Implementation/optimization of moving least squares response surfaces for approximation of hurricane/storm surge and wave responses

One of the important recent advances in the field of hurricane/storm modelling has been the development of high-fidelity numerical simulation models for reliable and accurate prediction of wave and surge responses. The computational cost associated with these models has simultaneously created an incentive for researchers to investigate surrogate modelling (i.e. metamodeling) and interpolation/regression methodologies to efficiently approximate hurricane/storm responses exploiting existing databases of high-fidelity simulations. Moving least squares (MLS) response surfaces were recently proposed as such an approximation methodology, providing the ability to efficiently describe different responses of interest (such as surge and wave heights) in a large coastal region that may involve thousands of points for which the hurricane impact needs to be estimated. This paper discusses further implementation details and focuses on optimization characteristics of this surrogate modelling approach. The approximation of different response characteristics is considered, and special attention is given to predicting the storm surge for inland locations, for which the possibility of the location remaining dry needs to be additionally addressed. The optimal selection of the basis functions for the response surface and of the parameters of the MLS character of the approximation is discussed in detail, and the impact of the number of high-fidelity simulations informing the surrogate model is also investigated. Different normalizations of the response as well as choices for the objective function for the optimization problem are considered, and their impact on the accuracy of the resultant (under these choices) surrogate model is examined. Details for implementation of the methodology for efficient coastal risk assessment are reviewed, and the influence in the analysis of the model prediction error introduced through the surrogate modelling is discussed. A case study is provided, utilizing a recently developed database of high-fidelity simulations for the Hawaiian Islands.     

边坡失效概率估计的高斯过程动态响应面法

针对传统响应面法在求解具有高度非线性隐式功能函数边坡可靠性问题上的局限性,采用适用于处理高维度、小样本、非线性回归问题的高斯过程回归模型构建隐式功能函数的响应面,将高斯过程响应面与蒙特卡罗模拟法相结合,通过构造合理的迭代方式,在利用高斯过程回归模型的不确定性评价功能获取最优采样点的基础上,实现了高斯过程响应面动态更新,由此提出了边坡失效概率快速估计的高斯过程动态响应面法。利用数值算例验证了该方法的有效性,在此基础上对3个边坡算例进行了可靠性分析。结果表明,与传统响应面法相比较,该方法计算精度与计算效率明显较高,易于与既有的边坡分析软件相结合,且实现容易,适用于边坡可靠性的快速分析。     

A reduced-order model for Monte Carlo simulations of stochastic groundwater flow

We explore the ability of the greedy algorithm to serve as an effective tool for the construction of reduced-order models for the solution of fully saturated groundwater flow in the presence of randomly distributed transmissivities. The use of a reduced model is particularly appealing in the context of numerical Monte Carlo (MC) simulations that are typically performed, e.g., within environmental risk assessment protocols. In this context, model order reduction techniques enable one to construct a surrogate model to reduce the computational burden associated with the solution of the partial differential equation governing the evolution of the system. These techniques approximate the model solution with a linear combination of spatially distributed basis functions calculated from a small set of full model simulations. The number and the spatial behavior of these basis functions determine the computational efficiency of the reduced model and the accuracy of the approximated solution. The greedy algorithm provides a deterministic procedure to select the basis functions and build the reduced-order model. Starting from a single basis function, the algorithm enriches the set of basis functions until the largest error between the full and the reduced model solutions is lower than a predefined tolerance. The comparison between the standard MC and the reduced-order approach is performed through a two-dimensional steady-state groundwater flow scenario in the presence of a uniform (in the mean) hydraulic head gradient. The natural logarithm of the aquifer transmissivity is modeled as a second-order stationary Gaussian random field. The accuracy of the reduced basis model is assessed as a function of the correlation scale and variance of the log-transmissivity. We explore the performance of the reduced model in terms of the number of iterations of the greedy algorithm and selected metrics quantifying the discrepancy between the sample distributions of hydraulic heads computed with the full and the reduced model. Our results show that the reduced model is accurate and is highly efficient in the presence of a small variance and/or a large correlation length of the log-transmissivity field. The flow scenarios associated with large variances and small correlation lengths require an increased number of basis functions to accurately describe the collection of the MC solutions, thus reducing significantly the computational advantages associated with the reduced model.     

