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.     

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.     

Hydrodynamic derivation of a variable parameter Muskingum method: 2. Verification

Abstract

The hydrodynamic derivation of a variable parameter Muskingum method and its solution procedure for estimating a routed hydrograph were presented in Part I of this series (Perumal, 1994a). In this paper, the limitations of the method, the criterion for its applicability and its accuracy are discussed based on the assumptions used. The method is verified by routing a given hypothetical inflow hydrograph through uniform rectangular cross-section channels and comparing the results with the corresponding numerical solutions of the St. Venant equations. The stage hydrographs as computed by the method are also compared with the corresponding St. Venant solutions. It is demonstrated that the method closely reproduces the St. Venant solutions for the discharge and stage hydrographs subject to the compliance of the assumptions of the method by the routing process.     

Diffusive wave solutions for open channel flows with uniform and concentrated lateral inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow into a river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form in terms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomes S-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usually resulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral inflow are analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively, hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infinite and finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channel types.     

Analysis of flood propagation changes in the Kienstock—Bratislava reach of the Danube River/Analyse des changements de propagation des crues dans le tronçon Kienstock—Bratislava du Fleuve Danube

Abstract

In the first part of this study, a flood wave transformation analysis for the largest historical floods in the Danube River reach Kienstock–Bratislava was carried out. For the simulation of the historical (1899 and 1954) flood propagation, the nonlinear river model NLN-Danube (calibrated on the recent river reach conditions) was used. It was shown that the simulated peak discharges were not changed significantly when compared to their historical counterparts. However, the simulated hydrographs exhibit a significant acceleration of the flood wave movement at discharges of between 5000 and 9000 m³ s^-1. In the second part, the travel time-water level relationships between Kienstock and Bratislava were analysed on a dataset of the flood peak water levels for the period 1991–2002. An empirical regression routing scheme for the Danube short-term water level forecast at Bratislava station was derived. This is based on the measured water level at Kienstock gauging station.     

A spatially distributed Clark’s unit hydrograph based hybrid hydrologic model (Distributed-Clark)

ABSTRACT

A hybrid hydrologic model (Distributed-Clark), which is a lumped conceptual and distributed feature model, was developed based on the combined concept of Clark’s unit hydrograph and its spatial decomposition methods, incorporating refined spatially variable flow dynamics to implement hydrological simulation for spatially distributed rainfall–runoff flow. In Distributed-Clark, the Soil Conservation Service (SCS) curve number method is utilized to estimate spatially distributed runoff depth and a set of separated unit hydrographs is used for runoff routing to obtain a direct runoff flow hydrograph. Case studies (four watersheds in the central part of the USA) using spatially distributed (Thiessen polygon-based) rainfall data of storm events were used to evaluate the model performance. Results demonstrate relatively good fit to observed streamflow, with a Nash-Sutcliffe efficiency (E_NS) of 0.84 and coefficient of determination (R²) of 0.86, as well as a better fit in comparison with outputs of spatially averaged rainfall data simulations for two models including HEC-HMS.     

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.     

Application of linear and nonlinear techniques in river flow forecasting in the Kilombero River basin,Tanzania / Application de techniques linéaires et non-linéaires à la prévision des débits dans le bassin de la Rivière Kilombero,en Tanzanie

Abstract

Modelling of the rainfall–runoff transformation process and routing of river flows in the Kilombero River basin and its five sub-catchments within the Rufiji River basin in Tanzania was undertaken using three system (black-box) models—a simple linear model, a linear perturbation model and a linear varying gain factor model—in their linear transfer function forms. A lumped conceptual model—the soil moisture accounting and routing model—was also applied to the sub-catchments and the basin. The HEC-HMS model, which is a distributed model, was applied only to the entire Kilombero River basin. River discharge, rainfall and potential evaporation data were used as inputs to the appropriate models and it was observed that sometimes the system models performed better than complex hydrological models, especially in large catchments, illustrating the usefulness of using simple black-box models in datascarce situations.     

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.     

Reservoir attenuation of floods from ungauged basins

Abstract

In a typical reservoir routing problem, the givens are the inflow hydrograph and reservoir characteristic functions. Flood attenuation investigations can be easily accomplished using a hydrological or hydraulic routing of the inflow hydrograph to obtain the reservoir outflow hydrograph, unless the inflow hydrograph is unavailable. Although attempts for runoff simulation have been made in ungauged basins, there is only a limited degree of success in special cases. Those approaches are, in general, not suitable for basins with a reservoir. The objective of this study is to propose a procedure for flood attenuation estimation in ungauged reservoir basins. In this study, a kinematic-wave based geomorphic IUH model was adopted. The reservoir inflow hydrograph was generated through convolution integration using the rainfall excess and basin geomorphic information. Consequently, a fourth-order Runge-Kutta method was used to route the inflow hydrograph to obtain the reservoir outflow hydrograph without the aid of recorded flow data. Flood attenuation was estimated through the analysis of the inflow and outflow hydrographs of the reservoir. An ungauged reservoir basin in southern Taiwan is presented as an example to show the applicability of the proposed analytical procedure. The analytical results provide valuable information for downstream flood control work for different return periods.     

