Predicting wetted width in any river at any discharge

Coefficients describing at‐a‐station power‐law relationships between discharge and width were calculated by applying multilevel models to field data collected during routine hydrological monitoring at 326 gauging stations across New Zealand. These hydraulic geometry coefficients were then estimated for each of these stations using standard stepwise multiple‐linear regression models. Analysis was carried out to quantify how the relationship between width and discharge changed in relation to several available explanatory variables. All coefficients describing the at‐a‐station hydraulic geometry were found to have statistically significant relationships with catchment area. Statistically significant relationships between each of the coefficients were also found with the addition of catchment climate as an explanatory variable. Further statistically significant relationships were found when station elevation and channel slope, as well as hydrological source of flow and landcover of the upstream catchment were added to the explanatory variables. The level of confidence that can be associated with estimates of width at ungauged sites, and sites with limited data availability, was then assessed by comparing model predictions with independent paired data on observed width and discharge from 197 sites. When compared against these independent data, model predictions of width were improved with the addition of predictor variables of the hydraulic geometry coefficients. The greatest improvements were made when climate was added to catchment area as predictor variables. Minor improvements were made when all available information was used to predict width at these independent sites. Although the analysis was purely empirical, results describing relationships between hydraulic geometry coefficients and catchment characteristics corresponded well with knowledge of the processes controlling at‐a‐station hydraulic geometry of river width. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of groundwater flow patterns using flux as upper boundary

Since the 1960s, most of the studies on groundwater flow systems by analytical and numerical modelling have been based on given‐head upper boundaries. The disadvantage of the given‐head approach is that the recharge into and discharge from a basin vary with changes in hydraulic conductivity and/or basin geometry. Consequently, flow patterns simulated with given‐head boundaries but with different hydraulic conductivities and/or basin geometry may not reflect the effects of these variables. We conducted, therefore, numerical simulations of groundwater flow in theoretical drainage basins using flux as the upper boundary and realistically positioned fluid‐potential sinks while changing the infiltration intensity, hydraulic conductivities, and geometric configuration of the basin. The simulated results demonstrate that these variables are dominant factors controlling the flow pattern in a laterally closed drainage basin. The ratio of infiltration intensity to hydraulic conductivity (R_ic) has been shown to be an integrated pattern‐parameter in a basin with a given geometric configuration and possible fluid‐potential‐sink distribution. Successively, the changes in flow patterns induced by stepwise reductions in R_ic are identical, regardless of whether the reductions are due to a decrease in infiltration intensity or an increase in hydraulic conductivity. The calculated examples show five sequential flow patterns containing (i) only local, (ii) local–intermediate, (iii) local–intermediate–regional, (iv) local–regional, and (v) just regional flow systems. The R_ic was found to determine also whether a particular sink is active or not as a site of discharge. Flux upper boundary is preferable for numerical simulation when discussing the flow patterns affected by a change of infiltration, the hydraulic conductivity, or the geometry of a basin. Copyright © 2012 John Wiley & Sons, Ltd.     

Adjustments in river channel geometry associated with hydraulic discontinuities across the fluvial–tidal transition of a regulated river

Major hydraulic discontinuities along lowland rivers may be caused by water impoundment behind weirs, by tributary floods, and by tides. An analysis of the geometry of 122 surveyed channel cross-sections located on an 18 km reach of the lower River Dee identifies up to three levels in the bank profile representing minima in the width:mean depth ratio, and distinct changes in the geometric properties of the channel to these three levels in a downstrem direction and within four stretches influenced to varying degrees by hydraulic discontinuities created by a weir and by tidal overtopping of the weir. Simple modelling combined with field observations suggest possible processes that may control the observed changes in channel morphology. © 1997 John Wiley & Sons, Ltd.     

Including geophysical data in ground water model inverse calibration

A nonlinear regression method is developed that can be used to estimate parameters of a ground waterflow model from a combination of observations of hydrological variables and observations of geophysical properties that are functionally related with the hydraulic conductivity. The procedure estimates: parameters characterizing the hydraulic conductivity field (e.g., zonal or pilot point values); geophysical properties that have been observed and that are functionally related with the hydraulic conductivity parameters; and a few parameters of the function that relates the hydraulic conductivity parameters with the geophysical properties (the type of function is assumed known). A fidelity factor, sigma(r)2, of a term of the minimized objective function reflects the faith one has in the validity of this functional relationship. The estimation methodology has been tested by means of synthetic models. The experimental results demonstrate that the number of estimated hydraulic conductivity parameters can be increased by adding geophysical observations to the set of hydrological observations that are traditionally used for model calibration. The improvement of the estimated hydraulic conductivity field and the simulated hydraulic head field can be significant but is dependent on the number, the locations, and the uncertainty of geophysical observations. The sensitivity of the estimation results to the value of sigma(r) is small for the studied problems except when the uncertainty of geophysical observations is high. In the latter case, a large sigma(r) value was found to be optimal to avoid that hydraulic conductivity estimates are closely tied to corresponding but highly uncertain geophysical observations.     

