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

Regression‐based regional flood frequency analysis (RFFA) methods are widely adopted in hydrology. This paper compares two regression‐based RFFA methods using a Bayesian generalized least squares (GLS) modelling framework; the two are quantile regression technique (QRT) and parameter regression technique (PRT). In this study, the QRT focuses on the development of prediction equations for a flood quantile in the range of 2 to 100 years average recurrence intervals (ARI), while the PRT develops prediction equations for the first three moments of the log Pearson Type 3 (LP3) distribution, which are the mean, standard deviation and skew of the logarithms of the annual maximum flows; these regional parameters are then used to fit the LP3 distribution to estimate the desired flood quantiles at a given site. It has been shown that using a method similar to stepwise regression and by employing a number of statistics such as the model error variance, average variance of prediction, Bayesian information criterion and Akaike information criterion, the best set of explanatory variables in the GLS regression can be identified. In this study, a range of statistics and diagnostic plots have been adopted to evaluate the regression models. The method has been applied to 53 catchments in Tasmania, Australia. It has been found that catchment area and design rainfall intensity are the most important explanatory variables in predicting flood quantiles using the QRT. For the PRT, a total of four explanatory variables were adopted for predicting the mean, standard deviation and skew. The developed regression models satisfy the underlying model assumptions quite well; of importance, no outlier sites are detected in the plots of the regression diagnostics of the adopted regression equations. Based on ‘one‐at‐a‐time cross validation’ and a number of evaluation statistics, it has been found that for Tasmania the QRT provides more accurate flood quantile estimates for the higher ARIs while the PRT provides relatively better estimates for the smaller ARIs. The RFFA techniques presented here can easily be adapted to other Australian states and countries to derive more accurate regional flood predictions. Copyright © 2011 John Wiley & Sons, Ltd.     

Development of regional flood frequency analysis techniques using generalized additive models for Australia

Estimation of flood quantiles in ungauged catchments is a common problem in hydrology. For this, the log-linear regression model is widely adopted. However, in many cases, a simple log transformation may not be able to capture the complexity and nonlinearity in flood generation processes. This paper develops generalized additive model (GAM) to deal with nonlinearity between the dependent and predictor variables in regional flood frequency analysis (RFFA) problems. The data from 85 gauged catchments from New South Wales State in Australia is used to compare the performances of a number of alternative RFFA methods with respect to variable selection, variable transformation and delineation of regions. Four RFFA methods are compared in this study: GAM with fixed region, log-linear model, canonical correlation analysis (to form neighbourhood in the space catchment attributes) and region-of-influence approach. Based on the outcome from a leave-one-out validation approach, it has been found that the GAM method generally outperforms the other methods even without linking GAM with a neighbourhood/region-of-influence approach. The main strength of GAM is that it captures the non-linearity between the dependent and predictor variables without any restrictive assumption. The findings of this study will encourage other researchers worldwide to apply GAM in RFFA studies, allowing development of more flexible and realistic RFFA models and their wider adoption in practice.     

Application of artificial neural networks in regional flood frequency analysis: a case study for Australia

Regional flood frequency analysis (RFFA) is widely used in practice to estimate flood quantiles in ungauged catchments. Most commonly adopted RFFA methods such as quantile regression technique (QRT) assume a log-linear relationship between the dependent and a set of predictor variables. As non-linear models and universal approximators, artificial neural networks (ANN) have been widely adopted in rainfall runoff modeling and hydrologic forecasting, but there have been relatively few studies involving the application of ANN to RFFA for estimating flood quantiles in ungauged catchments. This paper thus focuses on the development and testing of an ANN-based RFFA model using an extensive Australian database consisting of 452 gauged catchments. Based on an independent testing, it has been found that ANN-based RFFA model with only two predictor variables can provide flood quantile estimates that are more accurate than the traditional QRT. Seven different regions have been compared with the ANN-based RFFA model and it has been shown that when the data from all the eastern Australian states are combined together to form a single region, the ANN presents the best performing RFFA model. This indicates that a relatively larger dataset is better suited for successful training and testing of the ANN-based RFFA models.     

