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.     

Refinement of the channel response system by considering time-varying parameters for flood prediction

Impulse response functions derived from different types of flood wave equations (simplified shallow water equations) are continuously developed to conduct the linear channel routing (LCR), which is based on the linearized Saint Venant equation and has been widely applied to avoid any possibility of numerical instability. The impulse response function proposed by Dooge, Napiórkowski, and Strupczewski (1987) and derived from the dynamic wave equation with complete force terms has been acknowledged as a classic work to establish a good physical interpretation for the LCR model; however, the flexibility of altering the shape of impulse response still needs to be improved. Based on the concept of this work, this study intends to introduce the time-varying parameters in the model, so the values of parameters can be adjusted according to the inflow condition, flood stage, and the cross-sectional shape. Moreover, an integrated routing procedure is proposed to formulate the impulse response function for lateral-flow inputs and then to connect multiple inputs from subwatersheds or alongside the main channel with the impulse response function of each channel segment to reflect the spatial variation of hydraulic characteristics among different segments. In the discussion of this article, the impulse response function is analysed to show its sensitivity to hydraulic variables with spatial and temporary variations. Flood-event simulations of a studied watershed are also provided to verify the applicability of the proposed channel routing system.     

Genetic programming approach for flood routing in natural channels

In recognition of the non‐linear relationship between storage and discharge existing in most river systems, non‐linear forms of the Muskingum model have been proposed, together with methods to calibrate the model parameters. However, most studies have focused only on routing a typical hypothetical flood hydrograph characterized by a single peak. In this study, we demonstrate that the storage–discharge relationship adopted for the non‐linear Muskingum model is not adequate for routing flood hydrographs in natural channels, which are often characterized by multiple peaks. As an alternative, an evolutionary algorithm‐based modelling approach, i.e. genetic programming (GP), is proposed, which is found to route complex flood hydrographs accurately. The proposed method is applied for constructing a routing model for a channel reach along the Walla Walla River, USA. The GP model performs extremely well with a root‐mean‐square error (RMSE) of 0·73 m³ s^?1 as against an RMSE of 3·26 m³ s^?1 for routing the multi‐peaked hydrograph. The advantage of GP lies in the fact that, unlike other models, it establishes the routing relationship in an easy and simple mathematical form. Copyright © 2007 John Wiley & Sons, Ltd.     

Algorithms for solving the diffusive wave flood routing equation

Generally, the diffusive wave equation, obtained by neglecting the acceleration terms in the Saint-Venant equations, is used in flood routing in rivers. Methods based on the finite-difference discretization techniques are often used to calculate discharges at each time step. A modified form of the diffusive wave equation has been developed and new resolution algorithms proposed which are better adapted to flood routing along a complex river network. The two parameters of the equation, celerity and diffusivity, can then be taken as functions of the discharge. The resolution algorithm allows the use of any distribution of lateral inflow in space and time. The accuracy of the new algorithms were compared with a traditional algorithm by numerical experimentation. Special attention was given to the instability caused by the inflow signal which constitutes the upstream boundary condition. For the fully diffusive wave flood routing problem, all three algorithms tested gave good results. The results also indicate that the efficiency of the new algorithms could be significantly improved if the position of the x-axis is modified by rotation. The new algorithms were applied to flood routing simulation over the Gardon d'Anduze catchment (542 km²) in southern France.     

Multi-stage flood routing for gated reservoirs and conjunctive optimization of hydroelectricity income with flood losses

Abstract

A six-stage operation policy for routing of flood hydrographs of return periods from 1.01 year up to the Probable Maximum Flood (PMF) for any dam having a gated spillway is proposed. The gate opening rules are determined depending on the recent pool level. Regardless of the size and timing of any incoming floods, the fixed rules of the six-stage operation policy will provide optimum routing for all, which are classified into six different groups based on their return periods. 10-, 100-, 1000-, 10 000- 100 000-year floods, and PMF are the upper limits for the six groups. Next, an Incremental Dynamic Programming programme is developed to optimize both the firm and secondary energies of hydroelectric generation at monthly periods. First, the six-stage flood routing programme is applied sequentially to three dams, all on the Seyhan River in Turkey, for 18 combinations resulting from different active storages, and optimum flood operation policies for all three dams for all 18 combinations are determined. Second, the Dynamic Programming programme is applied to these three dams, and optimum hydroelectricity generation policies for all 18 combinations are computed. Finally, the optimum active and flood retention storages for the three dams are determined so as to maximize the net probability-weighted present worth of hydroelectricity benefits minus flood damage costs.     

