Agricultural effluent control under uncertainty: An inexact double-sided fuzzy chance-constrained model

An inexact double-sided fuzzy chance-constrained programming (IDFCCP) method was developed in this study and applied to an agricultural effluent control management problem. IDFCCP was formulated through incorporating interval linear programming (ILP) into a double-sided fuzzy chance-constrained programming (DFCCP) framework, and could be used to deal with uncertainties expressed as not only possibility distributions associated with both left- and right-hand-side components of constraints but also discrete intervals in the objective function. The study results indicated that IDFCCP allowed violation of system constraints at specified confidence levels, where each confidence level consisted of two reliability scenarios. This could lead to model solutions with high system benefits under acceptable risk magnitudes. Furthermore, the introduction of ILP allowed uncertain information presented as discrete intervals to be communicated into the optimization process, such that a variety of decision alternatives can be generated by adjusting the decision-variable values within their intervals. The proposed model could help decision makers establish various production patterns with cost-effective water quality management schemes under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability.     

Geophysical flows under location uncertainty,Part II Quasi-geostrophy and efficient ensemble spreading

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. In this paper, simplified geophysical dynamics are derived from a Boussinesq model under location uncertainty. Invoking usual scaling approximations and a moderate influence of the subgrid terms, stochastic formulations are obtained for the stratified Quasi-Geostrophy and the Surface Quasi-Geostrophy models. Based on numerical simulations, benefits of the proposed stochastic formalism are demonstrated. A single realization of models under location uncertainty can restore small-scale structures. An ensemble of realizations further helps to assess model error prediction and outperforms perturbed deterministic models by one order of magnitude. Such a high uncertainty quantification skill is of primary interests for assimilation ensemble methods. MATLAB^® code examples are available online.     

A simulation-based fuzzy chance-constrained programming model for optimal groundwater remediation under uncertainty

In this study a simulation-based fuzzy chance-constrained programming (SFCCP) model is developed based on possibility theory. The model is solved through an indirect search approach which integrates fuzzy simulation, artificial neural network and simulated annealing techniques. This approach has the advantages of: (1) handling simulation and optimization problems under uncertainty associated with fuzzy parameters, (2) providing additional information (i.e. possibility of constraint satisfaction) indicating that how likely one can believe the decision results, (3) alleviating computational burdens in the optimization process, and (4) reducing the chances of being trapped in local optima. The model is applied to a petroleum-contaminated aquifer located in western Canada for supporting the optimal design of groundwater remediation systems. The model solutions provide optimal groundwater pumping rates for the 3, 5 and 10 years of pumping schemes. It is observed that the uncertainty significantly affects the remediation strategies. To mitigate such impacts, additional cost is required either for increased pumping rate or for reinforced site characterization.     

Fluid flow dynamics under location uncertainty

We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent subgrid bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modeling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems.     

Optimal design and impact analysis of urban traffic regulations under ambient uncertainty

Decision-making in traffic regulations is challenging with uncertainty in the environment. In this research we extend probabilistic engineering design concepts to policy decision-making for urban traffic with variability from field data. City traffic is simulated using user equilibrium and cellular automata. A cellular automata (CA) model is developed by combing existing CA models with tailored rules for local traffic behaviors in Tainan, Taiwan. Both passenger sedans and motorcycles are considered with the possibility of passing between different types of vehicles. The tailpipe emissions from all mobile sources are modeled as Gaussian dispersion with finite line sources. Speed limits of all roads are selected as independent policy design variables, resulting in a problem with 50 dimensions. We first study the impacts of a particular policy-setting on traffic behaviors and on the environment under various sources of uncertainties. The genetic algorithm, combined with probabilistic analysis, is then used to obtain the optimal regulations with the minimal cost to the environment in compliance to the current ambient air quality standards.     

Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties

In this study, a two-stage fuzzy chance-constrained programming (TFCCP) approach is developed for water resources management under dual uncertainties. The concept of distribution with fuzzy probability (DFP) is presented as an extended form for expressing uncertainties. It is expressed as dual uncertainties with both stochastic and fuzzy characteristics. As an improvement upon the conventional inexact linear programming for handling uncertainties in the objective function and constraints, TFCCP has advantages in uncertainty reflection and policy analysis, especially when the input parameters are provided as fuzzy sets, probability distributions and DFPs. TFCCP integrates the two-stage stochastic programming (TSP) and fuzzy chance-constrained programming within a general optimization framework. TFCCP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. TFCCP is applied to a water resources management system with three users. Solutions from TFCCP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and fuzzy dominance indices.     

