Groundwater system response at sites with different agricultural land uses: case of the Guarani Aquifer outcrop area,Brotas/SP-Brazil

A system identification approach can be incorporated in groundwater time series analysis, revealing information concerning the local hydrogeological situation. The aim of this work was to analyse water table fluctuations in an outcrop area of the Guarani Aquifer System (GAS) in Brotas/SP, Brazil, using data from a groundwater monitoring network. The water table dynamic was modelled using continuous time series models that reference the hydrogeological system upon which they operate. The model’s climatological inputs of precipitation and evapotranspiration generate impulse response (IR) functions with parameters that can be related to the physical conditions concerning the hydrological processes involved. The interpretation of the model parameters from two sets of monitoring wells selected at different land-use sites is presented, exemplifying the effect of different water table depths and the distance to the nearest drainage location. Systematic trends of water table depths were also identified from model parameters at specific periods and related to plant development, crop harvest and land-use changes.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR L. Ruiz     

基于脉冲响应数据的ARMA法建模以及模态参数识别

本文提出了基于脉冲响应数据的ARMA法建模以及模态参数识别的新方法。该方法利用单位脉冲响应函数与ARMA模型G reen函数等价的特点,通过脉冲响应函数来估计系统响应的自相关系数,然后建立推广的Yu le-W alker方程以求得ARMA模型自回归系数并进行参数识别。最后通过算例,对一个模拟系统进行了参数识别,对采样频率、识别精度、模型阶数之间的影响规律进行了分析。     

A method for evaluating horizontal well pumping tests

Predicting the future performance of horizontal wells under varying pumping conditions requires estimates of basic aquifer parameters, notably transmissivity and storativity. For vertical wells, there are well-established methods for estimating these parameters, typically based on either the recovery from induced head changes in a well or from the head response in observation wells to pumping in a test well. Comparable aquifer parameter estimation methods for horizontal wells have not been presented in the ground water literature. Formation parameter estimation methods based on measurements of pressure in horizontal wells have been presented in the petroleum industry literature, but these methods have limited applicability for ground water evaluation and are based on pressure measurements in only the horizontal well borehole, rather than in observation wells. This paper presents a simple and versatile method by which pumping test procedures developed for vertical wells can be applied to horizontal well pumping tests. The method presented here uses the principle of superposition to represent the horizontal well as a series of partially penetrating vertical wells. This concept is used to estimate a distance from an observation well at which a vertical well that has the same total pumping rate as the horizontal well will produce the same drawdown as the horizontal well. This equivalent distance may then be associated with an observation well for use in pumping test algorithms and type curves developed for vertical wells. The method is shown to produce good results for confined aquifers and unconfined aquifers in the absence of delayed yield response. For unconfined aquifers, the presence of delayed yield response increases the method error.     

Stochastic models for simulation of strong ground motion in Iceland

Two types of modelling approaches for simulating ground motion in Iceland are studied and compared. The first type of models, named discrete‐time series models (ARMA), are based solely on measured acceleration in earthquakes occurring in Iceland. The second type of models are based on a theoretical seismic source model called the extended Brune model. Based on measured acceleration in Iceland during the period 1986–1996, the parameters for the extended Brune models have been estimated. The seismic source models are presented here as ARMA models, which simplifies the simulation process. A single‐layer soil amplification model is used in conjunction with the extended Brune model to estimate local site amplification. Emphasis is put on the ground motion models representing the variability in the measured earthquakes, with respect to energy, duration and frequency content. Demonstration is made using these models for constructing linear and non‐linear probabilistic response spectra using a discretised version of the Bouc–Wen model for the hysteresis of the second‐order system. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of arma models to estimate earthquake ground motion and structural response

This paper deals with the use of ARMA models in earthquake engineering. Tools and methods applied to strong ground motion are discussed emphasizing simulation of probabilistic earthquake response spectra. The ARMA models are applied to Icelandic earthquake data and a tentative model for Icelandic earthquakes is presented. This model, which is derived using 54 accelerograms, is based on a low-order, time-invariant ARMA process excited by Gaussian white noise and amplitude modulated using a simple envelope function to account for the non-stationary characteristics. This simple model gives a reasonable fit to the observed ground motion. Further, this model produces accurate earthquake response spectra, which, combined with accompanying attenuation and duration formulae, might be useful in earthquake hazard and risk assessment.     