MÉTHODE D'ÉTUDE DES NAPPES LIBRES DANS LES AQUIFÈRES ANISOTROPES

Abstract

The necessary and sufficient conditions for non-zero phase shift and non-zero attenuation in linear flood routing can be derived from the continuity equation alone and are found to depend on the existence of an imaginary part in the expression for frequency or in the expression for wave number. It is shown that in linear flood routing the phase lag between flow rate and area of flow is directly related to the attenuation per unit wave length. The effects of using various forms of the momentum equation, in addition to the continuity equation, are exemplified by deriving analytical expressions in terms of the frequency, both for attenuation per unit channel length and for phase shift, for the kinematic wave, the general diffusion analogy, and the complete St. Venant equation.     

Identification of rainfall–runoff models for operational applications / Identification de modèles pluie–débit pour des applications opérationnelles

Abstract

The problem of selecting appropriate objective functions for the identification of a lumped conceptual rainfall–runoff model is investigated, focusing on the value of the model in an operational setting. A probability-distributed soil moisture model is coupled with a linear parallel routing scheme, and conditioned on rainfall–runoff observations from three catchments in the southeast of England. Using an abstraction control problem, which requires accurate simulation of the intermediate flow range, it is shown that using the traditional RMSE fit criterion, produces operationally sub-optimal predictions. This is true in the identification period, when applied to a testing period, and to proxy catchment data. Using a second case study of the Leaf River in Mississippi (USA), where the focus changes to predicting flood peaks over a specified threshold, also suggests that the relevant flood threshold should govern the objective function choice. It is concluded that, due to limitations in the structure of the employed model, it would be counter-productive to try to achieve a good all-round representation of the rainfall–runoff processes, and that a more empirical approach to identification may be preferred for specific forecasting problems. This leaves us with the question of how far hydrological realism should be sacrificed in favour of purpose-driven objective functions.     

L'Opération Sources en Belgique: premières analyses statistiques des résultats et légitimité des cartes “nitrates”

Abstract

This work critically assesses the storage, or hydrological methods of flood routing, focusing on the Muskingum and Kalinin-Miljukov methods. The common hydraulic basis of these methods and their inter-relationships are established, emphasising hydraulic derivations of the Muskingum method's weighting coefficient. Important characteristics of the routing scheme are highlighted, especially the scheme's affinity to the pseudo-viscosity method of shock computation; the flow-dependence (nonlinearity) of routing parameters is analysed, as are mass balance errors. Options in calculating depths and in handling lateral flows are presented. Storage routing models are shown to be instances of a numerically equivalent convection—diffusion equation or kinematic wave-derived convection—diffusion routing model that is also able to relate depth and discharge at-a-section via loop-shaped rating curves; the consequences of ignoring the rating curves' transience are pointed out. System analytic parameter estimations are summarised, a routing option with direct use of the diffusion wave system response function (SRF) is reviewed, the selection of routing reaches based on the river morphology is discussed, and the extension of storage-type routing to mass transport simulation is indicated.     

复杂河道洪水预报系统研究——以淮河王家坝至小柳巷区间流域为例

随着社会经济的快速发展,洪水灾害造成的损失日益严重.洪水预报作为一项重要的防洪非工程措施,对防洪、抗洪工作起着至关重要的作用.淮河洪水危害的严重性和洪水演进过程的复杂性使得淮河洪水预报系统的研究长期以来受到高度重视.本文以王家坝至小柳巷区间流域为例,以河道洪水演算为主线,采用新安江三水源模型进行子流域降雨径流预报,概化具有行蓄洪区的干流河道,进行支流与干流、行蓄洪区与干流的洪水汇流耦合计算,采用实时更新的基于多元回归的方法确定水位流量关系,并以上游站点降雨径流预报模型提供的流量作为上边界条件、以下游站点的水位流量关系作为下边界条件,结合行蓄洪调度模型,建立具有行蓄洪区的河道洪水预报系统,再与基于K-最近邻(KNN)的非参数实时校正模型耦合,建立淮河中游河道洪水预报系统.采用多年资料模拟取得了较好的预报效果,并以2003和2007年大洪水为例进行检验,模拟结果精度较高,也证明了所建预报系统的合理性和适用性.     