Hydraulic Effects of Shales in Fluvial-Deltaic Deposits: Ground-Penetrating Radar, Outcrop Observations, Geostatistics, and Three-Dimensional Flow Modeling for the Ferron Sandstone, Utah

Ground-penetrating radar (GPR) surveys, outcrop measurements, and cores provide a high-resolution 3D geologic model to investigate the hydraulic effects of shales in marine-influenced lower delta-plain distributary channel deposits within the Cretaceous-age Ferron Sandstone at Corbula Gulch in central Utah, USA. Shale statistics are computed from outcrop observations. Although slight anisotropy was observed in mean length and variogram ranges parallel and perpendicular to pale of low , the anisotropy is not statistically significant and the estimated mean length is 5.4 m. Truncated Gaussian simulation was used to create maps of shales that are placed on variably dipping stratigraphic surfaces interpreted from high-resolution 3D GPR surveys, outcrop interpretations, and boreholes. Sandstone permeability is estimated from radar responses calibrated to permeability measurements from core samples. Experimentally designed flow simulations examine the effects of variogram range, shale coverage fraction, and trends in shale coverage on predicted upscaled permeability, breakthrough time, and sweep efficiency. Approximately 1500 flow simulations examine three different geologic models, flow in the 3 coordinate directions, 16 geostatistical parameter combinations, and 10 realizations for each model. ANOVA and response models computed from the flow simulations demonstrate that shales decrease sweep, recovery, and permeability, especially in the vertical direction. The effect on horizontal flow is smaller. Flow predictions for ideal tracer displacements at Corbula Gulch are sensitive to shale-coverage fraction, but are relatively insensitive to twofold variations in variogram range or to vertical trends in shale coverage. Although the hydraulic effects of shale are statistically significant, the changes in flow responses rarely exceed 20%. As a result, it may be reasonable to use simple models when incorporating analogous shales into models of reservoirs or aquifers.     

Current Trends and Demands in Visualization in the Geosciences

Geosciences, along with many other disciplines in science and engineering, faces an exponential increase in the amount of data generated from observation, experiment and large-scale, high-resolution 3-D numerical simulations. In this communication we describe the fundamentals of visualization necessary to meet these challenges. We present several alternative methodologies such as 2D/3D feature extraction, segmentation methods, and flow topology, to help better understand the physical structure of the data. We use AMIRA from TGS to demonstrate our concepts. Examples are drawn from fields in computational fluid dynamics, 3-D mantle convection and seismic tomography. Finally, we present our perspective on the future of visualization.     

Probabilistic assessment of rock slope stability using response surfaces determined from finite element models of geometric realizations

A methodology is developed for probabilistic rock slope stability assessment using numerical modelling that incorporates statistical analysis of the variability of joint set geometric parameters. Each probabilistic input parameter is substituted by its two point estimates. Half-factorial and central composite designs are implemented to obtain a minimum number of representative slope realizations to model. The output from the numerical models is used to construct mathematical prediction models or response surfaces. A response surface can be used to predict the factor of safety of arbitrary realizations without further numerical modelling and can be used to determine the probability of slope failure.     

An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics

In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed-stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high-fidelity model with the two-way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one-way formulation,” exhibiting substantial improvement in accuracy compared with the classical one-way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein.     

复杂地电模型的探地雷达时域有限差分正演

目前探地雷达正演模拟。都是针对简单的层状模型、圆状空洞、正方形空洞等单一的规则模型,而对于地下弯曲的界面或“V”字形等复杂模型的正演,实现起来较为困难。然而,地下构造是复杂的,因此,对复杂地电模型的正演研究显得更为重要。这里以麦克斯韦两个旋度方程为基本出发点,运用K.S.Yee的空间网格模型理论和时域有限差分法的基本原理,推导出二维空间的探地雷达正演方程组,通过讨论数值频散关系及其产生原因,推导出符合探地雷达实际传播规律的理想频散关系。为解决正演模拟时截断边界处的超强反射,采用了Mur超吸收边界条件．并以自制的探地雷达正演模拟程序为依托,对两个复杂的探地雷达模型进行了正演模拟,得到了正演剖面图。从其后模拟实例中的两正演剖面图可以看出,边界截断处的干扰波被大大地减少,消除边界反射后的雷达剖面能更好地指导工作人员进行地质解释,从而达到了把雷达的正演研究深入到复杂地电模型中去的目的,使正演研究更符合实际的地质情况。     

自适应网格在复杂地形浅水方程求解中的应用

计算域内地形的概化精度对模拟结果有较大影响,针对实际地形中同时存在狭长河谷与广阔泛洪区的问题,在层次自适应网格模型的基础上,研究了网格快速加密与合并的步骤,并以水位梯度与局部弗劳德数为基础设计了网格自适应准则,当水流运动情势变化时网格密度自动调整,实现计算精度与效率的平衡。在此网格模型基础上,采用有限体积法求解二维浅水方程,利用梯度限制器技术及龙格-库塔法提高模型的空间、时间计算精度。算例表明,层次自适应网格模型既能实现随水流运动动态变化并捕获水位计算敏感区,也能对局部区域进行静态固定加密,自适应性良好,具有较好的推广应用价值。     

