Investigating the behaviour of a small Mediterranean catchment using three different hydrological models as hypotheses

Mediterranean catchments are characterized by strong nonlinearities in their hydrological behaviour. Properly simulating those nonlinearities still represents a great challenge and, at the same time, an important issue in order to improve our knowledge of their hydrological behaviour. The main aim of this work is find out diverse modelling approaches to reproduce the observed nonlinear hydrological behaviour in a small Mediterranean catchment, Can Vila (Vallcebre, NE Spain). To this end, three hydrological models were considered: two lumped models called LU3 and LU4 of increasing complexity, and a distributed model called TETIS. The structures of these different models were used as hypotheses, which could explain and reproduce the observed nonlinear behaviour at the outlet. Four analyses were carried out: (i) goodness‐of‐fit criteria analysis, (ii) residual errors analysis, (iii) sensitivity analysis and (iv) multicriteria analysis based on the concept of Pareto Optimal. These analyses showed the higher capability and robustness of the distributed model to reproduce the observed complex hydrological behaviour in this catchment. Copyright © 2015 John Wiley & Sons, Ltd.     

Selection between the generalized Pareto and kappa distributions in peaks-over-threshold hydrological frequency modelling

Hydrologists use the generalized Pareto (GP) distribution in peaks-over-threshold (POT) modelling of extremes. A model with similar uses is the two-parameter kappa (KAP) distribution. KAP has had fewer hydrological applications than GP, but some studies have shown it to merit wider use. The problem of choosing between GP and KAP arises quite often in frequency analyses. This study, by comparing some discrimination methods between these two models, aims to show which method(s) is (are) recommended. Three specific methods are considered: one uses the Anderson-Darling goodness-of-fit (GoF) statistic, another uses the ratio of maximized likelihood (closely related to the Akaike information criterion and the Bayesian information criterion), and the third employs a normality transformation followed by application of the Shapiro-Wilk statistic. We show this last method to be the most recommendable, due to its advantages with sizes typically encountered in hydrology. We apply the simulation results to some flood POT datasets.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR E. Volpi     

Design event selection in bivariate hydrological frequency analysis

Abstract

In the bivariate analysis of hydrological events, such as rainfall storms or flood hydrographs, the choice of an appropriate return period for structure design leads to infinite combinations of values of the related random variables (e.g. peak and volume in the analysis of floods). These combinations are generally not equivalent, from a practical point of view. In this paper, a methodology is proposed to identify a subset of the critical combinations set that includes a fixed and arbitrarily chosen percentage in probability of the events, on the basis of their probability of occurrence. Therefore, several combinations can be selected within the subset, taking into account the specific characteristic of the design problem, in order to evaluate the effects of different hydrological loads on a structure. The proposed method is applicable to any type of bivariate distribution, thus providing a simple but effective rule to narrow down the infinite possible choices for the hydrological design variables. In order to illustrate how the proposed methodology can be easily used in practice, it is applied to a study case in the context of bivariate flood frequency analysis.

Editor Z.W. Kundzewicz; Associate editor Sheng Yue

Citation Volpi, E. and Fiori, A., 2012. Design event selection in bivariate hydrological frequency analysis. Hydrological Sciences Journal, 57 (8), 1506–1515.     

Comparative analysis of nonparametric change-point detectors commonly used in hydrology

ABSTRACT

Several commonly-used nonparametric change-point detection methods are analysed in terms of power, ability and accuracy of the estimated change-point location. The analysis is performed with synthetic data for different sample sizes, two types of change and different magnitudes of change. The methods studied are the Pettitt method, a method based on the Cramér von Mises (CvM) two-sample test statistic and a variant of the CUSUM method. The methods differ considerably in behaviour. For all methods the spread of estimated change-point location increases significantly for points near one of the ends of the sample. Series of annual maximum runoff for four stations on the Yangtze River in China are used to examine the performance of the methods on real data. It was found that the CvM-based test gave the best results, but all three methods suffer from bias and low detection rates for change points near the ends of the series.     

