An analytical method of stage–fall–discharge rating

This paper presents an analytical method for establishing a stage–fall–discharge rating using hydraulic performance graphs (HPG). The rating curves derived from the HPG are used as the basis to establish the functional relation of stage, fall and discharge through regression analysis following the USGS procedure. In doing so, the conventional trial‐and‐error process can be avoided and the associated uncertainties involved may be reduced. For illustration, the proposed analytical method is applied to establish stage–fall–discharge relations for the Keelung River in northern Taiwan to examine its accuracy and applicability in an actual river. Based on the data extracted from the HPG for the Keelung River, one can establish a stage–fall–discharge relation that is more accurate than the one obtained by the conventionally used relation. Furthermore, the discharges obtained from the proposed rating method are verified through backwater analysis for measured high water level events. The results indicate that the analytical stage–fall–discharge rating method is capable of circumventing the shortcomings of those based on single‐station data and, consequently, enhancing the reliability of flood estimation and forecasting. Copyright © 2008 John Wiley & Sons, Ltd.     

The effect of geometrical parameters on the discharge capacity of meandering compound channels

A number of methods and formulae has been proposed in the literature to estimate the discharge capacity of compound channels. When the main channel has a meandering pattern, a reduction in the conveyance capacity for a given stage is observed, which is due to the energy dissipations caused by the development of strong secondary currents and to the decrease of the main channel bed slope with respect to the valley bed slope. The discharges in meandering compound channels are usually assessed applying, with some adjustments, the same methods used in the straight compound channels. Specifically, the sinuosity of the main channel is frequently introduced to account for its meandering pattern, although some methods use different geometric parameters.In this paper the stage—discharge curves for several compound channels having identical cross-sectional area, roughness and bed slope but different planimetric patterns are numerically calculated and compared, in order to identify which geometric parameter should be efficaciously used in empirical formulae to account for meandering patterns. The simulations are carried out using a 3D finite-volume model that solves the RANS equations using a k-ε turbulence model. The numerical code is validated against experimental data collected in both straight and meandering compound channels.The numerical results show that the sinuosity is the main parameter to be accounted for in empirical formulae to assess the conveyance capacity of meandering compound channels. Comparison of the stage—discharge curves in the meandering compound channels with that obtained in a straight channel having identical cross-sectional area clearly shows the reduction of discharge due to the presence of bends in the main channel. The effect of other geometric parameters, such as the meander-belt width and the mean curvature radius, results very weak.     

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.     

Estimating river discharge from very high‐resolution satellite data: a case study in the Yangtze River,China

The measurement of river discharge is necessary for understanding many water‐related issues. Traditionally, river discharge is estimated by measuring water stage and converting the measurement to discharge by using a stage–discharge rating curve. Our proposed method for the first time couples the measurement of water‐surface width with river width–stage and stage–discharge rating curves by using very high‐resolution satellite data. We used it to estimate the discharge in the Yangtze (Changjiang) River as a case study. The discharges estimated at four stations from five QuickBird‐2 images matched the ground observation data very well, demonstrating that the proposed approach can be regarded as ancillary to traditional field measurement methods or other remote methods to estimate river discharge. Copyright © 2004 John Wiley & Sons, Ltd.     

Using width‐based rating curves from spatially discontinuous satellite imagery to monitor river discharge

Remote estimation of river discharge from river width variations is an intriguing method for gauging rivers without conventional measurements. Entirely cloud‐free imagery of an entire river reach is often rare, but partial coverage is more frequent. Discharge is estimated from spatially discontinuous imagery via construction of multiple width–discharge rating curves within a 62‐km reach of the Tanana River, Alaska. The resulting discharge error is as low as 6.7% root mean squared error. Imagery covering <20% of the study reach can be used. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling suspended sediment concentration using artificial neural networks for Gangotri glacier