Bayesian estimation of inflow hydrographs in ungauged sites of multiple reach systems

A Bayesian Geostatistical Approach to evaluate unknown upstream flow hydrographs in multiple reach systems is implemented. The methodology was, firstly, tested through three synthetic examples of river confluences, that differ in the available data, boundary conditions and number of the estimated inflow time series. Input discharge hydrographs were routed downstream by means of the widely known HEC-RAS river analysis system to obtain the downstream stage hydrographs used as known observations for the reverse procedure. In almost all cases, the observed water levels were corrupted with random errors to highlight the reliability of the methodology in preventing instabilities and overfitting. Then the procedure was applied to the real case study of the Parma–Baganza river confluence located at the city of Parma (Italy) to assess the tributary Baganza River inflow hydrograph (supposed completely ungauged) using water level data collected downstream on the main reach. The results show that the methodology properly reproduces the unknown inflows even in presence of errors affecting the downstream water levels. The practical applicability of the proposed approach is also demonstrated in complex river systems.     

Updating Real-Time Flood Forecasting Using a Fuzzy Rule-Based Model/Mise à Jour de Prévision de Crue en Temps Réel Grâce à un Modèle à Base de Règles Floues

Abstract

An updating technique is a tool to update the forecasts of mathematical flood forecasting model based on data observed in real time, and is an important element in a flood forecasting model. An error prediction model based on a fuzzy rule-based method was proposed as the updating technique in this work to improve one- to four-hour-ahead flood forecasts by a model that is composed of the grey rainfall model, the grey rainfall—runoff model and the modified Muskingum flow routing model. The coefficient of efficiency with respect to a benchmark is applied to test the applicability of the proposed fuzzy rule-based method. The analysis reveals that the fuzzy rule-based method can improve flood forecasts one to four hours ahead. The proposed updating technique can mitigate the problem of the phase lag in forecast hydrographs, and especially in forecast hydrographs with longer lead times.     

A hillslope-based hydrological model using catchment area and width functions

Abstract

A flow-interval hillslope discretization scheme is proposed for catchment hydrological modelling. By this scheme, a two-dimensional catchment is simplified into a one-dimensional cascade of flow intervals linked by the main stream. Each flow interval comprises a set of parallel hillslopes. The hillslope is the fundamental computational unit in the hydrological model providing lateral inflow to the main stream. The size of hillslope is determined by the catchment area and width functions. Catchment runoff is the total of hillslope responses through the river routing. Tests in four Japanese catchments showed that the model performed well on simulating the overall water balance, general flow pattern, and daily and hourly hydrographs of a whole catchment, as well as simultaneous simulation in different subcatchments. Characteristics of catchment hydrological responses and model applicability are discussed.     

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.     

Evaluation of storage–discharge relationships and recession analysis-based distributed hourly runoff simulation in large-scale,mountainous and snow-influenced catchment

ABSTRACT

Evaluation of a recession-based “top-down” model for distributed hourly runoff simulation in macroscale mountainous catchments is rare in the literature. We evaluated such a model for a 3090 km² boreal catchment and its internal sub-catchments. The main research question is how the model performs when parameters are either estimated from streamflow recession or obtained by calibration. The model reproduced observed streamflow hydrographs (Nash-Sutcliffe efficiency up to 0.83) and flow duration curves. Transferability of parameters to the sub-catchments validates the performance of the model, and indicates an opportunity for prediction in ungauged sites. However, the cases of parameter estimation and calibration excluding the effects of runoff routing underestimate peak flows. The lower end of the recession and the minimum length of recession segments included are the main sources of uncertainty for parameter estimation. Despite the small number of calibrated parameters, the model is susceptible to parameter uncertainty and identifiability problems.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Carsteanu     

Validation of a full hydrodynamic model for large‐scale hydrologic modelling in the Amazon