Estimating River Conductance from Prior Information to Improve Surface‐Subsurface Model Calibration

Most groundwater models simulate stream‐aquifer interactions with a head‐dependent flux boundary condition based on a river conductance (CRIV). CRIV is usually calibrated with other parameters by history matching. However, the inverse problem of groundwater models is often ill‐posed and individual model parameters are likely to be poorly constrained. Ill‐posedness can be addressed by Tikhonov regularization with prior knowledge on parameter values. The difficulty with a lumped parameter like CRIV, which cannot be measured in the field, is to find suitable initial and regularization values. Several formulations have been proposed for the estimation of CRIV from physical parameters. However, these methods are either too simple to provide a reliable estimate of CRIV, or too complex to be easily implemented by groundwater modelers. This paper addresses the issue with a flexible and operational tool based on a 2D numerical model in a local vertical cross section, where the river conductance is computed from selected geometric and hydrodynamic parameters. Contrary to other approaches, the grid size of the regional model and the anisotropy of the aquifer hydraulic conductivity are also taken into account. A global sensitivity analysis indicates the strong sensitivity of CRIV to these parameters. This enhancement for the prior estimation of CRIV is a step forward for the calibration and uncertainty analysis of surface‐subsurface models. It is especially useful for modeling objectives that require CRIV to be well known such as conjunctive surface water‐groundwater use.     

At‐a‐station hydraulic geometry relations, 2: calibration and testing

Using a large number of data sets obtained from various sources, the geometric relations derived in Part 1 are calibrated and verified using the split sampling approach. The calibration of parameters shows that the change in stream power is not shared equally among hydraulic variables and that the unevenness depends on the boundary conditions to be satisfied by the channel under consideration. The agreement between the observed values of the hydraulic variables and those predicted by the derived relations is close for the verification data set and lends credence to the hypotheses employed in this study. Copyright © 2007 John Wiley & Sons, Ltd.     

Predicting river width,depth and velocity at ungauged sites in England and Wales using multilevel models

Using a dataset of gauged river discharges taken from sites in England and Wales, linear multilevel models (also known as mixed effects models) were applied to quantify the variability in discharge and the discharge‐hydraulic geometry relationships across three nested spatial scales. A jackknifing procedure was used to test the ability of the multilevel models to predict hydraulic geometry, and therefore width, mean depth and mean velocity, at ungauged stations. These models provide a framework for making predictions of hydraulic geometry parameters, with associated levels of uncertainty, using different levels of data availability. Results indicate that as one travels downstream along a river there is greater variability in hydraulic geometry than is the case between rivers of similar sizes. This indicates that hydraulic geometry (and therefore hydrology) is driven by catchment area, to a greater extent than by natural geomorphological variations in the streamwise direction at the mesoscale, but these geomorphological variations can still have a major impact on channel structure. Copyright © 2008 John Wiley & Sons, Ltd.     

Sensitivity analysis of EUROSEM using Monte Carlo simulation I: hydrological,soil and vegetation parameters

Knowledge about model uncertainty is essential for erosion modelling and provides important information when it comes to parameterizing models. In this paper a sensitivity analysis of the European soil erosion model (EUROSEM) is carried out using Monte Carlo simulation, suitable for complex non‐linear models, using time‐dependent driving variables. The analysis revealed some important characteristics of the model. The variability of the static output parameters was generally high, with the hydrologic parameters being the most important ones, especially saturated hydraulic conductivity and net capillary drive followed by the percentage basal area for the hydrological and vegetation parameters and detachability and cohesion for the soil erosion parameters. Overall, sensitivity to vegetation parameters was insignificant. The coefficient of variation for the sedigraph was higher than for the hydrograph, especially from the beginning of the rainstorm and up to the peak, and may explain difficulties encountered when trying to match simulated hydrographs and sedigraphs with observed ones. The findings from this Monte Carlo simulation calls for improved within‐storm modelling of erosion processes in EUROSEM. Information about model uncertainty will be incorporated in a new EUROSEM user interface. Copyright © 2000 John Wiley & Sons, Ltd.     

