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.     

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.     

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.     

Variable power‐law scaling of hillslope Hortonian rainfall–runoff processes

Hydrological studies focused on Hortonian rainfall–run‐off scaling have found that the run‐off depth generally declines with the plot length in power‐law scaling. Both the power‐law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run‐off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell‐based rainfall‐infiltration‐run‐off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power‐law scaling at the initial stage of run‐off generation. Then, the magnitude of the power‐law scaling decreases gradually due to the decreasing run‐on effect. The power‐law scaling is most sensitive to the rainfall and soil infiltration parameters. When the ratio of rainfall to infiltration exceeds a critical value, the magnitude of the power‐law scaling tends to decrease notably. For different intermittent rainfall patterns, the power‐law exponent varies in the range of ?1.0 to ?0.113, which shows an approximately logarithmic increasing trend for the proportional coefficient as a function of the run‐off coefficient. The scaling is also sensitive to the surface roughness, soil sealing, slope angle, and hillslope geometry because these factors control the run‐off routing and run‐on infiltration processes. These results provide insights into the variable scaling of the Hortonian rainfall–run‐off process, which are expected to benefit modelling of large‐scale hydrological and ecological processes.     

The effects of discharge and slope on hyporheic flow in step‐pool morphologies

This paper focuses on surface–subsurface water exchange in a steep coarse‐bedded stream with a step‐pool morphology. We use both flume experiments and numerical modelling to investigate the influence of stream discharge, channel slope and sediment hydraulic conductivity on hyporheic exchange. The model step‐pool reach, whose topography is scaled from a natural river, consists of three step‐pool units with 0.1‐m step heights, discharges ranging between base and over‐bankfull flows (scaled values of 0.3–4.5 l/s) and slopes of 4% and 8%. Results indicate that the deepest hyporheic flow occurs with the steeper slope and at moderate discharges and that downwelling fluxes at the base of steps are highest at the largest stream discharges. In contrast to findings in a pool‐riffle morphology, those in this study show that steep slopes cause deeper surface–subsurface exchanges than gentle slopes. Numerical simulation results show that the portion of the hyporheic zone influenced by surface water temperature increases with sediment hydraulic conductivity. These experiments and numerical simulations emphasize the importance of topography, sediment permeability and roughness elements along the channel surface in governing the locations and magnitude of downwelling fluxes and hyporheic exchange. Our results show that hyporheic zones in these steep streams are thicker than previously expected by extending the results from streams with pool‐riffle bed forms. Copyright © 2014 John Wiley & Sons, Ltd.     

Freshwater flow to the San Francisco Bay‐Delta estuary over nine decades (Part 1): Trend evaluation

The San Francisco Bay‐Delta estuary and its upstream watershed have been highly modified since exploration and settlement by Europeans in the mid‐18th century. Although these hydrologic alterations supported the growth of California's economy to the eighth largest in the world, they have been accompanied by significant declines in native aquatic species and subsequent efforts to reverse these declines through flow management. To inform ongoing deliberations on management of freshwater flows to the estuary, we examined a recent nine‐decade hydrologic record to evaluate seasonal and annual trends in reported Delta outflow. Statistically significant trends were observed in seasonal outflows, with decreasing trends observed in 4 months (February, April, May, and November) and increasing trends observed in 2 months (July and August). Trend significance in early‐to‐mid autumn (September and October) is ambiguous due to uncertainty associated with in‐Delta agricultural water use. In spite of increasing water use over the period examined, we found no statistically significant annual trend in Delta outflow, a result likely due to large inter‐annual variability. Linkages between outflow trends and changes in upstream flows and coincident developments such as reservoir construction and operation, out‐of‐basin imports and exports, and expansion of irrigated agriculture are discussed. To eliminate inter‐annual variability as a factor, change attribution is explored using modelled flows and fixed climatology in a companion paper.     