The dynamics of suspended sediment involves inherent non‐linearity and complexity because of existence of both spatial variability of the basin characteristics and temporal climatic patterns. This complexity, therefore, leads to inaccurate prediction by the conventional sediment rating curve (SRC) and other empirical methods. Over past few decades, artificial neural networks (ANNs) have emerged as one of the advanced modelling techniques capable of addressing inherent non‐linearity in the hydrological processes. In the present study, feed‐forward back propagation (FFBP) algorithm of ANNs is used to model stage–discharge–suspended sediment relationship for ablation season (May–September) for melt runoff released from Gangotri glacier, one of the largest glaciers in Himalaya. The simulations have been carried out on primary data of suspended sediment concentration (SSC) discharge and stage for ablation season of 11‐year period (1999–2009). Combinations of different input vectors (viz. stage, discharge and SSC) for present and previous days are considered for development of the ANN models and examining the effects of input vectors. Further, based on model performance indices for training and testing phase, a suitable modelling approach with appropriate model input structure is suggested. The conventional SRC method is also used for modelling discharge–sediment relationship and performance of developed models is evaluated by statistical indices, namely; root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²). Statistically, the performance of ANN‐based models is found to be superior as compared to SRC method in terms of the selected performance indices in simulating the daily SSC. The study reveals suitability of ANN approach for simulation and estimation of daily SSC in glacier melt runoff and, therefore, opens new avenues of research for application of hybrid soft computing models in glacier hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

Stream channel erosion in a rapidly urbanizing region of the US–Mexico border: documenting the importance of channel hardpoints with Structure‐from‐Motion photogrammetry

Urbanization can lead to accelerated stream channel erosion, especially in areas experiencing rapid population growth, unregulated urban development on erodible soils, and variable enforcement of environmental regulations. A combination of field surveys and Structure‐from‐Motion (SfM) photogrammetry techniques was used to document spatial patterns in stream channel geometry in a rapidly urbanizing watershed, Los Laureles Canyon (LLCW), in Tijuana, Mexico. Ground‐based SfM photogrammetry was used to map channel dimensions with 1 to 2 cm vertical mean error for four stream reaches (100–300 m long) that were highly variable and difficult to survey with a differential GPS. Regional channel geometry curves for LLCW had statistically larger slopes and intercepts compared with regional curves developed for comparable, undisturbed reference channels. Cross‐sectional areas of channels downstream of hardpoints, such as concrete reaches or culverts, were up to 64 times greater than reference channels, with enlargement persisting, in some cases, up to 230 m downstream. Percentage impervious cover was not a good predictor of channel enlargement. Proximity to upstream hardpoint, and lack of riparian and bank vegetation paired with highly erodible bed and bank materials may account for the instability of the highly enlarged and unstable cross‐sections. Channel erosion due to urbanization accounts for approximately 25–40% of the total sediment budget for the watershed, and channel erosion downstream of hardpoints accounts for one‐third of all channel erosion. Channels downstream of hardpoints should be stabilized to prevent increased inputs of sediment to the Tijuana Estuary and local hazards near the structures, especially in areas with urban settlements near the stream channel. Copyright © 2017 John Wiley & Sons, Ltd.     

Uncertainty in stage–discharge rating curves: application to Australian Hydrologic Reference Stations data

The purpose of this paper is to determine uncertainty in the gauged range of the stage–gauged discharge relationship for 622 rating curves from 171 Australian Bureau of Meteorology Hydrologic Reference streamgauging Stations (HRS). Water agencies use many methods to establish rating curves. Here we adopt a consistent method across all stations and develop rating curves based on Chebyshev polynomials, and estimate uncertainties from standard regression errors in which residuals from the polynomials are adjusted to ensure they are homoscedastic and normally distributed. Uncertainty in input water level is also taken into account. The median uncertainties in mean response of the available gauged discharge relationship at median daily discharges for the HRS dataset range from +4.5 to ?4.2% (95% confidence band) and for individual gaugings from +29 to ?22% incorporating a water level uncertainty of ±4 mm. The uncertainties estimated are consistent with values estimated in Australia and elsewhere.     

Modeling River Stage‐Discharge Relationships Using Different Neural Network Computing Techniques

One of the most important problems in hydrology is the establishment of rating curves. The statistical tools that are commonly used for river stage‐discharge relationships are regression and curve fitting. However, these techniques are not adequate in view of the complexity of the problems involved. Three different neural network techniques, i. e., multi‐layer perceptron neural network with Levenberg‐Marquardt and quasi‐Newton algorithms and radial basis neural networks, are used for the development of river stage‐discharge relationships by constructing nonlinear relationships between stage and discharge. Daily stage and flow data from three stations, Yamula, Tuzkoy and Sogutluhan, on the Kizilirmak River in Turkey were used. Regression techniques are also applied to the same data. Different input combinations including the previous stages and discharges are used. The models' results are compared using three criteria, i. e., root mean square errors, mean absolute error and the determination coefficient. The results of the comparison reveal that the neural network techniques are much more suitable for setting up stage‐discharge relationships than the regression techniques. Among the neural network methods, the radial basis neural network is found to be slightly better than the others.     