Scale Dependence of Hydraulic and Structural Parameters in the Crystalline Rock of the KTB

— Knowledge of rock properties controlling the fluid movement is a basic prerequisite to understand the dynamical processes and the temperature and stress regime of the upper crust. Fracture networks were investigated on different scales to obtain quantitative results of fracture geometry like fracture length, orientation and fracture frequencies. Due to the scale effect, these parameters differ in several orders of magnitude in dependence of the scale of investigation. On the microscopic scale, fluorescent thin sections from cores were analysed and permeability was estimated for 2-D hydraulic networks. On the macroscopic scale, fracture parameters were determined from images of structural borehole measurements. The vicinity of the drill site represents the megascopic scale, where seismic reflectors were assumed as active hydraulic structures for construction of a fracture network. Compiling the fracture densities from all investigated scales and taking into consideration only the networks above the percolation threshold, the fracture length distribution follows a power law with an exponent of ?1.9 ± 0.05. Besides the scale differences of the geometric parameters like fracture density and length and the hydraulic parameters like permeability, the connectivity of the networks seems to be a confining characteristic. This is quantitatively described by the percolation parameter and the mean number of intersections per fracture. When assuming a macroscopic hydraulic system at the percolation threshold for the KTB site, the macroscopic mean fracture length can be estimated to approximately 30 m. This stands in agreement with the hydraulic experiments on site.     

STABLE CHANNEL OBJECTIVE FUNCTION

1 INTRODUCTIONA stable channel is a stream in equilibrium that is neither silting nor scouring over a period of time.Obviously, such a stream has developed a cross sectional area of flow through natural processes ofdeposition and scour. Gilbert (Chang 1988) in 1880 was perhaps the first to recognize the role ofndnilnization processes in arriving at an equilibrium cross-section of such a stream. Langbein (1964)gave an arbitrarily formed function of various knit powers obtained by dividing …     

Polynomial chaos expansion for global sensitivity analysis applied to a model of radionuclide migration in a randomly heterogeneous aquifer

We perform global sensitivity analysis (GSA) through polynomial chaos expansion (PCE) on a contaminant transport model for the assessment of radionuclide concentration at a given control location in a heterogeneous aquifer, following a release from a near surface repository of radioactive waste. The aquifer hydraulic conductivity is modeled as a stationary stochastic process in space. We examine the uncertainty in the first two (ensemble) moments of the peak concentration, as a consequence of incomplete knowledge of (a) the parameters characterizing the variogram of hydraulic conductivity, (b) the partition coefficient associated with the migrating radionuclide, and (c) dispersivity parameters at the scale of interest. These quantities are treated as random variables and a variance-based GSA is performed in a numerical Monte Carlo framework. This entails solving groundwater flow and transport processes within an ensemble of hydraulic conductivity realizations generated upon sampling the space of the considered random variables. The Sobol indices are adopted as sensitivity measures to provide an estimate of the role of uncertain parameters on the (ensemble) target moments. Calculation of the indices is performed by employing PCE as a surrogate model of the migration process to reduce the computational burden. We show that the proposed methodology (a) allows identifying the influence of uncertain parameters on key statistical moments of the peak concentration (b) enables extending the number of Monte Carlo iterations to attain convergence of the (ensemble) target moments, and (c) leads to considerable saving of computational time while keeping acceptable accuracy.     

Stochastic evolution of hydraulic geometry relations in the lower Yellow River of China under environmental uncertainties

Hydraulic geometry relations comprise a classic way to understand characteristics of a river. However, environmental changes pose large uncertainties for the reliability of such relations. In the current study, on the basis of the ordinary differential equations (ODEs) formed through linear treatment of the deterministic power-law hydraulic geometry relations, a set of stochastic differential equations (SDEs) driven by Fractional white noise and Poisson noise are developed to simulate the historical dynamic probability distributions of typical hydraulic geometry variables such as slope, width, depth, and velocity with bankfull discharge variation over time in the lower Yellow River of China. One group of possible stochastic average behaviors within the next 50 years are calculated under three different design incoming water-sediment conditions (including 300, 600, and 800 million t of annual average sediment discharge). In each part of the lower reaches, after estimation of the SDE parameters using a nonparametric maximum likelihood estimation (MLE) method, the model is carefully examined using Monte Carlo simulation as compared with the deterministic control models. The results of this comparison reveal the potential responses of hydraulic geometry characteristics to environmental disturbances, and the average trends mainly agree with the measurements. Comparisons among the three different prediction results reveal the stochastic average solution generally is greater than the deterministic solution. The results also confirm the severe negative impacts that result from the condition of 300 million t of incoming sediment, thus, pointing out the need to raise the level of river evolution alert for the lower Yellow River of China in the future. Moreover, with the help of the stochastic computation, the stream power and hydraulic width/depth ratio could be representative of an effective systematic measure for river dynamics. The proposed stochastic approach is not only important to development in the field of fluvial relations, but also beneficial to the practical design and monitoring of a river system according to specified accuracy requirements.     

