The impact of seasonal flood peak dependence on annual maxima design quantiles

If the maximum annual peak flow series are a mixture of summer and winter flows, a seasonal approach to flood frequency analysis is necessary. While considering seasonal maxima as mutually independent events, the annual maxima distribution is defined as the product of seasonal distributions. However, if the independency assumption does not hold, a bivariate approach with dependent margins should be applied, i.e. the copula approach. The impact of dependency on design quantiles is investigated here in the context of the Fréchet-Hoeffding inequality defining copula bounds and the definition of dependency. The results of the two approaches are compared using six catchments in the San River basin, where in four cases the dependency of seasonal maxima has been identified as positive significant and no strong dominance of any one season is observed. The product model leads to higher estimates of design quantiles than do models where the dependency is taken into account and, therefore, is safe.

EDITOR R. Woods ASSOCIATE EDITOR A. Fiori     

Frequency analysis of nonstationary annual maximum flood series using the time‐varying two‐component mixture distributions

The most popular practice for analysing nonstationarity of flood series is to use a fixed single‐type probability distribution incorporated with the time‐varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time‐varying under changing environments. To allow the investigation of this complex nature, the time‐varying two‐component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series of two stations in the Weihe River basin, with the model parameters calibrated by the meta‐heuristic maximum likelihood method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single‐type distributions, stationary mixture distributions and time‐varying single‐type distributions. The results highlighted the advantages of TTMD with physically‐based covariates for both stations. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. Copyright © 2016 John Wiley & Sons, Ltd.     

A note on asymptotic approximations of distributions for maxima of wave crests

The distribution of maxima during a given time interval is of interest in many applications in risk analysis. Within the framework of stationary Gaussian processes, several theoretical results considering asymptotics from different aspects have been derived for this distribution. In this note, we review results from the theory and study the accuracy of these approximations by exemplifying with a model for wave heights from oceanography. It turns out that for high values and the time periods normally encountered for buoy measurements, care should be taken in use of approximation based on the Gumbel distribution.     

On seasonal approach to flood frequency modelling. Part II: flood frequency analysis of Polish rivers

The annual peak flow series of Polish rivers are mixtures of summer and winter flows. As Part II of a sequence of two papers, practical aspects of applicability of seasonal approach to flood frequency analysis (FFA) of Polish rivers are discussed. Taking A Two‐Component Extreme Value (TCEV1) model as an example it was shown in the first part that regardless of estimation method, the seasonal approach can give profit in terms of upper quantile estimation accuracy that rises with the return period of the quantile and is the greatest for no seasonal variation. In this part, an assessment of annual maxima (AM) versus seasonal maxima (SM) approach to FFA was carried out with respect to seasonal and annual peak flow series of 38 Polish gauging stations. First, the assumption of mutual independence of the seasonal maxima has been tested. The smoothness of SM and AM empirical probability distribution functions was analysed and compared. The TCEV1 model with seasonally estimated parameters was found to be not appropriate for most Polish data as it considerably underrates the skewness of AM distributions and upper quantile values as well. Consequently, the discrepancies between the SM and AM estimates of TCEV1 are observed. Taking SM and TCEV1 distribution, the dominating season in AM series was confronted with predominant season for extreme floods. The key argument for presumptive superiority of SM approach that SM samples are more statistically homogeneous than AM samples has not been confirmed by the data. An analysis of fitness to SM and AM of Polish datasets made for seven distributions pointed to Pearson (3) distribution as the best for AM and Summer Maxima, whereas it was impossible to select a single best model for winter samples. In the multi‐model approach to FFA, the tree functions, i.e., Pe(3), CD3 and LN3, should be involved for both SM and AM. As the case study, Warsaw gauge on the Vistula River was selected. While most of AM elements are here from winter season, the prevailing majority of extreme annual floods are the summer maxima. The upper quantile estimates got by means of classical annual and two‐season methods happen to be fairly close; what's more they are nearly equal to the quantiles calculated just for the season of dominating extreme floods. Copyright © 2011 John Wiley & Sons, Ltd.     

基于二次重现期的多变量洪水风险评估

由于洪水是一种具有多个特征属性的随机事件,频率分析成为洪水风险评估的一种有效手段,多变量重现期与设计值的定义与计算则是洪水频率分析中的重点和难点.本文通过构造洪水历时、洪峰与洪量的联合分布,介绍了一种新的多变量重现期定义——二次重现期,并探讨了"或"重现期、"且"重现期和二次重现期对安全与危险域识别的差异性,以及在洪水风险管理与工程设计中的合理性与可靠性.传统的"或"和"且"多变量重现期对安全与危险域的识别存在局限性,利用Kendall函数定义的二次重现期则提供了更加合理的安全与风险域识别,避免了对安全事件与危险事件的错误判定,更有利于指导洪水风险的管理.在给定的二次重现期条件下,依据出现概率最大原则推算的历时、洪峰与洪量设计值组合可以满足工程设计以较低成本承受较大风险的追求,相比于单变量设计值,考虑了洪水多个属性联合特征的多变量设计值提供了更加全面和可靠的参考信息.     

