Rating Curve Model Research Articles

Estimating streamflow by an innovative rating curve model based on hydraulic parameters

Estimating streamflow by an innovative rating curve model based on hydraulic parameters

Development of Suspended Sediment Rating Curve Model by Statistical Classification of River Discharge Data (Case Study: Ghareh-Sou Coastal Watershed)

Development of Suspended Sediment Rating Curve Model by Statistical Classification of River Discharge Data (Case Study: Ghareh-Sou Coastal Watershed)

Estimation of daily suspended sediment concentration in the Ca River Basin using a sediment rating curve, multiple regression, and long short-term memory model

Abstract This study presents a sediment rating curve (SRC), multiple regression (MR), and long short-term memory (LSTM) model for estimating daily suspended sediment concentration (SSC). The data of daily SSC at Yen Thuong and daily flow at five locations in the Ca River Basin, Vietnam are used to demonstrate multiple approaches. Using the daily flow and SSC data in the period from 2009 to 2019, appropriate coefficients in each method are identified carefully using five popular criteria. The results showed that SRC and MR approaches reproduced acceptably the observed values, with the values of RMSE, MAE, and ME of daily SSC being less than 5% of daily SSC magnitude observed at the station, while NSE ranges from 0.47 to 0.63 and r coefficient varies between 0.69 and 0.80. The LSTM model represented the observed values of daily SSC very well. The values of two dimensionless criteria are greater than 0.94 and its values of three-dimensional criteria are smaller than 2.0% of the observed magnitude of daily SSC in both training and validation steps. The LSTM model is found to be the best among the three investigated approaches. Then, the model is applied to estimate daily SSC values for the period from 1969 to 2008 and the year 2020.

Prediction of Sediment Yields Using a Data-Driven Radial M5 Tree Model

Reliable estimations of sediment yields are very important for investigations of river morphology and water resources management. Nowadays, soft computing methods are very helpful and famous regarding the accurate estimation of sediment loads. The present study checked the applicability of the radial M5 tree (RM5Tree) model to accurately estimate sediment yields using daily inputs of the snow cover fraction, air temperature, evapotranspiration and effective rainfall, in addition to the flow, in the Gilgit River, Upper Indus Basin (UIB) tributary, Pakistan. The results of the RM5Tree model were compared with support vector regression (SVR), artificial neural network (ANN), multivariate adaptive regression spline (MARS), M5Tree, sediment rating curve (SRC) and response surface method (RSM) models. The resulting accuracy of the models was assessed using Pearson’s correlation coefficient (R2), the root-mean-square error (RMSE) and the mean absolute percentage error (MAPE). The prediction accuracy of the RM5Tree model during the testing period was superior to the ANN, MARS, SVR, M5Tree, RSM and SRC models with the R2, RMSE and MAPE being 0.72, 0.51 tons/day and 11.99%, respectively. The RM5Tree model predicted suspended sediment peaks better, with 84.10% relative accuracy, in comparison to the MARS, ANN, SVR, M5Tree, RSM and SRC models, with 80.62, 77.86, 81.90, 80.20, 74.58 and 62.49% relative accuracies, respectively.

Investigation of stage‐discharge model performance for streamflow estimating: A case study of the Gono River, Japan

AbstractIn water resource studies, long‐term measurements of river streamflow are essential. They allow us to observe trends and natural cycles and are prerequisites for hydraulic and hydrology models. This paper presents a new application of the stage‐discharge rating curve model introduced by Maghrebi et al. (2016) to estimate continuous streamflow along the Gono River, Japan. The proposed method, named single stage‐discharge (SSD) method, needs only one observed data to estimate the continuous streamflow. However, other similar methods require more than one observational data to fit the curve. The results of the discharge estimation by the SSD are compared with the improved fluvial acoustic tomography system (FATS), conventional rating curve (RC), and flow‐area rating curve (FARC). Some statistical indicators, such as the coefficient of determination (R2), root mean square error (RMSE), percent bias (PBAIS), mean absolute error (MAE), and Kling‐Gupta efficiency (KGE), are used to assess the performance of the proposed model. ADCP data are used as a benchmark for comparing four studied models. As a result of the comparison, the SSD method outperformed of FATS method. Also, the three studied RC methods were highly accurate at estimating streamflow if all observed data were used in calibration. However, if the observed data in calibration was reduced, the SSD method by R2 = 0.99, RMSE = 2.83 (m3/s), PBIAS = 0.715(%), MAE = 2.30 (m3/s), and KGE = 0.972 showed the best performance compared to other methods. It can be summarized that the SSD method is the feasible method in the data‐scarce region and delivers a strong potential for streamflow estimation.