Implication of evaporative loss estimation methods in discharge and water temperature modelling in cool temperate climates

Evaporative flux is a key component of hydrological budgets. Water loss through evapotranspiration reduces volumes available for run‐off. The transition from liquid to water vapour on open water surfaces requires heat. Consequently, evaporation act as a cooling mechanism during summer. Both river discharge and water temperature simulations are thus influenced by the methods used to model evaporation. In this paper, the impact of evapotranspiration estimation methods on simulated discharge is assessed using a semidistributed model on two Canadian watersheds. The impact of evaporation estimation methods on water temperature simulations is also evaluated. Finally, the validity of using the same formulation to simulate both of these processes is verified. Five well‐known evapotranspiration models and five evaporation models with different wind functions were tested. Results show a large disparity (18–22% of mean annual total evapotranspiration) among the evapotranspiration methods, leading to important differences in simulated discharge (3–25% of observed discharge). Larger differences result from evaporation estimation methods with mean annual divergences of 34–48%. This translates into a difference in mean summer water temperature of 1–15%. Results also show that the choice of model parameter has less influence than the choice of evapotranspiration method in discharge simulations. However, the parameter values influence thermal simulations in the same order of magnitude as the choice of evaporation estimation method. Overall, the results of this study suggest that evapotranspiration and open water evaporation should be represented separately in a hydrological modelling framework, especially when water temperature simulations are required.     

Defining and measuring braiding intensity

Geomorphological studies of braided rivers still lack a consistent measurement of the complexity of the braided pattern. Several simple indices have been proposed and two (channel count and total sinuosity) are the most commonly applied. For none of these indices has there been an assessment of the sampling requirements and there has been no systematic study of the equivalence of the indices to each other and their sensitivity to river stage. Resolution of these issues is essential for progress in studies of braided morphology and dynamics at the scale of the channel network. A series of experiments was run using small‐scale physical models of braided rivers in a 3 m ∞ 20 m flume. Sampling criteria for braid indices and their comparability were assessed using constant‐discharge experiments. Sample hydrographs were run to assess the effect of flow variability. Reach lengths of at least 10 times the average wetted width are needed to measure braid indices with precision of the order of 20% of the mean. Inherent variability in channel pattern makes it difficult to achieve greater precision. Channel count indices need a minimum of 10 cross‐sections spaced no further apart than the average wetted width of the river. Several of the braid indices, including total sinuosity, give very similar numerical values but they differ substantially from channel‐count index values. Consequently, functional relationships between channel pattern and, for example, discharge, are sensitive to the choice of braid index. Braid indices are sensitive to river stage and the highest values typically occur below peak flows of a diurnal (melt‐water) hydrograph in pro‐glacial rivers. There is no general relationship with stage that would allow data from rivers at different relative stage to be compared. At present, channel count indices give the best combination of rapid measurement, precision, and range of sources from which measurements can be reliably made. They can also be related directly to bar theory for braided pattern development. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of observation errors on the uncertainty of design floods

This study investigates the uncertainty in the estimation of the design flood induced by errors in flood data. We initially describe and critically discuss the main sources of uncertainty affecting river discharge data, when they are derived using stage-discharge rating curves. Then, different error structures are used to investigate the effects of flood data errors on design flood estimation. Annual maxima values of river discharge observed on the Po River (Italy) at Pontelagoscuro are used as an example. The study demonstrates that observation errors may have a significant impact on the uncertainty of design floods, especially when the rating curve is affected by systematic errors.     

Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions

In order to quantify total error affecting hydrological models and predictions, we must explicitly recognize errors in input data, model structure, model parameters and validation data. This paper tackles the last of these: errors in discharge measurements used to calibrate a rainfall‐runoff model, caused by stage–discharge rating‐curve uncertainty. This uncertainty may be due to several combined sources, including errors in stage and velocity measurements during individual gaugings, assumptions regarding a particular form of stage–discharge relationship, extrapolation of the stage–discharge relationship beyond the maximum gauging, and cross‐section change due to vegetation growth and/or bed movement. A methodology is presented to systematically assess and quantify the uncertainty in discharge measurements due to all of these sources. For a given stage measurement, a complete PDF of true discharge is estimated. Consequently, new model calibration techniques can be introduced to explicitly account for the discharge error distribution. The method is demonstrated for a gravel‐bed river in New Zealand, where all the above uncertainty sources can be identified, including significant uncertainty in cross‐section form due to scour and re‐deposition of sediment. Results show that rigorous consideration of uncertainty in flow data results in significant improvement of the model's ability to predict the observed flow. Copyright © 2010 John Wiley & Sons, Ltd.     

