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.     

Complementary aspects of linear flood routing modelling and flood frequency analysis

Similarity and differences between linear flood routing modelling (LFRM) and flood frequency analysis (FFA) techniques are presented. The moment matching used in LFRM to approximate the impulse response function (IRF) was applied in FFA to derive the asymptotic bias caused by the false distribution assumption. Proceeding in this way, other estimation methods were used as approximation methods in FFA to derive the asymptotic bias. Using simulation experiments, the above investigation was extended to evaluate the sampling bias. As a feedback, the maximum likelihood method (MLM) can be used for approximating linear channel response (LCR) by the IRFs of conceptual models. Impulse responses of the convective diffusion and kinematic diffusion models were applied and developed as FFA models. Based on kinematic diffusion LFRM, the equivalence of estimation problems of discrete‐continuous distribution and single‐censored sample are shown both for the method of moments (MOM) and the MLM. Hence, the applicability of MOM is extended for the case of censored samples. Owing to the complexity and non‐linearity of hydrological systems and resulting processes, the use of simple models is often questionable. The rationale of simple models is discussed. The problems of model choice and overparameterization are common in mathematical modelling and FF modelling. Some results for the use of simple models in the stationary FFA are presented. The problems of model discrimination are then discussed. Finally, a conjunction of linear stochastic processes and LFRM is presented. The influence of river courses on stochastic properties of the runoff process is shown by combining Gaussian input with the LCR of the simplified Saint Venant model. It is shown that, from the classification of the ways of their development, both LFRM and FFA can benefit. Copyright © 2006 John Wiley & Sons, Ltd.     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi     

Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. I. A re-visit to regional homogeneity

As part I of a sequence of two papers, previously developed L-moments by Hosking (J R Stat Soc Ser B Methodol 52(2):105–124, 1990), and the LH-moments by Wang (Water Resour Res 33(12):2841–2848, 1997) are re-visited. New relationships are developed for regional homogeneity analysis by the LH-moments, and further establishment of regional homogeneity is investigated. Previous works of Hosking (J R Stat Soc Ser B Methodol 52(2):105–124, 1990) and Wang (Water Resour Res 33(12):2841–2848, 1997) on L-moments and LH-moments for the generalized extreme value (GEV) distribution are extended to the generalized Pareto (GPA) and the generalized logistic (GLO) distributions. The Karkhe watershed, located in western Iran is used as a case study area. Regional homogeneity was investigated by first assuming the entire study area as one regional cluster. Then the entire study area was designated “homogeneous” by the L-moments (L); and was designated “heterogeneous” by all four levels of the LH-moments (L₁ to L₄). The k-means method was used to investigate the case of two regional clusters. All levels of the L- and LH-moments designated the upper watershed (region A), “homogeneous”, and the lower watershed (region B) “possibly-homogeneous”. The L₃ level of the GPA and the L₄ level of the GLO were selected for regions A and B, respectively. Wang (Water Resour Res 33(12):2841–2848, 1997) identified a reversing trend in improved performance of the GEV distribution at the LH-moments level of L₃ (during the goodness-of-fit test). Similar results were also obtained in this research for the GEV distribution. However, for the case of the GPA distribution the reversing trend started at L₄ for region A; and at L₂ for region B. As for the case of the GLO, an improved performance was observed for all levels (moving from L to L₄); for both regions.     

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.     

A Multiple Criteria Decision Modelling approach to selection of estimation techniques for fitting extreme floods

The problem of fitting a probability distribution, here log-Pearson Type III distribution, to extreme floods is considered from the point of view of two numerical and three non-numerical criteria. The six techniques of fitting considered include classical techniques (maximum likelihood, moments of logarithms of flows) and new methods such as mixed moments and the generalized method of moments developed by two of the co-authors. The latter method consists of fitting the distribution using moments of different order, in particular the SAM method (Sundry Averages Method) uses the moments of order 0 (geometric mean), 1 (arithmetic mean), –1 (harmonic mean) and leads to a smaller variance of the parameters. The criteria used to select the method of parameter estimation are:

Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part II: Experimental verification