Dynamic aspects of suspended-sediment-concentration recession curves

Understanding and modeling suspended sediment concentration (C) dynamics in river channels are essential for many theoretical as well as practical purposes. The sediment rating curve approach that relates C with river discharge (Q) is among the most followed modeling approaches, mainly because of its simplicity and effectiveness. Although studies in the past have suggested the possibility of C-Q relationship for a basin not being unique, how the relationship evolves with time is not yet fully understood. In this study, we limit our analysis to recession periods when both C and Q continuously decrease with time and show that the coefficient of C-Q power-law equation changes across recession events. Furthermore, we propose to express -dC/dt as a function of C for recession periods: -dC/dt=fCe. The exponent e is assumed to be related to static catchment characteristics and the coefficient f to dynamic factors, namely catchment-water storage and sediment availability condition. Assuming the dynamic factors controlling f to evolve slowly with time, we propose that it is possible to predict f for a recession event considering only past C data. Once f is estimated, we can predict C for anytime during the recession event. The advantage of the proposed model is that it can predict future suspended sediment concentration at a river cross section during a recession event. We applied the proposed model to 35 US Geological Survey basins and found the 25th, 50th, and 75th values of NSE, respectively, to be 0.55, 0.64, and 0.78, and the corresponding values for the rating curve model - 0.05, 0.01 and 0.20. The results here essentially highlight the importance of recognizing the dynamic nature of suspended sediment concentration-discharge relationship.

An Improved Unique Fatigue Crack Growth Rate Curve Model and Determination of the Model Shape Exponents

An Improved Unique Fatigue Crack Growth Rate Curve Model and Determination of the Model Shape Exponents

Capability and Robustness of Novel Hybridized Artificial Intelligence Technique for Sediment Yield Modeling in Godavari River, India

Suspended sediment yield (SSY) prediction plays a crucial role in the planning of water resource management and design. Accurate sediment prediction using conventional models is very difficult due to many complex processes. We developed a fully automatic highly generalized accurate and robust artificial intelligence models for SSY prediction in Godavari River Basin, India. The genetic algorithm (GA), hybridized with an artificial neural network (ANN) (GA-ANN), is a suitable artificial intelligence model for SSY prediction. The GA is used to concurrently optimize all ANN’s parameters. The GA-ANN was developed using daily water discharge, with water level as the input data to estimate the daily SSY at Polavaram, which is the farthest gauging station in the downstream of the Godavari River Basin. The performances of the GA-ANN model were evaluated by comparing with ANN, sediment rating curve (SRC) and multiple linear regression (MLR) models. It is observed that the GA-ANN contains the highest correlation coefficient (0.927) and lowest root mean square error (0.053) along with lowest biased (0.020) values among all the comparative models. The GA-ANN model is the most suitable substitute over traditional models for SSY prediction. The hybrid GA-ANN can be recommended for estimating the SSY due to comparatively superior performance and simplicity of applications.

Improving rating curve accuracy by incorporating water balance closure at river bifurcations

Accurate discharge records are essential for flood frequency analyses, hydraulic model calibration and flood forecasting. Discharge records are often obtained via a transformation of water levels to discharges using a rating curve. For accurate rating curves, a physical basis is important, particularly in the extrapolation domain towards extreme discharges. In this study, physical processes and constraints are incorporated in a rating curve model: water balance closure at a bifurcation and bed level degradation. The aim is to assess the effect of incorporating these physical processes and constraints for rating curves at two bifurcations of the Rhine river in the Netherlands. Intermittent gaugings are available for a 31 year period at these bifurcations. Bayesian inference and Markov Chain Monte Carlo sampling is used to estimate the posterior distributions of the rating curves. If rating curves are constructed independently, they show a large water balance error at bifurcations of up to 10%. Incorporating bed level degradation is required for accurate rating curves as it reduces the residual errors by up to 50%. If explicitly accounting for water balance closure, the water balance error can be reduced to 1%, while residual errors remain equally small. As water balance closure is a physical constraint at a river bifurcation, the rating curves that account for water balance closure are expected to be more physically realistic. Therefore, it is recommended to specifically gauge at river bifurcations and confluences, such that the constraint of water balance closure can be used to improve the accuracy of rating curves and discharge records.

