Hysteresis‐based analysis of overland metal transport

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.     

On the Seddon speed formula

Abstract

The Seddon speed formula expressed mathematically as c = dQ/dA (or alternatively, as c = (1 + m)u_o; where Q is the discharge, A is the area of cross-section, c is the wave speed, u_o is the normal flow velocity, and m is a dimensionless parameter) is revisited in the context of elasticity and thermodynamics. Its link with the linearized solution of St Venant's equations for wave celerity, which does not appear to have been reported in the hydrological literature, is established. The rating exponent m is shown to be equivalent to the dimensionless relative celerity and is found to be the ratio of two specific heats, viz. c_p and c_v which are the specific heats at constant pressure and volume, respectively. The use of the parameter m as a complex variable helps describe shallow wave characteristics, the damping capacity of a wave, and the mechanism of occurrence of the hysteretic phenomenon. The damping capacity is found to describe the magnitude of wave subsidence, whereas the hysteresis also describes the speed of subsidence.     

Relative velocities of discharge and sediment waves for the River Severn,UK

Abstract

It is generally accepted that the celerity of a discharge wave exceeds that of a floodwave. The discharge wave is the initial wavefront (shown by an increase in stage at a particular site), whereas the floodwave refers to the body of water moving downstream. Yet, few studies have investigated the varying relationship between discharge and suspended sediment concentration as floods propagate downstream. This paper examines the relative velocities of the discharge and sediment waves for natural flood events on the River Severn, UK. Four monitoring stations were established within the upper 35 km reach of the River Severn (drainage basin area 380 km2). Discharge was monitored using fixed structures, and suspended sediment concentrations were monitored at similar locations using Partech IR40C turbidity meters. Results showed discharge wave celerity increased with flood magnitude, but relationships were more complex for sediment wave celerity. Sediment wave celerity was greater than discharge wave celerity, and is attributed to the dominant source of sediment, which is most probably bank erosion.     

A three‐component end‐member analysis of streamwater hydrochemistry in a small Japanese forested headwater catchment

Intensive water sampling in conjunction with hydrological observations was conducted during three different rainstorms in order to understand the effects of rainfall events on the temporal variation of streamwater chemistry in a small headwater forest catchment. Concentrations of Na⁺ and SO₄^2? decreased as the discharge rate increased. Hydrograph separation of the components was made using the three‐component model based on the end‐members mixing analysis (EMMA). The three end‐members were:

• 1 the groundwater in the saturated zone that prescribes the chemistry of the baseflow;
• 2 the throughfall that dilutes the streamwater;
• 3 the groundwater in the transient saturated zone prescribed, which was dependent on the groundwater level.

When the groundwater level was lower, only the two components, groundwater in the saturated zone and throughfall, affected the streamwater chemistry. When the groundwater level rose and the saturated zone spread, the groundwater in the transient saturated zone became the third component. When the groundwater in the transient saturated zone contributed to the discharge, this component became the dominant source and the streamwater chemistry was affected by the groundwater chemistry in the transient saturated zone. When this component was discharged as the saturation overland flow, the streamwater chemistry was greatly affected by this component. Copyright © 2001 John Wiley & Sons, Ltd.     

Time‐varying suspended sediment‐discharge rating curves to estimate climate impacts on fluvial sediment transport

This study presents time‐varying suspended sediment‐discharge rating curves to model suspended‐sediment concentrations (SSCs) under alternative climate scenarios. The proposed models account for hysteresis at multiple time scales, with particular attention given to systematic shifts in sediment transport following large floods (long‐term hysteresis). A series of nested formulations are tested to evaluate the elements embedded in the proposed models in a case study watershed that supplies drinking water to New York City. To maximize available data for model development, a dynamic regression model is used to estimate SSC based on denser records of turbidity, where the parameters of this regression are allowed to vary over time to account for potential changes in the turbidity‐SSC relationship. After validating the proposed rating curves, we compare simulations of SSC among a subset of models in a climate change impact assessment using an ensemble of flow simulations generated using a stochastic weather generator and hydrologic model. We also examine SSC estimates under synthetic floods generated using a peaks‐over‐threshold model. Our results indicate that estimates of extreme SSC under new climate and hydrologic scenarios can vary widely depending on the selected model and may be significantly underestimated if long‐term hysteresis is ignored when simulating impacts under sequences of large storm event. Based on the climate change scenarios explored here, average annual maximum SSC could increase by as much as 2.45 times over historical values.     

