Sediment-discharge Relationship Research Articles

Quantifying and interpreting the hysteresis patterns of monthly sediment concentration and water discharge in karst watersheds

Hysteresis loop models are one of the most common and effective tools for quantifying time-scale dynamics of sediment-discharge relationships. These models can successfully characterize sediment dynamics in watersheds and facilitate developing effective measures to manage sediment-discharge resources. Considering the characteristics of a proportional hysteresis index, an improved differential hysteresis index was developed. The improved model was used to quantify typical patterns of monthly sediment-discharge relationships in six karst watersheds in southwest China during 2003–2019. Partial least squares structural equation modeling was conducted to decouple the effects of climatic factors and vegetation extent on the hysteresis index. The results indicate that clockwise hysteresis accounted for 74 % of the total hysteresis occurring in the watersheds, whereas counterclockwise and 8-shaped hysteresis accounted for only 22 % and 3.9 %, respectively. The improved hysteresis index varied from −10 to 10, effectively reflecting the degree of hysteresis occurring in the watersheds. Partial least squares structural equation modeling shows that climatic factors (e.g., temperature and precipitation) and vegetation extent in the Hongshui, Yujiang, Liujiang and Wujiang watersheds explained 50 %∼75 % of the hysteresis between sediment concentration and water discharge. The combined effect of temperature and precipitation on the hysteresis index was larger than that of vegetation extent. The improved differential hysteresis index proposed in this study effectively extended the applicability of differential hysteresis indices and facilitated comparing the degree of hysteresis among watersheds with different sediment concentrations. This study can improve the understanding of sediment sources and transport pathways and provide valuable information for decision making on soil erosion control in karst watersheds.

Copula-Based Infilling Methods for Daily Suspended Sediment Loads

Less-frequent and inadequate sampling of sediment data has negatively impacted the long and continuous records required for the design and operation of hydraulic facilities. This data-scarcity problem is often found in most river basins of Taiwan. This study aims to propose a parsimonious probabilistic model based on copulas to infill daily suspended sediment loads using streamflow discharge. A copula-based bivariate distribution model of sediment and discharge of the paired recorded data is constructed first. The conditional distribution of sediment load given observed discharge is used to provide probabilistic estimation of sediment loads. In addition, four different methods based on the derived conditional distribution of sediment load are used to give single-value estimations. The obtained outcomes of these methods associated with the results of the traditional sediment rating curve are compared with recorded data and evaluated in terms of root mean square error (RMSE), mean absolute percentage error (MAPE), Nash-Sutcliffe efficiency (NSE), and modified Nash-Sutcliffe efficiency (MNSE). The proposed approach is applied to the Janshou station located in eastern Taiwan with recorded daily data for the period of 1960–2019. The results indicate that the infilled sediments by the sediment rating curve exhibit better performance in RMSE and NSE, while the copula-based methods outperform in MAPE and MNSE. Additionally, the infilled sediments by the copula-based methods preserve scattered characteristics of observed sediment-discharge relationships and exhibit similar frequency distributions to that of recorded sediment data.

Time‐varying, nonlinear suspended sediment rating curves to characterize trends in water quality: An application to the Upper Hudson and Mohawk Rivers, New York

AbstractThis work proposes two modelling frameworks for diagnosing temporal variations in nonlinear rating curves that describe suspended sediment–discharge relationships. A variant of the weighted regression on time, discharge, and season model is proposed and is compared against dynamic nonlinear modelling, a newly developed nonlinear time series filter based on sequential Monte Carlo sampling. Both approaches estimate a time series of rating curve parameters, with uncertainty, that can be used to diagnose variability in the sediment–discharge relationship over time. We evaluate the models with a variety of synthetic scenarios to highlight their ability to estimate signals of known rating curve change. Results reveal important bias‐variance trade‐offs unique to each approach, and in general, suggest that dynamic nonlinear modelling is better suited for rapid rating curve changes, whereas the weighted regression on time, discharge, and season variant more precisely estimates slow change. The techniques are then applied in two case studies in the Upper Hudson and Mohawk Rivers in New York. We conclude with a discussion of the implications of dynamic rating curves for the management of water quality in riverine and estuary systems.