Generalization of the power‐law rating curve using hydrodynamic theory and Bayesian hierarchical modeling

AbstractThe power‐law rating curve has been used extensively in hydraulic practice and hydrology. It is given by , where is discharge, is water elevation, , , and are unknown parameters. We propose a novel extension of the power‐law rating curve, referred to as the generalized power‐law rating curve. It is constructed by linking the physics of open channel flow to a model of the form . The function is referred to as the power‐law exponent and it depends on the water elevation. The proposed model and the power‐law model are fitted within the framework of Bayesian hierarchical models. By exploring the properties of the proposed rating curve and its power‐law exponent, we find that cross‐sectional shapes that are likely to be found in nature are such that the power‐law exponent will usually be in the interval . This fact is utilized for the construction of prior densities for the model parameters. An efficient Markov chain Monte Carlo sampling scheme, that utilizes the lognormal distributional assumption at the data level and Gaussian assumption at the latent level, is proposed for the two models. The two statistical models were applied to four datasets. In the case of three datasets the generalized power‐law rating curve gave a better fit than the power‐law rating curve while in the fourth case the two models fitted equally well and the generalized power‐law rating curve mimicked the power‐law rating curve. We developed an R package, bdrc, for fitting the power‐law and generalized power‐law rating curve models. It is available on CRAN.

Predictability performance enhancement for suspended sediment in rivers: Inspection of newly developed hybrid adaptive neuro-fuzzy system model

Reliable modeling of river sediments transport is important as it is a defining factor of the economic viability of dams, the durability of hydroelectric-equipment, river susceptibility to pollution, suitability for navigation, and potential for aesthetics and fish habitat. The capability of a new machine learning model, fuzzy c-means based neuro-fuzzy system calibrated using the hybrid particle swarm optimization-gravitational search algorithm (ANFIS-FCM-PSOGSA) in improving the estimation accuracy of river suspended sediment loads (SSLs) is investigated in the current study. The outcomes of the proposed method were compared with those obtained using the fuzzy c-means based neuro-fuzzy system calibrated using particle swarm optimization (ANFIS-FCM-PSO), ANFIS-FCM, and sediment rating curve (SRC) models. Various input combinations involving lagged river flow (Q) and suspended sediment (S) values were used for model development. The effect of Q and S on the model's accuracy also was assessed by including the difference between lagged Q and S values as inputs. The model performance was assessed using the root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe Efficiency (NSE), and coefficient of determination (R2) and several graphical comparison methods. The results showed that the proposed model enhanced the prediction performance of the ANFIS-FCM-PSO (or ANFIS-FCM) models by 8.14% (1.72%), 14.7% (5.71%), 12.5% (2.27%), and 25.6% (1.86%), in terms of the RMSE, MAE, NSE and R2, respectively. The current study established the potential of the proposed ANFIS-FCM-PSOGSA model for simulation of the cumulative sediment load. The modeling results revealed the potential effects of the river flow lags on the sediment transport quantification.

Fitting Rating Curves to Selected Streams in Southeast Nigeria

Lack of funds and political will have made continuous gauging of rivers in Nigeria impossible, thus stalling the development of surface water resources. In order to address this anomaly; this study is focused on developing discharge rating curve, for selected streams in Imo-Anambra river basin of southeast Nigeria, which is capable of predicting discharge from stage. Ten years monthly stage and discharge records, measured with stream gauges, for Rivers Adada in Enugu state, Ajali in Anambra state, Ivo in Ebonyi State, Otamiri in Imo state, and Imo (Umuopara) in Abia state, were used in estimating the rating curve models using simple linear regression as: , and . All the rating curve equations were validated using coefficient of determination which yielded values of 98.54%, 97.38%, 17.31%, 89.98% and 99.43%, but the empirical discharge-stage model of River Ivo was discarded as the model produced poor performance and lacked the features of a rating curve. The rating curve of Imo River predicted the highest discharge for equivalent input values of stage because of its large cross-section at the gauging station. The developed rating curve models are therefore recommended for discharge prediction in these catchment areas with limited streamflow records.Keywords— fitting, rating curve, southeast Nigeria, stream discharge

A Rating Curve Model Accounting for Cyclic Stage‐Discharge Shifts due to Seasonal Aquatic Vegetation