Data-Worth Assessment for a Three-Dimensional Optimal Design in Nonlinear Groundwater Systems

Groundwater model predictions are often uncertain due to inherent uncertainties in model input data. Monitored field data are commonly used to assess the performance of a model and reduce its prediction uncertainty. Given the high cost of data collection, it is imperative to identify the minimum number of required observation wells and to define the optimal locations of sampling points in space and depth. This study proposes a design methodology to optimize the number and location of additional observation wells that will effectively measure multiple hydrogeological parameters at different depths. For this purpose, we incorporated Bayesian model averaging and genetic algorithms into a linear data-worth analysis in order to conduct a three-dimensional location search for new sampling locations. We evaluated the methodology by applying it along a heterogeneous coastal aquifer with limited hydrogeological data that is experiencing salt water intrusion (SWI). The aim of the model was to identify the best locations for sampling head and salinity data, while reducing uncertainty when predicting multiple variables of SWI. The resulting optimal locations for new observation wells varied with the defined design constraints. The optimal design (OD) depended on the ratio of the start-up cost of the monitoring program and the installation cost of the first observation well. The proposed methodology can contribute toward reducing the uncertainties associated with predicting multiple variables in a groundwater system.     

Analytic modeling of groundwater dynamics with an approximate impulse response function for areal recharge

An analytic approach is presented for the simulation of variations in the groundwater level due to temporal variations of recharge in surficial aquifers. Such variations, called groundwater dynamics, are computed through convolution of the response function due to an impulse of recharge with a measured time series of recharge. It is proposed to approximate the impulse response function with an exponential function of time which has two parameters that are functions of space only. These parameters are computed by setting the zeroth and first temporal moments of the approximate impulse response function equal to the corresponding moments of the true impulse response function. The zeroth and first moments are modeled with the analytic element method. The zeroth moment may be modeled with existing analytic elements, while new analytic elements are derived for the modeling of the first moment. Moment matching may be applied in the same fashion with other approximate impulse response functions. It is shown that the proposed approach gives accurate results for a circular island through comparison with an exact solution; both a step recharge function and a measured series of 10 years of recharge were used. The presented approach is specifically useful for modeling groundwater dynamics in aquifers with shallow groundwater tables as is demonstrated in a practical application. The analytic element method is a gridless method that allows for the precise placement of ditches and streams that regulate groundwater levels in such aquifers; heads may be computed analytically at any point and at any time. The presented approach may be extended to simulate the effect of other transient stresses (such as fluctuating surface water levels or pumping rates), and to simulate transient effects in multi-aquifer systems.     

Automated Time Series Modeling for Piezometers in the National Database of the Netherlands

The Geological Survey of the Netherlands (TNO-GSN) maintains a public national database of groundwater head observations. Transfer function-noise modeling has been applied to the time series in order to extract the impulse response functions for precipitation and evaporation for each piezometer. An automated procedure has been developed to assess the quality of the time series and of the models. The time series models of sufficient quality offer far more homogeneous data on the piezometric head than the original measurements. This allows for improved mapping of the head at a specific date or of characteristics of the head like average summer or winter levels. Also, the separation of precipitation and evaporation from other influences is useful for groundwater management and policy. The individual time series models are available online with interactive graphics ( https://www.grondwatertools.nl/grondwatertools-viewer ). The spatial patterns of the impulse response function characteristics can support analyses of the groundwater system.     