Implications of heterogeneous flood‐frequency distributions on traditional stream‐discharge prediction techniques

Traditional flood‐frequency analysis involves the assumption of homogeneity of the flood distribution. However, floods are often generated by heterogeneous distributions composed of a mixture of two or more populations. Differences between the populations may be the result of a number of factors, including seasonal variations in the flood‐producing mechanisms, changes in weather patterns resulting from low‐frequency climate shifts and/or El Niño/La Nina oscillations, changes in channel routing owing to the dominance of within‐channel or floodplain flow, and basin variability resulting from changes in antecedent soil moisture. Not recognizing these physical processes in conventional flood‐frequency analysis probably is the main reason that many frequency distributions do not provide an acceptable fit to flood data. In this paper, we use long‐term hydroclimatic records from the Gila River basin of south‐east and central Arizona in the USA to explore the extent and significance of mixed populations. First, we discuss the probable causes of heterogeneity in the frequency distribution of annual flood and present evidence of its occurrence. Second, we investigate the implications of using various popular homogeneous distributions for predicting peak flows for basins that exhibit mixed population characteristics. Third, we demonstrate how alternative frequency models that explicitly account for floods generated by a mixture of two or more populations are both hydrologically and statistically more appropriate. We illustrate how the selection of the most plausible distribution for flood‐frequency analysis also should be based on hydrological reasoning as opposed to the sole application of the traditional statistical goodness‐of‐fit tests. Copyright © 2002 John Wiley & Sons, Ltd.     

A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses: I. Known pdf

Abstract

Two probability density functions (pdf), popular in hydrological analyses, namely the log-Gumbel (LG) and log-logistic (LL), are discussed with respect to (a) their applicability to hydrological data and (b) the drawbacks resulting from their mathematical properties. This paper—the first in a two-part series—examines a classical problem in which the considered pdf is assumed to be the true distribution. The most significant drawback is the existence of the statistical moments of LG and LL for a very limited range of parameters. For these parameters, a very rapid increase of the skewness coefficient, as a function of the coefficient of variation, is observed (especially for the log-Gumbel distribution), which is seldom observed in the hydrological data. These probability distributions can be applied with confidence only to extreme situations. For other cases, there is an important disagreement between empirical data and theoretical distributions in their tails, which is very important for the characterization of the distribution asymmetry. The limited range of shape parameters in both distributions makes the analyses (such as the method of moments), that make use of the interpretation of moments, inconvenient. It is also shown that the often-used L-moments are not sufficient for the characterization of the location, scale and shape parameters of pdfs, particularly in the case where attention is paid to the tail part of probability distributions. The maximum likelihood method guarantees an asymptotic convergence of the estimators beyond the domain of the existence of the first two moments (or L-moments), but it is not sensitive enough to the upper tails shape.     

A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses: II. Assumed pdf

Abstract

Applicability of log-Gumbel (LG) and log-logistic (LL) probability distributions in hydrological studies is critically examined under real conditions, where the assumed distribution differs from the true one. The set of alternative distributions consists of five two-parameter distributions with zero lower bound, including LG and LL as well as lognormal (LN), linear diffusion analogy (LD) and gamma (Ga) distributions. The log-Gumbel distribution is considered as both a false and a true distribution. The model error of upper quantiles and of the first two moments is analytically derived for three estimation methods: the method of moments (MOM), the linear moments method (LMM) and the maximum likelihood method (MLM). These estimation methods are used as methods of approximation of one distribution by another distribution. As recommended in the first of this two-part series of papers, MLM turns out to be the worst method, if the assumed LG or LL distribution is not the true one. It produces a huge bias of upper quantiles, which is at least one order higher than that of the other two methods. However, the reverse case, i.e. acceptance of LN, LD or Ga as a hypothetical distribution, while the LG or LL distribution is the true one, gives the MLM bias of reasonable magnitude in upper quantiles. Therefore, one should avoid choosing the LG and LL distributions in flood frequency analysis, especially if MLM is to be applied.     

On the use of partial probability weighted moments in the analysis of hydrological extremes

The use of partial probability weighted moments (PPWM) for estimating hydrological extremes is compared to that of probability weighted moments (PWM). Firstly, estimates from at‐site data are considered. Two Monte Carlo analyses, conducted using continuous and empirical parent distributions (of peak discharge and daily rainfall annual maxima) and applying four different distributions (Gumbel, Fréchet, GEV and generalized Pareto), show that the estimates obtained from PPWMs are better than those obtained from PWMs if the parent distribution is unknown, as happens in practice. Secondly, the use of partial L‐moments (obtained from PPWMs) as diagnostic tools is considered. The theoretical partial L‐diagrams are compared with the experimental data. Five different distributions (exponential, Pareto, Gumbel, GEV and generalized Pareto) and 297 samples of peak discharge annual maxima are considered. Finally, the use of PPWMs with regional data is investigated. Three different kinds of regional analyses are considered. The first kind is the regression of quantile estimates on basin area. The study is conducted applying the GEV distribution to peak discharge annual maxima. The regressions obtained with PPWMs are slightly better than those obtained with PWMs. The second kind of regional analysis is the parametric one, of which four different models are considered. The congruence between local and regional estimates is examined, using peak discharge annual maxima. The congruence degree is sometimes higher for PPWMs, sometimes for PWMs. The third kind of regional analysis uses the index flood method. The study, conducted applying the GEV distribution to synthetic data from a lognormal joint distribution, shows that better estimates are obtained sometimes from PPWMs, sometimes from PWMs. All the results seem to indicate that using PPWMs can constitute a valid tool, provided that the influence of ouliers, of course higher with censored samples, is kept under control. Copyright © 2007 John Wiley & Sons, Ltd.     