Artificial intelligence for identifying hydrologically homogeneous regions: A state‐of‐the‐art regional flood frequency analysis

Due to the severity related to extreme flood events, recent efforts have focused on the development of reliable methods for design flood estimation. Historical streamflow series correspond to the most reliable information source for such estimation; however, they have temporal and spatial limitations that may be minimized by means of regional flood frequency analysis (RFFA). Several studies have emphasized that the identification of hydrologically homogeneous regions is the most important and challenging step in an RFFA. This study aims to identify state‐of‐the‐art clustering techniques (e.g., K ‐means, partition around medoids, fuzzy C‐means, K ‐harmonic means, and genetic K ‐means) with potential to form hydrologically homogeneous regions for flood regionalization in Southern Brazil. The applicability of some probability density function, such as generalized extreme value, generalized logistic, generalized normal, and Pearson type 3, was evaluated based on the regions formed. Among all the 15 possible combinations of the aforementioned clustering techniques and the Euclidian, Mahalanobis, and Manhattan distance measures, the five best were selected. Several watersheds' physiographic and climatological attributes were chosen to derive multiple regression equations for all the combinations. The accuracy of the equations was quantified with respect to adjusted coefficient of determination, root mean square error, and Nash–Sutcliffe coefficient, whereas, a cross‐validation procedure was applied to check their reliability. It was concluded that reliable results were obtained when using robust clustering techniques based on fuzzy logic (e.g., K ‐harmonic means), which have not been commonly used in RFFA. Furthermore, the probability density functions were capable of representing the regional annual maximum streamflows. Drainage area, main river length, and mean altitude of the watershed were the most recurrent attributes for modelling of mean annual maximum streamflow. Finally, an integration of all the five best combinations stands out as a robust, reliable, and simple tool for estimation of design floods.     

Regional flood frequency analysis using support vector regression in arid and semi-arid regions of Iran

Regional flood frequency analysis (RFFA) was carried out on data for 55 hydrometric stations in Namak Lake basin, Iran, for the period 1992–2012. Flood discharge of specific return periods was computed based on the log Pearson Type III distribution, selected as the best regional distribution. Independent variables, including physiographic, meteorological, geological and land-use variables, were derived and, using three strategies – gamma test (GT), GT plus classification and expert opinion – the best input combination was selected. To select the best technique for regionalization, support vector regression (SVR), adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN) and nonlinear regression (NLR) techniques were applied to predict peak flood discharge for 2-, 5-, 10-, 25-, 50- and 100-year return periods. The GT + ANFIS and GT + SVR models gave better performance than the ANN and NLR models in the RFFA. The results of the input variable selection showed that the GT technique improved the model performance.     

Application of L‐moments and Bayesian inference for low‐flow regionalization in Sefidroud basin,Iran

Reliable estimation of low flows at ungauged catchments is one of the major challenges in water‐resources planning and management. This study aims at providing at‐site and ungauged sites low‐flow frequency analysis using regionalization approach. A two‐stage delineating homogeneous region is proposed in this study. Clustering sites with similar low‐flow L‐moment ratios is initially conducted, and L‐moment‐based discordancy and heterogeneity measures are then used to detect unusual sites. Based on the goodness‐of‐fit test statistic, the best‐fit regional model is identified in each hydrologically homogeneous region. The relationship between mean annual 7‐day minimum flow and hydro‐geomorphic characteristics is also constructed in each homogeneous region associated with the derived regional model for estimating various low‐flow quantiles at ungauged sites. Uncertainty analysis of model parameters and low‐flow estimations is carried out using the Bayesian inference. Applied in Sefidroud basin located in northwestern Iran, two hydrologically homogeneous regions are identified, i.e. the east and west regions. The best‐fit regional model for the east and west regions are generalized logistic and Pearson type III distributions, respectively. The results show that the proposed approach provides reasonably good accuracy for at‐site as well as ungauged‐site frequency analysis. Besides, interval estimations for model parameters and low flows provide uncertainty information, and the results indicate that Bayesian confidence intervals are significantly reduced when comparing with the outcomes of conventional t‐distribution method. Copyright © 2013 John Wiley & Sons, Ltd.     

