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.     

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.     

How well can the subsurface storage–discharge relation be interpreted and predicted using the geometric factors in headwater areas?

Headwater storage–discharge (S–Q) remains one of the least understood processes, and there is renewed interest in the S–Q relation. How well can the S–Q relation be interpreted mechanistically using geometric factors? In this paper, the hillslope storage Boussinesq and hillslope storage kinematic wave equation were adopted to guide the theoretical derivations. Analytical solutions were derived based on the hsKW equation for nine idealized hillslope aquifers, which were subdivided into two groups, i.e. hillslope aquifers with exponential hillslope width function (C1) and hillslope aquifers with Gaussian hillslope width function (C2). We found that analytical expressions of the S–Q relation can be derived for C1 hillslope aquifers. For more compound hillslope aquifers, i.e. C2, no explicit S–Q relation can be obtained. The whole subsurface recession after a rainstorm is simulated by applying the initial saturation condition. We found that the simulated S–Q processes can be characterized by a two‐phase recession, i.e. quick and slow recession. The time (t_b) at the dividing point of the quick and slow recessions depends on the geometric factors, such as the plan and profile curvature. In the quick recession for C1, many of the S–Q curves can be described as linear or quasi‐linear functions, which indicate that linear reservoir models can be applied approximately for recession simulations. However, during the slow recession phase of C1 and during the whole recession of C2, the S–Q relations are highly non‐linear. Finally, we compared the hillslope storage kinematic wave and hillslope storage Boussinesq models for simulating subsurface water recession after a rainstorm event in a real‐world headwater catchment (G5) in China. Through comparison of the recession slope curves, we found that the simulated results of the models employing the Gaussian hillslope width function match the observed hydrograph. The results indicated that appropriate organization of the hillslope geometric factors enhances our ability to make S–Q predictions. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Models for recession flows in the upper Blue Nile River

Stream‐flow recessions are commonly characterized by the exponential equation or in the alternative power form equation of a single linear reservoir. The most common measure of recession is the recession constant K, which relates to the power function form of the recession equation for a linear reservoir. However, in reality it can be seen that the groundwater dynamics of even the simplest of aquifers may behave in a non‐linear fashion. In this study three different storage–outflow algorithms; single linear, non‐linear and multiple linear reservoir were considered to model the stream‐flow recession of the upper Blue Nile. The recession parameters for the linear and non‐linear models were derived by the use of least‐squares regression procedures. Whereas, for the multiple linear reservoir model, a second‐order autoregressive AR (2) model was applied first in order to determine the parameters by the least‐squares method. The modelling of the upper Blue Nile recession flow performed shortly after the wet season, when interflow and bank storage may be contributing considerably to the river flow, showed that the non‐linear reservoir model simulates well with the observed counterparts. The variation related to preceding flow on a recession parameter of the non‐linear reservoir remains significant, which was obtained by stratification of the recession curves. Although a similar stratification did not show any systematic variation on the recession parameters for the linear and multiple linear reservoir models. Copyright © 2004 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.     

Regional variation of recession flow power‐law exponent

Recession flows of a basin provide valuable information about its storage–discharge relationship as during recession periods discharge occurs due to depletion of storage. Storage–discharge analysis is generally performed by plotting ?dQ/dt against Q , where Q is discharge at time t . For most real world catchments, ?dQ/dt versus Q show a power‐law relationship of the type: ?dQ/dt = kQ^α . Because the coefficient k varies across recession events significantly, the exponent α needs to be computed separately for individual recession events. The median α can then be considered as the representative α for the basin. The question that arises here is what are the basin characteristics that influence the value of α ? Studies based on a small number of basins (up to 50 basins) reveal that α has good relationship with several basin characteristics. However, whether such a relationship is universal remains an important question, because a universal relationship would allow prediction of the value of α for any ungauged basin. To test this hypothesis, here, we study data collected from a relatively large number of basins (358 basins) in USA and examine the influence of 35 different physio‐climatic characteristics on α . We divide the basins into 2 groups based on their longitudes and test the relationship between α and basin characteristics separately for the two groups. The results indicate that α is not identically influenced by different basin characteristics for the two datasets. This may suggest that the power‐law exponent α of a region is determined by the way local physio‐climatic forces have shaped the landscape.     