Copula‐based flood frequency (COFF) analysis at the confluences of river systems

Many civil infrastructures are located near the confluence of two streams, where they may be subject to inundation by high flows from either stream or both. These infrastructures, such as highway bridges, are designed to meet specified performance objectives for floods of a specified return period (e.g. the 100 year flood). Because the flooding of structures on one stream can be affected by high flows on the other stream, it is important to know the relationship between the coincident exceedence probabilities on the confluent stream pair in many hydrological engineering practices. Currently, the National Flood Frequency Program (NFF), which was developed by the US Geological Survey (USGS) and based on regional analysis, is probably the most popular model for ungauged site flood estimation and could be employed to estimate flood probabilities at the confluence points. The need for improved infrastructure design at such sites has motivated a renewed interest in the development of more rigorous joint probability distributions of the coincident flows. To accomplish this, a practical procedure is needed to determine the crucial bivariate distributions of design flows at stream confluences. In the past, the copula method provided a way to construct multivariate distribution functions. This paper aims to develop the Copula‐based Flood Frequency (COFF) method at the confluence points with any type of marginal distributions via the use of Archimedean copulas and dependent parameters. The practical implementation was assessed and tested against the standard NFF approach by a case study in Iowa's Des Moines River. Monte Carlo simulations proved the success of the generalized copula‐based joint distribution algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of area under‐estimations of sloped mountain terrain on simulated hydrological behaviour: a case study using the ACRU model

Sloped areas calculated from a GIS raster file, such as a digital elevation model, are smaller than the true surface area, because they are projected to a planimetric plane. In mountainous regions this sloped area under‐estimation (SAUE) can have significant consequences on hydrological calculations. A sensitivity analysis is conducted, using the ACRU agro‐hydrological modelling system in a small watershed in Glacier National Park, Montana, USA, to investigate the sensitivity of the SAUE on key elements of the hydrological cycle, including precipitation depth, April snow depth, August soil moisture deficit, actual evapotranspiration depth, and runoff depth. The sensitivity analysis is based on 224 unique combinations of slope, soil and land cover types, elevation with associated precipitation depths, and north and south facing radiation regimes. Results revealed an increasing influence of the SAUE on all hydrological processes with increasing slope steepness. Distinct differences and magnitudes between different land cover types, different elevations, and, in particular, different exposition were quantified. Actual evapotranspiration increases with SAUE, while runoff decreases. April soil water is simulated to decrease with an increase in SAUE. Finally, a comparison of a streamflow simulation of a small and steep alpine watershed with and without consideration of the SAUE is carried out. The sloped area of the small watershed is under‐estimated by 20·9%, and the difference in simulated runoff is 12·3%. When the SAUE was not considered, runoff was simulated to be higher, the associated coefficient of determination was slightly lower, and the slope of the regression line was flatter. Copyright © 2010 John Wiley & Sons, Ltd.     

Impact of climate change on hydrological processes over a basin scale in northern Taiwan

This study investigates the impact of climate change on rainfall, evapotranspiration, and discharge in northern Taiwan. The upstream catchment of the Shihmen reservoir in northern Taiwan was chosen as the study area. Both observed discharge and soil moisture were simultaneously adopted to optimize the HBV‐based hydrological model, clearly improving the simulation of the soil moisture. The delta change of monthly temperature and precipitation from the grid cell of GCMs (General Circulation Models) that is closest to the study area were utilized to generate the daily rainfall and temperature series based on a weather generating model. The daily rainfall and temperature series were further inputted into the calibrated hydrological model to project the hydrological variables. The studies show that rainfall and discharge will be increased during the wet season (May to October) and decreased during the dry season (November to April of the following year). Evapotranspiration will be increased in the whole year except in November and December. Copyright © 2009 John Wiley & Sons, Ltd.     

