Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback.Results indicate: (1) The new method exhibits quadratic convergence for homogenous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%.     

地下水渗流沉降的三维耦合模型及程序的研制

研制可合理模拟预测基坑降水过程中引起地面沉降的计算机程序,并提出最优化降水方案。基于三维全耦合数值模型,笔者开发了GWS软件。GWS软件是以比奥固结理论为基础,将土体的非线性特征及土的渗透性随应力状态的动态变化考虑进去,通过耦合地下水渗流场和土体应力场进行模拟预测基坑降水过程中渗流场及地面沉降的变化。以一个实际基坑降水工程为例,经GWS软件计算得出5口井联合抽水方案,后续工程证明此方案正确、可靠。以三维全耦合数值理论为基础的GWS软件,可以为基坑降水工程引起的地下水渗流场变化及地面沉降量提供可靠的预测。     

P- and S-wavefield simulations using both the first- and second-order separated wave equations through a high-order staggered grid finite-difference method

In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equations. In this study, we compare two kinds of such wave equations: the first-order (velocity–stress) and the second-order (displacement–stress) separate elastic wave equations, with the first-order (velocity–stress) and the second-order (displacement–stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-difference method. Comparisons are given of wavefield snapshots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corresponding first-order or second-order full elastic wave equations. These mixed equations are computationally slightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-component processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.     

高精度瑞雷波有限差分数值模拟及波场分析

应用2×12阶高精度交错网格有限差分法,建立了震源位于自由表面时模拟瑞雷波的边界条件,通过对均匀半空间模型模拟得到的结果与解析解完全一致,证明了波场模拟的正确性.针对模拟得到的波场记录,从瑞雷波的传播速度、传播深度、能量衰减和频散特性等几个方面进行了分析,从波场模拟的角度完全证实了弹性波传播理论中的瑞雷波传播特征,加深了对瑞雷波传播过程的认识.在均匀介质模拟的基础上,对含有软弱夹层的三层介质模型进行了模拟,获得了更加接近实际情况的地震记录.为进一步开展对高模式下瑞雷波的反演研究和促进对瑞雷波勘探的应用提供了有益的帮助.     

Stochastic modelling and risk analysis of groundwater pollution using FORM coupled with automatic differentiation

The first order reliability method (FORM) has been widely used in probabilistic modelling of groundwater problems. The FORM approach requires an iterative optimization procedure to find out the system failure point (the most probable point).The advantages of this approach are that it does not require many computations in comparison with other methods when applied to simple problems, and it produces reasonably accurate results. However, it has been found that the computations of FORM can equal or exceed that of other methods in case of large number of variables.In this paper, a new implementation of FORM was proposed with more efficiency and accuracy than the traditional FORM method. In the proposed approach, automatic differentiation is used to obtain the gradient vector of the limit state function, which is required by FORM, instead of using finite difference estimation. This way, the first order derivative was obtained with a very good accuracy, and with less computational effort. Based on the obtained results, it is found that the proposed implementation of FORM is a very good tool for probabilistic risk assessment and uncertainty analysis in groundwater problems.     

Flood frequency analysis using historical data: accounting for random and systematic errors

Abstract

Flood frequency analysis based on a set of systematic data and a set of historical floods is applied to several Mediterranean catchments. After identification and collection of data on historical floods, several hydraulic models were constructed to account for geomorphological changes. Recent and historical rating curves were constructed and applied to reconstruct flood discharge series, together with their uncertainty. This uncertainty stems from two types of error: (a) random errors related to the water-level readings; and (b) systematic errors related to over- or under-estimation of the rating curve. A Bayesian frequency analysis is performed to take both sources of uncertainty into account. It is shown that the uncertainty affecting discharges should be carefully evaluated and taken into account in the flood frequency analysis, as it can increase the quantiles confidence interval. The quantiles are found to be consistent with those obtained with empirical methods, for two out of four of the catchments.

Citation Neppel, L., Renard, B., Lang, M., Ayral, P.-A., Coeur, D., Gaume, E., Jacob, N., Payrastre, O., Pobanz, K. & Vinet, F. (2010) Flood frequency analysis using historical data: accounting for random and systematic errors. Hydrol. Sci. J. 55(2), 192–208.     