A canonical correlation approach to the determination of homogeneous regions for regional flood estimation of ungauged basins

Abstract

A canonical correlation method for determining the homogeneous regions used for estimating flood characteristics of ungauged basins is described. The method emphasizes graphical and quantitative analysis of relationships between the basin and flood variables before the data of the gauged basins are used for estimating the flood variables of the ungauged basin. The method can be used for both homogeneous regions, determined a priori by clustering algorithms in the space of the flood-related canonical variables, as well as for “regions of influence” or “neighbourhoods” centred on the point representing the estimated location of the ungauged basin in that space.     

Flood frequency analysis of southern Africa: II. Identification of regional distributions

Abstract

Regional frequency analysis of annual maximum flood data comprising 407 stations from 11 countries of southern Africa is presented. Forty-one homogeneous regions are identified. The L-moments of the observed data indicate that the possible underlying frequency distributions are Pearson type 3 (P3), lognormal 3-parameter (LN3), General Pareto (GPA) or General Extreme Value (GEV). Simulation experiments for the selection of the most suitable flood frequency procedure indicate that Pearson type 3/Probability Weighted Moments (P3/PWM) and log-Pearson type 3/Method of Moments (LP3/MOM) are suitable procedures for the region.     

Have applications of continuous rainfall–runoff simulation realized the vision for process‐based flood frequency analysis?

Keith Beven was amongst the first to propose and demonstrate a combination of conceptual rainfall–runoff modelling and stochastically generated rainfall data in what is known as the ‘continuous simulation’ approach for flood frequency analysis. The motivations included the potential to establish better links with physical processes and to avoid restrictive assumptions inherent in existing methods applied in design flood studies. Subsequently, attempts have been made to establish continuous simulation as a routine method for flood frequency analysis, particularly in the UK. The approach has not been adopted universally, but numerous studies have benefitted from applications of continuous simulation methods. This paper asks whether industry has yet realized the vision of the pioneering research by Beven and others. It reviews the generic methodology and illustrates applications of the original vision for a more physically realistic approach to flood frequency analysis through a set of practical case studies, highlighting why continuous simulation was useful and appropriate in each case. The case studies illustrate how continuous simulation has helped to offer users of flood frequency analysis more confidence about model results by avoiding (or exposing) bad assumptions relating to catchment heterogeneity, inappropriateness of assumptions made in (UK) industry‐standard design event flood estimation methods, and the representation of engineered or natural dynamic controls on flood flows. By implementing the vision for physically realistic analysis of flood frequency through continuous simulation, each of these examples illustrates how more relevant and improved information was provided for flood risk decision‐making than would have been possible using standard methods. They further demonstrate that integrating engineered infrastructure into flood frequency analysis and assessment of environmental change are also significant motivations for adopting the continuous simulation approach in practice. Copyright © 2016 John Wiley & Sons, Ltd.     

An evaluation of a traditional and a neural net modelling approach to flood forecasting for an upland catchment

This study evaluates two (of the many) modelling approaches to flood forecasting for an upland catchment (the River South Tyne at Haydon Bridge, England). The first modelling approach utilizes ‘traditional’ hydrological models. It consists of a rainfall–runoff model (the probability distributed model, or PDM) for flow simulation in the upper catchment. Those flows are then routed to the lower catchment using two kinematic wave (KW) routing models. When run in forecast‐mode, the PDM and KW models utilize model updating procedures. The second modelling approach uses neural network models, which use a ‘pattern‐matching’ process to produce model forecasts.Following calibration, the models are evaluated in terms of their fit to continuous stage data and flood event magnitudes and timings within a validation period. Forecast times of 1 h, 2 h and 4 h are selected (the catchment has a response time of approximately 4 h). The ‘traditional’ models generally perform adequately at all three forecast times. The neural networks produce reasonable forecasts of small‐ to medium‐sized flood events but have difficulty in forecasting the magnitude of the larger flood events in the validation period. Possible modifications to the latter approach are discussed. © Crown copyright 2002. Reproduced with the permission of Her Majesty's stationery office. Published by John Wiley & Sons, Ltd.     

