous clusters, while the goodness of fit measure tests the data to distinguish the preferred distribution for the purpose of calculating the growth curves. A comparative study is made with the other linear algorithms such as K-means and C-means, which reveals the better performance of the proposed nonlinear model for identifying the homogeneous regions, in arriving at precise estimates of flood quantiles for various return periods up to 160 years.

The paper illustrates the results of regional flood frequency analysis of eleven sites of the four major rivers of Punjab, Pakistan. The discordancy measure (D i ) shows that none of the site, in the cluster of eleven sites, is discordant. Timing of the flood occurrences has been used, initially, for the formation of homogeneous region, but the heterogeneity measure (H) has shown a small amount of heterogeneity. To reduce the amount of heterogeneity, a subjective adjustment has been made considering the fact that a couple of site is located at the confluence of rivers. As a result, two homogeneous regions have been identified, i.e., Region 1 having nine sites and Region 2 containing couple of site located at the confluence of the rivers. In order to find out suitable candidate(s) for regional distribution L-moment ration diagram, average weighted distance and Z DIST statistics have been used. To obtain the flood quantiles at ungauged sites, multiple linear regression relationship has been developed, between mean of annual maximum peak flows (AMPF) at gauged sites (l 1) and best subset of site characteristics, i.e., average rainfall during monsoon and catchment area of the rivers to which the sites belong. A cross-validation with the observed AMPF from 2010 to 2014 and historical data (the highest of the AMPF attained so far at various sites of Region 1) showed that the estimates based on this model/procedure are accurate and useful, especially for the longer return periods.

<strong class="journal-contentHeaderColor">Abstract.</strong> A reliable flood frequency analysis (FFA) requires selection of an appropriate statistical distribution to model historic streamflow data and, where streamflow data are not available (ungauged sites), a regression-based regional flood frequency analysis (RFFA) often correlates well with downstream channel discharge to drainage area relations. However, the predictive strength of the accepted RFFA relies on an assumption of homogeneous watershed conditions. For glacially conditioned fluvial systems, inherited glacial landforms, sediments, and variable land use can alter flow paths and modify flow regimes. This study compares a multi-variate RFFA that considers 28 explanatory variables to characterize variable watershed conditions (i.e., surficial geology, climate, topography, and land use) to an accepted power-law relationship between discharge and drainage area. Archived gauge data from southern Ontario, Canada are used to test these ideas. Mathematical goodness-of-fit criteria best estimate flood discharge for a broad range of flood recurrence intervals, i.e., 1.25, 2, 5, 10, 25, 50, and 100 years. The LN, EV1, LP3, and GEV distributions are found most appropriate in 42.5 %, 31.9 %, 21.7 %, and 3.9 % of cases, respectively, suggesting that systematic model selection criterion is required for FFA in heterogeneous landscapes. Multi-variate regression of estimated flood quantiles with backward elimination of explanatory variables using principal component and discriminant analyses reveal that precipitation provides a greater predictive relationship for more frequent flood events, whereas surficial geology demonstrates more predictive ability for high magnitude, less frequent flood events. In this study, all seven flood quantiles identify a statistically significant two-predictor model that incorporates upstream drainage area and the percentage of naturalized landscape <em>with 5 % improvement</em> in predictive power over the commonly used single-variable drainage area model (<em>p</em> &lt; 2.2e&minus;16). An analysis of variance (ANOVA) further supports the two-predictor model indicating a decrease in the sum of squares of residuals and an F statistic (<em>p</em> &lt; 0.001) that demonstrates very strong evidence in favour of the two-predictor model (i.e., drainage area and land use) when estimating flood discharge in this low-relief landscape with pronounced glacial legacy effects and heterogenous land use.