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.     

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

Parsimonious 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 & Sons, Ltd.     

The frictional resistance characteristics of a bedrock‐influenced river channel

Much of the published literature relating to reach‐scale total ?ow resistance concentrates on alluvial rivers and little mention is made of the more extreme resistance found in bedrock‐in?uenced river systems. This paper presents the results of a detailed investigation of total ?ow resistance variation for ?ve channel types on the Sabie River, South Africa (cohesive mixed anastomosed, uncohesive mixed anastomosed, mixed pool–rapid, alluvial braided and alluvial single thread) over a range of discharges. Manning's ‘n’ and Darcy‐Weisbach f resistance coef?cients are calculated using Barnes' methodology (H. H. Barnes, US Geological Survey Water Supply Paper 1849, 1967). These data are analysed at the scales of channel type and morphologic unit and the resultant resistance values are compared with the literature. Generally the low‐?ow friction values estimated for the bedrock‐in?uenced channel types are higher than any reported. Flow resistance quanti?cation of the alluvial channel type study sites on the Sabie River produced values slightly higher than earlier studies of similar morphologies. In situations where signi?cant areas of irregular bedrock are exposed (cohesive mixed anastomosed and mixed pool–rapid channel types) the high ?ow resistance coef?cients at low discharges probably re?ect energy dissipation due to hydraulic jumps and internal distortions; however, these values fall as discharge increases to values comparable to those recorded for step–pool rivers. It is suggested that the slightly elevated resistance coef?cients recorded in the alluvial channel types are the result of the vegetation roughness component, operating when the macro‐channel bar features are inundated. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Causes for the decline of suspended‐sediment discharge in the Mississippi River system, 1940–2007

Before 1900, the Missouri–Mississippi River system transported an estimated 400 million metric tons per year of sediment from the interior of the United States to coastal Louisiana. During the last two decades (1987–2006), this transport has averaged 145 million metric tons per year. The cause for this substantial decrease in sediment has been attributed to the trapping characteristics of dams constructed on the muddy part of the Missouri River during the 1950s. However, reexamination of more than 60 years of water‐ and sediment‐discharge data indicates that the dams alone are not the sole cause. These dams trap about 100–150 million metric tons per year, which represent about half the decrease in sediment discharge near the mouth of the Mississippi. Changes in relations between water discharge and suspended‐sediment concentration suggest that the Missouri–Mississippi has been transformed from a transport‐limited to a supply‐limited system. Thus, other engineering activities such as meander cutoffs, river‐training structures, and bank revetments as well as soil erosion controls have trapped sediment, eliminated sediment sources, or protected sediment that was once available for transport episodically throughout the year. Removing major engineering structures such as dams probably would not restore sediment discharges to pre‐1900 state, mainly because of the numerous smaller engineering structures and other soil‐retention works throughout the Missouri–Mississippi system. Published in 2009 by John Wiley & Sons, Ltd.     

Concentration–discharge relationships reflect chemostatic characteristics of US catchments

Concentration–discharge relationships have been widely used as clues to the hydrochemical processes that control runoff chemistry. Here we examine concentration–discharge relationships for solutes produced primarily by mineral weathering in 59 geochemically diverse US catchments. We show that these catchments exhibit nearly chemostatic behaviour; their stream concentrations of weathering products such as Ca, Mg, Na, and Si typically vary by factors of only 3 to 20 while discharge varies by several orders of magnitude. Similar patterns are observed at the inter‐annual time scale. This behaviour implies that solute concentrations in stream water are not determined by simple dilution of a fixed solute flux by a variable flux of water, and that rates of solute production and/or mobilization must be nearly proportional to water fluxes, both on storm and inter‐annual timescales. We compared these catchments' concentration–discharge relationships to the predictions of several simple hydrological and geochemical models. Most of these models can be forced to approximately fit the observed concentration–discharge relationships, but often only by assuming unrealistic or internally inconsistent parameter values. We propose a new model that also fits the data and may be more robust. We suggest possible tests of the new model for future studies. The relative stability of concentration under widely varying discharge may help make aquatic environments habitable. It also implies that fluxes of weathering solutes in streams, and thus fluxes of alkalinity to the oceans, are determined primarily by water fluxes. Thus, hydrology may be a major driver of the ocean‐alkalinity feedback regulating climate change. Copyright © 2009 John Wiley & Sons, Ltd.     