A numerical study on response factors for steel wall–frame systems

A numerical investigation was undertaken to evaluate the response of dual structural systems that consisting of steel plate shear walls and moment‐resisting frames. The primary objective of the study was to investigate the influence of elastic base shear distribution between the wall and the frame on the global system response. A total of 10 walls and 30 wall–frame systems, ranging from 3 to 15 stories, were selected for numerical assessment. These systems represent cases in which the elastic base shear resisted by the frame has a share of 10, 25, or 50% of the total base shear resisted by the dual system. The numerical study consisted of 1600 time history analyses employing three‐dimensional finite elements. All 40 structures were separately analyzed for elastic and inelastic response by subjecting them to the selected suite of earthquake records. Interstory drifts, top story drift, base shears resisted by the wall, and the frame were collected during each analysis. Based on the analysis results, important response quantities, such as the strength reduction, the overstrength, and the displacement amplification factors, are evaluated herein. Results are presented in terms of displacement measures, such as the interstory drift ratio and the top story drift ratio. Analysis results revealed that the increase in the strength reduction factor with the amount of load share is insignificant. Furthermore, there is an inverse relationship between the ductility reduction and the overtsrength. Copyright © 2010 John Wiley & Sons, Ltd.     

Modelling stage–discharge relationships in anastomosed bedrock-influenced sections of the Sabie River system

Flow dynamics in a bedrock-influenced river system, the Sabie River, South Africa, have been found to be significantly different from those in temperate alluvial systems. The lack of lateral water connectivity leads to multiple bedrock distributaries with varying water surface elevations across a cross-section. Distributary activation is dependent on upstream breaching of bedrock barriers between distributaries by rising discharge. Where measurement of individual stage–discharge relationships in each distributary was not possible, a ‘Multiple Stage’ model was developed to predict hydraulic conditions in each distributary, using a single measured rating curve and knowledge of individual distributary water surface elevations at a low flow. Use of the ‘Multiple Stage’ model has enabled realistic prediction of channel geometry and hydraulic variables, that accounts for the different stages found in bedrock-influenced sections, yet is not prohibitively data intensive. Predicted ‘Multiple Stage’ results for maximum depth and velocity demonstrate the vast improvement on modelling flow dynamics, when compared to the conventional assumption of a single stage representing the whole cross-section. © 1998 John Wiley & Sons, Ltd.     

Direct finite element method for nonlinear earthquake analysis of 3‐dimensional semi‐unbounded dam–water–foundation rock systems

A direct finite element method for nonlinear earthquake analysis of 2‐dimensional dam–water–foundation rock systems has recently been presented. The analysis procedure uses standard viscous‐damper absorbing boundaries to model the semi‐unbounded foundation‐rock and fluid domains and specifies the seismic input as effective earthquake forces at these boundaries. Presented in this paper is a generalization of the direct finite element method with viscous‐damper boundaries to 3‐dimensional dam–water–foundation rock systems. Step‐by‐step procedures for determining the effective earthquake forces starting from a ground motion specified at a control point on the foundation‐rock surface is developed, and several numerical examples are computed and compared with independent benchmark solutions to demonstrate the effectiveness of the analysis procedure for modeling 3‐dimensional systems.     

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.     

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.     

Analysis of RC slab–beam–column sub‐assemblages subjected to bidirectional lateral cyclic loading using a new 3D macroelement

An existing two‐dimensional macroelement for reinforced concrete beam–column joints is extended to a three‐dimensional macroelement. The three‐dimensional macroelement for beam–column joints consists of six rigid interface plates and uniaxial springs for concrete, steel, and bond–slip, which model the inside of a beam–column joint. The mechanical models for the materials and the stiffness equation for the springs are also presented. To validate the model, we used test results from three slab–beam–column sub‐assemblages subjected to bi‐lateral cyclic load. It is revealed that the new joint model is capable of capturing the strength of beam–column joints and the bidirectional interaction in joint shear response, including the concentration of damage in the beam–column joint, the pinching nature in hysteretic behavior, the stiffness degradation, and strength deterioration resulting from cyclic and bidirectional loading. Copyright © 2017 John Wiley & Sons, Ltd.     