Morphology and sedimentology of a complex debris flow in a clay‐shale basin

Coupling morphological, sedimentological, and rheological studies to numerical simulations is of primary interest in defining debris‐flow hazard on alluvial fans. In particular, numerical runout models must be carefully calibrated by morphological observations. This is particularly true in clay‐shale basins where hillslopes can provide a large quantity of poorly sorted solid materials to the torrent, and thus change both the mechanics of the debris flow and its runout distance. In this context, a study has been completed on the Faucon stream (southeastern French Alps), with the objectives of (1) defining morphological and sedimentological characteristics of torrential watersheds located in clay‐shales, and (2) evaluating through a case study the scouring potential of debris flows affecting a clay‐shale basin. Morphological surveys, grain‐size distributions and petrographic analyses of the debris‐flow deposits demonstrate the granular character of the flow during the first hectometre, and its muddy character from there to its terminus on the debris fan. These observations and laboratory tests suggest that the contributing areas along the channel have supplied the bulk of the flow material. Copyright © 2005 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.     

Stability of the time‐domain analysis method including a frequency‐dependent soil–foundation system

A number of methods have been proposed that utilize the time‐domain transformations of frequency‐dependent dynamic impedance functions to perform a time‐history analysis. Though these methods have been available in literature for a number of years, the methods exhibit stability issues depending on how the model parameters are calibrated. In this study, a novel method is proposed with which the stability of a numerical integration scheme combined with time‐domain representation of a frequency‐dependent dynamic impedance function can be evaluated. The method is verified with three independent recursive parameter models. The proposed method is expected to be a useful tool in evaluating the potential stability issue of a time‐domain analysis before running a full‐fledged nonlinear time‐domain analysis of a soil–structure system in which the dynamic impedance of a soil–foundation system is represented with a recursive parameter model. Copyright © 2015 John Wiley & Sons, Ltd.     

Curve‐Number/Green–Ampt mixed procedure for streamflow predictions in ungauged basins: Parameter sensitivity analysis

A procedure combining the Soil Conservation Service‐Curve Number (SCS‐CN) method and the Green–Ampt (GA) infiltration equation was recently developed to overcome some of the drawbacks of the classic SCS‐CN approach when estimating the volume of surface runoff at a sub‐daily time resolution. The rationale of this mixed procedure, named Curve Number for Green–Ampt (CN4GA), is to use the GA infiltration model to distribute the total volume of the net hyetograph (rainfall excess) provided by the SCS‐CN method over time. The initial abstraction and the total volume of rainfall given by the SCS‐CN method are used to identify the ponding time and to quantify the hydraulic conductivity parameter of the GA equation. In this paper, a sensitivity analysis of the mixed CN4GA parameters is presented with the aim to identify conditions where the mixed procedure can be effectively used within the Prediction in Ungauged Basin perspective. The effects exerted by changes in selected input parameters on the outputs are evaluated using rectangular and triangular synthetic hyetographs as well as 100 maximum annual storms selected from synthetic rainfall time series. When applied to extreme precipitation events, which are characterized by predominant peaks of rainfall, the CN4GA appears to be rather insensitive to the input hydraulic parameters of the soil, which is an interesting feature of the CN4GA approach and makes it an ideal candidate for the rainfall excess estimation at sub‐daily temporal resolution at ungauged sites. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling three‐dimensional non‐linear seismic performance of elevated bridges with emphasis on pounding of girders

Unseating of bridge girders/decks during earthquakes is very harmful to the safety and serviceability of bridges. Evidence from recent severe earthquakes indicates that in addition to damage along longitudinal direction, lateral displacement and rotation of bridge girders caused by pounding to adjacent girders can also lead to unseating. To simulate this effect, 3D modelling of the dynamic performance of whole bridge structures, including pounding, is needed strongly. This paper presents a 3D model that is practically suitable to precisely analyse pounding between bridge girders. Experiments have been conducted to verify the proposed pounding model. The 3D non‐linear modelling of steel elevated bridges is also discussed. A general‐purpose dynamic analysis program for bridges, namely dynamic analysis of bridge systems (DABS) has been developed. Seismic analyses on a chosen three‐span steel bridge are conducted for several cases including pounding as a case study. The applicability of the proposed pounding model is illustrated by the computations. The effects of poundings on the response of bridge girders are discussed and the computation results are given. Copyright © 2002 John Wiley & Sons, Ltd.     