Sensitivity analysis of the probability distribution of groundwater level series based on information entropy

Information entropy is an effective method to analyze uncertainty in various processes. The principle of maximum entropy (POME) provides a guide line for the parameter estimation of probability density function (PDF). Mutual entropy analysis is well qualified for delineating the nonlinear and complex multivariable relationship. The probability distribution of model output is the element of model uncertainty analysis. In this paper, a synthetic groundwater flow field is build to produce groundwater level series (GLS). The probability distribution of GLS is obtained by the frequency analysis method based on POME and Chi-Squared test. The important uncertainty factors that affect the parameters of PDF of GLS are assessed by the sensitivity analysis methods, which include stepwise regression analysis and mutual entropy analysis. Results of this analysis indicate that most of the GLS follow normal distribution (or log-normal distribution), while a few obey others. The mean and variance of normal GLS are affected differently by the input variables of groundwater model. Mutual entropy analysis is more competitive and appropriate for delineating the nonlinear and nonmonotonic multivariable relationship than stepwise regression analysis.     

A dual two-stage stochastic model for flood management with inexact-integer analysis under multiple uncertainties

This study introduces a hybrid optimization approach for flood management under multiple uncertainties. An inexact two-stage integer programming (ITIP) model and its dual formation are developed by integrating the concepts of mixed-integer and interval-parameter programming techniques into a general framework of two-stage stochastic programming. The proposed approach provides a linkage to pre-defined management policies, deals with capacity-expansion planning issues, and reflects various uncertainties expressed as probability distributions and discrete intervals for a flood management system. Penalties are imposed when the policies are violated. The marginal costs are determined based on dual formulation of the ITIP model, and their effects on the optimal solutions are investigated. The developed model is applied to a case study of flood management. The solutions of binary variables represent the decisions of flood-diversion–capacity expansion within a multi-region, multi-flow-level, and multi-option context. The solutions of continuous variables are related to decisions of flood diversion toward different regions. The solutions of dual variables indicate the decisions of marginal costs associated with the resources of regions’ capacity, water availability, and allowable diversions. The results show that the proposed approach could obtain reliable solutions and adequately support decision making in flood management.     

Regional flood frequency and spatial patterns analysis in the Pearl River Delta region using L-moments approach

The Pearl River Delta (PRD) has one of the most complicated deltaic drainage systems with probably the highest density of crisscross-river network in the world. This article presents a regional flood frequency analysis and recognition of spatial patterns for flood-frequency variations in the PRD region using the well-known index flood L-moments approach together with some advanced statistical test and spatial analysis methods. Results indicate that: (1) the whole PRD region is definitely heterogeneous according to the heterogeneity test and can be divided into three homogeneous regions; (2) the spatial maps for annual maximum flood stage corresponding to different return periods in the PRD region suggest that the flood stage decreases gradually from the riverine system to the tide dominated costal areas; (3) from a regional perspective, the spatial patterns of flood-frequency variations demonstrate the most serious flood-risk in the coastal region because it is extremely prone to the emerging flood hazards, typhoons, storm surges and well-evidenced sea-level rising. Excessive rainfall in the upstream basins will lead to moderate floods in the upper and middle PRD region. The flood risks of rest parts are identified as the lowest in entire PRD. In order to obtain more reliable estimates, the stationarity and serial-independence are tested prior to frequency analysis. The characterization of the spatial patterns of flood-frequency variations is conducted to reveal the potential influences of climate change and intensified human activities. These findings will definitely contribute to formulating the regional development strategies for policymakers and stakeholders in water resource management against the menaces of frequently emerged floods and well-evidenced sea level rising.     