Toward petascale earthquake simulations

Earthquakes are among the most complex terrestrial phenomena, and modeling of earthquake dynamics is one of the most challenging computational problems in science. Computational capabilities have advanced to a state where we can perform wavefield simulations for realistic three-dimensional earth models, and gain more insights into the earthquakes that threaten California and many areas of the world. The Southern California Earthquake Center initiated a major earthquake research program called TeraShake to perform physics-based numerical simulations of earthquake processes for large geographical regions, at high resolution, and for high frequencies. For a large scale simulation such as TeraShake, optimization problems tend to emerge that are not significant in smaller scale simulations. This involves both large parallel computation and also massive data management and visualization coordination. In this paper, we describe how we performed single-processor optimization of the TeraShake AWM application, optimization of the I/O handling, and optimization of initialization. We also look at the challenges presented by run-time data archive management and visualization. The improvements made to the TeraShake AWM code enabled execution on the 40k IBM Blue Gene processors and have created a community code that can be used by seismologists to perform petascale earthquake simulations.     

煤火区浅部松散煤体及采空区的探地雷达响应特征

探地雷达对浅层勘探具有较高分辨率,为煤田火区浅部松散煤体或采空区等典型火源地质结构探测提供了重要手段。然而如何识别各种火源地质结构体,确定火区重点范围还存在一定的理论不足。基于电磁波理论,采用时域有限差分法正演模拟了火区典型地质体地电模型雷达响应,其特征表现为：松散跨塌煤体对应雷达响应绕射波严重,其内部波形紊乱;空洞区顶界面回波能量强,较为连续,其内部无绕射。正演模拟和现场测试研究表明：探地雷达对识别浅埋火区煤层松散跨落程度,圈定火烧重点区域,减少灭火成本和火区开采安全事故具有重要的现实意义。     

Accuracy and efficiency of time integration methods for 1D diffusive wave equation

The diffusive wave approximation of the Saint-Venant equations is commonly used in hydrological models to describe surface flow processes. Numerous numerical approaches can be used to solve this highly nonlinear equation. Nonlinear time integration schemes—also called methods of lines (MOL)—were proven very efficient to solve other nonlinear problems in geosciences but were never considered to deal with surface flow modeling with the diffusive wave equation. In this paper, we study the relative performance of different time and space integration schemes by comparing the results obtained with classical approaches and with nonlinear time integration approaches. The results show that (i) the integration method with a higher order in space shows high accuracy regarding an integrated indicator such as the global mass balance error but is less accurate regarding local indicators, and (ii) nonlinear time integration techniques perform better than classical ones. Overall, it seems that integration techniques combining nonlinear time integration and a low spatial order need to be considered when developing hydrological modeling tools owing to their simplicity of implementation and very good performance.     

Validation of a three‐dimensional constitutive model for nonlinear site response and soil‐structure interaction analyses using centrifuge test data

The capability of a bounding surface plasticity model with a vanishing elastic region to capture the multiaxial dynamic hysteretic responses of soil deposits under broadband (eg, earthquake) excitations is explored by using data from centrifuge tests. The said model was proposed by Borja and Amies in 1994 (J. Geotech. Eng., 120, 6, 1051‐1070), which is theoretically capable of representing nonlinear soil behavior in a multiaxial setting. This is an important capability that is required for exploring and quantifying site topography, soil stratigraphy, and kinematic effects in ground motion and soil‐structure interaction analyses. Results obtained herein indicate that the model can accurately predict key response data recorded during centrifuge tests on embedded specimens—including soil pressures and bending strains for structural walls, structures' racking displacements, and surface settlements—under both low‐ and high‐amplitude seismic input motions, which was achieved after performing only a basic material parameter calibration procedure. Comparisons are also made with results obtained using equivalent linear models and a well‐known pressure‐dependent multisurface plasticity model, which suggested that the present model is generally more accurate. The numerical convergence behavior of the model in nonlinear equilibrium iterations is also explored for a variety of numerical implementation and model parameter options. To facilitate broader use by researchers and practicing engineers alike, the model is implemented as a “user material” in ABAQUS Standard for implicit time stepping.     