Hydrological runoff modelling by the use of remote sensing data with reference to the 1993–1994 and 1995 floods in the river Rhine catchment

In hydrological modelling of runoff processes, including water balance, various input data and parameters can be acquired or estimated by the use of remote sensing (RS) techniques.The acquisition and use of synoptic RS areal information rather than traditional point information is an important issue in hydrology. Hydrological models allow runoff/water balance in catchments to be calculated and flow routing within flow channels to be done. For runoff and water balance computations land use, soil moisture, detection of snow and ice, digital terrain models (DTM), as well as hydrometeorological information and discharge are important. For flow routing, water level information, geometric–topographic information such as cross-sections for normal and flood conditions, coefficient of roughness and velocity of flow and its cross-sectional distribution are required. In addition, water level information (lower and upper level) is needed for shipping and for design purposes. In the German part of the River Rhine catchment, several focus areas in the December 1993–January 1994 and January 1995 floods were covered with RS data [ERS-1 and airborne SAR, both C-band VV, passive microwave (18·7, 36·5, 89 GHz), TIR, UV, aerial photographs (b/w PAN, b/w NIR)], giving a good opportunity for a comparison of methods. Evaluation is still continuing. The importance of soil saturation for flood generation and, therefore, for flood monitoring, was shown on this occasion. The use of ERS SAR data for soil moisture estimation is currently being investigated by the Federal Institute of Hydrology. Also, the need for emergency schemes for data acquisition and easy, quick and affordable RS data dissemination was demonstrated. The assimilation of RS data with GIS information such as DTMs, including relevant topographic features like dams, which is omitted in currently available raster digital elevation models, is promising. RS altimetry techniques can be a step towards high resolution DTMs for hydrological purposes. Ground truth reference data are still needed. © 1997 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.     

ANALYTICAL HAYAMI SOLUTION FOR THE DIFFUSIVE WAVE FLOOD ROUTING PROBLEM WITH LATERAL INFLOW

The diffusive wave equation is generally used in flood routing in rivers. The two parameters of the equation, celerity and diffusivity, are usually taken as functions of the discharge. If these two parameters can be assumed to be constant without lateral inflow, the diffusive wave equation may have an analytical solution: the Hayami model. A general analytical method, based on ‘Hayami’s hypothesis, is developed here which resolves the diffusive wave flood routing equation with lateral inflow or outflow uniformly distributed over a channel reach. Flood routing parameters are then identified using observed inflow and outflow and the Hayami model used to simulate outflow. Two examples are discussed. Firstly, the prediction of the hydrograph at a downstream section on the basis of a knowledge of the hydrograph at an upstream section and the lateral inflow. The second example concerns lateral inflow identification between an upstream and a downstream section on the basis of a knowledge of hydrographs at the upstream and downstream sections. The new general Hayami model was applied to flood routing simulation and for lateral inflow identification of the River Allier in France. The major advantages of the method relate to computer simulation, real-time forecasting and control applications in examples where numerical instabilities, in the solution of the partial differential equations must be avoided.     

BMA集合预报在淮河流域应用及参数规律初探

以淮河流域吴家渡水文站作为试验站点,采用基于贝叶斯平均法(BMA)的集合预报模型处理来源于马斯京根法、一维水动力学方法、BPNN(Back Propagation Neural Network)的预报流量序列,通过分析BMA的参数以及其预报结果,对各方法在淮河典型站点流量预报中的适用性进行验证与分析.经2003—2016年19场洪水模拟检验可知,BMA模型能够有效避免模型选择带来的洪水预报误差放大效应,可以提供高精度、鲁棒性强的洪水预报结果.通过进一步比较各模型统计最优的频率与BMA权重值之间的相关性,发现权重值不适用于对单场洪水预报精度评定,而适用于描述多场洪水预报中,模型为最优的统计频率;基于大量先验信息,提前获取BMA的权重等参数,将是指导模型选择、降低洪水预报不确定性、改进洪水预报技术的有效手段.     

