Stochastic estimation of facies using ground penetrating radar data

Explicitly defining large-scale heterogeneity is a necessary step of groundwater model calibration if accurate estimates of flow and transport are to be made. In this work, neural networks are used to estimate radar facies probabilities from ground penetrating radar (GPR) images, yielding stochastic facies-based models that honour the large-scale architecture of the subsurface. For synthetic GPR images, a neural network was able to correctly identify radar facies with an accuracy of approximately 90%. Manual interpretation of a set of 450 MHz GPR field data from the Borden aquifer resulted in the identification of four radar facies. Of these, a neural network was able to identify two facies with an accuracy of near 80% and one with an accuracy of 44%. The neural network was not able to identify the fourth facies, likely due to the choice of defining facies characteristics. Sequential indicator simulation was used to generate facies realizations conditioned to the radar facies probabilities. Numerical simulations indicate that significant improvements in the prediction of solute transport are possible when GPR is used to constrain the facies model compared to using well data alone, especially when data are sparse.This work was supported by funding to R. Knight under Grant No. DE-FG07–00ER15118-A000, Environmental Management Science Program, Office of Science and Technology, Office of Environment Management, United States Department of Energy (DOE). However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE. Further support was provided by a Stanford Graduate Fellowship to S. Moysey. The authors would also like to thank James Irving for his assistance with processing of the radar data.     

An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty

In this study, an interval-parameter multi-stage stochastic linear programming (IMSLP) method has been developed for water resources decision making under uncertainty. The IMSLP is a hybrid methodology of inexact optimization and multi-stage stochastic programming. It has three major advantages in comparison to the other optimization techniques. Firstly, it extends upon the existing multi-stage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Secondly, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. Thirdly, it cannot only handle uncertainties through constructing a set of scenarios that is representative for the universe of possible outcomes, but also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The developed IMSLP method is applied to a hypothetical case study of water resources management. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.     

Steady- and transient-state inversion in hydrogeology by successive flux estimation

A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors.     

Modeling the length of day and extrapolating the rotation of the Earth

The stochastic behavior of the length of day (LOD) process is analyzed and is modeled within statistical accuracy on a time-scale ranging from weeks to millennia by a three-component model comprising a global Brownian motion process, decadal fluctuations, and a 50-day Madden–Julian oscillation. While the model is intended to be phenomenological, some possible physical models underlying the three components are speculated upon. The model is applied to estimate long-range extrapolation errors. For example, it predicts a standard error of 1 h in the clock-time correction ΔT for extrapolation by 1,500 years from 500 to 2000 BC.     

Ground water contaminant transport by nondivergence-free, unsteady and nonstationary velocity fields

Pore flow velocity is assumed to be a nondivergence-free, unsteady, and nonstationary random function of space and time for ground water contaminant transport in a heterogeneous medium. The laboratory-scale stochastic contaminant transport equation is up scaled to field scale by taking the ensemble average of the equation by using the cumulant expansion method. A new velocity correction, which is a function of mean pore flow velocity divergence, is obtained due to strict second order cumulant expansion (without omitting any term after the expansion). The field scale transport equations under the divergence-free pore flow velocity field assumption are also derived by simplifying the nondivergence-free field scale equation. The significance of the new velocity correction term is investigated on a two dimensional transport problem driven by a density dependent flow.     

A stochastic model of surface contaminant releases to support assessment of site contamination at a former industrial site

An industrial site is usually contaminated by accidental (and occasionally intentional) releases of pollutants to the environment from various operations carried out on that site. Consequently, the pattern of contamination created during the life of the site depends in part, at least, on the pattern of operations. Thus, the assessment of the pattern of contamination over the site should be improved: if it is possible to identify the pattern of operations on the site, the duration of the different activities and the perceived likelihood of releases from the different operations. A stochastic model has been developed that can be used to simulate alternative realizations of contaminant releases (duration, extent and timing). The model employs release zones associated with particular activities or groups of activities on the site and the areas of each of the zones may be independent or overlapping. The period of activity in each zone is obtained from the site records, while the likelihood and extent of contamination in each zone is inferred from an analysis of the contamination data obtained by point sampling. The form of the model, the method of inference of the model parameter values from the site data and the application of the model to the study site are presented. The release model has been developed as part of a suite of stochastic models for site ground contamination analysis. The stochastic soil and transport models and the application of the integrated modelling system are described in separate papers.     

Stochastic generation of hourly rainstorm events

Occurrence of rainstorm events can be characterized by the number of events, storm duration, rainfall depth, inter-event time and temporal variation of rainfall within a rainstorm event. This paper presents a Monte-Carlo based stochastic hourly rainfall generation model considering correlated non-normal random rainstorm characteristics, as well as dependence of various rainstorm patterns on rainfall depth, duration, and season. The proposed model was verified by comparing the derived rainfall depth–duration–frequency relations from the simulated rainfall sequences with those from observed annual maximum rainfalls based on the hourly rainfall data at the Hong Kong Observatory over the period of 1884–1990. Through numerical experiments, the proposed model was found to be capable of capturing the essential statistical features of rainstorm characteristics and those of annual extreme rainstorm events according to the available data.     

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。     

Applications of the random model of drainage basin composition

The random model of drainage basin composition is founded on the assumptions that (a) natural channels are topologically random in the absence of geological controls and (b) for channel networks developed in similar environments, the exterior and interior link lengths are independent random variables with a common distribution for each type. The effectiveness of this model in estimating the values of geomorphic variables and in explaining and predicting geomorphic relationships is illustrated by several examples. The data required for these examples were obtained from map studies of 30 channel networks, comprising a total of about 8700 links, in eastern Kentucky. A common factor in the success of all three applications of the model is the way in which the planimetric features of drainage basins are determined by their underlying topologic structure.     

不同洞口位置节能砌块隐形密框复合墙体恢复力模型研究

为研究洞口位置对节能砌块隐形密框复合墙体滞回特性的影响,对6个采用低周反复加载方式的1/2缩尺试件的试验现象及数据进行分析。基于试验结果和现有恢复力模型理论,对试验数据进行拟合分析,利用退化四折线模型和回归方法,建立节能砌块隐形密框复合墙体的四折线恢复力模型。试验结果表明:当洞口位于墙体中间时,试件滞回环愈加丰满,试件初始刚度有所增加,承载力衰减速率减小,卸载刚度退化速率变慢。通过对骨架曲线特征参数的计算,并和试验骨架曲线对比,两者吻合较好,表明该恢复力模型可以较好的反映出不同洞口位置对其滞回特性的影响,可为节能砌块隐形密框复合墙体的弹塑性分析及工程应用提供参考。