Assessment of flooding in urbanized ungauged basins: a case study in the Upper Tiber area,Italy

The reliability of a procedure for investigation of flooding into an ungauged river reach close to an urban area is investigated. The approach is based on the application of a semi‐distributed rainfall–runoff model for a gauged basin, including the flood‐prone area, and that furnishes the inlet flow conditions for a two‐dimensional hydraulic model, whose computational domain is the urban area. The flood event, which occurred in October 1998 in the Upper Tiber river basin and caused significant damage in the town of Pieve S. Stefano, was used to test the approach. The built‐up area, often inundated, is included in the gauged basin of the Montedoglio dam (275 km²), for which the rainfall–runoff model was adapted and calibrated through three flood events without over‐bank flow. With the selected set of parameters, the hydrological model was found reasonably accurate in simulating the discharge hydrograph of the three events, whereas the flood event of October 1998 was simulated poorly, with an error in peak discharge and time to peak of −58% and 20%, respectively. This discrepancy was ascribed to the combined effect of the rainfall spatial variability and a partial obstruction of the bridge located in Pieve S. Stefano. In fact, taking account of the last hypothesis, the hydraulic model reproduced with a fair accuracy the observed flooded urban area. Moreover, incorporating into the hydrological model the flow resulting from a sudden cleaning of the obstruction, which was simulated by a ‘shock‐capturing’ one‐dimensional hydraulic model, the discharge hydrograph at the basin outlet was well represented if the rainfall was supposed to have occurred in the region near the main channel. This was simulated by reducing considerably the dynamic parameter, the lag time, of the instantaneous unit hydrograph for each homogeneous element into which the basin is divided. The error in peak discharge and time to peak decreased by a few percent. A sensitivity analysis of both the flooding volume involved in the shock wave and the lag time showed that this latter parameter requires a careful evaluation. Moreover, the analysis of the hydrograph peak prediction due to error in rainfall input showed that the error in peak discharge was lower than that of the same input error quantity. Therefore, the obtained results allowed us to support the hypothesis on the causes which triggered the complex event occurring in October 1998, and pointed out that the proposed procedure can be conveniently adopted for flood risk evaluation in ungauged river basins where a built‐up area is located. The need for a more detailed analysis regarding the processes of runoff generation and flood routing is also highlighted. Copyright © 2005 John Wiley & Sons, Ltd.     

Comprehensive assessment of flood risk using the classification and regression tree method

The Evaluation of flood risk is a difficult task due to its numerous and complex impact factors. This article built a classification and regression tree (CART) model for the flood risk assessment with the available data of Hunan Province. This model is able to extract the major impact factors from many complex variables, determine the factors’ thresholds, and evaluate the levels of flood risk objectively. To construct the model, 18 explanatory variables were selected as the influential factors, including meteorological conditions, surface conditions and social vulnerability. Economic loss density from flood was chosen as the response variable for the quantitative and comprehensive evaluation of flood risk. The final model showed that meteorological conditions have the most significant influence on flood risk. Additionally, the relationship between meteorological factors and flood risk is rather complex. The variability of rainstorm days during the seasonal alternate period from the end of spring (May) to the early summer (June) is the source of the highest flood risk. In addition, the regional embankment density and population density as social vulnerability indicators and the relief degree of land surface as a surface condition indicator were also included in the flood risk assessment for Hunan. A region with dense dams appeared at a relatively higher risk. Densely inhabited areas with greater topographical relief also demonstrated a higher flood risk in the study area. The conditions obtained from the final tree for different levels of risk demonstrate the objectivity of selecting impact factors and a reduction of complexity for the risk evaluation process. Furthermore, the evaluation of high-level risk using the proposed method requires fewer conditions, which allows for a rapid risk assessment of serious floods. The CART method shows a decreased root mean squared error compared with that of a multiple linear regression model. In addition, the cross-validation error was improved for the high-risk levels that represent the most important classes in risk management. The verification with the available historical records showed that the output of the model is reliable. In summary, the CART method is feasible for extracting the main impact factors and their associated thresholds for the comprehensive assessment of regional flood risk.     