我国东南沿海中小流域洪水模拟研究

我国东南沿海多为独流入海的中小流域,河流短小,流域调节能力弱.该区洪水历时较短,但危害较大,加之近年来区内经济的迅速发展,洪水造成损失日趋加剧,因此开展此区洪水特性和防洪减灾研究意义重大.本文以中国东南沿海曹娥江流域为典型,根据中小流域洪水的特点,在初步分析流域降雨径流的成因和洪水演进规律的基础上,开展了流域洪水模拟研究, 选择建立了流域降雨径流模型以及洪水演进模型,重点探讨了利用遥感信息和GIS相结合确定水文模型参数的方法和途径,经实验流域资料检验分析,其模拟结果计算精度满足要求.该研究将有助于该区流域降雨径流特性及洪水演变规律的深入研究,同时为东南沿海中小流域洪水模拟预测和防洪减灾研究提供了经验和模式.     

G) Personalia

Abstract

This paper proposes a framework for identifying the parameters of a lumped routing model in small to medium sized catchments where lateral inflows can be large but poorly defined. In a first step, a priori estimates of the parameters are made based on topography, aerial photographs, flood marks and field surveys. In a second step, runoff data are analysed of reservoir release events and convective events where no rainfall in the direct catchments occurred. In a third step the routing model is calibrated to the results of hydrodynamic models for scenarios of different magnitudes. In a fourth step, these pieces of information are combined, allowing for soft expert judgement to be incorporated. In a fifth step, the routing parameters are fine tuned to observed flood events where lateral inflows are estimated by a rainfall—runoff model. The framework is illustrated by the Kamp flood forecasting system in Austria that has been in operational use since 2006.     

Fifteen-stage operation of gated spillways for flood routing management through artificial reservoirs

Abstract

A procedure to identify sets of operational rules for gated spillways for optimal flood routing management of artificial reservoirs is proposed. The flood retention storage of a dam having a gated flood spillway is divided into 15 sub-storages whose surface elevations are identified as critical levels. The most suitable operation set for the downstream conditions and for the dam can be chosen from many derived operation sets. The spillway gates are operated in an optimum way for any floods from very small magnitudes to the probable maximum flood (PMF), without having to forecast the actual magnitude of the incoming flood hydrograph. Decision floods are formed by dividing the PMF into 15 sub-hydrographs by 5 and 10% increments in the ranges 5–50% and 50–100% of the PMF, respectively. Many potential spillway gate openings from closed to fully open are chosen initially. As a result of a series of routing simulations of 15 decision floods, a set of 15 gate openings is determined such that all floods from very small magnitudes to the PMF may be routed without overtopping the dam crest. Next, a few more 15-stage operation rules are determined such that the gate openings of the initial stages are decreased as their critical levels are increased stepwise, with the objective of attenuating smaller floods more effectively and releasing higher outflows for larger floods close to and including the PMF. The developed model is applied to the Catalan and Aslantas dams in Turkey, both of which serve for flood mitigation as well as hydropower generation.

Citation Haktanir, T., Citakoglu, H., and Acanal, N., 2013. Fifteen-stage operation of gated spillways for flood routing management through artificial reservoirs. Hydrological Sciences Journal, 58 (5), 1013–1031.