Water–air temperature relationships in a Devon river system and the role of flow

The nature of the water–air temperature relationship, and its moderation by discharge, were investigated for catchments ranging in size from 2·1 to 601 km² in the Exe basin, Devon, UK and for data relating to hourly, daily and weekly time bases. The sensitivity and explanatory power of simple water–air temperature regression models based on hourly data were improved by incorporation of a lag, which increased with catchment size, although relationships became more sensitive and less scattered as the time base of data increased from hourly to weekly mean values. Significant departures from linearity in water–air temperature relationships were evident for hourly, but not for daily mean or weekly mean, data. A clear tendency for relationships between water and air temperatures to be stronger and more sensitive for flows below median levels was apparent, and multiple regression analysis also revealed water temperature to be inversely related to discharge for all catchments and time‐scales. However, discharge had a greater impact in accounting for water temperature variation at shorter time‐scales and in larger catchments. Copyright © 2003 John Wiley & Sons, Ltd.     

Concentration–discharge relationships describe solute and sediment mobilization,reaction, and transport at event and longer timescales

Concentration–discharge (C‐Q) relationships reflect material sources, storage, reaction, proximity, and transport in catchments. Differences in hydrologic pathways and connectivity influence observed C‐Q patterns at the catchment outlet. We examined solute and sediment C‐Q relationships at event and interannual timescales in a small mid‐Atlantic (USA) catchment. We found systematic differences in the C‐Q behaviour of geogenic/exogenous solutes (e.g., calcium and nitrate), biologically associated solutes (e.g., dissolved organic carbon), and particulate materials (e.g., total suspended solids). Negative log(C)–log(Q) regression slopes, indicating dilution, were common for geogenic solutes whereas positive slopes, indicating concentration increase, were common for biologically associated solutes. Biologically associated solutes often exhibited counterclockwise hysteresis during events whereas geogenic solutes exhibited clockwise hysteresis. Across event and interannual timescales, solute C‐Q patterns are linked to the spatial distribution of hydrologic sources and the timing and sequence of hydro‐biogeochemical source contributions to the stream. Groundwater is the primary source of stormflow during the earliest and latest stages of events, whereas precipitation and soil water become increasingly connected to the stream near peakflow. This sequence and timing of flowpath connectivity results in dilution and clockwise hysteresis for geogenic/exogenous solutes and concentration increase and counterclockwise hysteresis for biologically associated solutes. Particulate materials demonstrated positive C‐Q slopes over the long‐term and clockwise hysteresis during individual events. Drivers of particulate and solute C‐Q relationships differ, based on longitudinal and lateral expansion of active channels and changing shear stresses with increasing flows. Although important distinctions exist between the drivers of solute and sediment C‐Q relationships, overall solute and sediment C‐Q patterns at event and interannual timescales reflect consistent catchment hydro‐biogeochemical processes.     

Modelling the rainfall–runoff process of the Mara River basin using the Soil and Water Assessment Tool

The delicate balance between human utilization and sustaining its pristine biodiversity in the Mara River basin (MRB) is being threatened because of the expansion of agriculture, deforestation, human settlement, erosion and sedimentation and extreme flow events. This study assessed the applicability of the Soil and Water Assessment Tool (SWAT) model for long‐term rainfall–runoff simulation in MRB. The possibilities of combining/extending gage rainfall data with satellite rainfall estimates were investigated. Monthly satellite rainfall estimates not only overestimated but also lacked the variability of observed rainfall to substitute gage rainfall in model simulation. Uncertainties related to the quality and availability of input data were addressed. Sensitivity and uncertainty analysis was reported for alternative model components and hydrologic parameters used in SWAT. Mean sensitivity indices of SWAT parameters in MRB varied with and without observed discharge data. The manual assessment of individual parameters indicated heterogeneous response among sub‐basins of MRB. SWAT was calibrated and validated with 10 years of discharge data at Bomet (Nyangores River), Mulot (Amala River) and Mara Mines (Mara River) stations. Model performance varied from satisfactory at Mara Mines to fair at Bomet and weak at Mulot. The (Nash–Sutcliff efficiency, coefficient of determination) results of calibration and validation at Mara Mines were (0.68, 0.69) and (0.43, 0.44), respectively. Two years of moving time window and flow frequency analysis showed that SWAT performance in MRB heavily relied on quality and abundance of discharge data. Given the 5.5% area contribution of Amala sub‐basin as well as uncertainty and scarcity of input data, SWAT has the potential to simulate the rainfall runoff process in the MRB. Copyright © 2012 John Wiley & Sons, Ltd.     