Visual Analysis to Investigate the Capability of ANFIS in Modelling Hydrological Relationship Using Synthetic Dataset

ANFIS (Adaptive Neuro Fuzzy Inference System), for its advantages of having linguistic representation of models has been the interests of both hydrological operational modellers and scientists/theorists. In hydrology especially, every process is unique and dependent on large number of natural factors hence modelling using machine learning algorithm without considering hydrological insight is very dangerous. In using most of the machine learning algorithms including ANFIS, to obtain the best model, the common and normal approach is always by comparing models of different parameter settings based on the goodness-offit statistical measures. This approach is not always accurate, as each statistical measure has its drawbacks in terms of how accurate it is presenting the model depending on the condition and complexity of the data involved. This research proposes the use of synthetic data in order to explore and understand the behaviour of ANFIS parameters on hydrological data, specifically hysteresis effect in sediment-discharge relationship, in order to improve the efficiency of the modelling process. The results of simulation on the synthetic datasets are then presented and analysed visually. The modelling process is then repeated on real datasets in order to validate the findings.

Erratum to: A New Approach for Modeling Sediment-Discharge Relationship: Local Weighted Linear Regression

Erratum to: A New Approach for Modeling Sediment-Discharge Relationship: Local Weighted Linear Regression

The effect of El Niño Southern Oscillation cycles on the decadal scale suspended sediment behavior of a coastal dry‐summer subtropical catchment

AbstractRivers display temporal dependence in suspended sediment–water discharge relationships. Although most work has focused on multi‐decadal trends, river sediment behavior often displays sub‐decadal scale fluctuations that have received little attention. The objectives of this study were to identify inter‐annual to decadal scale fluctuations in the suspended sediment–discharge relationship of a dry‐summer subtropical river, infer the mechanisms behind these fluctuations, and examine the role of El Niño Southern Oscillation climate cycles. The Salinas River (California) is a moderate sized (11 000 km2), coastal dry‐summer subtropical catchment with a mean discharge (Qmean) of 11.6 m3 s−1. This watershed is located at the northern most extent of the Pacific coastal North America region that experiences increased storm frequency during El Niño years. Event to inter‐annual scale suspended sediment behavior in this system was known to be influenced by antecedent hydrologic conditions, whereby previous hydrologic activity regulates the suspended sediment concentration–water discharge relationship. Fine and sand suspended sediment in the lower Salinas River exhibited persistent, decadal scale periods of positive and negative discharge corrected concentrations. The decadal scale variability in suspended sediment behavior was influenced by inter‐annual to decadal scale fluctuations in hydrologic characteristics, including: elapsed time since small (~0.1 × Qmean), and moderate (~10 × Qmean) threshold discharge values, the number of preceding days that low/no flow occurred, and annual water yield. El Niño climatic activity was found to have little effect on decadal‐scale fluctuations in the fine suspended sediment–discharge relationship due to low or no effect on the frequency of moderate to low discharge magnitudes, annual precipitation, and water yield. However, sand concentrations generally increased in El Niño years due to the increased frequency of moderate to high magnitude discharge events, which generally increase sand supply. Copyright © 2014 John Wiley & Sons, Ltd.

Eel River margin source-to-sink sediment budgets: Revisited

Abstract The Eel River coastal margin has been used as a representative source-to-sink sediment dispersal system owing to its steep, high-sediment yield river and the formation of sedimentary strata on its continental shelf. One finding of previous studies is that the adjacent continental shelf retains only ~ 25% of the Eel River fine-grained sediment (less than 63 μm) discharged over time scales of both individual floods and the 20th century, thus suggesting that the Eel shelf trapping-efficiency is uniquely lower than other similar systems. Here I provide data and analyses showing that sediment discharge relationships in the Eel River have varied strongly with time and include substantial decreases in suspended-sediment concentrations during the latter 20th century. Including these trends in margin-wide sediment budgets, I show that previous Eel River sediment discharge rates were overestimated by a factor of two. Thus, revised sediment budgets shown here reveal that the Eel shelf retained ~ 50% of the discharged river fine-grained suspended sediment during intensively sampled events of 1995–97 and over the 20th century. In light of this, hypotheses about high rates of sediment export away from the primary shelf depocenter should be reevaluated.