Determination of specific yield for the Biscayne Aquifer with a canal-drawdown test

Data from a large-scale canal-drawdown test were used to estimate the specific yield (sy) of the Biscayne Aquifer, an unconfined limestone aquifer in southeast Florida. The drawdown test involved dropping the water level in a canal by about 30 cm and monitoring the response of hydraulic head in the surrounding aquifer. Specific yield was determined by analyzing data from the unsteady portion of the drawdown test using an analytical stream-aquifer interaction model (Zlotnik and Huang 1999). Specific yield values computed from drawdown at individual piezometers ranged from 0.050 to 0.57, most likely indicating heterogeneity of specific yield within the aquifer (small-scale variation in hydraulic conductivity may also have contributed to the differences in sy among piezometers). A value of 0.15 (our best estimate) was computed based on all drawdown data from all piezometers. We incorporated our best estimate of specific yield into a large-scale two-dimensional numerical MODFLOW-based ground water flow model and made predictions of head during a 183-day period at four wells located 337 to 2546 m from the canal. We found good agreement between observed and predicted heads, indicating our estimate of specific yield is representative of the large portion of the Biscayne Aquifer studied here. This work represents a practical and novel approach to the determination of a key hydrogeological parameter (the storage parameter needed for simulation and calculation of transient unconfined ground water flow), at a large spatial scale (a common scale for water resource modeling), for a highly transmissive limestone aquifer (in which execution of a traditional pump test would be impractical and would likely yield ambiguous results). Accurate estimates of specific yield and other hydrogeological parameters are critical for management of water supply, Everglades environmental restoration, flood control, and other issues related to the ground water hydrology of the Biscayne Aquifer.     

Co-Seismic Groundwater Level Changes Induced by the May 12, 2008 Wenchuan Earthquake in the Near Field

The large scales of co-seismic water level changes in mainland China were observed in response to the tragic 2008 Ms 8.0 Wenchuan earthquake. To better understand the mechanism of these hydrogeological phenomena, groundwater-level data at 17 confined wells, with an epicentral distance of <500 km, were collected. We compare the static strain predicted by dislocation theory with the volumetric strain calculated by the tide effect of the groundwater based on poroelastic theory. The results show that the sign of the co-seismic groundwater level change is consistent with the sign predicted by dislocation theory. Additionally, the magnitude of the strain calculated by the two methods is also concordant in half of the wells. In the rest of the wells, the strains inversed from the groundwater level are one or two orders of magnitude larger than the fault dislocation model. These wells mostly have an epicenter distance larger than 300 km; therefore, the dynamic stress induced by the seismic wave may be responsible for the co-seismic water level changes in these wells. According to these results, we roughly estimate that the effect range of the static stress is approximately 300 km for the Wenchuan earthquake, and the dynamic stresses dominate beyond this epicenter distance. In addition, geological and hydrogeological conditions and other mechanisms may be responsible for these changes.     

Poroelastic Loading of an Aquifer Due to Upstream Dam Releases

Short-term changes in the hydraulic head of surface water bodies are known to influence the shallow response of hydraulically connected groundwaters. Associated with these fluctuations is the physical increase in stream water creating a mechanical load on the ground surface. This load is supported by the geologic materials (sediment or rock) and the pore fluid contained within the pores. Changes in this surface load have a direct effect on the total stress of the aquifer causing either a change in effective stress or fluid pressure. This response, predicted by the framework of linear poroelasticity, is a well-understood phenomenon in geologic materials. Currently, field measurements of the hydraulic response (i.e., fluid pressure) of aquifer materials are undergoing poroelastic loading due to dam releases in the Deerfield River Watershed in Massachusetts. An increase in stream stage from upstream dam releases causes an instantaneous pore fluid pressure increase at multiple depths and locations in the aquifer. This increase lasts anywhere from 15 to 40 minutes depending on the magnitude of the rise in the stream stage. Pore-pressure changes are well correlated to stream stage fluctuations for all of the recorded events. Poroelastic models created using basin stratigraphy and hydraulic properties of the aquifer response match the field observations well. Model results suggest that the overall stratigraphy is important in controlling the magnitude and duration of the poroelastic response. An improved understanding of responses such as these can be used to constrain uncertainties in model calibration and simulations of the contaminant migration in low permeability fine-grained (compressive) materials.     

