Discharge Rating Curves Research Articles

Analysis of runoff, sediment dynamics and sediment yield of subcatchments in the highly erodible Isábena catchment, Central Pyrenees

The Isabena catchment (445 km2), Spain, features highly diverse spatial heterogeneity in land use, lithology and rainfall. Consequently, the relative contribution in terms of water and sediment yield varies immensely between its subcatchments, and also temporally. This study presents the synthesis of ~2.5 years of monitoring rainfall, discharge and suspended sediment concentration (SSC) in the five main subcatchments of the Isabena and its outlet. Continuous discharge at the subcatchment outlets, nine tipping bucket rainfall and automatic SSC samplers (complemented by manual samples), were collected from June 2011 until November 2013. The water stage records were converted to discharge using a rating curve derived with Bayesian regression. For reconstructing sediment yields, the data from the intermittent SSC sampling needed to be interpolated. We employed non-parametric multivariate regression (Quantile Regression Forests, QRF) using the discharge and rainfall data plus different aggregation levels of these as ancillary predictors. The subsequent Monte Carlo simulations allowed the determination of monthly sediment yields and their uncertainty. The stage–discharge rating curves showed wide credibility intervals for the higher stages, with great uncertainties associated with the discharge rates, especially during floods. The water yield of the subcatchments differed considerably. The entire catchment’s output was dominated by the northernmost subcatchment (~360 mm year−1). The smaller, southern subcatchments featured much higher variability and lower runoff rates (55–250 mm year−1). The SSCs exhibited a wide range and can exceed 100 g l−1 for the central subcatchments, where most of the badlands are located. For the reconstruction of the sedigraphs, the QRF method proved suitable with Nash–Sutcliffe indices of 0.50 to 0.84. The specific sediment yield ranges from relatively low (32 t km−2 year−1) in the highly vegetated north to high values (3,651 t km−2 year−1) in areas with many badland formations. The Isabena catchment shows high erosion dynamics with great variability in space and time, with stark contrasts even between adjacent subcatchments. The natural conditions make water and sediment monitoring and instrumentation very challenging; the measurement of discharge is particularly prone to considerable uncertainties. The QRF method employed for reconstructing sedigraphs and monthly yields proved well suited for the task.

Remotely sensed estimation of water discharge into the rapidly dwindling Dead Sea

The Dead Sea is shrinking as its water level drops at the alarming rate of about 1 m year-1. The Dead Sea is important to the economies of Israel and Jordan due to the extracted minerals (primarily potassium, also magnesium and bromide). It is also central to regional tourism. It is the lowest place on Earth and its endorheic, saline basin attracts international research in various disciplines. Additional to the Lower Jordan River, the discharge of which has been decreased to a small fraction of its original value, fresh to brackish springs are the main source of water to the rapidly dwindling Dead Sea. Although the existence of these springs has been known for decades, until recently estimates of spring water discharge into the Dead Sea were scarce. In this study, we developed a methodology of water discharge estimation for channels incising into a lacustrine bed using remotely sensed data and a single hydraulic geometry variable, water-surface width. Based on calibration of over 400 in situ measurements and simultaneous hydrometric data from aerial images, width–discharge rating curves were established, tested, and found suitable (r2 = 0.92, p = 0.001) for the estimation of water discharge, with ±5% uncertainty. Furthermore, we used these relationships to estimate retrospectively the temporal changes in water discharge of seven main channels traceable in historical aerial images. The reconstructed trend reveals a major (63%) reduction in average freshwater inflow between 1990 and 2006. Our results maximize the use of water-surface width information from aerial imagery, and suggest applicability to areas experiencing rapid exposure of sea/lake bed and consequent access difficulties in in situ discharge monitoring.Editor Z.W. KundzewiczCitation Vachtman, D. and Laronne, J.B., 2014. Remotely sensed estimation of water discharge into the rapidly dwindling Dead Sea. Hydrological Sciences Journal, 59 (8), 1593–1605. http://dx.doi.org/10.1080/02626667.2013.852278

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.

