Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Sea-level rise and flooding in coastal riverine flood plains

Abstract

This work presents a method for calculating the contributions of sea-level rise and urban growth to flood risk in coastal flood plains. The method consists of hydraulic/hydrological, urban growth and flood-damage quantification modules. The hydraulic/hydrological module estimates peak annual flows to generate flood stages impacted by sea-level rise within flood plains. A model for urban growth predicts patterns of urbanization within flood plains over the period 2010–2050. The flood-damage quantification module merges flood maps and urbanization predictions to calculate the expected annual flood damage (EAFD) for given scenarios of sea-level rise. The method is illustrated with an application to the Tijuana River of southern California, USA, and northwestern Mexico, where the EAFD is predicted to increase by over US$100 million because of sea-level rise of 0.25–1.0 m and urban growth by the year 2050. It is shown that urbanization plays a principal role in increasing the EAFD in the study area for the range of sea-level rise considered.

Editor Z.W. Kundzewicz

Citation Garcia, E.S. and Loáiciga, H.A., 2013. Sea-level rise and flooding in coastal riverine flood plains. Hydrological Sciences Journal, 59 (1), 204–220.     

地震活动的随机标度和非线性标度律

把地震作为一个复杂系统,研究了地震活动的随机性质．当不考虑震级范围时,全球地震活动、人震的余震和区域震群均有以幂次律为特征的长尾现象．地震的强度由震级确定,具有一特定震级的地震可形成一个地震活动系列,很多这样的地震活动系列就形成具有各种震级的地震的集合．不同地震系列间的统计特征由随机标度来表征,随机标度表明了由地震震级分类的不同地震系列间统计时刻的标度关系．为了统一地方、区域和全球地震活动性的统计特性,引入了非线性标度率．     

Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion

Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment).     

棉花耗水规律和灌溉随机控制

根据5年田间试验资料,分析了棉花产量与耗水量的抛物线关系,确定了棉花最佳耗水量;根据棉花植株在不同土壤湿度情况下气孔阻力、蒸腾强度和蕾铃脱落率的变化,确定了不同生育阶段的适宜水分指标和干旱指标。在此基础上,研制了棉花灌溉随机控制模型,可以动态预报棉田土壤有效水分含量和实际蒸散量,并从经济效益和水分利用效率的角度提出优化灌溉决策。     

A BME solution of the inverse problem for saturated groundwater flow

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.     

Stability and capsizing analysis of nonlinear ship rolling in wind and stochastic beam seas

Considering the actual seaway condition, stability and capsizing of nonlinear ship rolling system in stochastic beam seas is of significant importance for voyage safety. Safe zone are defined in the phase space plan of the unperturbed Hamilton system to qualitatively distinguish ship motions as capsize and noncapsize. Capsize events are defined by solutions passing out of the safe zone. The probability of such an occurrence is studied by virtue of the random Melnikov function and the concept of phase space flux. In this paper, besides conventional wave excitation, the effect of wind load is also taken into account. The introduction of wind load will lead to asymmetry, in other words, it transforms the symmetric heteroclinic orbits into asymmetric homoclinic orbits. For asymmetric dynamical system, the orbital analytic solutions and its power spectrum are not readily available, and the technique of discrete time Fourier transformation (DTFT) is used. In the end, as verification of theoretical critical significant wave height, capsizing probability contour diagram is generated by means of numerical simulation. The contour diagram shows that these analytical methods provide reliable and predictive results about the likelihood of a vessel capsizing in a given seaway condition.     

多股水平淹没射流水力特性的影响因素研究

采用数值模拟和模型试验相结合的方法,分析了水股分层、坎高、出口体型和跌坎形式等因素对多股水平淹没射流的流态稳定性和水力特性的影响。研究表明,多股多层水平淹没射流较单层多股水平淹没射流流态稳定性好、临底流速低、消能率高,是一种高效的新型消能方式。结合试验结果,提出中孔泄槽以等宽或微收缩为宜、表中孔最优坎高差应大于中孔水流的主流水深、跌坎形式的选择应结合具体工程特点等建议。     

1D elastic full‐waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm–Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic‐algorithm‐sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis–Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one‐dimensional elastic full‐waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the “genetic drift” effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step.     

Détermination expérimentale des paramètres équivalents d'un milieu poreux hétérogène en écoulements uniforme ou radial

Tracer tests are carried out in a heterogeneous porous medium that has a 3D correlated random distribution of the permeabilities. The fitting of numerical models provides the values of equivalent permeability and macrodispersivity characterizing a 2D homogeneous horizontal medium. Different flow configurations are studied: uniform, radial and pump and treat (doublet). The fitted parameter sets are independent of the flow type, except for the doublet. They are greater than the values predicted by stochastic theories, due to the small number of correlation lengths explored by the tracer and the limited extension of the experimental set-up. To cite this article: C. Danquigny, P. Ackerer, C. R. Geoscience 337 (2005).