Factors controlling variations in suspended sediment concentration for single-valued sediment rating curves,Fraser River,British Columbia,Canada

Functional (regression) and cause-and-effect analytical methods were employed in the investigation of factors controlling single-value sediment–discharge relationships for individual hydrological events in the Fraser River Basin. Of 1025 hydrological events identified in the 97 years of the 9-stations discharge record monitored by the Water Survey of Canada (1960–1988), 49 were associated with linear, non-linear (concave and convex) sediment rating curves. Analysis revealed that time of events offered a partial explanation for the occurrence of single-valued curves because events occurring in isolation or in quick succession did not always produce single-valued curves owing to variations in hydrograph characteristics and temporal and spatial peak attenuation factors. Hydrologically, linear and non-linear sediment rating curves were distinguished by the influence of preceding discharge or antecedent moisture, which tends to generate quick or delayed runoff, thereby causing rapid or slow increases in sediment concentration in concert with discharge changes. Hydraulically, linear curves were shown to be controlled by rates of stream bed scour (rising stage) similar to those for channel filling (falling stage); concave curves by rates of scouring (rising stage) similar to those of filling but different from those of rescouring (falling stage); and convex curves by rates of filling and scouring (rising stage) different from those of filling and rescouring (falling stages), all in relation to the timing of the exceedance of the threshold discharge for stream bed scour. Meteorologically, bed scour and fill approximately coincided with the timing of precipitation, if any, on the rising and/or falling stages under subzero (T≤0 °C), low (1≤T≤9 °C) and moderate (10≤T≤19 °C) temperature conditions. It is concluded that a combination of temporal, spatial, hydrological, hydraulic and meteorological factors control variations in sediment concentration during single hydrological events on the Fraser River in a complex fashion. Multivariate analysis of these factors should greatly improve prediction of sediment transport in the Fraser River Basin. © 1998 John Wiley & Sons, Ltd.     

Magnitude‐frequency characteristics of effective discharge for suspended sediment transport,Fraser River,British Columbia,Canada

This study analyses archival discharge and sediment concentration data (1965–1988), monitored by Water Survey of Canada, to examine suspended sediment transport rates and their relationship to effective discharge (Q_eff) based on daily discharge duration curves. Effective discharge was determined as the mid‐point of the discharge class transporting the greatest portion of the suspended sediment load (hence class‐based Q_eff). Results showed that the concept of effective discharge was applicable to the Fraser River basin where the average class‐based Q_eff occurred during 8·4% of the study period with individual values ranging from 0·03% to 16·1%. The durations of effective discharge classes ranged from 0·02% to 19·6% while the transport of 50% of total sediment loads ranged from 3% to 22% with an average of 14% of the time. Equations for predicting the class‐based Q_eff in the Fraser River basin from bankfull discharge and drainage area are presented. The observed variations among stations in sediment‐discharge regimes based on subjectively selected 20 discharge classes, seem to reflect the influence of sediment controlling factors such as geology, physiography, catchment size and land use practice in the basin. Future directions of research on applications of the effective discharge concept are explored. As a solution to the problem of lack of an objective method for determining the effective discharge, the effective discharge should be determined from event based assessments of sediment transport (event‐based Q_eff), avoiding any subjectivity in the selection of number of discharge classes used for its determination. In conclusion, it is proposed that continued use of the conventional method of determining Q_eff should cease. Copyright © 1999 John Wiley & Sons, Ltd.     