Water Management Solution of Reservoir Storage Function Under Condition of Measurement Uncertainties in Hydrological Input Data

The paper describes a possible procedure of the rate uncertainty implementation to the continuous water stage measurement and uncertainties of state - discharge rating curve point positions, which the stage -discharge rating curves were fitted into the uncertainties of the real discharge series members. Then the members of discharge series under uncertainty impact were tested on the calculated values of the reservoir storage volume. The next step was the implementation of the uncertainties of the real discharge series members on the generation of the artificial discharge series of mean monthly discharge using the AR and ARMA generators and the determination of their impact on the calculated values of the reservoir storage volume.

Rainfall and Runoff Observations in the Subtropical Forest of Okinawa Island, Japan

We set up two experimental catchments to provide an improved understanding of hydrological processes in a subtropical forested area in the northern part of Okinawa Island, Japan. We calculated runoff using water level data (recorded by a pressure-type water level gauge installed in a box culvert) and a discharge rating curve (derived from in situ observations). Water balance calculations for 2010 showed that the rainfall, runoff and evapotranspiration losses (= rainfall – runoff) were 3403.6 mm, 2285.7 mm and 1117.4 mm, respectively. This result was in agreement with previous results from other forested experimental catchments in this region. Direct runoff, as a proportion of event total rainfall, can be expressed by the empirical equation (Qdirect = 0.0048, Pevent 1.7971, R2 = 0.9599). When Pevent was 100 mm or less, the ratios of Qdirect to Pevent were less than 15% in general. When Pevent exceeded 100 mm, the ratios were 20% - 30%.

Flood modelling: parameterisation and inflow uncertainty

This paper presents an analysis of uncertainty in hydraulic modelling of floods, focusing on the inaccuracy caused by inflow errors and parameter uncertainty. In particular, the study develops a method to propagate the uncertainty induced by, firstly, application of a stage–discharge rating curve and, secondly, parameterisation of a one-dimensional hydraulic model by way of the power function and the conditioning of Manning's roughness coefficients. The proposed methodology was applied to a 98 km reach of the River Po, Italy. Model performance was evaluated using two independent sets of observed water levels in the river reach within a generalised likelihood uncertainty estimation framework. The inflow uncertainty was found to have a greater contribution to the overall uncertainty of the 1D model than the roughness parameters. Independent parameter conditioning and validation, as well as the uncertainty analysis, showed satisfactory model performance. When conditioned on one flood event, the model adequately simulated flood levels and high water marks for another (independent) event, as the observations were within 90% confidence interval of the simulation ensemble.

Monte Carlo Simulation을 이용한 도시하천의 고수위 Rating Curve 개발

본 연구에서는 도시하천을 대상으로 Monte Carlo Simulation (MCS)에 의한 모의발생 기법 적용으로 최적화된 강우-유출 모형과 홍수위 추적모형 연계를 통한 고수위 Rating Curve 작성법을 제안하였다. 대상유역의 관측 자료로부터 작성된 수위-유량곡선식은 유량측정의 오차와 더불어 고수위에 대한 불확실성을 내포하고 있음을 확인할 수 있었으며, 관측치와의 표준오차(<TEX>$S_e$</TEX>)는 0.056으로, 무작위 불확실성(<TEX>$2S_{mr}$</TEX>)은 평균 <TEX>${\pm}1.43%$</TEX>, 최대 <TEX>${\pm}4.27%$</TEX>로 분석되었다. 또한, 전대수지법과 Stevens방법에 의한 고수위 연장은 도시하천 유역 규모에 비하여 수위에 따른 홍수량이 과대 산정되는 문제점이 있는 것으로 분석되었다. 마지막으로, MCS에 의한 다량의 수문자료군 확보를 통한 수위-유량 관계곡선의 연장방법은 고수위에 대한 불확실성을 감소시켜며, 보다 신뢰성 있는 고수위 연장이 가능하였다. 향후 본 연구의 결과는 MCS에 의한 고수위 연장 시스템 구축을 통한 도시하천유역의 실시간 홍수 예 경보 활용에 적용이 가능할 것으로 사료된다. In this study, we proposed a methodology to develop Rating Curves for high water level using rainfall generation by the Monte Carlo Simulation (MCS) technique, optimized rainfall-runoff model, and flood routing model in an urban stream. The developed stage discharge Rating Curve based on observed data was contained flow measurement errors and uncertainties. The standard error (<TEX>$S_e$</TEX>) for observations was 0.056, and the random uncertainty (<TEX>$2S_{mr}$</TEX>) was analyzed by <TEX>${\pm}1.43%$</TEX> on average, and up to <TEX>${\pm}4.27%$</TEX>. Moreover, it was found that the Rating Curve extensions by way of logarithmic and Stevens methods were overestimated to compare with the urban basin scale. Finally, we confirmed that the high water level extension by random generation of hydrological data using MCS can be reduced uncertainty of the high water level, and it will consider as a more reliable approach for high water level extension. In the near future, this results can be applied to real-time flood alert system for urban streams through construction of the high water level extension system using MCS procedures.