Complex patterns of catchment solute–discharge relationships for coastal plain rivers

Riverine solute versus discharge (C–Q) relationships provide information about the magnitude and dynamics of material fluxes from landscapes. We analysed long‐term patterns of C–Q relationships for 44 rivers in Florida across a suite of geogenic, nutrient, and organic solutes and investigated land cover, watershed size, and surficial geology as controls on these patterns. Solute concentrations generally exhibited far less variability than did discharge, with coherent solute‐specific behaviours repeated across watersheds. Geogenic solutes generally diluted with increasing discharge, whereas organic solutes generally enriched; patterns for nutrients were highly variable across watersheds, but on average exhibited chemostasis. Despite strong evidence of both geologic and land cover controls on solute flow‐weighted concentrations, these variables were poor predictors of C–Q slopes (β) or relative coefficients of variation (CV_C:CV_Q). CV_C:CV_Q generally increased with watershed size, and wetland area appeared to influence C–Q patterns for base cations and organic solutes. Perhaps most importantly, we observed significant slope breaks in C–Q association in approximately half of our observations, challenging the generality of using single power functions to describe catchment solute export patterns. For all solutes except phosphorus (P), C–Q slopes decreased above statistically identified breaks (slopes for P increased), with breaks consistently at or near median flow (i.e., 50% flow exceedance probability). This common pattern significantly impacts solute load estimates; failing to account for slope breaks overestimates nitrate and total organic carbon loads as much as 125% and underestimates P loads as much as 35%. In addition to challenging generic power‐law characterization of C–Q relationships for these coastal plain rivers, and exploring the load estimate consequences thereof, our study supports emerging insights about watershed hydrochemical behaviours across a wide array of solutes.     

Evaluation of basin storage–discharge sensitivity in Taiwan using low‐flow recession analysis

Sensitivity analysis of the hydrological behaviour of basins has mainly focused on the correlation between streamflow and climate, ignoring the uncertainty of future climate and not utilizing complex hydrological models. However, groundwater storage is affected by climatic change and human activities. The streamflow of many basins is primarily sourced from the natural discharge of aquifers in upstream regions. The correlation between streamflow and groundwater storage has not been thoroughly discussed. In this study, the storage–discharge sensitivity of 22 basins in Taiwan was investigated by means of daily streamflow and rainfall data obtained over more than 30 years. The relationship between storage and discharge variance was evaluated using low‐flow recession analysis and a water balance equation that ignores the influence of rainfall and evapotranspiration. Based on the obtained storage–discharge sensitivity, this study explored whether the water storage and discharge behaviour of the studied basins is susceptible to climate change or human activities and discusses the regional differences in storage–discharge sensitivity. The results showed that the average storage–discharge sensitivities were 0.056 and 0.162 mm^?1 in the northern and southern regions of Taiwan, respectively. In the central and eastern regions, the values were both 0.020 mm^?1. The storage–discharge sensitivity was very high in the southern region. The regional differences in storage–discharge sensitivity with similar climate conditions are primarily due to differences in aquifer properties. Based on the recession curve, other factors responsible for these differences include land utilization, land coverage, and rainfall patterns during dry and wet seasons. These factors lead to differences in groundwater recharge and thus to regional differences in storage–discharge sensitivity.     

Analysis of the nonlinear storage–discharge relation for hillslopes through 2D numerical modelling

Storage–discharge curves are widely used in several hydrological applications concerning flow and solute transport in small catchments. This article analyzes the relation Q(S) (where Q is the discharge and S is the saturated storage in the hillslope), as a function of some simple structural parameters. The relation Q(S) is evaluated through two‐dimensional numerical simulations and makes use of dimensionless quantities. The method lies in between simple analytical approaches, like those based on the Boussinesq formulation, and more complex distributed models. After the numerical solution of the dimensionless Richards equation, simple analytical relations for Q(S) are determined in dimensionless form, as a function of a few relevant physical parameters. It was found that the storage–discharge curve can be well approximated by a power law function Q/(LK_s) = a(S/(L²(? ? θ_r)))^b, where L is the length of the hillslope, K_s the saturated conductivity, ? ? θ_r the effective porosity, and a, b two coefficients which mainly depend on the slope. The results confirm the validity of the widely used power law assumption for Q(S). Similar relations can be obtained by performing a standard recession curve analysis. Although simplified, the results obtained in the present work may serve as a preliminary tool for assessing the storage–discharge relation in hillslopes. Copyright © 2012 John Wiley & Sons, Ltd.     