Stochastic–conceptual analysis of near‐surface hydrological response

The stochastic–conceptual rainfall–runoff simulator (SCRRS) developed by R. A. Freeze in 1980 was used in this study to demonstrate quantitatively the interplay of the factors that control the occurrence of overland flow by the Horton and Dunne mechanisms. The simulation domain and input data for the SCRRS simulations reported here were abstracted from the R‐5 catchment (Chickasha, OK) data sets. The results illustrate that the identification of a dominant hydrological response process may not be as simple as a singular Horton or Dunne characterization. The SCRRS simulations show that the Horton and Dunne processes can (i) occur simultaneously at different locations during a given rainfall event, (ii) change from one process to the other with time depending on the characteristics of the rainfall event, and (iii) be strongly dependent on the initial conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

Bias compensation in flood frequency analysis

Abstract

Flood frequency analysis (FFA) is essential for water resources management. Long flow records improve the precision of estimated quantiles; however, in some cases, sample size in one location is not sufficient to achieve a reliable estimate of the statistical parameters and thus, regional FFA is commonly used to decrease the uncertainty in the prediction. In this paper, the bias of several commonly used parameter estimators, including L-moment, probability weighted moment and maximum likelihood estimation, applied to the general extreme value (GEV) distribution is evaluated using a Monte Carlo simulation. Two bias compensation approaches: compensation based on the shape parameter, and compensation using three GEV parameters, are proposed based on the analysis and the models are then applied to streamflow records in southern Alberta. Compensation efficiency varies among estimators and between compensation approaches. The results overall suggest that compensation of the bias due to the estimator and short sample size would significantly improve the accuracy of the quantile estimation. In addition, at-site FFA is able to provide reliable estimation based on short data, when accounting for the bias in the estimator appropriately.

Editor D. Koutsoyiannis; Associate editor Sheng Yue     

Hydrological effects of water reservoirs on hydrological processes in the East River (China) basin: complexity evaluations based on the multi‐scale entropy analysis

Using the multi‐scale entropy analysis (MSE), we study the effects of water reservoirs on the river flow records based on long streamflow series covering January 1, 1954 and December 31, 2009 at four representative hydrological stations, i.e. the Longchuan, the Heyuan, the Lingxia and the Boluo stations. Hydrological effects of two major water reservoirs, the Xinfengjiang and the Fengshuba water reservoirs, are evaluated. The results indicate that: (1) before the construction of the water reservoirs, the complexity of the streamflow series comes to be decreasing from the upper to the lower East River and which should be attributed to the topographical properties and buffering effects of the river channel; (2) construction of water reservoirs greatly increases the complexity degree of the hydrological processes, and this influence is subjected to a damping process with the increase of distance between the water reservoirs and the hydrological stations; (3) power generation is the major function of the water reservoirs in the East River basin. The results of this study should be of theoretical and scientific merits in terms of conservation of the ecological environment and also water resources management under the influences of climate changes and intensifying human activities. Copyright © 2011 John Wiley & Sons, Ltd.     

Configuration of hydrological processes in a steep hillslope through causality analysis of soil moisture measurements

The vertical and lateral profiles of temporal variations in soil moisture are important for understanding the hydrological process along hillside transects. In this study, relationships among measured soil moistures were explored to configure the hydrological contributions of different flowpaths. All the measured soil moistures included a common stochastic structure because rainfall, the hydrometeological driver, is the main factor that determines the soil moisture response feature, and the infiltration process through the topsoil at a shallow depth is also common in all measured soil moisture histories. Therefore, the relationships between the measured series are also affected by both rainfall and topsoil infiltration. The common stochastic structure of the soil moisture series was removed via a prewhitening procedure. A systematic analysis procedure is presented to delineate the exclusive causal relationships among multiple soil moisture measurements. A monitoring system based on multiplexed time domain reflectometry was used to obtain soil moisture time series along two transects on a steep hillslope during the rainy season. The application of the proposed method for monitoring points in two adjacent locations provided 8, 12, 14, and 13, 16, 22 causal relationships for vertical, lateral in parallel, and diagonal directions, respectively, along the two transects. The point‐based contributions of the internal flowpath can be evaluated as the correlation is normalized in the context of inflow and outflow. The hydrological processes in the soil layer, vertical flow, lateral flow, downslope recharge, and return flow were quantified, and the relative importance of each hydrological component was determined to improve our understanding of the hydrological processes along the two transects of the study area. Copyright © 2011 John Wiley & Sons, Ltd.     