Water flow measurements in Turkey&#039;s rivers and evaluation of alternative methods

The accuracy and sustainability in the flow measurement of rivers has a great importance for the water management, planning of water storage structures and prediction of floods. Flow measurements include some difficulty due to the variability of many hydrologic factors. Current rivers flow measurement in Turkey is generally based on the use of limnograph and discharge rating curve and, advances has mostly been made the improvement of reading of limnograph. In this study, at the stage of the discharge measurement, giving priority to the improvement in the measurements of flow velocity and cross-section has been emphasized. Then, while obtaining discharge rating curve, it was expressed that not only the depth of water but also flow velocity values have to be taken into account for the preparing and using the discharge rating curve. A field study conducted by the acoustic method sampled for the assessments that were made. From findings, It was concluded that the use of flow velocity values for the discharge rating curve gives better estimate results.

Flood discharge measurement of a mountain river – Nanshih River in Taiwan

Abstract. This study proposes a more efficient method of flood discharge measurement in mountain rivers that accounts for personal safety, accuracy, and reliability. Because it is based on the relationships between mean and maximum velocities and between cross-sectional area and gauge height, the proposed method utilizes a flood discharge measurement system composed of an acoustic Doppler profiler and crane system to measure velocity distributions, cross-sectional area, and water depths. The flood discharge measurement system can be used to accurately and quickly measure flood data that is difficult to be collected by the conventional instruments. The measured data is then used to calibrate the parameters of the proposed method for estimating mean velocity and cross-sectional area. Then these observed discharge and gauge height can be used to establish the water stage–discharge rating curve. Therefor continuous and real-time estimations of flood discharge of a mountain river can become possible. The measurement method and system is applied to the Nanshih River at the Lansheng Bridge. Once the method is established, flood discharge of the Nanshih River could be efficiently estimated using maximum velocity and the water stage. Results of measured and estimated discharges of the Nanshih River at the Lansheng Bridge differed only slightly from each other, demonstrating the efficiency and accuracy of the proposed method.

Discharge estimation of the Shin-Yuan Canal using indirect method

This study presents an indirect method for estimating the discharge of the Shin-Yuan Canal. It includes a new tool of velocity measurement, a method of discharge computation, and some technology. When the Shin-Yuan Canal was built, the issue of discharge measurement was not considered. The Shin-Yuan Canal was co-constructed with the Wan-Dan Canal. Therefore, direct discharge measurement was impossible. This study indirectly estimated the discharge of the Shin-Yuan Canal by controlling the pump discharge through a pumping station. And a stage-discharge rating curve was created for continuous and real-time monitoring of canal discharge. In order to improve measurement accuracy and reliability, this study adopted the acoustic digital current meter (ADC) for discharge measurement. The probabilistic velocity distribution equation was used to accurately calculate the average vertical velocity and the area-velocity principle was used to estimate the water discharge of the Wan-Dan Canal. According to the measurement results, the discharge rating curve of the Shin-Yuan Canal could be accurately established with the precise device, ADC, and the technologies which could effectively measure velocity. This method should be promoted and applied to other similar discharge measurement and monitoring issues of irrigation canals.