Long‐term variations and temporal scaling of hydroclimatic time series with focus on the German part of the Elbe River Basin

Long‐term variations and temporal scaling of mean monthly time series of river flow, precipitation, temperature, relative humidity, air pressure, duration of bright sunshine, degree of cloud cover, short wave radiation, wind speed and potential evaporation within or in vicinity of the German part of the Elbe River Basin are analyzed. Statistically significant correlations between the 2–15 year scale‐averaged wavelet spectra of the hydroclimatic variables and the North Atlantic Oscillation‐ and Arctic Oscillation index are found which suggests that such long‐term patterns in hydroclimatic time series are externally forced. The Hurst parameter estimates (H) based on the Detrended Fluctuation Analysis (DFA) indicate persistence for discharge, precipitation, wind speed, air pressure and the degree of cloud cover, all having an annual cycle and a broad low‐frequency distribution. Also, DFA H parameter estimates are higher for discharge than for precipitation. The major long‐term quasi‐periodic variability modes of precipitation detected using Singular Spectrum Analysis coincide with those detected in the discharge time series. Upon subtraction of these low‐frequency quasi‐periodic modes, the DFA H parameter estimates suggest absence of the persistence for both precipitation and discharge. Copyright © 2013 John Wiley & Sons, Ltd.     

Interaction of multiple courses of wave‐induced fluid flow in layered porous media

Different theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.     

Predicting suspended sediment concentrations in the Meuse river using a supply‐based rating curve

A rating curve provides a reasonable estimate of the suspended sediment concentration at a given discharge. However, analysis of a detailed 9‐year time‐series of suspended sediment concentration (SSC) and discharge Q of the Meuse River in The Netherlands indicates that SSC is (besides discharge) controlled by exhaustion and replenishment of different sediment sources. Clockwise hysteresis and other effects of sediment exhaustion can be observed during and after flood events, and the effects of stockpiling of sediment in the river bed during low‐discharge periods are obvious in the SSC of the next flood. In a single regression equation we have implemented a parameter that represents the presence or absence of stock for sediment uptake. In comparison with a rating curve of SSC and Q, adding this parameter is shown to be a more reliable and comprehensive method to predict SSCs at all discharge regimes with all preceding discharge conditions, for single‐peaked and multi‐peaked runoff events as well as for low flow conditions. The method is probably applicable to other small‐ to medium‐scaled river basins. Copyright © 2007 John Wiley & Sons, Ltd.     

Bedload hysteresis in a glacier‐fed mountain river

Sediment transport during flood events often reveals hysteretic patterns because flow discharge can peak before (counterclockwise hysteresis) or after (clockwise hysteresis) the peak of bedload. Hysteresis in sediment transport has been used in the literature to infer the degree of sediment availability. Counterclockwise and clockwise hysteresis have been in fact interpreted as limited and unlimited sediment supply conditions, respectively. Hysteresis has been mainly explored for the case of suspended sediment transport, but it was rarely reported for bedload transport in mountain streams. This work focuses on the temporal variability of bedload transport in an alpine catchment (Saldur basin, 18.6 km², Italian Alps) where bedload transport was monitored by means of an acoustic pipe sensor which detects the acoustic vibrations induced by particles hitting a 0.5m‐long steel pipe. Runoff dynamics are dominated by snowmelt in late spring/early summer, mostly by glacier melt in late summer/early autumn, and by a combination of the snow and glacier melt in mid‐summer. The results indicate that hysteretic patterns during daily discharge fluctuations are predominantly clockwise during the snowmelt period, likely due to the ready availability of unpacked sediments within the channel or through bank erosion in the lower part of the basin. On the contrary, counterclockwise hysteresis tend to be more frequent during late glacier melting period, possibly due to the time lag needed for sediment provided by the glacial and peri‐glacial area to be transported to the monitoring section. However, intense rainfall events occurring during the glacier melt period generated predominantly clockwise hysteresis, thus indicating the activation of different sediment sources. These results indicate that runoff generation processes play a crucial role on sediment supply and temporal availability in mountain streams. Copyright © 2014 John Wiley & Sons, Ltd.     

Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media

In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf.     