Numerical modeling of local scour at a submerged weir with a downstream slope using a coupled moving-mesh and maskedelement approach

This paper presents a model for local scour at submerged weirs with downstream slopes that uses a coupled moving-mesh and masked-element approach.In the developed model,the fluid-sediment interface is tracked using a moving-mesh technique,and the effects of the structure on the hydrodynamics and bed morphology are resolved using a masked-element technique.Compared to traditional sediment scour models,based on the moving-mesh technique,the present model has the advantage of allowing for a simpler setup of the computational grids and a larger-amplitude deformation.Laboratory experiments on local scour at a submerged weir with a downstream slope were conducted,which provided bed profiles at different time instants.The results obtained by the present model are compared to the experimental data.The comparisons demonstrate the performance of the model in satisfactorily predicting local scour at a submerged weir with a downstream slope.The model was further modified and employed to carry out additional computations to investigate the influence of various parameters and sub-models.     

Detecting volcanic eruption precursors: a new method using gravity and deformation measurements

One of the fundamental questions in modern volcanology is the manner in which a volcanic eruption is triggered; the intrusion of fresh magma into a reservoir is thought to be a key component. The amount by which previously ponded reservoir magma interacts with a newly intruded magma will determine the nature and rate of eruption as well as the chemistry of erupted lavas and shallow dykes. The physics of this interaction can be investigated through a conventional monitoring procedure that incorporates the simple and much used Mogi model relating ground deformation (most simply represented by Δh) to changes in volume of a magma reservoir. Gravity changes (Δg) combined with ground deformation provide information on magma reservoir mass changes. Our models predict how, during inflation, the observed Δg/Δh gradient will evolve as a volcano develops from a state of dormancy through unrest into a state of explosive activity. Calderas in a state of unrest and large composite volcanoes are the targets for the methods proposed here and are exemplified by Campi Flegrei, Rabaul, Krafla, and Long Valley. We show here how the simultaneous measurement of deformation and gravity at only a few key stations can identify important precursory processes within a magma reservoir prior to the onset of more conventional eruption precursors.     

Catchment-scale vulnerability assessment of groundwater pollution from diffuse sources using the DRASTIC method: a case study

Abstract

The catchment-scale groundwater vulnerability assessment that delineates zones representing different levels of groundwater susceptibility to contaminants from diffuse agricultural sources has become an important element in groundwater pollution prevention for the implementation of the EU Water Framework Directive (WFD). This paper evaluates the DRASTIC method using an ArcGIS platform for assessing groundwater vulnerability in the Upper Bann catchment, Northern Ireland. Groundwater vulnerability maps of both general pollutants and pesticides in the study area were generated by using data on the factors depth to water, net recharge, aquifer media, soil media, topography, impact of vadose zone, and hydraulic conductivity, as defined in DRASTIC. The mountain areas in the study area have “high” (in 4.5% of the study area) or “moderate” (in 25.5%) vulnerability for general pollutants due to high rainfall, net recharge and soil permeability. However, by considering the diffuse agricultural sources, the mountain areas are actually at low groundwater pollution risk. The results of overlaying the maps of land use and the groundwater vulnerability are closer to the reality. This study shows that the DRASTIC method is helpful for guiding the prevention practices of groundwater pollution at the catchment scale in the UK.

Citation Yang, Y. S. & Wang, L. (2010 Yang, Y. S. and Wang, L. 2010. A review of modelling tools for implementation of the EU Water Framework Directive in handling diffuse water pollution. Water Resour. Manage., 24: 1819–1843.  [Google Scholar]) Catchment scale vulnerability assessment of groundwater pollution from diffuse sources using the DRASTIC method: a case study. Hydrol. Sci. J. 55(7), 1206–1216.     

A new tool for hillslope hydrologists: spatially distributed groundwater level and soilwater content measured using electromagnetic induction

New methods for obtaining and quantifying spatially distributed subsurface moisture are a high research priority in process hydrology. We use simple linear regression analyses to compare terrain electrical conductivity measurements (EC) derived from multiple electromagnetic induction (EMI) frequencies to a distributed grid of water‐table depth and soil‐moisture measurements in a highly instrumented 50 by 50 m hillslope in Putnam County, New York. Two null hypotheses were tested: H0₍₁₎, there is no relationship between water table depth and EC; H0₍₂₎, there is no relationship between soil moisture levels and EC. We reject both these hypotheses. Regression analysis indicates that EC measurements from the low frequency EM31 meter with a vertical dipole orientation could explain over 80% of the variation in water‐table depth across the test hillslope. Despite zeroing and sensitivity problems encountered with the high frequency EM38, EC measurements could explain over 70% of the gravimetrically determined soil‐moisture variance. The use of simple moisture retrieval algorithms, which combined EC measurements from the EM31 and EM38 meters in both their vertical and horizontal orientations, helped increase the r² coefficients slightly. This first hillslope hydrological analysis of EMI technology in this way suggests that it may be a promising method for the collection of a large number of distributed soilwater and groundwater depth measurements with a reasonable degree of accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法

本文基于Biot的饱和多孔介质本构方程,考察具有辐射阻尼的外行球面波,推导了饱和多孔介质三维黏弹性人工边界的法向和切向边界方程;在已有的饱和多孔介质二维显式有限元数值计算方法基础上,提出该理论的三维方法,并开发了实现该三维方法的有限元程序.算例表明饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法具有较好的精度和稳定性.     