Uncertainty and sensitivity analysis of runoff and sediment yield in a small agricultural watershed with KINEROS2 / Analyse d'incertitude et de sensibilité des simulations d'écoulement et de transport solide de KINEROS2 dans un petit bassin versant agricole

Abstract

Using the Monte Carlo (MC) method, this paper derives arithmetic and geometric means and associated variances of the net capillary drive parameter, G, that appears in the Parlange infiltration model, as a function of soil texture and antecedent soil moisture content. Approximate expressions for the arithmetic and geometric statistics of G are also obtained, which compare favourably with MC generated ones. This paper also applies the MC method to evaluate parameter sensitivity and predictive uncertainty of the distributed runoff and erosion model KINEROS2 in a small experimental watershed. The MC simulations of flow and sediment related variables show that those parameters which impart the greatest uncertainty to KINEROS2 model outputs are not necessarily the most sensitive ones. Soil hydraulic conductivity and wetting front net capillary drive, followed by initial effective relative saturation, dominated uncertainties of flow and sediment discharge model outputs at the watershed outlet. Model predictive uncertainty measured by the coefficient of variation decreased with rainfall intensity, thus implying improved model reliability for larger rainfall events. The antecedent relative saturation was the most sensitive parameter in all but the peak arrival times, followed by the overland plane roughness coefficient. Among the sediment related parameters, the median particle size and hydraulic erosion parameters dominated sediment model output uncertainty and sensitivity. Effect of rain splash erosion coefficient was negligible. Comparison of medians from MC simulations and simulations by direct substitution of average parameters with observed flow rates and sediment discharges indicates that KINEROS2 can be applied to ungauged watersheds and still produce runoff and sediment yield predictions within order of magnitude of accuracy.     

A geostatistical approach to an inverse problem: Identification of geometry and estimate of equivalent conductivities for highly heterogeneous porous media with the differential system method

A methodology for identifying the geometry of different materials in highly heterogeneous porous media in discrete inverse problems (DIP) is described. It applies a geostatistical approach within the differential system method (DSM). DSM calculates conductivity values along an integration path beginning at a point with known conductivity. In aquifers with zero source terms, DSM completely describes the conductivity field through a spatially distributed parameter depending on hydraulic head gradients and integration path. A factor analysis of the structural components of this parameter (i.e. coregionalisation analysis) was carried out to identify the geometry of different materials, corresponding to distinct statistically homogeneous areas. The equivalent conductivity values for homogeneous areas were estimated.This approach was applied for a synthetic aquifer. The identification of geometry was accurate and the estimates of equivalent parameters were good, compared with reference values. The accuracy of the results depended on errors in hydraulic gradients, compared with conductivity gradients.     

Anisotropic dispersive Henry problem

The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer.     

基于多波束地形测量的上荆江典型河段沙波形态特征分析

沙波形态影响水流结构、泥沙输移及动床阻力。本研究采用多波束测深系统首次精细测量了上荆江典型河段的床面地形,采用改进后的沙波形态量化算法统计了各类沙波形态参数,分析了不同水流强度下沙波形态的变化特征。计算结果表明:(1)测量河段小型与大型沙波的平均波高分别为0.16～0.81和0.96～2.31 m,波长分别为13～27和16～41m;沙波尺度相较于水深较小,小型与大型沙波的波高分别不超过水深的0.045和0.150倍;(2)沙波背流面坡度基本不超过14°,小于泥沙水下休止角,其与陡度之间的关系可以用线性方程描述;(3)中洪水流量对沙波形态尺度的塑造作用强于枯水流量,且对浅水区大型沙波形态尺度的塑造作用强于深水区。本研究量化了天然河流的沙波形态,较好地反映了沙波形态特征,能为大型冲积河流沙波形态的量化及特征参数的统计分析提供参考。     

A geostatistically based inverse model for three-dimensional variably saturated flow

We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.     

A geostatistically based inverse model for three-dimensional variably saturated flow

We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

Live-bed scour downstream of block ramps for low densimetric Froude numbers

Sediment load plays a major role in the morphological evolution of rivers.Therefore,the analysis of the sediment load interaction with hydraulic structures is of main importance in order to enhance the preservation of fish habitats and river morphological characteristics.The present study analyzes the scour mechanisms downstream of a block ramp in live bed conditions,when the sediment supplied by the approaching flow is balanced by the sediment transported out of the scour hole.Experiments were performed in a model flume and the effect of the approaching sediment concentration on the scour geometry was analyzed.It was observed that the scour features depend deeply on the approaching sediment concentration and four main profile configurations were distinguished.The experimental data were analyzed and empirical relationships were developed in order to evaluate the depth and length of a scour hole,the dune height and the distance of the transversal section of maximum dune height from the ramp toe for different hydraulic and geometric conditions.It was also proved that the dynamic equilibrium shape of a scour hole does not depend on the sediment load time history.