Sedimentation of overbank floods in the confined complex channel–floodplain system of the Lower Yellow River,China

The channel boundary conditions along the Lower Yellow River (LYR) have been altered significantly since the 1950s with the continual reinforcement and construction of both main and secondary dykes and river training works. To evaluate how the confined complex channel–floodplain system of the LYR responds to floods, this study presents a detailed investigation of the relationship between the tempo‐spatial distribution of sedimentation/erosion and overbank floods occurred in the LYR. For large overbank floods, we found that when the sediment transport coefficient (ratio of sediment concentration of flow to flow discharge) is less than 0.034, the bankfull channel is subject to significant erosion, whereas the main and secondary floodplains both accumulate sediment. The amount of sediment deposited on the main and secondary floodplains is closely related to the ratio of peak discharge to bankfull discharge, volume of water flowing over the floodplains, and sediment concentration of overbank flow, whereas the degree of erosion in the bankfull channel is related to the amount of sediment deposited on the main and secondary floodplains, water volume, and sediment load in flood season. The significant increase in erosion in the bankfull channel is due to the construction of the main and secondary dykes and river training works, which are largely in a wide and narrow alternated pattern along the LYR such that the water flowing over wider floodplains returns to the channel downstream after it drops sediment. For small overbank floods, the bankfull channel is subject to erosion when the sediment transport coefficient is less than 0.028, whereas the amount of sediment deposited on the secondary floodplain is associated closely with the sediment concentration of flow. Over the entire length of the LYR, the situation of erosion in the bankfull channel and sediment deposition on the main and secondary floodplains occurred mainly in the upper reach of the LYR, in which a channel wandering in planform has been well developed.     

Recent variation in reach‐scale bankfull discharge in the Lower Yellow River

Bankfull discharge is a key parameter in the context of river engineering and geomorphology, as an indicator of flood discharge capacity in alluvial rivers, and varying in response to the incoming flow and sediment regimes. Bankfull channel dimensions have significantly adjusted along the Lower Yellow River (LYR) due to recent channel degradation, caused by the operation of the Xiaolangdi Reservoir, which has led to longitudinal variability in cross‐sectional bankfull discharges. Therefore, it is more representative to describe the flood discharge capacity of the LYR, using the concept of reach‐averaged bankfull discharge. Previous simple mean methods to estimate reach‐scale bankfull discharge cannot meet the condition of flow continuity or account for the effect of different spacing between two sections. In this study, a general method to calculate cross‐sectional bankfull discharge using the simulated stage‐discharge relation is outlined briefly, and an integrated method is then proposed for estimating reach‐scale bankfull discharge. The proposed method integrates a geometric mean based on the log‐transformation with a weighted average based on the spacing between two consecutive sections, which avoids the shortcomings of previous methods. The post‐flood reach‐scale bankfull discharges in three different channel‐pattern reaches of the LYR were estimated annually during the period from 1999 to 2010 using the proposed method, based on surveyed post‐flood profiles at 91 sedimentation sections and the measured hydrological data at seven hydrometric sections. The calculated results indicate that: (i) the estimated reach‐scale bankfull discharges can effectively represent the flood discharge capacity of different reaches, with their ranges of variation being less than those of typical cross‐sectional bankfull discharges; and (ii) the magnitude of the reach‐scale bankfull discharge in each reach can respond well to the accumulative effect of incoming flow and sediment conditions. Finally, empirical relationships for different reaches in the LYR were developed between the reach‐scale bankfull discharge and the previous four‐year average discharge and incoming sediment coefficient during flood seasons, with relatively high correlation coefficients between them being obtained, and the reach‐scale bankfull discharges in different reaches predicted by the delayed response model were also presented for a comparison. These relations for the prediction of reach‐scale bankfull discharges were validated using the cross‐sectional profiles and hydrological data measured in 2011. Copyright © 2013 John Wiley & Sons, Ltd.     