On seasonal approach to flood frequency modelling. Part I: Two‐component distribution revisited

The annual peak flow series of the Polish rivers are mixtures of summer and winter flows. In the Part I of a sequence of two papers, theoretical aspects of applicability of seasonal approach to flood frequency analysis (FFA) in Poland are discussed. A testing procedure is introduced for the seasonal model and the data overall fitness. Conditions for objective comparative assessment of accuracy of annual maxima (AM) and seasonal maxima (SM) approaches to FFA are formulated and finally Gumbel (EV1) distribution is chosen as seasonal distribution for detailed investigation. Sampling properties of AM quantile x(F) estimates are analysed and compared for the SM and AM models for equal seasonal variances. For this purpose, four estimation methods were used, employing both asymptotic approach and sampling experiments. Superiority of the SM over AM approach is stated evident in the upper quantile range, particularly for the case of no seasonal variation in the parameters of Gumbel distribution. In order to learn whether the standard two‐ and three‐parameter flood frequency distributions can be used to model the samples generated from the Two‐Component Extreme Value 1 (TCEV1) distribution, the shape of TCEV1 probability density function (PDF) has been tested in terms of bi‐modality. Then the use of upper quantile estimate obtained from the dominant season of extreme floods (DEFS) as AM upper quantile estimate is studied and respective systematic error is assessed. The second part of the paper deals with advantages and disadvantages of SM and AM approach when applied to real flow data of Polish rivers. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

The two-component extreme value distribution for flood frequency analysis: Derivation of a new estimation method

The two component extreme value (TCEV) distribution has recently been shown to account for most of the characteristics of the real flood experience. A new method of parameter estimation for this distribution is derived using the principle of maximum entropy (POME). This method of parameter estimation is suitable for application in both the site-specific and regional cases and appears simpler than the maximum likelihood estimation method. Statistical properties of the regionalized estimation were evaluated using a Monte Carlo approach and compared with those of the maximum likelihood regional estimators.     

Statistical analysis of flash flood events for designing water harvesting systems in an extremely arid environment

A water harvesting system for research purposes has been established in the Lisan Peninsula of the Dead Sea in the middle of the Jordan Rift Valley, where no authorized guideline is available for designing water harvesting systems. Rainfall and runoff, which occurred as flash floods, were observed at the downstream end of a gorge with a 1.12 km² barren catchment area from October 2014 through July 2019. Due to the extremely arid environment, runoff from the catchment is ephemeral, and the flash flood events can be clearly distinguishable from each other. Thirteen flash flood events with a total runoff volume of more than 100 m³ were successfully recorded during the five rainy seasons. Pearson and Spearman correlations between duration, total rainfall depths at two points, total runoff volume, maximum runoff discharge, bulk runoff coefficient, total variation in runoff discharge and maximum variation in runoff discharge of each flash flood event were examined, revealing no straightforward relationship between rainfall and runoff. The performance of the conventional SCS runoff curve number method was also deficient in reproducing any rainfall–runoff relationship. Therefore, probability distribution fitting was performed for each random variable, focusing on the lognormal distribution with three parameters and the generalized extreme value distribution. The maximum goodness-of-fit estimation turns out to be a more rational and efficient method in obtaining the parameter values of those probability distributions rather than the standard maximum likelihood estimation, which has known disadvantages. Results support the design of the water harvesting system and provide quantitative information for designing and operating similar systems in the future.     

Flood frequency under the influence of trends in the Pearl River basin,China: changing patterns,causes and implications

Using a nonstationary flood frequency model, this study investigates the impact of trends on the estimation of flood frequencies and flood magnification factors. Analysis of annual peak streamflow data from 28 hydrological stations across the Pearl River basin, China, shows that: (1) northeast parts of the West and the North River basins are dominated by increasing annual peak streamflow, whereas decreasing trends of annual peak streamflow are prevailing in other regions of the Pearl River basin; (2) trends significantly impact the estimation of flood frequencies. The changing frequency of the same flood magnitude is related to the changing magnitude or significance/insignificance of trends, larger increasing frequency can be detected for stations with significant increasing trends of annual peak streamflow and vice versa, and smaller increasing magnitude for stations with not significant increasing annual peak streamflow, pointing to the critical impact of trends on estimation of flood frequencies; (3) larger‐than‐1 flood magnification factors are observed mainly in the northeast parts of the West River basin and in the North River basin, implying magnifying flood processes in these regions and a higher flood risk in comparison with design flood‐control standards; and (4) changes in hydrological extremes result from the integrated influence of human activities and climate change. Generally, magnifying flood regimes in the northeast Pearl River basin and in the North River basin are mainly the result of intensifying precipitation regime; smaller‐than‐1 flood magnification factors along the mainstream of the West River basin and also in the East River basin are the result of hydrological regulations of water reservoirs. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison of scenario‐neutral approaches for estimation of climate change impacts on flood characteristics

Scenario‐neutral assessments of climate change impact on floods analyse the sensitivity of a catchment to a range of changes in selected meteorological variables such as temperature and precipitation. The key challenges of the approach are the choice of the meteorological variables and statistics thereof and how to generate time series representing altered climatologies of the selected variables. Different methods have been proposed to achieve this, and it remains unclear if and to which extent they result in comparable flood change projections. Here, we compare projections of annual maximum floods (AMFs) derived from three different scenario‐neutral methods for a prealpine study catchment. The methods chosen use different types of meteorological data, namely, observations, regional climate model output, and weather generator data. The different time series account for projected changes in the seasonality of temperature and precipitation, in the occurrence statistics of precipitation, and of daily precipitation extremes. Resulting change in mean AMF peak magnitudes and volumes differs in sign between the methods (range of ?6% to +7% for flood peak magnitudes and ?11% to +14% for flood volumes). Moreover, variability of projected peak magnitudes and flood volumes depends on method with one approach leading to a generally larger spread. The differences between the methods vary depending on whether peak magnitudes or flood volumes are considered and different relationships between peak magnitude and volume change result. These findings can be linked to differing flood regime changes among the three approaches. The study highlights that considering selected aspects of climate change only when performing scenario‐neutral studies may lead to differing representations of flood generating processes by the approaches and thus different quantifications of flood change. As each method comes with its own strengths and weaknesses, it is recommended to combine several scenario‐neutral approaches to obtain more robust results.