The two-component extreme value distribution for flood frequency analysis: Derivation of a new estimation method

The two component extreme value (TCEV) distribution has recently been shown to account for most of the characteristics of the real flood experience. A new method of parameter estimation for this distribution is derived using the principle of maximum entropy (POME). This method of parameter estimation is suitable for application in both the site-specific and regional cases and appears simpler than the maximum likelihood estimation method. Statistical properties of the regionalized estimation were evaluated using a Monte Carlo approach and compared with those of the maximum likelihood regional estimators.     

Investigation of submarine groundwater discharge to tidal rivers: Evidence for regional and local scale seepage

Fluxes of submarine groundwater discharge (SGD) were investigated into two tidal rivers on the north and south shore of Long Island, NY, during July 2015. Ground‐based handheld thermal infrared (TIR) imagery, combined with direct push‐point piezometer sampling, documented spatially heterogeneous small‐scale intertidal seepage zones. Pore waters were relatively fresh and enriched in nitrogen (N) within these small‐scale seeps. Pore waters sampled just 20 cm away, outside the boundary of the ground‐based TIR‐located seepage zone, were more saline and lower in N. These ground‐based TIR‐identified seeps geochemically represented the terrestrial fresh groundwater endmember, whereas N in pore waters sampled outside of the TIR‐identified seeps was derived from the remineralization of organic matter introduced into the sediment by tidal seawater infiltration. A ²²²Rn (radon‐222) time‐series was used to quantify fresh SGD‐associated N fluxes using the N endmembers sampled from the ground‐based TIR pore water profiles. N fluxes were up‐scaled to groundwater seepage zones identified from high‐resolution airborne TIR imagery using the two‐dimensional size of the airborne TIR surface water anomalies, relative to the N flux from the time‐series sampling location. Results suggest that the N load from the north‐shore tidal river to Long Island Sound is underrepresented by at least 1.6–3.6%, whereas the N load from SGD to a south‐shore tidal river may be up to 9% higher than previous estimates. These results demonstrate the importance of SGD in supplying nutrients to the lower reaches of tidal rivers and suggest that N loads in other tidal river environments may be underestimated if SGD is not accounted for.     

Monitoring and forecasting nitrate concentration in the groundwater using statistical process control and time series analysis: a case study

Contaminated water resources have important implications on health and the environment. Nitrate contamination of the groundwater is a serious problem in the European Union. A method based on the statistical process control (SPC) and time series analysis is developed to monitoring and to predict the concentration evolution of nitrate (NO₃ ⁻) in groundwater. In many pumping wells the NO₃ ⁻concentration ([NO₃ ⁻]) increases and approaches or even passes the European Community standard of 50 mg l⁻¹. The objective of this paper is to show the application of statistical process control as a monitoring tool for groundwater pollution from agricultural practices. We propose the autoregressive integrated moving average (ARIMA) model as a management tool to monitoring and reduction of the intrusion of nitrate into the groundwater. This tool should help in setting up useful guidelines for evaluating actual environmental performance against the firm’s environmental objectives and targets and regulatory requirements. We concluded that the statistical process control method may be a potentially important way of monitoring groundwater quality that also permits rapid response to serious increases in pollutants concentrations. In doing so, the paper fills an important gap in the water pollution standards and emerging polices (Water Framework directives).     

Experimental analysis of groundwater flow through a landslide slip surface using natural and artificial water chemical tracers

Artificial and natural tracer tests combined with high accurate electronic distancemeter measurements are conducted on a small landslide with a well known slip surface geometry. Outflow yields and chemical contents are monitored for all the experiment duration and they analyzed to estimate the slip surface hydraulic parameters. The main result is that the slip surface acts as a drain for groundwater flows that evacuates interstitial pressures in the slope and brings the sliding mass to be more stable one. Copyright © 2007 John Wiley & Sons, Ltd.