Testing a conceptual hillslope recession model based on the storage–discharge relationship with the Richards equation

The conceptual recession model based on the storage–discharge relationship was proposed to account for the unsaturated–saturated water storage interaction. The recession model was formulated by combining the constitutive storage–discharge relationship with the integral balance equation for unsaturated and saturated water storage. The functional form of the constitutive storage–discharge relationship was determined from the spatial integration of the Richards equation. The performance of the recession model was tested by comparing with the solution of the Richards equation for different simulation geometric shapes and soil types. The conceptual recession model incorporating the unsaturated–saturated water storage interaction was in good agreement with the recession response of the Richards equation. However, the recession model that neglected the unsaturated–saturated water storage interaction was comparable to the Richards equation only for soils with the weak interaction between unsaturated water storage and saturated water storage. This result suggests the important role of the unsaturated–saturated water storage interaction in the formulation of the recession process when the derivative of the functional relationship between the unsaturated water storage and saturated water storage becomes significant. Copyright © 2007 John Wiley & Sons, Ltd.     

Multiple temporal scale relationships of bankfull discharge with streamflow and sediment transport in the Yellow River in China

This paper presents a study on the characteristics of multiple time scales of bankfull discharge and its delayed response to changes of flow conditions using continuous wavelet analysis for data from selected hydrological stations in the Yellow River basin. Results showed that bankfull discharge series had one or two dominant time scales. For example, the Huayuankou station in the lower reach of the Yellow River had two dominant time scales of 19-20 years and 545 years. The dominant time scales of the bankfull discharge series were generally consistent with the dominant time scales of water discharge and sediment concentration series, indicating that the channel morphology inherits the characteristics of the hydrological system in terms of multiple time scales. In addition, the wavelet coefficients of the bankfull discharge series had a phase difference in relation to those of the sediment concentration series, with a delay time that varied from 3 to 16 years at different sites. This delay time or relaxation time is a result of the delayed response of bankfull discharge to flow conditions, which was significant for channel adjustments in response to changes of flow conditions. The findings of the multiple time scales and the delayed response are of importance for further study of channel morphology of fluvial systems.     

Bed morphology and generation of step–pool channels

Flume experiments have been carried out to study the formation processes and the bed morphology of step–pool channels. From the experiments different step types and step configurations could be distinguished depending on the stream power. These step types can be seen as an image of the generation mechanisms of step–pool systems. These results suggest that the bed roughness geometry develops towards a condition that provides the maximum possible bed stability for a given grain size distribution. In contrast to a variety of other studies, antidunes did not contribute to the generation of the step structures. However, the data of the presented study fits well into the region of antidune formation proposed by Kennedy for sand‐bed rivers. This observation points out that step–pool field‐data located in the Kennedy region do not inevitably prove that antidunes played a role in step development. It is rather proposed that in Kennedy's region of antidune formation there exist hydraulic conditions where the flow resistance is maximized. It is suggested that such maximum flow resistance is associated with an optimal distance between the bedforms and their height, independently of whether these are antidunes in sand‐ and gravel‐bed rivers or step–pool units in boulder‐bed streams. The considerations of the Kennedy region of antidune formation and the analysis of planform step types depending on stream power both suggest that steep channels have a potential for self‐stabilization by modifying the step–pool structure towards a geometry that provides maximum flow resistance and maximum bed stability. Copyright © 2008 John Wiley & Sons, Ltd.     

特征差分法在水位推流上的应用

本文阐述了在符合明渠非恒定流一维定床条件的水文测站,应用变化的特征差分格式,将两断面实测水位过程线推算为流量过程线的原理、方法和应用实例,对理论推算的流量过程和实测流量过程进行了比较分析。从泗洪站和运河站的成果看出,推流和实测过程线基本吻合,精度较高。因此可以明显看出,应用本法推流,不但安全可靠,具有节约人力、物力等经济效益,还可提高测验精度、防止高洪期流量的错测、漏测,保证洪水资料的连续和完整。在湖泊水量平衡计算中,同样可以借助两组水尺获得的水位资料进行推流,无需设置专用流量站。