Development of stage–discharge rating curve using model tree and neural networks: An application to Peachtree Creek in Atlanta

The applicability and the performance of the M5P model tree machine learning technique is investigated in modeling of the stage–discharge problem for Peachtree Creek in Atlanta, Georgia. The stage–discharge relationship has an important bearing on the correct assessment of discharge. This technique is compared to three different algorithms of artificial neural network and conventional rating curve. It is shown that the model trees, being analogous to piecewise linear functions, have certain advantages over neural networks; they are more transparent and hence acceptable by decision makers, they are very fast in training, and they always converge. The accuracy of M5P trees is superior to neural network models and conventional model. It was found that M5P outperformed when fewer data events were available for model development. In other words, M5P has potential to be a useful and practical tool for cases where less measured data is available for modeling stage–discharge problem. This study has also showed high consistency between the training and testing phases of modeling when using M5P compared to neural network models and conventional method. Furthermore, a partition analysis has been performed. This analysis reveals that the results obtained using M5P model performed better than ANN for both the high flows and the low flows.

Modeling discharge rating curves with Bayesian B-splines

River discharges are traditionally modeled by employing a standard power-law methodology. Recently, the Bayesian approached has successfully been applied to improve the estimates of the standard power-law. In this article, an extension to the standard power-law based on Bayesian B-splines is developed and tested on data sets from 61 different rivers. The extended model is evaluated against the standard power-law using two measures, the Deviance Information Criterion and Bayes factor. The extended model captures deviations in the data from the standard power-law but reduces to the standard power-law when that model is adequate. The standard power-law is inadequate for 26% of the rivers while the extended model provides an adequate fit in all of those cases and for the remaining 74% of the rivers the extended model and the power-law model both give adequate fit with almost identical estimates.

Sediment Delivery Assessment for a Transboundary Mediterranean Catchment: The Example of Nestos River Catchment

Nestos River flows through Bulgaria and Greece and discharges into the North Aegean Sea. Its total catchment area is around 6,200 km2, while the mean annual precipitation and runoff are 680 mm and 40 m3/s, respectively. The Hellenic part of the catchment has undergone a substantial hydroelectric development, since two dams associated with major hydropower pumped-storage facilities are in operation. The main objective of the paper is to assess the expected sediment delivery of Nestos R. at the uppermost Thisavros reservoir site. This has been carried out by implementing the Universal Soil Loss Equation in a GIS environment for determining the mean annual soil erosion in conjunction with a suspended sediment measurement program (114 measurements in total) accomplished between 1965 and 1983 adjacent to the dam site. The sediment discharge rating curve between sediment and river discharges in a power form has been constructed using five alternative techniques, namely (a) the linear regression of the log-transformed variables, (b) the same as (a) but with the Ferguson correction, (c) different ratings for the dry and wet seasons of the year, (d) the nonlinear regression, and (e) the broken line interpolation that utilizes different rating parameters for two discharge classes. It is shown that the mean annual sediment yield is almost equal for all rating curve formulations and varies between 178.5 t km−2 and 203.4 t km−2 and the highest value results from the broken line interpolation method. Accordingly, the sediment delivery ratios vary slightly between 17% and 19% of the upstream soil erosion.

Remote Sensing and Hydrological Measurements for Irrigation Performance Assessments in a Water User Association in the Lower Amu Darya River Basin