Trends in the suspended-sediment yields of coastal rivers of northern California, 1955–2010

Time-dependencies of suspended-sediment discharge from six coastal watersheds of northern California – Smith River, Klamath River, Trinity River, Redwood Creek, Mad River, and Eel River – were evaluated using monitoring data from 1955 to 2010. Suspended-sediment concentrations revealed time-dependent hysteresis and multi-year trends. The multi-year trends had two primary patterns relative to river discharge: (i) increases in concentration resulting from both land clearing from logging and the flood of record during December 1964 (water year 1965), and (ii) continual decreases in concentration during the decades following this flood. Data from the Eel River revealed that changes in suspended-sediment concentrations occurred for all grain-size fractions, but were most pronounced for the sand fraction. Because of these changes, the use of bulk discharge-concentration relationships (i.e., “sediment rating curves”) without time-dependencies in these relationships resulted in substantial errors in sediment load estimates, including 2.5-fold over-prediction of Eel River sediment loads since 1979. We conclude that sediment discharge and sediment discharge relationships (such as sediment rating curves) from these coastal rivers have varied substantially with time in response to land use and climate. Thus, the use of historical river sediment data and sediment rating curves without considerations for time-dependent trends may result in significant errors in sediment yield estimates from the globally-important steep, small watersheds.

EXPLICIT NEURAL NETWORK IN SUSPENDED SEDIMENT LOAD ESTIMATION

Correct estimation of sediment volume carried by a river is very im- portant for many water resources projects. Traditionally, artificial neural networks (ANNs) are used as black-box models without understanding what happens inside the box. The question is that, how anyone who may be unfamiliar with ANNs can apply this kind of models in any other study, while the model has not been formu- lated. This paper proposes an explicit neural network (ENN) formulation which is simple and can be used, by anyone who is even not familiar with ANNs, for mod- eling daily suspended sediment-discharge relationship. The daily streamflow and suspended sediment data from two stations on Tongue River in Montana are used as case studies. Two different sediment rating curves (SRC), multi-linear regres- sion (MLR) and nonlinear regression (NLR) are also applied to the same data. The ENN estimates are compared with those of the SRC, MLR and NLR models. The root mean square errors (RMSE), mean absolute errors (MAE), correlation coeffi- cient (R) and model efficiency (E) statistics are used to evaluate the performance of the models. The comparison results reveal that the suggested model performs better than the conventional SRC, MLR and NLR.

A methodological approach for estimating turbidity in a river

During the operations of purging and disposal of sediments of a reservoir it is necessary to know the values of turbidity in the river downstream in natural condition, in the absence of dams or river training works. The paper shows that under these conditions the ratio of the average values of sediment discharge to the annual maximum value of water discharge is a function of the average annual turbidity. Turbidity can be considered as representative synthetic index of the climatic conditions, the lithological features and the land cover of the basin, and the geometric characteristics of the river network. The proposed relationship of sediment discharge as a function of water discharge were validated on the basis of data collected from different Italian regions that have very different morphological, geo-lithological and rainfall features and that are characterised by a basin area changing between a few dozen and thousands of square kilometres. The results can be considered satisfying.

Daily suspended sediment estimation using neuro-wavelet models

This paper proposes the application of neuro-wavelet technique for modeling daily suspended sediment–discharge relationship. The neuro-wavelet models are obtained by combining two methods, artificial neural networks (ANN) and discrete wavelet transform. The accuracy of the neuro-wavelet and the ANN models is compared with each other in suspended sediment load estimation. The daily streamflow and suspended sediment data from two stations on Tongue River in Montana are used as case studies. The comparison results reveal that the suggested model could increase the estimation accuracy.

Multi-year precipitation variations and watershed sediment yield in a CEAP benchmark watershed

A case study was conducted on the Fort Cobb Reservoir watershed in central Oklahoma to investigate impacts and implications of persistent multi-year precipitation variations on watershed runoff and sediment yield. Sediment yield was calculated from a sediment-discharge relationship representing 2004 to 2005 land use, agronomic practices, and conservation measures. Several persistent multi-year precipitation variations, called wet and dry periods, occurred in central Oklahoma between 1940 and 2005. The difference in mean annual precipitation between wet and dry periods was 33% of the long-term mean. As a result of nonlinear hydrologic linkages between precipitation, runoff and sediment yield, corresponding variations in watershed runoff and calculated sediment yield were comparatively larger. The difference in mean annual runoff between wet and dry periods was 100% of the long-term mean, and for mean annual calculated sediment yield it was 183% of the long-term mean. With regard to the Conservation Effects Assessment Project (CEAP), the sensitivity of runoff and therefore of sediment yield to wet and dry periods suggests that measures of conservation program effectiveness depend on climatic conditions used in their evaluation and that great care should be taken to select a climate record representative of prevailing climate conditions. Furthermore, it was inferred that the calibration of simulation models used in the conservation effects assessment may be biased if performed with climatic data representing either just a wet or a dry period. In the presence of multi-year precipitation variations, a thorough model validation for both wet and dry periods is recommended to ensure accurate simulation results over the full range of prevailing climatic conditions.