AbstractManaging stage‐discharge relations at hydrometric stations affected by seasonal aquatic vegetation is challenging. Their ratings vary continuously in time so that establishing the streamflow time series is difficult. To the best of our knowledge, no rating curve model exists to deal with a vegetated channel control, only manual adjustment methods. To address this issue, a temporal rating curve model accounting for transient changes due to vegetation is developed. The model is built on basic concepts from open‐channel hydraulics and plant physiology. In the model, the flow resistance varies through time as a function of the plant development (growth and decay) and of the plant ability to reconfigure. Model parameters and uncertainty are estimated through Bayesian inference combining prior knowledge on the hydraulic controls at the station and observational data. In addition to the traditionally used stage‐discharge gaugings, the model allows the use of qualitative observations on the plant development state (e.g., no plant, growth, and decay). The model is tested and validated for a French hydrometric station where frequent gaugings (twice a month) and written comments about vegetation are available over more than 20 years. Relative errors between the simulated discharges and the observed discharges mostly range between ±20% for the temporal rating curve. In contrast, they are higher than ±50% with a standard model with no vegetation module. This case study highlights the importance of using observations about plant development to predict water discharge. We finally discuss some possible improvements and extensions of the model and recommend methods for data collection.

Unbiased Estimates and Confidence Intervals for Riverine Loads

AbstractEstimating the uncertainty in annual riverine constituent loads, which is the mass that passes through a river cross‐section into a receiving water body, using infrequent water quality (WQ) observations is a difficult and unsolved task. Therefore, we propose an unbiased point estimation method and interval estimation method for river loads based on the rating curve (RC) method using importance sampling and the bootstrap method, respectively. In this paper, we first statistically explain the unbiasedness of load estimates using the proposed method. Second, the effectiveness of point and interval estimates by the proposed method is demonstrated for river loads from a small catchment and from large watersheds based on discharge and WQ data of solutes, nutrients, and suspended sediments with 10‐min to daily intervals. The results show that the proposed method provides unbiased estimates and appropriate coverage of confidence intervals regardless of the RC model used. The results also reveal that the dominant cause of bias in load estimates based on ordinary RC methods, such as the Loadest model, is not due to the poor simulation of observed loading rates by the RCs or because of the nonnormality of the regression residuals but rather improper sampling strategies. The proposed method is currently not feasible for WQ monitoring sites in large rivers due to the unmanageability of missing observations or censored data and an inefficient sampling strategy, although the requirement of unbiased estimation explained here can aid in scheduling high‐flow sampling for monitoring sites.

Application of Soft Computing Models with Input Vectors of Snow Cover Area in Addition to Hydro-Climatic Data to Predict the Sediment Loads

The accurate estimate of sediment load is important for management of the river ecosystem, designing of water infrastructures, and planning of reservoir operations. The direct measurement of sediment is the most credible method to estimate the sediments. However, this requires a lot of time and resources. Because of these two constraints, most often, it is not possible to continuously measure the daily sediments for most of the gauging sites. Nowadays, data-based sediment prediction models are famous for bridging the data gaps in the estimation of sediment loads. In data-driven sediment predictions models, the selection of input vectors is critical in determining the best structure of models for the accurate estimation of sediment yields. In this study, time series inputs of snow cover area, basin effective rainfall, mean basin average temperature, and mean basin evapotranspiration in addition to the flows were assessed for the prediction of sediment loads. The input vectors were assessed with artificial neural network (ANN), adaptive neuro-fuzzy logic inference system with grid partition (ANFIS-GP), adaptive neuro-fuzzy logic inference system with subtractive clustering (ANFIS-SC), adaptive neuro-fuzzy logic inference system with fuzzy c-means clustering (ANFIS-FCM), multiple adaptive regression splines (MARS), and sediment rating curve (SRC) models for the Gilgit River, the tributary of the Indus River in Pakistan. The comparison of different input vectors showed improvements in the prediction of sediments by using the snow cover area in addition to flows, effective rainfall, temperature, and evapotranspiration. Overall, the ANN model performed better than all other models. However, as regards sediment load peak time series, the sediment loads predicted using the ANN, ANFIS-FCM, and MARS models were found to be closer to the measured sediment loads. The ANFIS-FCM performed better in the estimation of peak sediment yields with a relative accuracy of 81.31% in comparison to the ANN and MARS models with 80.17% and 80.16% of relative accuracies, respectively. The developed multiple linear regression equation of all models show an R2 value of 0.85 and 0.74 during the training and testing period, respectively.