An integrative approach to robust design and probabilistic risk assessment for CO<Subscript>2</Subscript> storage in geological formations

CO₂ storage in geological formations is currently being discussed intensively as a technology with a high potential for mitigating CO₂ emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis or stochastic approaches based on a brute-force approach of repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a higher-order orthogonal basis of polynomials to approximate dependence on uncertain parameters (porosity, permeability, etc.) and design parameters (injection rate, depth, etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation, and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs with a minimum failure probability. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al., Comput Geosci 13:451–467, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speed-up by a factor of 100 compared with the Monte Carlo evaluation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO₂ injection, including uncertainty in the analysis leads to a systematic and significant shift of the predicted leakage rates toward higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios.     

Vulnerability and resistance to neoliberal environmental changes: An assessment of agriculture and forestry in the Biobio region of Chile (1974–2014)

This article examines the dynamics of double exposure, vulnerability, and resistance to neoliberal globalization and environmental change in the Chilean agricultural region of Biobio. By using climatic models and secondary Agricultural Census data from 1997 and 2007, we assess how Chilean neoliberal reforms have, since 1974, facilitated land use changes and forestry investments. We demonstrate that policy changes which incentivize forestry investments have reduced cultivated agricultural lands and native forest, and concentrated land in the hands of global agribusiness corporations. Compounding these issues, Biobio shows a climatic trend towards aridity coupled with an increasing demand for irrigation. Analyzing these conditions, we argue that the neoliberal globalization of regional agriculture under the context of climatic changes has produced a regional space of increasing vulnerabilities and uneven geographical development in Biobio. We particularly demonstrate that the Chilean mode of agricultural neoliberalization has been conducive to land dispossession—to the detriment of traditional agriculture —and has homogenized the biophysical landscape, replacing traditional crops and native forests with exotic species like pines and eucalyptus. We also examine how local producers are using resistance movements to cope with and contest neoliberal environmental changes. We conclude by evaluating the implications of these spaces of agricultural vulnerabilities and local resistances in the context of uneven geographical development at a regional and global scale.     

螺旋面的拟合应用研究

提出了一种螺旋面的拟合算法。利用参数方程建立独立参数与直角坐标的代数关系,构建出误差方程组,再利用非线性方程的多维数值寻根方法求解出螺旋面的各项参数。用模拟数据进行了算法的验证,并给出了误差的评定方法。此法可拓展到对其它参数曲面的拟合。     

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.     

Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations

Model calibration and history matching are important techniques to adapt simulation tools to real-world systems. When prediction uncertainty needs to be quantified, one has to use the respective statistical counterparts, e.g., Bayesian updating of model parameters and data assimilation. For complex and large-scale systems, however, even single forward deterministic simulations may require parallel high-performance computing. This often makes accurate brute-force and nonlinear statistical approaches infeasible. We propose an advanced framework for parameter inference or history matching based on the arbitrary polynomial chaos expansion (aPC) and strict Bayesian principles. Our framework consists of two main steps. In step 1, the original model is projected onto a mathematically optimal response surface via the aPC technique. The resulting response surface can be viewed as a reduced (surrogate) model. It captures the model’s dependence on all parameters relevant for history matching at high-order accuracy. Step 2 consists of matching the reduced model from step 1 to observation data via bootstrap filtering. Bootstrap filtering is a fully nonlinear and Bayesian statistical approach to the inverse problem in history matching. It allows to quantify post-calibration parameter and prediction uncertainty and is more accurate than ensemble Kalman filtering or linearized methods. Through this combination, we obtain a statistical method for history matching that is accurate, yet has a computational speed that is more than sufficient to be developed towards real-time application. We motivate and demonstrate our method on the problem of CO₂ storage in geological formations, using a low-parametric homogeneous 3D benchmark problem. In a synthetic case study, we update the parameters of a CO₂/brine multiphase model on monitored pressure data during CO₂ injection.     

城市下垫面空间特征对地表产汇流过程的影响研究综述

快速城市化显著改变了城市下垫面空间特征,对地表产汇流过程产生了重要影响。综述城市下垫面空间特征对地表产汇流过程的影响研究进展,以下垫面空间特征对产汇流过程的影响为主线,聚焦不透水面和微地形两类空间特征,总结城市下垫面空间特征及其表征方法;从不透水率与不透水面空间变化、数值模拟与物理实验等方面,分别梳理不透水面和微地形等空间特征对地表产汇流过程的影响研究成果。展望未来城市下垫面空间特征对地表产汇流过程的影响研究重点和发展方向,主要包括影响机理解析、主控空间特征参数识别与敏感性分析、城市水文效应适应性应对等,以期为快速城市化下城市水文效应解析和城市洪涝灾害防治提供一定参考。