Irrigation water management in Central Asia is notorious for its inefficiency. We assessed the operational performance of the irrigation scheme in one Water Users Association (WUA), Shomakhulum, in Khorezm district, Uzbekistan, in 2007 to provide recommendations for strategic water management planning. Relative evapotranspiration (RET), delivery performance ratio (DPR), drainage ratio (DR), depleted fraction (DF), overall consumed ratio (OCR), field application ratio (FAR) and conveyance ratio (CR) were used as performance indicators. The components of the water balance were obtained through remote sensing techniques and hydrological field measurements. The surface energy balance algorithm for land (SEBAL) was applied to MODIS satellite data to derive actual and potential evapotranspiration. Inflows and outflows were quantified with field measurements in the irrigation and drainage network using discharge rating curves. Ponding experiments allowed determining canal seepage losses. Water balances at field level were established for application efficiency estimations. The indicator values were then compared to efficiency target values taken from the literature in order to assess the operational capabilities of the irrigation scheme. The general performance of the irrigation scheme is very poor. DPRs exceeding 1.0 indicate that more water is delivered to the system than is demanded. The seasonal DF of 0.4 is lower than the target value of 0.6. Losses during the field application averaged at 57%, which is 24% above target values. Seasonal DR, OCR, CR and RET are 0.55, 0.51, 0.76 and 0.82 against the target values of 0.1, 0.54, 0.84 and 0.75, respectively. We conclude that the distribution mechanism can be considerably improved. Besides improving water distribution (timing and equity) in the network, another recommended intervention would be to increase the DF, particularly by interventions at field level that raise the FAR, which in turn will improve DR and OCR. This can be achieved by introducing modern water management approaches such as laser leveling, double-sided irrigation, and control of inflow through flow-measuring devices installed at farm gates, and adequate water pricing.

A hydraulic study on the applicability of flood rating curves

Several hydrological studies have shown that river discharge records are affected by significant uncertainty. This uncertainty is expected to be very high for river flow data referred to flood events, when the stage–discharge rating curve is extrapolated far beyond the measurement range. This study examines the standard methodologies for the construction and extrapolation of rating curves to extreme flow depths and shows the need of proper approaches to reduce the uncertainty of flood discharge data. To this end, a comprehensive analysis is performed on a 16km reach of the River Po (Italy) where five hydraulic models (HEC-RAS) were built. The results of five topographical surveys conducted during the last 50 years are used as geometric input. The application demonstrates that hydraulically built stage–discharge curves for the five cases differ only for ordinary flows, so that a common rating curve for flood discharges can be derived. This result confirms the validity of statistical approaches to the estimation of the so-called ‘flood rating curve’, a unique stage–discharge curve based on data of contemporaneous annual maxima of stage and discharge values, which appears insensitive to marginal changes in river geometry.

Stochastic modeling of nutrient losses in streams: Interactions of climatic, hydrologic, and biogeochemical controls

We present an analytical, stochastic approach for quantifying intra‐annual fluctuations of in‐stream nutrient losses induced by naturally variable hydrologic conditions. The relevance of the problem we address lies in the growing concern for the major environmental impacts of increasing nutrient loads from watersheds to freshwater bodies and coastal waters. Here we express the first‐order nutrient loss rate constant, ke, as a function of key biogeochemical and hydrologic controls, in particular the stream depth (h). The stage h modulates the impact of natural streamflow temporal fluctuations (induced by intermittent rainfall forcings) on the underlying biogeochemical processes and thus represents the major driver of at‐a‐site fluctuations of ke. Novel expressions for the probability distribution function (pdf) of h and ke are derived as a function of a few eco‐hydrologic, morphologic and biogeochemical parameters. The shape of such pdf's chiefly depends on the following attributes: (1) the average frequency of streamflow‐producing rainfall events, λ; (2) the inverse of mean catchment residence time, k; and (3) a stream channel shape factor, identified through the discharge rating curve exponent b. For λ/(kb) &gt; 1, h and ke have lower intra‐annual variability and lower sensitivity to climatic and morphologic controls, leading to improved predictability and ease of measurement of these attributes. Moment analyses suggest that the variability of ke, relative to that of h, is attenuated for λ/(kb) &gt; 1. Thus, the interplay between climate‐landscape parameters and the stream shape factor b controls the temporal variability induced by stochastic rainfall forcings on stream stages and nutrient removal rates.