A multi‐azimuth seismic refraction study for a horizontal transverse isotropic medium: physical modelling results

To investigate the characteristics of the anisotropic stratum, a multi‐azimuth seismic refraction technique is proposed in this study since the travel time anomaly of the refraction wave induced by this anisotropic stratum will be large for a far offset receiver. To simplify the problem, a two‐layer (isotropy–horizontal transverse isotropy) model is considered. A new travel time equation of the refracted P‐wave propagation in this two‐layer model is derived, which is the function of the phase and group velocities of the horizontal transverse isotropic stratum. In addition, the measured refraction wave velocity in the physical model experiment is the group velocity. The isotropic intercept time equation of a refraction wave can be directly used to estimate the thickness of the top (isotropic) layer of the two‐layer model because the contrast between the phase and group velocities of the horizontal transverse isotropic medium is seldom greater than 10% in the Earth. If the contrast between the phase and group velocities of an anisotropic medium is small, the approximated travel time equation of a refraction wave is obtained. This equation is only dependent on the group velocity of the horizontal transverse isotropic stratum. The elastic constants A₁₁, A₁₃, and A₃₃ and the Thomsen anisotropic parameter ε of the horizontal transverse isotropic stratum can be estimated using this multi‐azimuth seismic refraction technique. Furthermore, under a condition of weak anisotropy, the Thomsen anisotropic parameter δ of the horizontal transverse isotropic stratum can be estimated by this technique as well.     

Modelling the effects of land‐use change on water and salt delivery from a catchment affected by dryland salinity in south‐east Australia

A comprehensive framework for the assessment of water and salt balance for large catchments affected by dryland salinity is applied to the Boorowa River catchment (1550 km²), located in south‐eastern Australia. The framework comprised two models, each focusing on a different aspect and operating on a different scale. A quasi‐physical semi‐distributed model CATSALT was used to estimate runoff and salt fluxes from different source areas within the catchment. The effects of land use, climate, topography, soils and geology are included. A groundwater model FLOWTUBE was used to estimate the long‐term effects of land‐use change on groundwater discharge. Unlike conventional salinity studies that focus on groundwater alone, this study makes use of a new approach to explore surface and groundwater interactions with salt stores and the stream. Land‐use change scenarios based on increased perennial pasture and tree‐cover content of the vegetation, aimed at high leakage and saline discharge areas, are investigated. Likely downstream impacts of the reduction in flow and salt export are estimated. The water balance model was able to simulate both the daily observed stream flow and salt load at the catchment outlet for high and low flow conditions satisfactorily. Mean leakage rate of about 23·2 mm year^?1 under current land use for the Boorowa catchment was estimated. The corresponding mean runoff and salt export from the catchment were 89 382 ML year^?1 and 38 938 t year^?1, respectively. Investigation of various land‐use change scenarios indicates that changing annual pastures and cropping areas to perennial pastures is not likely to result in substantial improvement of water quality in the Boorowa River. A land‐use change of about 20% tree‐cover, specifically targeting high recharge and the saline discharge areas, would be needed to decrease stream salinity by 150 µS cm^?1 from its current level. Stream salinity reductions of about 20 µS cm^?1 in the main Lachlan River downstream of the confluence of the Boorowa River is predicted. The FLOWTUBE modelling within the Boorowa River catchment indicated that discharge areas under increased recharge conditions could re‐equilibrate in around 20 years for the catchment, and around 15 years for individual hillslopes. Copyright © 2004 John Wiley & Sons, Ltd.     

A layered micropolar half space

Summary Wave propagation in a semi-infinite micropolar isotropic elastic solid lying over another micropolar isotropic elastic solid is considered using the theory of micropolar elasticity initiated byEringen [3]²). The relation between the group velocity and the speed of propagation is obtained for the new type of surface wave.     

Estimating suspended sediment concentrations in areas with limited hydrological data using a mixed‐effects model

Sediment rating curves are commonly used to estimate the suspended sediment load in rivers and streams under the assumption of a constant relation between discharge (Q) and suspended sediment concentrations (SSC) over time. However, temporal variation in the sediment supply of a watershed results in shifts in this relation by increasing variability and by introducing nonlinearities in the form of hysteresis or a path‐dependent relation. In this study, we used a mixed‐effects linear model to estimate an average SSC–Q relation for different periods of time within the hydrologic cycle while accounting for seasonality and hysteresis. We tested the performance of the mixed‐effects model against the standard rating curve, represented by a generalized least squares regression, by comparing observed and predicted sediment loads for a test case on the Chilliwack River, British Columbia, Canada. In our analyses, the mixed‐effects model reflected more accurate patterns of interpolated SSC from Q data than the rating curve, especially for the low‐flow summer months when the SSC–Q relation is less clear. Akaike information criterion scores were lower for the mixed‐effects model than for the standard model, and the mixed‐effects model explained nearly twice as much variance as the standard model (52% vs 27%). The improved performance was achieved by accounting for variability in the SSC–Q relation within each month and across years for the same month using fixed and random effects, respectively, a characteristic disregarded in the sediment rating curve. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.     