Multi-year precipitation variations and watershed sediment yield in a CEAP benchmark watershed

A case study was conducted on the Fort Cobb Reservoir watershed in central Oklahoma to investigate impacts and implications of persistent multi-year precipitation variations on watershed runoff and sediment yield. Sediment yield was calculated from a sediment-discharge relationship representing 2004-2005 land use, agronomic practices and conservation measures. Several persistent multi-year precipitation variations, called wet and dry periods, occurred in central Oklahoma between 1940 and 2005. The difference in mean annual precipitation between wet and dry periods was 33% of the long-term mean. As a result of non- linear hydrologic linkages between precipitation, runoff and sediment yield, corresponding variations in watershed runoff and calculated sediment yield were comparatively larger. The difference in mean annual runoff between wet and dry periods was 100% of the long-term mean, and for mean annual calculated sediment yield it was 183% of the long-term mean. With regard to the Conservation Effects Assessment Project (CEAP), the sensitivity of runoff and therefore of sediment yield to wet and dry periods suggests that measures of conservation program effectiveness depend on climatic conditions used in their evaluation, and that great care should be taken to select a climate record representative of prevailing climate conditions. Furthermore, it was inferred that the calibration of simulation models used in the conservation effects assessment may be biased if performed with climatic data representing either just a wet or a dry period. In the presence of multi-year precipitation variations, a thorough model validation for both wet and dry periods is recommended to ensure accurate simulation results over the full range of prevailing climatic conditions. Sediment yield from agricultural watersheds is traditionally ascribed to land use, land management and agronomic practices. However, soil erosion and sediment transport and yield are in fact caused by rainfall and runoff, whereas land use, land management and agronomic practices affect the location's erosion potential. Thus, rainfall-runoff is a primary determinant in watershed sediment yield, and any lasting change in rainfall and runoff should be expected to lead to a corresponding change in sediment yield, assuming all other factors remain the same. Lasting changes in rainfall and runoff can be caused by persistent, multi-year precipitation variations which are defined as sequences of consecutive years that have annual precipitation values predominantly above or below the long-term average. Precipitation variations that last 5 or more years are termed wet or dry periods, or pluvial and drought periods. Wet or dry periods in a precipitation record are not uncommon (Gray et al., 2004; Garbrecht and Rossel, 2002; NRC, 1998). Notable examples include the Dust Bowl years

A genetic programming approach to suspended sediment modelling

This study proposes genetic programming (GP) as a new approach for the explicit formulation of daily suspended sediment–discharge relationship. Empirical relations such as sediment rating curves are often applied to determine the average relationship between discharge and suspended sediment load. This type of models generally underestimates or overestimates the amount of sediment. During recent decades, some black box models based on artificial neural networks have been developed to overcome this problem. But these type of models are implicit that can not be simply used by other investigators. Therefore it is still necessary to develop an explicit model for the discharge–sediment relationship. It is aimed in this study, to develop an explicit model based on genetic programming. Explicit models obtained using the GP are compared with rating curves and multi-linear regression techniques in suspended sediment load estimation. The daily streamflow and suspended sediment data from two stations on Tongue River in Montana are used as case studies. The results indicate that the proposed GP formulation performs quite well compared to sediment rating curves and multi-linear regression models and is quite practical for use.

Effective discharge recurrence intervals of Illinois streams

Abstract Effective discharge values are routinely used to characterize the geomorphic impact/work that different flows have on streams and watersheds. Effective discharge values are also routinely employed in stream restoration design. Reliable flow frequency and sediment-rating curves are needed to compute effective discharge values, but are not available for many streams. In lieu of regional effective discharge data, researchers/engineers often assume that a stream's effective discharge is the same as the 1.5-year flow event for that stream. However, research shows that this is not always true. Hence, demand exists for developing regional effective discharge values that can be applied at ungaged stream locations. A regional study of effective discharge values within Illinois is performed. Eighty-eight monitoring sites were identified as locations where effective discharge values could potentially be computed. Twenty of these sites were determined to have sufficient data to compute effective discharge values. For these stations, effective discharge values were computed using two different sediment–discharge relationships (a power curve and an alternative “mean approach”). The mean approach estimates effective discharge values that are, on average, 1.9 times larger than those estimated using the power curve. The sediment load carried by flows less than or equal to the effective discharge value are, on average, 2.7 times larger when the mean approach is used. Both the power curve and mean approaches typically yield effective discharge values greater than the stream's mean flow and less than its 1.1-year (annual maximum series) flow event. Some of the computed effective discharge values are less than the stream's mean flow. Computing effective discharge values remains a subjective process with large uncertainties involved. Class interval size, sediment-rating curve fitting techniques, and available sediment data influence effective discharge results. A paucity of monitoring data for Illinois streams draining <518 km 2 (where many geomorphic analyses and stream restoration projects take place) hinders the regional applicability of effective discharge results. The uncertainties associated with effective discharge values and the inability to validate effective discharge values as a stream's dominant discharge makes channel design using effective and dominant discharge theory problematic. Suggestions for improving regional effective discharge studies and effective discharge estimates are provided.