In a companion paper two different modelling approaches have been described, operating at the meso‐scale of the fibre elements and at the micro‐scale of the finite element (FE) method. The aim of this paper is to explore the efficiency of these models in the pushover analysis for the seismic assessment of existing reinforced concrete (RC) structures. To this purpose a prototype reference structure, one of the RC shear walls designed according to the multi‐fuse concept and tested on shaking table for the CAMUS Project, is modelled at different levels of refinement. At the micro‐scale the reinforcement and anchorage details are described with increasing accuracy in separate models, whereas at the meso‐scale one single model is used, where each element represents a large part of the structure. Static incremental non‐linear analyses are performed with both models to derive a capacity curve enveloping the experimental results and to reproduce the damage pattern at the displacement level where failure is reached. The comparison between experimental and numerical results points out the strong and weak points of the different models inside the procedure adopted, and the utility of an integration of results from both approaches. This study confirms, even for the rather difficult case at study, the capability of the pushover in reproducing the non‐linear dynamic response, both at a global and a local level, and opens the way to the use of the models within a displacement‐based design and assessment procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Changes to flood peaks of a mountain river: implications for analysis of the 2013 flood in the Upper Bow River,Canada

The mountain headwater Bow River at Banff, Alberta, Canada, was subject to a large flood in June 2013, over which considerable debate has ensued regarding its probability of occurrence. It is therefore instructive to consider what information long‐term streamflow discharge records provide about environmental change in the Upper Bow River basin above Banff. Though protected as part of Banff National Park, since 1885, the basin has experienced considerable climate and land cover changes, each of which has the potential to impact observations, and hence the interpretations of flood probability. The Bow River at Banff hydrometric station is one of Canada's longest‐operating reference hydrological basin network stations and so has great value for assessing changes in flow regime over time. Furthermore, the station measures a river that provides an extremely important water supply for Calgary and irrigation district downstream and so is of great interest for assessing regional water security. These records were examined for changes in several flood attributes and to determine whether flow changes may have been related to landscape change within the basin as caused by forest fires, conversion from grasslands to forest with fire suppression, and regional climate variations and/or trends. Floods in the Upper Bow River are generated by both snowmelt and rain‐on‐snow (ROS) events, the latter type which include flood events generated by spatially and temporally large storms such as occurred in 2013. The two types of floods also have different frequency characteristics. Snowmelt and ROS flood attributes were not correlated significantly with any climate index or with burned area except that snowmelt event duration correlated negatively to the Pacific Decadal Oscillation. While there is a significant negative trend in all floods over the past 100 years, when separated based on generating process, neither snowmelt floods nor large ROS floods associated with mesoscale storms show any trends over time. Despite extensive changes to the landscape of the basin and in within the climate system, the flood regime remains unchanged, something identified at smaller scales in the region but never at larger scales. Copyright © 2016 John Wiley & Sons, Ltd.     

Textural analysis and modelling of a flood deposit: River severn,U.K.

Samples of sediment collected from the Severn floodplain between Worcester and Gloucester following the severe flooding in January and February 1990, were analysed for their grain size distribution. The results show that most sand was deposited within 20 m of the channel bank, but that fine sand may contribute to flood sediment across the width of the floodplain. James' (1985) numerical model of overbank sedimentation attempts to predict the transfer of sediment to the floodplain during flooding. Geometrical and hydraulic data relating to the Severn flood are used as input for a computer program of James' (1985) model. The pattern of sediment concentrations predicted by the model was compared with that obtained from statistical analysis of the flood sediment. The patterns were found to be similar, so James' (1985) model was considered to predict in a relative sense the distribution of flood sediment.     

Impulse response of a linear diffusion analogy model as a flood frequency probability density function

Abstract

The impulse response of a linear convective-diffusion analogy (LD) model used for flow routing in open channels is proposed as a probability distribution for flood frequency analysis. The flood frequency model has two parameters, which are derived using the methods of moments and maximum likelihood. Also derived are errors in quantiles for these parameter estimation methods. The distribution shows that the two methods are equivalent in terms of producing mean values—the important property in case of unknown true distribution function. The flood frequency model is tested using annual peak discharges for the gauging sections of 39 Polish rivers where the average value of the ratio of the coefficient of skewness to the coefficient of variation equals about 2.52, a value closer to the ratio of the LD model than to the gamma or the lognormal model. The likelihood ratio indicates the preference of the LD over the lognormal for 27 out of 39 cases. It is found that the proposed flood frequency model represents flood frequency characteristics well (measured by the moment ratio) when the LD flood routing model is likely to be the best of all linear flow routing models.     

Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part I: Model formulation

This work focuses on the modelling issues related to the adoption of the pushover analysis for the seismic assessment of existing reinforced concrete (RC) structures. To this purpose a prototype reference structure, one of the RC shear walls designed according to the multi‐fuse concept and tested on shaking table for the CAMUS project, is modelled at different levels of refinement. The meso‐scale of a stiffness‐based fibre element and the micro‐scale of the finite element (FE) method are herein adopted; in the latter separate elements are adopted for the concrete, the steel and the steel–concrete interface. This first of the two companion papers presents in detail the wall under study, illustrating the design philosophy, the geometry of the wall, the instrumentation set‐up and the test programme. The two modelling approaches are then described; the most important points in terms of element formulation and constitutive relations for materials are presented and discussed for each approach, in the light of the particular design of the wall and of its experimental behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Three‐dimensional modal pushover analysis of buildings subjected to two components of ground motion,including its evaluation for tall buildings

The modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three‐dimensional analysis of buildings—symmetric or unsymmetric in plan—subjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Stiffened steel box columns. Part 1: Cyclic behaviour

This paper aims to study the cyclic inelastic behaviour of stiffened steel box columns failed by local and overall interaction instability under a constant compressive axial force and cyclic lateral loading. Such columns find broad application in steel bridge piers. The columns are of box sections with longitudinal stiffeners. In the analysis, a modified two‐surface plasticity model developed at Nagoya University is employed to model material non‐linearity. For comparison, analyses using classical isotropic‐ and kinematic‐hardening models are also carried out. Hysteretic curves and buckling modes obtained from analysis using the two‐surface model and classical models are compared with experimental results. Moreover, the progression of deformation from occurrence of local buckling to structural failure is discussed in detail. The comparisons show that the use of an accurate plasticity model is quite important in the prediction of both the cyclic inelastic behaviour and failure characteristic of steel box columns failed by coupled local and overall instability. It is found that the modified two‐surface model is a satisfactory model in predicting the cyclic hysteretic behaviour of both the thin‐ and thick‐walled steel box columns. Copyright © 2000 John Wiley & Sons, Ltd.     

Water reservoirs and the risk of accidental flood occurrence. Case study: Stanca–Costesti reservoir and the historical floods of the Prut river in the period July–August 2008, Romania

In the summer of 2008 the Prut river recorded a historical flow of 7140 m³/s at its entrance into Romania. This flow was the highest ever recorded of any Romanian river. The high value was generated by high amounts of rainfall recorded first on the territory of Ukraine and then in Romania. Unfortunately, there were some discrepancies between the data transmitted and intercepted from the Meteorology National Agency and Hydrology and Water Management National Agency. This is why the amount of precipitation which fell over the territory of Ukraine could not be monitored in time and punctually. Nor could the high flood wave moving rapidly from the upper basin to the lower basin. The high flow of the upper Prut caused the accumulation of an immense quantity of water in the Stanca–Costesti reservoir. Under the conditions of precipitation occurring in the lower river basin as well, the levels reached the flood quota and the reservoir reached the maximum accepted capacity, with 0·1% insurance. The release of supplementary water quantities from the reservoir would have produced catastrophic floods downstream. Keeping the water in the reservoir could have broken it and the flooding, through backwater eddies, or the riverbank settlements. In such a case, it would have produced the greatest tragedy in the hydrological history of Europe. The most significant damage was produced upstream of the barrage, next to the localities of Radauti Prut and Baranca–Hudesti, as well as in the area of the reservoir, as a result of the phenomenon known as ‘remuu’, or backwater eddies. The floods of the Prut river occurred between the end of July and the end of August. Copyright © 2011 John Wiley & Sons, Ltd.     

Stiffened steel box columns. Part 2: Ductility evaluation

The purpose of this study is to evaluate the ultimate strength and ductility capacity of stiffened steel box columns failed by local and overall interaction instability under a constant compressive axial force and cyclic lateral loading. In a companion paper, a finite element formulation accounting for both geometrical and material non‐linearity was developed to obtain cyclic hysteretic behaviour of such columns. In this paper, the effect of loading patterns on the cyclic inelastic behaviour is first studied; then, a parametric study is carried out to investigate the effects of flange plate width–thickness ratio parameter, column slenderness ratio parameter, stiffener's equivalent slenderness ratio parameter, magnitude of axial load, and material type of stiffeners on the strength and ductility of the columns. Last but not least, empirical formulae of both the ultimate strength and ductility capacities are proposed for stiffened steel box columns, and the limit values of various parameters for the required ductility demand are also discussed. Copyright © 2000 John Wiley & Sons, Ltd.