Deep learning long short-term memory combined with discrete element method for porosity prediction in gravel-bed rivers

The porosity of gravel riverbed material often is an essential parameter to estimate the sediment transport rate, groundwater-river flow interaction, river ecosystem, and fluvial geomorphology. Current methods of porosity estimation are time-consuming in simulation. To evaluate the relation between porosity and grain size distribution (GSD), this study proposed a hybrid model of deep learning Long Short-Term Memory (LSTM) combined with the Discrete Element Method (DEM). The DEM is applied to model the packing pattern of gravel-bed structure and fine sediment infiltration processes in three-dimensional (3D) space. The combined approaches for porosity calculation enable the porosity to be determined through real time images, fast labeling to be applied, and validation to be done. DEM outputs based on the porosity dataset were utilized to develop the deep learning LSTM model for predicting bed porosity based on the GSD. The simulation results validated with the experimental data then segregated into 800 cross sections along the vertical direction of gravel pack. Two DEM packing cases, i.e., clogging and penetration are tested to predict the porosity. The LSTM model performance measures for porosity estimation along the z-direction are the coefficient of determination (R²), root mean squared error (RMSE), and mean absolute error (MAE) with values of 0.99, 0.01, and 0.01 respectively, which is better than the values obtained for the Clogging case which are 0.71, 0.14, and 0.03, respectively. The use of the LSTM in combination with the DEM model yields satisfactory results in a less complex gravel pack DEM setup, suggesting that it could be a viable alternative to minimize the simulation time and provide a robust tool for gravel riverbed porosity prediction. The simulated results showed that the hybrid model of the LSTM combined with the DEM is reliable and accurate in porosity prediction in gravel-bed river test samples.     

Total least square method applied to rating curves

The ordinary least square method (OLS) has been the most frequently used least square method in hydrological data analysis. Its computational algorithm is simple, and the error analysis is also simple and clear. However, the primary assumption of the OLS method, which states that the dependent variable is the only error‐contaminated variable and all other variables are error free, is often violated in hydrological data analyses. Recently, a matrix algorithm using the singular value decomposition for the total least square (TLS) method has been developed and used in data analyses as errors‐in‐variables model where several variables could be contaminated with observational errors. In our study, the algorithm of the TLS is introduced in the evaluation of rating curves between the flow discharge and the water level. Then, the TLS algorithm is applied to real data set for rating curves. The evaluated TLS rating curves are compared with the OLS rating curves, and the result indicates that the TLS rating curve and the OLS rating curve are in good agreement. The TLS and OLS rating curves are discussed about their algorithms and error terms in the study. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Estimation of river discharge from non-trapezoidal open channel using QuickBird-2 satellite imagery/Utilisation des images satellites de Quickbird-2 pour le calcul des débits fluviaux en chenaux ouverts non-trapézoïdaux

Abstract

Abstract River discharge is traditionally acquired by measuring water stage and then converting the water stage to discharge by using a stage–discharge rating curve. The possibility of monitoring river discharge by satellite has not been adequately studied hitherto, because of the difficulty in making sufficiently precise measurements of the water surface. Since the successful launch of commercial satellites with very-high-resolution sensors, it has become possible to derive ground information from satellite data. To determine river discharge in a non-trapezoidal open channel, an efficient approach has been developed that uses mainly satellite data. The method, which focuses on the measurement of surface water width coupled with river width–stage and ?remote? stage–discharge rating curves, was applied to the Yangtze River (Changjiang) and an accurate estimate of river discharge was obtained. The method can be regarded as ancillary to traditional field measurement methods or other remote sensing methods.     

Stage‐discharge uncertainty derived with a non‐stationary rating curve in the Choluteca River,Honduras

Uncertainty in discharge data must be critically assessed before data can be used in, e.g. water resources estimation or hydrological modelling. In the alluvial Choluteca River in Honduras, the river‐bed characteristics change over time as fill, scour and other processes occur in the channel, leading to a non‐stationary stage‐discharge relationship and difficulties in deriving consistent rating curves. Few studies have investigated the uncertainties related to non‐stationarity in the stage‐discharge relationship. We calculated discharge and the associated uncertainty with a weighted fuzzy regression of rating curves applied within a moving time window, based on estimated uncertainties in the observed rating data. An 18‐year‐long dataset with unusually frequent ratings (1268 in total) was the basis of this study. A large temporal variability in the stage‐discharge relationship was found especially for low flows. The time‐variable rating curve resulted in discharge estimate differences of ? 60 to + 90% for low flows and ± 20% for medium to high flows when compared to a constant rating curve. The final estimated uncertainty in discharge was substantial and the uncertainty limits varied between ? 43 to + 73% of the best discharge estimate. Copyright © 2010 John Wiley & Sons, Ltd.