Regional estimation of catchment‐scale soil properties by means of streamflow recession analysis for use in distributed hydrological models

The estimation of catchment‐scale soil properties, such as water storage capacity and hydraulic conductivity, is of primary interest for the implementation of distributed hydrological models at the regional scale. This estimation is generally performed on the basis of information provided by soil databases. However, such databases are often established for agronomic uses and generally do not document deep‐weathered rock horizons (i.e. pedologic horizons of type C and deeper), which can play a major role in water transfer and storages. Here, we define the Drainable Storage Capacity Index (DSCI), an indicator that relies on the comparison between cumulated streamflow and precipitation to assess catchment‐scale storage capacities. DSCI is found to be reliable to detect underestimation of soil storage capacities in soil databases. We also use the streamflow recession analysis methodology defined by Brutsaert and Nieber in 1977 to estimate water storage capacities and lateral saturated hydraulic conductivities of the nondocumented deep horizons. The analysis is applied to a sample of 23 catchments (0.2–291 km²) located in the Cévennes‐Vivarais region (south of France). For regionalization purposes, the obtained results are compared with the dominant catchment geology and present a clear hierarchy between the different geologies of the area. Hard crystalline rocks are found to be associated with the thickest and less conductive deep soil horizons. Schist rocks present intermediate values of thickness and of saturated hydraulic conductivity, whereas sedimentary rocks and alluvium are found to be less thick and most conductive. These results are of primary interest in view of the future set‐up of distributed hydrological models over the Cévennes‐Vivarais region. Copyright © 2013 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.     

Comparison of P‐wave attenuation models of wave‐induced flow

Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with White's and Johnson's models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.     

Free‐vibration analysis of a three‐dimensional soil–structure system

A procedure which involves a non‐linear eigenvalue problem and is based on the substructure method is proposed for the free‐vibration analysis of a soil–structure system. In this procedure, the structure is modelled by the standard finite element method, while the unbounded soil is modelled by the scaled boundary finite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam–foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also verified by the Fourier transform of the impulsive response calculated in the time domain by the three‐dimensional soil–structure–wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are significantly different due to the different definition of damping ratio. This study shows that although the classical mode‐superposition method is not applicable to a soil–structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil–structure system. Copyright © 2001 John Wiley & Sons, Ltd.     

Composition and origin of a lithalsa related to lake‐level recession and Holocene terrestrial emergence,Northwest Territories,Canada

Lithalsas of the Great Slave Lowland, Northwest Territories, occur within fine‐grained glaciolacustrine, lacustrine, and alluvial deposits. Detailed investigations of a lithalsa revealed that it is composed of ice‐rich sediments with ice lenses up to 0.2 m thick below 4 m depth. The observed ice accounted for about 2 m of the 4 m between the top of the lithalsa and adjacent terrain. The ice is isotopically similar to modern surface water, but enriched in δ¹⁸O relative to local precipitation. Total soluble cation concentrations are low in the basal, Shield‐derived and unweathered glaciolacustrine sediments of the lithalsa. Higher concentrations in the overlying Holocene‐aged lacustrine and alluvial deposits may be due to greater ion availability in Holocene surface waters. Increasing Cl^‐ and Na⁺ concentrations in clays at depth likely relate to exclusion and migration of these dissolved ions in pore water during ice lens formation though total soluble cations remain comparatively low. The lithalsa developed 700 to 300 cal yr BP. A conceptual model of lithalsa formation and landscape evolution illustrates that this feature and more than 1800 other lithalsas in the region have developed in association with Holocene terrestrial emergence following lake‐level recession. Copyright © 2017 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure

A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.     

A regional model of low flow for southern Taiwan

The primary purpose of this study is to develop regional models of the lower part of flow duration curves (LPFDCs) to synthesize low‐flow characteristics at ungauged sites in southern Taiwan. Because of the close relationship between low streamflow regimes and hydrogeological features, the model development first involved delimiting homogeneous hydrogeological regions by using two‐step cluster analysis. Each homogeneous region was then discriminated by an equation developed on the basis of its hydrogeological features, which was then used to determine which of three sets of regional LPFDC models would be appropriate for a particular ungauged site. Each of the three sets of regional LPFDC models were developed using both conventional multivariate statistical regression and fuzzy regression. Thirty‐four stream‐gauged watersheds located in southern Taiwan provide the data set. The study results reveal that the regional LPFDC models developed in this study could be applied reasonably at ungauged sites. Copyright © 2002 John Wiley & Sons, Ltd.