Comparative evaluation of statistical tests for time series analysis: application to hydrological time series / Evaluation comparative de tests statistiques pour l'analyse de séries temporelles: application à des séries temporelles hydrologiques

Abstract

Statistical analyses of hydrological time series play a vital role in water resources studies. Twenty-nine statistical tests for detecting time series characteristics were evaluated by applying them to analyse 46 years of annual rainfall, 47 years of 1-day maximum rainfall and consecutive 2-, 3-, 4-, 5- and 6-day maximum rainfalls at Kharagpur, West Bengal, India. The performance of all the tests was evaluated. No severe outliers were found, and both the annual and maximum rainfall series were found to be normally distributed. Based on the known physical parameters affecting the homogeneity, the cumulative deviations and the Bayesian tests were found to be superior to the classical von Neumann test. Similarly, the Tukey test proved excellent among all the multiple comparison tests. These tests indicated that all the seven rainfall series are homogeneous. Two parametric t tests and the non-parametric Mann-Whitney test indicated stationarity in all the rainfall series. Of 12 trend detection tests, nine tests indicated no trends in the rainfall series. The Kendall's Rank Correlation test and the Mann-Kendall test were found equally powerful. Moreover, the Fourier series analysis revealed no apparent periodicities in all the seven rainfall series. The annual rainfall series was found persistent with a time lag of nine years. All the rainfall series were subjected to stochastic analysis by fitting 35 autoregressive moving-average (ARMA) models of different orders. The best-fit models for the original annual rainfall and 1-, 2- and 3-day maximum rainfall series were found to be ARMA(0,4), ARMA(0,2), ARMA(0,2) and ARMA(3,0), respectively. The best-fit model for the logarithmically transformed 4-day maximum rainfall was found to be ARMA(0,2). However, for the inversely transformed 4-, 5- and 6-day maximum rainfall series, ARMA(0,1) was obtained as the best-fit model. It is concluded that proper selection of time series tests and use of several tests is indispensable for making useful and reliable decisions.     

Visualization of aquifer response to periodic forcing

Many studies of periodic forcing and response in aquifers have focused on describing the induced fluctuations in hydraulic head, without much consideration of the time-dependent flows. Visualization techniques presented in this paper can be applied to obtain a more physically intuitive impression of groundwater motion in aquifers that undergo periodic fluctuations of hydraulic head. The concepts of velocity ellipse and displacement ellipse are introduced as methods for visualizing oscillatory flows associated with individual forcing modes. Cyclical trajectories illustrate the potential complexity of flow paths that can arise due to superposition of modal responses. The full periodic motion that results due to superposition of the mean flow and modal flows is visualized using streaklines. An animated time series of streaklines provides an intuitive impression of the flow and affords insight into apparent dispersion phenomenon that can arise due to periodic fluctuations in both the strength and direction of groundwater flow. Electronic animations are available from the authors.     

Exploratory spectral analysis of hydrological times series

Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.     

Use of point scale models to improve conceptual understanding in complex aquifers: An example from a sandstone aquifer in the Eden valley,Cumbria, UK

Understanding catchment functioning is increasingly important to enable water resources to be quantified and used sustainably, flood risk to be minimized, as well as to protect the system from degradation by pollution. Developing conceptual understanding of groundwater systems and their encapsulation in models is an important part of this understanding, but they are resource intensive to create and calibrate. The relative lack of data or the particular complexity of a groundwater system can prevent the development of a satisfactory conceptual understanding of the hydrological behaviour, which can be used to construct an adequate distributed model. A time series of daily groundwater levels from the Permo-Triassic sandstones situated in the River Eden Valley, Cumbria, UK have been analysed. These hydrographs show a range of behaviours and therefore have previously been studied using statistical and time series analysis techniques. This paper describes the application of AquiMOD, impulse response function (IRF) and combined AquiMOD-IRF methods to characterize the daily groundwater hydrographs. The best approach for each characteristic type of response has been determined and related to the geological and hydrogeological framework found at each borehole location. It is clear that AquiMOD, IRF and a combination of AquiMOD with IRF can be deployed to reproduce hydrograph responses in a range of hydrogeological settings. Importantly the choice of different techniques demonstrates the influence of differing processes and hydrogeological settings. Further they can distinguish the influences of differing hydrogeological environments and the impacts these have on the groundwater flow processes. They can be used, as shown in this paper, in a staged approach to help develop reliable and comprehensive conceptual models of groundwater flow. This can then be used as a solid basis for the development of distributed models, particularly as the latter are resource expensive to build and to calibrate effectively. This approach of using simple models and techniques first identifies specific aspects of catchment functioning, for example influence of the river, that can be later tested in a distributed model.     