Multivariate homogeneity testing in a northern case study in the province of Quebec,Canada

In regional frequency analysis, the examination of the regional homogeneity represents an important step of the procedure. Flood events possess multivariate characteristics which can not be handled by classical univariate regional procedures. For instance, classical procedures do not allow to assess regional homogeneity while taking into consideration flood peak, volume and duration. Chebana and Ouarda proposed multivariate discordancy and homogeneity tests. They carried out a simulation study to evaluate the performance of these tests. In the present paper, practical aspects are investigated jointly on flood peak and flood volume of a data set from the Côte‐Nord region in the province of Quebec, Canada. It is shown that, after removing the discordant sites, the remaining ones constitute a homogeneous region for the volumes and heterogeneous region for the peaks. However, if both variables are jointly considered, the obtained region is possibly homogeneous. Furthermore, the results demonstrate the usefulness of the bivariate test to take into account the dependence structure between the variables representing the event, and to take advantage of more information from the hydrograph. Copyright © 2009 John Wiley & Sons, Ltd.     

Spatial prediction on river networks: comparison of top‐kriging with regional regression

Top‐kriging is a method for estimating stream flow‐related variables on a river network. Top‐kriging treats these variables as emerging from a two‐dimensional spatially continuous process in the landscape. The top‐kriging weights are estimated by regularising the point variogram over the catchment area (kriging support), which accounts for the nested nature of the catchments. We test the top‐kriging method for a comprehensive Austrian data set of low stream flows. We compare it with the regional regression approach where linear regression models between low stream flow and catchment characteristics are fitted independently for sub‐regions of the study area that are deemed to be homogeneous in terms of flow processes. Leave‐one‐out cross‐validation results indicate that top‐kriging outperforms the regional regression on average over the entire study domain. The coefficients of determination (cross‐validation) of specific low stream flows are 0.75 and 0.68 for the top‐kriging and regional regression methods, respectively. For locations without upstream data points, the performances of the two methods are similar. For locations with upstream data points, top‐kriging performs much better than regional regression as it exploits the low flow information of the neighbouring locations. Copyright © 2012 John Wiley & Sons, Ltd.     

A feature weighting and selection method for improving the homogeneity of regions in regionalization of watersheds

The method used for feature selection or feature weighting in regionalization of watersheds may affect the results of regionalization methods considerably. It can play a key role in forming hydrologically homogeneous regions for regional flood frequency analysis. In this study, a method based on exploring the nearest and farthest neighbours of data points is introduced for identifying salient features for regionalization of watersheds. The method includes options to relate watershed features to flood data records in order to increase the homogeneity of the regions. The nearest and farthest neighbours are identified based on the criteria such as the mutual information criterion and Spearman's rank correlation coefficient. Then, the watershed features more able to explain the relationships between the nearest and farthest neighbours are identified as salient features to form homogeneous features for regional flood frequency analysis. The results show that the optimum option of the proposed method improves the performances of the hard and fuzzy clustering algorithms in more than half of the cases based on the cluster validity indices. Furthermore, the results reveal that the optimum option can increase the number of the homogeneous regions formed by clustering algorithms to a great extent. By using the optimum option with 5 nearest and 5 farthest neighbours, longitude, drainage area, and run‐off coefficient are identified as the salient features to regionalize Sefidrud basin. The results show that the proposed method can be considered as an efficient method to form homogeneous regions for regional flood frequency analysis.     

Regional flood frequency analysis using residual kriging in physiographical space

In this article, an approach using residual kriging (RK) in physiographical space is proposed for regional flood frequency analysis. The physiographical space is constructed using physiographical/climatic characteristics of gauging basins by means of canonical correlation analysis (CCA). This approach is a modified version of the original method, based on ordinary kriging (OK). It is intended to handle effectively any possible spatial trends within the hydrological variables over the physiographical space. In this approach, the trend is first quantified and removed from the hydrological variable by a quadratic spatial regression. OK is therefore applied to the regression residual values. The final estimated value of a specific quantile at an ungauged station is the sum of the spatial regression estimate and the kriged residual. To evaluate the performance of the proposed method, a cross‐validation procedure is applied. Results of the proposed method indicate that RK in CCA physiographical space leads to more efficient estimates of regional flood quantiles when compared to the original approach and to a straightforward regression‐based estimator. Copyright © 2010 John Wiley & Sons, Ltd.