An expanded rating curve model to estimate river discharge during tidal influences across the progressive-mixed-standing wave systems.

Empirically quantifying tidally-influenced river discharge is typically laborious, expensive, and subject to more uncertainty than estimation of upstream river discharge. The tidal stage-discharge relationship is not monotonic nor necessarily single-valued, so conventional stage-based river rating curves fail in the tidal zone. Herein, we propose an expanded rating curve method incorporating stage-rate-of-change to estimate river discharge under tidal influences across progressive, mixed, and standing waves. This simple and inexpensive method requires (1) stage from a pressure transducer, (2) flow direction from a tilt current meter, and (3) a series of ADP surveys at different flow rates for model calibration. The method was validated using excerpts from 12 tidal USGS gauging stations during baseflow conditions. USGS gauging stations model discharge using a different more complex and expensive method. Comparison of new and previous models resulted in good R2 correlations (min 0.62, mean 0.87 with S.D. 0.10, max 0.97). The method for modeling tidally-influenced discharge during baseflow conditions was applied de novo to eight intertidal stations in the Mission and Aransas Rivers, Texas, USA. In these same rivers, the model was further expanded to identify and estimate tidally-influenced stormflow discharges. The Mission and Aransas examples illustrated the potential scientific and management utility of the applied tidal rating curve method for isolating transient tidal influences and quantifying baseflow and storm discharges to sensitive coastal waters.

Developing a Sediment Rating Curve Model Using the Curve Slope

Developing a Sediment Rating Curve Model Using the Curve Slope

Presenting a New Approach to Increase the Efficiency of the Sediment Rating Curve Model in Estimating Suspended Sediment Load in Watersheds (Case Study: Mahabad-Chai River, Lake Urmia Basin, West Azarbayejan Province, Iran)

Presenting a New Approach to Increase the Efficiency of the Sediment Rating Curve Model in Estimating Suspended Sediment Load in Watersheds (Case Study: Mahabad-Chai River, Lake Urmia Basin, West Azarbayejan Province, Iran)

Revisiting conceptual stormwater quality models by reconstructing virtual state variables

This work proposes a Bayesian non-informative reconstruction of virtual state variables in the representation of stormwater total suspended solids pollutographs by the traditional wash-off models, based on 255 rainfall events measured in a 185 ha French urban catchment. Results from event-based analyses revealed the missing representation of an essential process in the traditional rating curve (RC) model (simplest wash-off model) for 56% of the rainfall events. The unsatisfactory performances of the RC model are found to be not necessarily linked to antecedent dry weather conditions, as assumed by a great number of accumulation/wash-off models. Statistical tests suggest that non-representable rainfall events by the RC model are randomly distributed in time. The proposed Bayesian reconstructions of a potential process missed by the RC model exhibit a suitable identifiability at an intra-event scale. However, these reconstructions are not interpretable from the traditional accumulation/wash-off notions, i.e. in terms of a unique state of virtual available mass over the catchment that is decreasing over time, due to their high unrepeatability regarding their shape and their low prediction capacity for other rainfall events.

Modeling Hydrological Appraisal of Potential Land Cover Change and Vegetation Dynamics under Environmental Changes in a Forest Basin

An integrated multi-model approach to predict future land cover in the Da River Basin in Vietnam was developed to analyze future impacts of land cover change on streamflow and sediment load. The framework applied a land cover change model and an ecological model to forecast future land cover and leaf area index (LAI) based on the historical land cover change, and these data were then used in a calibrated distributed hydrological model and a new sediment rating curve model to assess hydrological changes and sediment load in the river basin. Results showed that deforestation would likely continue, and that forest area would decrease by up to 21.3% by 2050, while croplands and shrublands would replace forests and increase by over 11.7% and 10%, respectively. Streamflow and sediment load would generally increase due to deforestation in the Da River Basin in the 2050s, in both the wet and dry seasons, but especially in the wet season. In this case, the predicted annual sediment load was expected to increase by about 9.7% at the Lai Chau station. As deforestation increased, sediment load and reservoir siltation could likely shorten the lifespan of the recently constructed Son La Reservoir. The applied integrated modeling approach provides a comprehensive evaluation of land/forest cover change effects on the river discharge and sediment load, which is essential in understanding human impacts on the river environment and in designing watershed management policies.