A fuzzy dynamic wave routing model

In this paper a fuzzy dynamic wave routing model (FDWRM) for unsteady flow simulation in open channels is presented. The continuity equation of the dynamic wave routing model is preserved in its original form while the momentum equation is replaced by a fuzzy rule based model which is developed on the principle that during unsteady flow the disturbances in the form of discontinuities in the gradient of the physical parameters will propagate along the characteristics with a velocity equal to that of velocity of the shallow water wave. The model gets rid off the assumptions associated with the momentum equation by replacing it with the fuzzy rule based model. It overcomes the necessity of calculating friction slope (S_f) in flow routing and hence the associated uncertainties are eliminated. The robustness of the fuzzy rule based model enables the FDWRM to march the solution even in regions where the aforementioned assumptions are violated. Also the model can be used for flow routing in curved channels. When the model is applied to hypothetical flood routing problems in a river it is observed that the results are comparable to those of an implicit numerical model (INM) which solves the dynamic wave equations using an implicit numerical scheme. The model is also applied to a real case of flow routing in a field canal. The results match well with the measured data and the model performs better than the INM. Copyright © 2007 John Wiley & Sons, Ltd.     

A fuzzy logic based dynamic wave model inversion algorithm for canal regulation

A fuzzy logic based centralized control algorithm for irrigation canals is presented. Purpose of the algorithm is to control downstream discharge and water level of pools in the canal, by adjusting discharge release from the upstream end and gates settings. The algorithm is based on the dynamic wave model (Saint‐Venant equations) inversion in space, wherein the momentum equation is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. The fuzzy rule based model is developed on fuzzification of a new mathematical model for wave velocity, the derivational details of which are given. The advantages of the fuzzy control algorithm, over other conventional control algorithms, are described. It is transparent and intuitive, and no linearizations of the governing equations are involved. Tuning of the algorithm and method of computation are explained. It is shown that the tuning is easy and the computations are straightforward. The algorithm provides stable, realistic and robust outputs. The disadvantage of the algorithm is reduced precision in its outputs due to the approximation inherent in the fuzzy logic. Feed back control logic is adopted to eliminate error caused by the system disturbances as well as error caused by the reduced precision in the outputs. The algorithm is tested by applying it to water level control problem in a fictitious canal with a single pool and also in a real canal with a series of pools. It is found that results obtained from the algorithm are comparable to those obtained from conventional control algorithms. Copyright © 2009 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.     

A practical method for analysis of river waves and for kinematic wave routing in natural channel networks

The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Empirical assessment of flood wave celerity–discharge relationships at local and reach scales

ABSTRACT

An accurate comprehension of celerity (flood wave speed) dynamics is a key step for understanding flood wave propagation in rivers. We present the results of empirically estimated celerity values in 12 Brazilian rivers, and analyse the behaviour of celerity–discharge relationships (CxQ). Celerity was estimated with a reach-scale (RS) method, based on the peak travel time between stations; and with a local-scale (LS) method, based on the derivative of discharge–cross-section area relationships surveyed at gauging stations. The results indicate that the magnitudes of celerity values obtained by the methods are reasonably comparable, and can rarely be considered constant, varying with river discharge. Three reaches presented differing CxQ relationships at local and reach scales, which suggests that in situ cross-sections at gauging stations should not be extrapolated as representative of the whole reach for flood routing studies, and that CxQ relationship assessments might provide relevant insights for hydrological modelling.     

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.     

Assessment of river flow with significant lateral inflow through reverse routing modeling

The discharge hydrograph estimation in rivers based on reverse routing modeling and using only water level data at two gauged sections is here extended to the most general case of significant lateral flow contribution, without needing to deploy rainfall–runoff procedures. The proposed methodology solves the Saint‐Venant equations in diffusive form also involving the lateral contribution using a “head‐driven” modeling approach where lateral inflow is assumed to be function of the water level at the tributary junction. The procedure allows to assess the discharge hydrograph at ends of a selected river reach with significant lateral inflow, starting from the stage recorded there and without needing rainfall data. Specifically, the MAST 1D hydraulic model is applied to solve the diffusive wave equation using the observed stage hydrograph at the upstream section as upstream boundary condition. The other required data are (a) the observed stage hydrograph at the downstream section, as benchmark for the parameter calibration, and (b) the bathymetry of the river reach, from the upstream section to a short distance after the downstream gauged section. The method is validated with different flood events observed in two river reaches with a significant intermediate basin, where reliable rating curves were available, selected along the Tiber River, in central Italy, and the Alzette River, in Luxembourg. Very good performance indices are found for the computed discharge hydrographs at both the channel ends and along the tributaries. The mean Nash‐Sutcliffe value (NS_q) at the channel ends of two rivers is found equal to 0.99 and 0.86 for the upstream and downstream sites, respectively. The procedure is also validated on a longer stretch of the Tiber River including three tributaries for which appreciable results are obtained in terms of NS_q for the computed discharge hydrographs at both the channel ends for three investigated flood events.     

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.     