HydRun: A MATLAB toolbox for rainfall–runoff analysis

Understanding the nature of streamflow response to precipitation inputs is at the core of hydrological applications and water resource management. Indices such as the base flow index, recession constant, and response lag of a watershed retain an important place in hydrology as metrics to compare watersheds and understand the impact of human activity, geology, geomorphology, soils, and climate on precipitation–runoff relations. Extracting characteristics of the hyetograph–hydrograph relationship is often done manually, which is time consuming and may result in subjective and potentially inconsistent outcomes. Here, we present a MATLAB‐based toolbox, called HydRun, for rapid and flexible rainfall–runoff analysis. HydRun uses a series of flexible routines to extract base flow from the hydrograph and then computes commonly used time instants of the rainfall–runoff relationship. HydRun provides users the flexibility to decide thresholds and limits of analysis, but objectively computes hydrometric indices. The toolkit includes a graphical user interface and example files. In this paper, we apply HydRun to 4 watersheds, 3 in Scotland and 1 in Canada, to demonstrate the software functions and highlight important decisions the user must make in its application.     

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.     

Nonstationary seismic responses of structure with nonlinear stiffness subject to modulated Kanai–Tajimi excitation

A simple structure under earthquake excitation is modeled as a single‐degree‐of‐freedom system with nonlinear stiffness subject to modulated Kanai–Tajimi excitation. The nonstationary responses including the nonstationary probability densities of the system responses and the statistical moments are obtained in semi‐analytical form. By applying the stochastic averaging method based on the generalized harmonic functions, the averaged Fokker–Planck–Kolmogorov(FPK) equation governing the nonstationary probability density of the amplitude is derived. Then, the solution of the FPK equation is approximately expressed by a series expansion in terms of a set of properly selected basis functions with time‐dependent coefficients. According to the Galerkin method, the time‐dependent coefficients are solved from a set of linear first‐order differential equations. Thus, the nonstationary probability densities of the amplitude and the state responses as well as the statistic moments of the amplitude are obtained. Finally, two types of the modulating functions, i.e. constant function and exponential function, are considered to give some semi‐analytical formulae. The proposed procedures are checked against the Monte Carlo simulation. The effects of the structure natural frequency and the intensity of the excitation as well as the ground stiffness on the system responses are discussed. It should be pointed out that the proposed method is good for broadband excitation and light damping. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

Complex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 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.     

Estimating parameters of the channel width–flow discharge relation using rill and gully channel junction data

Eroding channels can usually be characterized by a power relationship between channel width (W) and channel discharge (Q). This paper examines the WQ relation using a recently developed channel junction approach to extend the validity of the WQ relation and to develop a procedure for estimating the WQ exponent and proportionality coefficient. Rill and gully channel data from the literature, and new data collected in different badland areas and in a few forest mountain streams, are analysed. Analysis shows that the WQ relation for channel width collected in badlands and forests agrees with trends observed for cropland. The exponent increases with increasing channel width in a continuous fashion rather than in a step‐like way and tends to a maximum whose value ranges between 0·5 and 0·6. The proportionality coefficient can be split into two terms, one expressing the case in which an eroding channel can broaden, the other reflecting the difficulties in removing the less erodible clods or rock fragments from the channel bed. Its splitting allows the development of a more correct form of the WQ relation in agreement with modern approaches of channel geometry: one part has the dimension of a discharge and makes the power base dimensionless, while the other brings the dimension of a length, needed for the channel width, into the WQ relation. The interpretation of the two constants is supported by data collected in rainfall‐runoff simulation experiments conducted in the field. Values characterizing the two constants in some environments are also given. Nevertheless the approach is not sufficiently parameterized yet to be of practical use (e.g. in models or for estimating peak discharge in areas where rill channels have formed). Copyright © 2009 John Wiley & Sons, Ltd.