A depth-averaged two-phase model for debris flows over fixed beds

A depth-averaged two-phase model is proposed for debris flows over fixed beds, explicitly incorporating interphase and particle-particle interactions, fluid and solid fluctuations and multi grain sizes. A first-order model based on the kinetic theory of granular flows is employed to determine the stresses due to solid fluctuations, while the turbulent kinetic energy - dissipation rate model is used to determine the stresses from fluid fluctuations. A well-balanced numerical algorithm is applied to solve the governing equations. The present model is benchmarked against USGS experimental debris flows over fixed beds. Incorporating the stresses due to fluid and solid fluctuations and properly estimating the bed shear stresses are shown to be crucial for reproducing the debris flows. Longitudinal particle segregation is resolved, demonstrating coarser sediments around the fronts and finer grains trailing the head. Based on extended modeling exercises, debris flow efficiency is shown to increase with initial volume, which is underpinned by observed datasets.     

Modelling of groundwater flow in heterogeneous porous media by finite element method

The HySuf‐FEM code (Hydrodynamic of Subsurface Flow by Finite Element Method) is proposed in this article in order to estimate the spatial variability of the transmissivity values of the Berrechid aquifer (Morocco). The calibration of the model is based on the hydraulic head, hydraulic conductivity and recharge. Three numerical tests are used to validate the model and verify its convergence. The first test case consists in using the steady analytical solution of the Poisson equation. In the second, the model has been compared with the hydrogeological system which is characterized by an unconfined monolayer (isotropic layer) and computed by using PMWIN‐MODFLOW software. The third test case is based on the comparison between the results of HySuf‐FEM and the multiple cell balance method in the aquifer system with natural boundaries case. Good agreement between the Hydrodynamic of Subsurface Flow, the numerical tests and the spatial distribution of the thickening of the hydrogeological system is deduced from the analysis and the interpretations of hydrogeological wells. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling effects of multinode wells on solute transport

Long-screen wells or long open boreholes with intraborehole flow potentially provide pathways for contaminants to move from one location to another in a ground water flow system. Such wells also can perturb a flow field so that the well will not provide water samples that are representative of ground water quality a short distance away from the well. A methodology is presented to accurately and efficiently simulate solute transport in ground water systems that include wells longer than the grid spacing used in a simulation model of the system and hence are connected to multiple nodes of the grid. The methods are implemented in a MODFLOW-compatible solute-transport model and use MODFLOW's Multi-Node Well Package but are generic and can be readily implemented in other solute-transport models. For nonpumping multinode wells (used to simulate open boreholes or observation wells, for example) and for low-rate pumping wells (in which the flow between the well and the ground water system is not unidirectional), a simple routing and local mixing model was developed to calculate nodal concentrations within the borehole. For high-rate pumping multinode wells (either withdrawal or injection, in which flow between the well and the ground water system is in the same direction at all well nodes), complete and instantaneous mixing in the wellbore of all inflows is assumed.     

Writing Analytic Element Programs in Python

The analytic element method is a mesh-free approach for modeling ground water flow at both the local and the regional scale. With the advent of the Python object-oriented programming language, it has become relatively easy to write analytic element programs. In this article, an introduction is given of the basic principles of the analytic element method and of the Python programming language. A simple, yet flexible, object-oriented design is presented for analytic element codes using multiple inheritance. New types of analytic elements may be added without the need for any changes in the existing part of the code. The presented code may be used to model flow to wells (with either a specified discharge or drawdown) and streams (with a specified head). The code may be extended by any hydrogeologist with a healthy appetite for writing computer code to solve more complicated ground water flow problems.