Editor Z.W. Kundzewicz; Associate editor A. Montanari     

Coupling the Xinanjiang model to a kinematic flow model based on digital drainage networks for flood forecasting

The Xinanjiang model, which is a conceptual rainfall‐runoff model and has been successfully and widely applied in humid and semi‐humid regions in China, is coupled by the physically based kinematic wave method based on a digital drainage network. The kinematic wave Xinanjiang model (KWXAJ) uses topography and land use data to simulate runoff and overland flow routing. For the modelling, the catchment is subdivided into numerous hillslopes and consists of a raster grid of flow vectors that define the water flow directions. The Xinanjiang model simulates the runoff yield in each grid cell, and the kinematic wave approach is then applied to a ranked raster network. The grid‐based rainfall‐runoff model was applied to simulate basin‐scale water discharge from an 805‐km² catchment of the Huaihe River, China. Rainfall and discharge records were available for the years 1984, 1985, 1987, 1998 and 1999. Eight flood events were used to calibrate the model's parameters and three other flood events were used to validate the grid‐based rainfall‐runoff model. A Manning's roughness via a linear flood depth relationship was suggested in this paper for improving flood forecasting. The calibration and validation results show that this model works well. A sensitivity analysis was further performed to evaluate the variation of topography (hillslopes) and land use parameters on catchment discharge. Copyright © 2009 John Wiley & Sons, Ltd.     

Flood routing model incorporating intensive streambed infiltration

Flood routing models are critical to flood forecasting and confluence calculations. In the streams that dry up and disconnect from groundwater, the streambed infiltration is intensive and has a significant effect on flood wave movement. Streambed infiltration should be considered in flood routing. A flood routing model incorporating intensive streambed infiltration is proposed. In the model a streambed infiltration simulation method based on soil infiltration theory is developed. In this method the Horton equation is used to calculate infiltration capacity. A trial-and-error method is developed to calculate infiltration rate and determine whether the flood wave can travel downstream. A formula is derived to calculate infiltration flow per unit length. The Muskingum-Cunge method with streambed infiltration flow as lateral outflow is used for flood routing. The proposed model is applied to the stream from the downstream of the Yuecheng Reservoir to the Caixiaozhuang Hydrometric Station in the Zhangwei River of the Haihe River Basin. Simulation results show that the accuracy of the model is high, and the infiltration simulation method can represent infiltration processes well. The proposed model is simple and practical for flood simulation and forecasting, and can be used in river confluence calculations in a rainfall-runoff model for arid and semiarid regions.     

基于连续方程的河道水流双变量耦合演算模型

针对现有的河道水流洪水演算模型只能模拟单一变量(流量或水位)的问题,以水流连续方程和河段蓄水量的两种不同表达形式(蓄水量等于平均过水断面面积与河段长乘积,蓄水量等于河段平均流量与传播时间的乘积)为基础,对马斯京根模型进行了通用性改进,提出了双变量耦合通用演算模型.选取了四大水系(包括内陆河流和入海河流)的16个河段汛期洪水资料进行模型检验,模型验证考虑了地理范围、不同的河段特征和水力特征、洪水量级等因素,全面地检验了模型结构的合理性和模拟实际洪水的有效性.将双变量耦合通用演算模型与传统的马斯京根法进行了效果比较,结果表明双变量耦合通用演算模型的模拟精度高于马斯京根法,模拟效果比马斯京根法稳定一些,而且具有较好的通用性.     

An event simulation approach to the assessment of flood level frequencies: risk maps for the Warsaw reach of the River Vistula

Flood risk assessment is customarily performed using a design flood. Observed past flows are used to derive a flood frequency curve which forms the basis for a construction of a design flood. The simulation of a distributed model with the 1‐in‐T year design flood as an input gives information on the possible inundation areas, which are used to derive flood risk maps. The procedure is usually performed in a deterministic fashion, and its extension to take into account the design flood‐and flow routing model uncertainties is computer time consuming. In this study we propose a different approach to flood risk assessment which consists of the direct simulation of a distributed flow routing model for an observed series of annual maximum flows and the derivation of maps of probability of inundation of the desired return period directly from the obtained simulations of water levels at the model cross sections through an application of the Flood Level Frequency Analysis. The hydraulic model and water level quantile uncertainties are jointly taken into account in the flood risk uncertainty evaluation using the Generalized Likelihood Uncertainty Estimation (GLUE) approach. An additional advantage of the proposed approach lies in smaller uncertainty of inundation predictions for long return periods compared to the standard approach. The approach is illustrated using a design flood level and a steady‐state solution of a hydraulic model to derive maps of inundation probabilities. Copyright © 2016 John Wiley & Sons, Ltd.