Inbank and overbank velocity conditions in an arid zone anastomosing river

Relative to those at sub‐bankfull flow, hydraulic conditions at overbank flow, whether in the channel or on the floodplain, are poorly understood. Here, velocity conditions are analysed over an unusually wide range of flows in the arid zone river of Cooper Creek with its complex system of anastomosing channels and large fluctuations in floodplain width. At‐a‐station hydraulic geometry relationships reveal sharp discontinuities in velocity at the inbank–overbank transition, the nature of the discontinuity varying with the degree of flow confinement and the level of channel–floodplain interaction. However, despite inter‐sectional differences, velocities remain modest throughout the flow range in this low‐gradient river, and the large increases in at‐a‐station discharge are principally accommodated by changes in cross‐sectional area. Velocity distribution plots suggest that within‐channel conditions during overbank flow are characterized by a central band of high velocity which penetrates far toward the bed, helping to maintain already deep cross‐sections. Floodplain resistance along Cooper Creek is concentrated at channel bank tops where vegetation density is highest, and the subsequent flow retardation is transmitted across the surface of the channels over distances as large as 50–70 m. The rough floodplain surface affects flood wave transmission, producing significant decreases in wave speeds downstream. The character of the wave‐speed–discharge relationship also changes longitudinally, from log–linear in the upper reaches to nonlinear where the floodplain broadens appreciably. The nonlinear form is similar in several respects to relationships proposed for more humid rivers, with flood wave speed reaching an intermediate maximum at about four‐fifths bankfull discharge before decreasing to a minimum at approximately Q_2·33. It does not regain the value at the intermediate maximum until the 10 year flood, by which time floodplain depths have become relatively large and broad floodways more active. Copyright © 2002 John Wiley & Sons, Ltd.     

Recent variation in reach‐scale bankfull discharge in the Lower Yellow River

Bankfull discharge is a key parameter in the context of river engineering and geomorphology, as an indicator of flood discharge capacity in alluvial rivers, and varying in response to the incoming flow and sediment regimes. Bankfull channel dimensions have significantly adjusted along the Lower Yellow River (LYR) due to recent channel degradation, caused by the operation of the Xiaolangdi Reservoir, which has led to longitudinal variability in cross‐sectional bankfull discharges. Therefore, it is more representative to describe the flood discharge capacity of the LYR, using the concept of reach‐averaged bankfull discharge. Previous simple mean methods to estimate reach‐scale bankfull discharge cannot meet the condition of flow continuity or account for the effect of different spacing between two sections. In this study, a general method to calculate cross‐sectional bankfull discharge using the simulated stage‐discharge relation is outlined briefly, and an integrated method is then proposed for estimating reach‐scale bankfull discharge. The proposed method integrates a geometric mean based on the log‐transformation with a weighted average based on the spacing between two consecutive sections, which avoids the shortcomings of previous methods. The post‐flood reach‐scale bankfull discharges in three different channel‐pattern reaches of the LYR were estimated annually during the period from 1999 to 2010 using the proposed method, based on surveyed post‐flood profiles at 91 sedimentation sections and the measured hydrological data at seven hydrometric sections. The calculated results indicate that: (i) the estimated reach‐scale bankfull discharges can effectively represent the flood discharge capacity of different reaches, with their ranges of variation being less than those of typical cross‐sectional bankfull discharges; and (ii) the magnitude of the reach‐scale bankfull discharge in each reach can respond well to the accumulative effect of incoming flow and sediment conditions. Finally, empirical relationships for different reaches in the LYR were developed between the reach‐scale bankfull discharge and the previous four‐year average discharge and incoming sediment coefficient during flood seasons, with relatively high correlation coefficients between them being obtained, and the reach‐scale bankfull discharges in different reaches predicted by the delayed response model were also presented for a comparison. These relations for the prediction of reach‐scale bankfull discharges were validated using the cross‐sectional profiles and hydrological data measured in 2011. Copyright © 2013 John Wiley & Sons, Ltd.     

Developing a hybrid multi‐model for peak flood forecasting

The present study aims to develop a hybrid multi‐model using the soft computing approach. The model is a combination of a fuzzy logic, artificial neural network (ANN) and genetic algorithm (GA). While neural networks are low‐level computational structures that perform well dealing with raw data, fuzzy logic deal with reasoning on a higher level by using linguistic information acquired from domain experts. However, fuzzy systems lack the ability to learn and cannot adjust themselves to a new environment. Moreover, experts occasionally make mistakes and thus some rules used in a system may be false. A network type structure of the present hybrid model is a multi‐layer feed‐forward network, the main part is a fuzzy system based on the first‐order Sugeno fuzzy model with a fuzzification and a defuzzification processes. The consequent parameters are determined by least square method. The back‐propagation is applied to adjust weights of network. Then, the antecedent parameters of the membership function are updated accordingly by the gradient descent method. The GA was applied to select the fuzzy rule. The hybrid multi‐model was used to forecast the flood level at Chiang Mai (under the big flood 2005) and the Koriyama flood (2003) in Japan. The forecasting results are evaluated using standard global goodness of fit statistic, efficient index (EI), the root mean square error (RMSE) and the peak flood error. Moreover, the results are compared to the results of a neuro‐genetic model (NGO) and ANFIS model using the same input and output variables. It was found that the hybrid multi‐model can be used successfully with an efficiency index (EI) more than 0·95 (for Chiang Mai flood up to 12 h ahead forecasting) and more than 0·90 (for Koriyama flood up to 8 h ahead forecasting). In general, all of three models can predict the water level with satisfactory results. However, the hybrid model gave the best flood peak estimation among the three models. Therefore, the use of fuzzy rule base, which is selected by GA in the hybrid multi‐model helps to improve the accuracy of flood peak. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