A key aspect of large river basins partially neglected in large‐scale hydrological models is river hydrodynamics. Large‐scale hydrologic models normally simulate river hydrodynamics using simplified models that do not represent aspects such as backwater effects and flood inundation, key factors for some of the largest rivers of the world, such as the Amazon. In a previous paper, we have described a large‐scale hydrodynamic approach resultant from an improvement of the MGB‐IPH hydrological model. It uses full Saint Venant equations, a simple storage model for flood inundation and GIS‐based algorithms to extract model parameters from digital elevation models. In the present paper, we evaluate this model in the Solimões River basin. Discharge results were validated using 18 stream gauges showing that the model is accurate. It represents the large delay and attenuation of flood waves in the Solimões basin, while simplified models, represented here by Muskingum Cunge, provide hydrographs are wrongly noisy and in advance. Validation against 35 stream gauges shows that the model is able to simulate observed water levels with accuracy, representing their amplitude of variation and timing. The model performs better in large rivers, and errors concentrate in small rivers possibly due to uncertainty in river geometry. The validation of flood extent results using remote sensing estimates also shows that the model accuracy is comparable to other flood inundation modelling studies. Results show that (i) river‐floodplain water exchange and storage, and (ii) backwater effects play an important role for the Amazon River basin hydrodynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Using unsteady-state water level data to estimate channel roughness and discharge hydrograph

A novel methodology for simultaneous discharge and channel roughness estimation is developed and applied to data sets available at three experimental sites. The methodology is based on the synchronous measurement of water level data in two river sections far some kilometers from each other, as well as on the use of a diffusive flow routing solver and does not require any direct velocity measurement. The methodology is first analyzed for the simplest case of a channel with a large slope, where the kinematic assumption holds. A sensitivity and a model error analysis are carried out in this hypothesis in order to show the stability of the results with respect to the error in the input parameters in the case of homogeneous roughness and to analyze the effect of unknown roughness heterogeneity on the estimated discharges. The methodology is then extended to the more general case of channels with mild slope and validated using field data previously collected in three Italian rivers: the Arno (in Tuscany), the Tiber (in Latium) and the Vallo di Diana, a small tributary of the Tanagro river (in Southern Italy). The performance of the proposed algorithm has been investigated according to three performance criteria estimating the quality of the match between the measured and the computed stage and discharge hydrographs. Results of the field tests can be considered good, despite the uncertainties of the field data and of the measured values.     

A combined rotated general regression neural network method for river flow forecasting

ABSTRACT

This study focused on the performance of the rotated general regression neural network (RGRNN), as an enhancement of the general regression neural network (GRNN), in monthly-mean river flow forecasting. The study of forecasting of monthly mean river flows in Heihe River, China, was divided into two steps: first, the performance of the RGRNN model was compared with the GRNN model, the feed-forward error back-propagation (FFBP) model and the soil moisture accounting and routing (SMAR) model in their initial model forms; then, by incorporating the corresponding outputs of the SMAR model as an extra input, the combined RGRNN model was compared with the combined FFBP and combined GRNN models. In terms of model efficiency index, R², and normalized root mean squared error, NRMSE, the performances of all three combined models were generally better than those of the four initial models, and the RGRNN model performed better than the GRNN model in both steps, while the FFBP and the SMAR were consistently the worst two models. The results indicate that the combined RGRNN model could be a useful river flow forecasting tool for the chosen arid and semi-arid region in China.

Editor D. Koutsoyiannis; Associate editor not assigned     

Real-time flood forecasting by relating local stage and remote discharge

Abstract

The rating curve model (RCM) proposed by Moramarco and co-authors is modified here for flood forecasting purposes without using rainfall information. The RCM is a simple approach for discharge assessment at a river site of interest based on relating the local recorded stage and the remote discharge monitored at an upstream gauged river site located some distance away. The proposed RCM for real-time application (RCM-RT), involves only two parameters and can be used for river reaches where significant lateral flows occur. The forecast lead time depends on the mean wave travel time of the reach. The model is found to be accurate for a long reach of the Po River (northern Italy) and for two branches of the Tiber River (central Italy) characterized by different intermediate drainage areas and wave travel times. Moreover, the assessment of the forecast uncertainty coming from the model parameters is investigated by performing a Monte Carlo simulation. Finally, the model capability to accurately forecast the exceedence of fixed hydrometric thresholds is analysed.

Editor D. Koutsoyiannis; Associate editor C. Perrin     

Application of a land surface model for simulating rainfall streamflow hydrograph: 2. Comparison with hydrological models

Rainfall runoff hydrographs for 12 river basins ∼10³ km² in area, simulated using land surface model SWAP, are compared with analogous hydrographs obtained using hydrological models that took part in the International Model Parameter Estimation Experiment project and demonstrated the best results. All models were calibrated against data on daily river runoff from each basin over a 20-year period (1960–1979). Optimized model parameters were used to simulate runoff hydrographs for the following 19 years (1980–1998). The comparison of the modeled hydrographs for 12 basins in different calculational periods demonstrated that the SWAP model can simulate river runoff with an accuracy comparable with that of hydrological models.