Estimation of Sediment Yield for a Rain, Snow and Glacier Fed River in the Western Himalayan Region

Assessment of soil erosion, sediment transport and deposition of sediment in the reservoirs, irrigation and hydropower systems are considered essential for the land and water management. The magnitude of sediment transported by rivers has become a serious concern for the water resources planning. In the present study, an assessment of sediment yield has been made for the Satluj River, which flows through the western Himalayan region. Two approaches have been used for the assessment of sediment yield (i) relationship between suspended sediment load and discharge and (ii) empirical relationship. The first approach was used for Satluj Basin up to Suni (52 983 km2), Kasol (53 768 km2) and also for the intermediate basin between Kasol and Suni (785 km2). The sediment-discharge relationship was developed using daily data for a period of three years (1991–1993) for different basins and was applied for each basin for the years 1994 and 1996 for estimation of sediment yield. The second approach, which gives annual sediment yield, has been used for a small intermediate basin only because of data availability constraints. For estimation of the sediment yield using the empirical relationship, various geographical parameters such as land use, topographical etc. were generated using Geographic Information System (GIS) technique. The annual sediment yield for the intermediate basin was estimated for three years and compared with observed values. The trend of difference between computed and observed sediment yield suggested an effect of physical features of mountainous basins. The available empirical relationship was, therefore, revised by incorporating a basin parameter in the equation. This basin parameter represented an integrated effect of slope and spatial distribution of rainfall in the mountainous basin. Using the revised empirical relationship, the sediment yield was estimated for two independent years and a good correlation was found between computed and observed sediment yield.

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.

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.

Sediment yield estimation in small watersheds based on streamflow and suspended sediment discharge measurements

In the past, the watershed sediment yield estimation, in rivers where hydrometric information is available, has been done using the sediment rating curve, which is obtained fitting theoretical functions to the water and sediment discharge relationship. Once this relationship is defined, it can be used along with the flow duration curve of a given year (or runoff-frequency data) to obtain the annual sediment yield prediction. Sometimes, specially in recent years, a better estimation has been developed using the same procedure but replacing the flow duration curve for the daily flow series, transforming each daily flow in suspended sediment discharge, by means of the sediment rating curve, and accumulating this information to monthly and annual levels. This procedure is judged adequate for large watersheds, where the differences among the mean daily flow and the maximum and minimum streamflow during the day are not very large. Generally the equations that fit best the sediment rating curves are highly nonlinear, therefore, in small watersheds where the differences among mean daily flows and the extreme instantaneous flows during the day are important, working with mean daily flows (and even worse with flow duration curves) introduces large errors in sediment yield estimations. In addition to this, there also exists other problems related to the previous procedure, namely the extrapolation errors, that can be very important. Also the quality of the basic information is of paramount importance in this type of analysis. This paper discusses all the above problems analyzing case studies related to two important Venezuelans reservoirs: Dos Cerritos in the Tocuyo River and Cumaripa in the Yaracuy river. An evaluation is made of the effects of these sources of errors in the sediment yield estimation of both cases.

Mobile boundary flow: an assessment of velocity and sediment discharge relationships

Using the data from Brownlie's update of the Compendium of Solids Transport Data, velocity and sediment discharge equations have been derived using regression analysis. Two velocity equations have been determined, one for the lower flow regime and the other for the upper flow regime. A single equation for sediment discharge covers both flow regimes. The equations provide estimation/prediction of sediment discharge and velocity that are simple to use.Plots of over 3000 test results show the relationship of sediment discharge, velocity, flow depth, energy gradient, and sediment size for the lower and upper flow regimes. Included in the plots are estimation and prediction limits for the velocity and sediment discharge relationships. Key words: sediment discharge, velocity, flow regime, weighted least squares, regression, prediction.