消能支撑框架结构的低周往复水平荷载试验仿真分析方法

本文提出了低周往复水平荷载试验仿真分析方法，该法既不同于弹塑性地震反应时程分析，又不同于常见的弹塑性静力分析。它能模拟低周往复水荷载试验的过程，既避免了地震波频谱的影响又体现了水平荷载的往复作用，可用于计算结构和构件的滞回曲线、截面的屈服顺序及相应的荷载和位移，尤其适用于分析消能支撑框架结构等耗能减震结构。本文用此方法分析了在框架柱轴压比超过限值要求时消能支撑的作用。     

磁流变变阻尼半主动控制结构的仿真分析

由于高阶单步法已成功地应用于结构非线性分析及考虑时滞的主动控制等，显示了它的稳定、精度高和计算迅速等特点。用于结构振动控制的磁流变阻尼器属于速度相关型变阻尼半主动控制器，已有的一些算法，或因计算时间过长不能用于实际控制，或因需要事先经过学习训练，控制效果取决于训练学习的情况。因此，本文将高阶单步法应用于磁流变变阻尼半主动控制系统，采用开关控制和连续控制两种控制率对磁流变液的剪切强度进行调节。仿真计算表明，该控制算法是一种能用于结构实际控制的变阻尼有效算法.     

Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia

Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log‐Pearson type 3 distribution. This paper examines the suitability of a five‐parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas. Copyright © 2014 John Wiley & Sons, Ltd.     

Non-stationary frequency analysis of heavy rainfall events in southern France

Abstract

Heavy rainfall events often occur in southern French Mediterranean regions during the autumn, leading to catastrophic flood events. A non-stationary peaks-over-threshold (POT) model with climatic covariates for these heavy rainfall events is developed herein. A regional sample of events exceeding the threshold of 100 mm/d is built using daily precipitation data recorded at 44 stations over the period 1958–2008. The POT model combines a Poisson distribution for the occurrence and a generalized Pareto distribution for the magnitude of the heavy rainfall events. The selected covariates are the seasonal occurrence of southern circulation patterns for the Poisson distribution parameter, and monthly air temperature for the generalized Pareto distribution scale parameter. According to the deviance test, the non-stationary model provides a better fit to the data than a classical stationary model. Such a model incorporating climatic covariates instead of time allows one to re-evaluate the risk of extreme precipitation on a monthly and seasonal basis, and can also be used with climate model outputs to produce future scenarios. Existing scenarios of the future changes projected for the covariates included in the model are tested to evaluate the possible future changes on extreme precipitation quantiles in the study area.

Editor Z.W. Kundzewicz; Associate editor K. Hamed

Citation Tramblay, Y., Neppel, L., Carreau, J., and Najib, K., 2013. Non-stationary frequency analysis of heavy rainfall events in southern France. Hydrological Sciences Journal, 58 (2), 280–294.     

Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. II. Development of LH-moments parameters for the generalized Pareto and generalized logistic distributions

As part II of a sequence of two papers, previously developed L-moments by Hosking (1990), and the LH-moments by Wang (1997) are further investigated. The LH-moments (L to L₄) are used to develop the regional parameters of the generalized extreme value distribution, generalized Pareto (GPA) distribution and the generalized logistic (GLO) distributions. These respective probability distribution functions (PDFs) are evaluated in terms of their performances. Flood peaks by the corresponding PDFs are compared with those generated by Monte Carlo simulation of randomized data, considering the respective LH-moments. The influence of the LH-moments on estimated PDFs are studied by evaluating the relative bias (RBIAS) in quantile estimation due to variability of the k parameter. Karkhe watershed located in western Iran was used as a case study area. Part I of this study identified the study area as regions A and B. The minimum calculated relative root mean square error (RRMSE) and RBIAS between simulated flood peaks and flood peaks by the corresponding PDFs were used in PDF selection, considering the respective LH-moments. The boxplots of the RRMSE tests identified the L₃ level of the GPA distribution as the suitable PDF for sample sizes 20 and 80; for region A. Similar results were found for the RBIAS test. As for region B, the boxplots of the RRMSE tests indicated similar results for the three PDFs. However, the boxplots of the RBIAS tests identified the L₄ level of the GLO most suitable for sample sizes 20 and 80. Relative efficiencies of the LH-moments were investigated, measured as RRMSE ratios of L-moments over the respective LH-moments. For the most parts the findings of this part of the study were similar to those of part I.