An alternative Boussinesq equation considering the effect of hysteresis on coastal groundwater waves

This paper presents an alternative Boussinesq equation considering hysteresis effect via a third‐order derivative term. By introducing an improved moisture–pressure retention function, this equation describes, with reasonable precision, groundwater propagation in coastal aquifers subject to Dirichlet boundary condition of different oscillation frequencies. Test results confirmed that it is necessary to consider horizontal and vertical flows in unsaturated zone, because of their variable influences on hysteresis. Hysteresis in unsaturated zone can affect the water table wave number of groundwater wave motion, such as wave damping rate and phase lag. Oscillations with different periods exert different hysteresis effect on wave propagation. Truncation/shrinkage of unsaturated zones also affects the strength of hysteresis. These impacts can be reflected in the alternative Boussinesq equation by adjusting the parameter representing the variation rate of moisture associated with pressure change, as opposed to traditional computationally expensive hysteresis algorithms. The present Boussinesq equation is simple to use and can provide feasible basis for future coupling of groundwater and surface water models. Copyright © 2016 John Wiley & Sons, Ltd.     

Concentration–discharge relationships in the coal mined region of the New River basin and Indian Fork sub‐basin,Tennessee, USA

For many basins, identifying changes to water quality over time and understanding current hydrologic processes are hindered by fragmented and discontinuous water‐quality and hydrology data. In the coal mined region of the New River basin and Indian Fork sub‐basin, muted and pronounced changes, respectively, to concentration–discharge (C–Q) relationships were identified using linear regression on log‐transformed historical (1970s–1980s) and recent (2000s) water‐quality and streamflow data. Changes to C–Q relationships were related to coal mining histories and shifts in land use. Hysteresis plots of individual storms from 2007 (New River) and the fall of 2009 (Indian Fork) were used to understand current hydrologic processes in the basins. In the New River, storm magnitude was found to be closely related to the reversal of loop rotation in hysteresis plots; a peak‐flow threshold of 25 cubic meters per second (m³/s) segregates hysteresis patterns into clockwise and counterclockwise rotational groups. Small storms with peak flow less than 25 m³/s often resulted in dilution of constituent concentrations in headwater tributaries like Indian Fork and concentration of constituents downstream in the mainstem of the New River. Conceptual two or three component mixing models for the basins were used to infer the influence of water derived from spoil material on water quality. Copyright © 2012 John Wiley & Sons, Ltd.     

Pore fluid viscosity effects on P‐ and S‐wave anisotropy in synthetic silica‐cemented sandstone with aligned fractures

Ultrasonic (500 kHz) P‐ and S‐wave velocity and attenuation anisotropy were measured in the laboratory on synthetic, octagonal‐shaped, silica‐cemented sandstone samples with aligned penny‐shaped voids as a function of pore fluid viscosity. One control (blank) sample was manufactured without fractures, another sample with a known fracture density (measured from X‐ray CT images). Velocity and attenuation were measured in four directions relative to the bedding fabric (introduced during packing of successive layers of sand grains during sample construction) and the coincident penny‐shaped voids (fractures). Both samples were measured when saturated with air, water (viscosity 1 cP) and glycerin (100 cP) to reveal poro‐visco‐elastic effects on velocity and attenuation, and their anisotropy. The blank sample was used to estimate the background anisotropy of the host rock in the fractured sample; the bedding fabric was found to show transverse isotropy with shear wave splitting (SWS) of 1.45 ± 1.18% (i.e. for S‐wave propagation along the bedding planes). In the fractured rock, maximum velocity and minimum attenuation of P‐waves was seen at 90° to the fracture normal. After correction for the background anisotropy, the fractured sample velocity anisotropy was expressed in terms of Thomsen's weak anisotropy parameters ε, γ & δ. A theory of frequency‐dependent seismic anisotropy in porous, fractured, media was able to predict the observed effect of viscosity and bulk modulus on ε and δ in water‐ and glycerin‐saturated samples, and the higher ε and δ values in air‐saturated samples. Theoretical predictions of fluid independent γ are also in agreement with the laboratory observations. We also observed the predicted polarisation cross‐over in shear‐wave splitting for wave propagation at 45° to the fracture normal as fluid viscosity and bulk modulus increases.     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.