THE DISTRIBUTION OF FLOOD HYDROGRAPH RECESSION CONSTANT FOR CHARACTERIZATION OF KARST SPRING AND UNDERGROUND RIVER FLOW COMPONENTS RELEASING WITHIN GUNUNG SEWU KARST REGION

This research is carried out within two caves with underground river and one karst spring, which is located in Gunung Sewu karst area, Gunung Kidul. The objective of this research is to recognize some flood hydrograph properties of karst aquifer characterization in order to compare the comportment of aquifer to release its flow components between underground river and karst spring. Water level data loggers are installed within two caves and one karst spring represent upper, middle, and lower elevation of karst topography, which are Beton, Seropan, and Toto Cave, respectively. In addition, time series discharge measurement in correspond to minimum, average, and maximum flow events is conducted to formulate the Annual Stage Discharge Rating Curve. Thereby, the full year river hydrograph may be defined. Afterwards, by selecting several flood hydrograph events, the recession constant in each cave including diffuse flow (Kb), and fissure flow (Ki), and conduit flow (Kc) recession constant, is then calculated and compared in every location. The result shows that Beton Spring that represents the upper part of research area confirms the quickest respond towards rainfall events. Also, this point specifies the medium number of diffuse recession constant (Kb=0.983), compared to Seropan (0.996), and Toto (0.937), means that the aquifer surrounding Toto Cave release its groundwater storage faster than Beton Spring and Seropan Cave. On the contrary, Seropan Cave performs the highest value of diffuse recession constant (0.996) and this situation is confirmed by its dry season discharge that still above 810 lt/second.

Combined sewer overflow over an oblique weir at Rat Creek in Edmonton, Alberta

Oblique weirs are commonly used in urban drainage systems to remove excess flow from a sewer, in particular, a combined sewer system that has limited conveyance capacity. It is important to understand the hydraulics of these weirs to properly monitor the amount of the overflows as well as to design and improve sewer systems. The Rat Creek structure in Edmonton, Alberta, is a combined sewer overflow structure with a weir at an oblique alignment to the centerline of the sewer. A physical model study of the structure was conducted. The results show that both the approach flow conditions and the chamber geometry can significantly affect the hydraulic performance of the weir and invalidate the application of standard weir equations. A unique flow regime with a linear head–discharge rating curve was observed. The effects of modifying the weir and the hanging baffle wall downstream of the weir were also studied and reported. The results of this case study help to improve the understanding of the hydraulics of oblique weirs in sewer systems.

Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

AbstractParsimonious stage–fall–discharge rating curve models for gauging stations subject to backwater complications are developed from simple hydraulic theory. The rating curve models are compounded in order to allow for possible shifts in the hydraulics when variable backwater becomes effective. The models provide a prior scientific understanding through the relationship between the rating curve parameters and the hydraulic properties of the channel section under study. This characteristic enables prior distributions for the rating curve parameters to be easily elicited according to site‐specific information and the magnitude of well‐known hydraulic quantities. Posterior results from three Norwegian and one American twin‐gauge stations affected by variable backwater are obtained using Markov chain Monte Carlo simulation techniques. The case studies demonstrate that the proposed Bayesian rating curve assessment is appropriate for developing rating procedures for gauging stations that are subject to variable backwater. Copyright © 2009 John Wiley &amp; Sons, Ltd.

The Development of Rating Curve Considering Variance Function Using Pseudo-likelihood Estimation Method

This paper employs a new estimation method for estimating stage–discharge rating curve parameters. In typical practical applications, the original non-linear rating curve is transformed into a simple linear regression model by log-transforming the measurement without examining the effect of heteroscedasticity of residuals. Therefore, the model with pseudo-likelihood estimation is developed in this study to deal with heteroscedasticity of residuals in the original non-linear model. The parameters of rating curves and variance functions of errors are simultaneously estimated by the pseudo-likelihood estimation (P-LE) method. Also simulated annealing, a sort of global optimization techniques, is adapted to minimize the log likelihood of the weighted residuals. At first, the developed P-LE model was applied to a hypothetical site where stage–discharge data were generated by incorporating various errors for statistical test. Also, the limit of stages for segmentation is estimated in the process of P-LE using the Heaviside function. For the validation of effects of the developed P-LE model, the results of the conventional log-transformed linear regression (LT-LR) model and the P-LE model are estimated and compared. After statistical simulation, the developed P-LE model is then applied to the real data sets from six gauge stations in the Geum River basin. It can be suggested that this new estimation method is applied to real river sites to successfully determine the weights taking into account error distributions from observed discharge data.