The strategy of building a flood forecast model by neuro‐fuzzy network

A methodology is proposed for constructing a flood forecast model using the adaptive neuro‐fuzzy inference system (ANFIS). This is based on a self‐organizing rule‐base generator, a feedforward network, and fuzzy control arithmetic. Given the rainfall‐runoff patterns, ANFIS could systematically and effectively construct flood forecast models. The precipitation and flow data sets of the Choshui River in central Taiwan are analysed to identify the useful input variables and then the forecasting model can be self‐constructed through ANFIS. The analysis results suggest that the persistent effect and upstream flow information are the key effects for modelling the flood forecast, and the watershed's average rainfall provides further information and enhances the accuracy of the model performance. For the purpose of comparison, the commonly used back‐propagation neural network (BPNN) is also examined. The forecast results demonstrate that ANFIS is superior to the BPNN, and ANFIS can effectively and reliably construct an accurate flood forecast model. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

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

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

FLOOD MODELLING WITH GIS-DERIVED DISTRIBUTED UNIT HYDROGRAPHS

The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time–area curve of a watershed by the S-curve method. The time–area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time–area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km² watershed, using 1 km × 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km × 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time–area curve. The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology.     

Quantifying peakflow attenuation/amplification in a karst river using the diffusive wave model with lateral flow

The aim of this paper is to quantify peakflow attenuation and/or amplification in a river, investigating lateral flow from the intermediate catchment during floods. This is a challenge for the study of the hydrological response of permeable/intermittent streams, and our contribution refers to a modelling framework based on the inverse problem for the diffusive wave model applied in a karst catchment. Knowing the upstream and downstream hydrographs on a reach between two stations, we can model the lateral one, given information on the hydrological processes involved in the intermediate catchment. The model is applied to 33 flood events in the karst reach of the Iton River in French Normandy where peakflow attenuation is observed. The monitored zone consists of a succession of losing and gaining reaches controlled by strong surface‐water/groundwater (SW/GW) interactions. Our results show that despite a high baseflow increase in the reach, peakflow is attenuated. Model application shows that the intensity of lateral outflow for the flood component is linked to upstream discharge. A combination of river loss and overbank flow for highest floods is proposed for explaining the relationships. Our approach differentiates the role of outflow (river loss and overbank flow) and that of wave diffusion on peakflow attenuation. Based on several sets of model parameterization, diffusion is the main attenuation process for most cases, despite high river losses of up to several m³/s (half of peakflow for some parameterization strategies). Finally, this framework gives new insight into the SW/GW interactions during floods in karst basins, and more globally in basins characterized by disconnected river‐aquifer systems.     

Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment,part 1: mesh resolution effects

High‐resolution data obtained from airborne remote sensing is increasing opportunities for representation of small‐scale structural elements (e.g. walls, buildings) in complex floodplain systems using two‐dimensional (2D) models of flood inundation. At the same time, 2D inundation models have been developed and shown to provide good predictions of flood inundation extent, with respect to both full solution of the depth‐averaged Navier–Stokes equations and simplified diffusion‐wave models. However, these models have yet to be applied extensively to urban areas. This paper applies a 2D raster‐based diffusion‐wave model to determine patterns of fluvial flood inundation in urban areas using high‐resolution topographic data and explores the effects of spatial resolution upon estimated inundation extent and flow routing process. Model response shows that even relatively small changes in model resolution have considerable effects on the predicted inundation extent and the timing of flood inundation. Timing sensitivity would be expected, given the relatively poor representation of inertial processes in a diffusion‐wave model. Sensitivity to inundation extent is more surprising, but is associated with: (1) the smoothing effect of mesh coarsening upon input topographical data; (2) poorer representation of both cell blockage and surface routing processes as the mesh is coarsened, where the flow routing is especially complex; and (3) the effects of (1) and (2) upon water levels and velocities, which in turn determine which parts of the floodplain the flow can actually travel to. It is shown that the combined effects of wetting and roughness parameters can compensate in part for a coarser mesh resolution. However, the coarser the resolution, the poorer the ability to control the inundation process, as these parameters not only affect the speed, but also the direction of wetting. Thus, high‐resolution data will need to be coupled to a more sophisticated representation of the inundation process in order to obtain effective predictions of flood inundation extent. This is explored in a companion paper. Copyright © 2005 John Wiley & Sons, Ltd.     

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.