Comparison of sparse‐grid geometric and random sampling methods in nonlinear inverse solution uncertainty estimation

A new uncertainty estimation method, which we recently introduced in the literature, allows for the comprehensive search of model posterior space while maintaining a high degree of computational efficiency. The method starts with an optimal solution to an inverse problem, performs a parameter reduction step and then searches the resulting feasible model space using prior parameter bounds and sparse‐grid polynomial interpolation methods. After misfit rejection, the resulting model ensemble represents the equivalent model space and can be used to estimate inverse solution uncertainty. While parameter reduction introduces a posterior bias, it also allows for scaling this method to higher dimensional problems. The use of Smolyak sparse‐grid interpolation also dramatically increases sampling efficiency for large stochastic dimensions. Unlike Bayesian inference, which treats the posterior sampling problem as a random process, this geometric sampling method exploits the structure and smoothness in posterior distributions by solving a polynomial interpolation problem and then resampling from the resulting interpolant. The two questions we address in this paper are 1) whether our results are generally compatible with established Bayesian inference methods and 2) how does our method compare in terms of posterior sampling efficiency. We accomplish this by comparing our method for two electromagnetic problems from the literature with two commonly used Bayesian sampling schemes: Gibbs’ and Metropolis‐Hastings. While both the sparse‐grid and Bayesian samplers produce compatible results, in both examples, the sparse‐grid approach has a much higher sampling efficiency, requiring an order of magnitude fewer samples, suggesting that sparse‐grid methods can significantly improve the tractability of inference solutions for problems in high dimensions or with more costly forward physics.     

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.     

Assessing the impact of ground-motion variability and uncertainty on empirical fragility curves

Empirical fragility curves, constructed from databases of thousands of building-damage observations, are commonly used for earthquake risk assessments, particularly in Europe and Japan, where building stocks are often difficult to model analytically (e.g. old masonry structures or timber dwellings). Curves from different studies, however, display considerable differences, which lead to high uncertainty in the assessed seismic risk. One potential reason for this dispersion is the almost universal neglect of the spatial variability in ground motions and the epistemic uncertainty in ground-motion prediction. In this paper, databases of building damage are simulated using ground-motion fields that take account of spatial variability and a known fragility curve. These databases are then inverted, applying a standard approach for the derivation of empirical fragility curves, and the difference with the known curve is studied. A parametric analysis is conducted to investigate the impact of various assumptions on the results. By this approach, it is concluded that ground-motion variability leads to flatter fragility curves and that the epistemic uncertainty in the ground-motion prediction equation used can have a dramatic impact on the derived curves. Without dense ground-motion recording networks in the epicentral area empirical curves will remain highly uncertain. Moreover, the use of aggregated damage observations appears to substantially increase uncertainty in the empirical fragility assessment. In contrast, the use of limited randomly-chosen un-aggregated samples in the affected area can result in good predictions of fragility.     

基于匹配追踪和遗传算法的大地电磁噪声压制

针对匹配追踪计算量大、大地电磁数据处理效率低的问题,提出基于匹配追踪和遗传算法的大地电磁噪声压制方法.首先,利用Gabor原子构建过完备原子库,并对过完备原子库集合进行划分.然后,借助遗传算法的自适应性,快速搜寻最优匹配原子及所在位置.最后,运用最优匹配原子对待处理信号进行稀疏分解,重构有用信号.通过对计算机模拟的典型强干扰和矿集区实测大地电磁数据进行分析处理,实验结果表明,相对于匹配追踪和正交匹配追踪,文中所提方法能从过完备原子库中快速、自适应地选取最优匹配原子与不同噪声干扰类型高精度的匹配,极大地提升了计算效率;大地电磁时间域序列中的大尺度强干扰被有效剔除,视电阻率曲线更为光滑、连续,低频段的数据质量得到明显改善.

     

基于同步大地电磁时间序列依赖关系的噪声处理

本文从信号与系统的角度讨论了同步大地电磁时间序列信号之间的依赖关系,选取高信噪比的时间序列信号作为先验数据,用最小二乘法估算依赖关系;结合参考道的数据,合成本地道含噪声时段的数据,最后用合成数据替代噪声段数据,组成新数据,从而在时域中去除大地电磁噪声.西藏地区高信噪比实测数据的试算结果表明,无论电场还是磁场,信号之间的依赖关系是相对稳定的,只与先验数据的长度有关,与时间无关;虽然不同参考点之间的依赖关系不同,但都可以精确合成本地点数据,与参考点地下电性结构和参考距离无关.仿真实验显示,去噪后的信号与原始信号基本一致.实测数据处理结果表明,该方法可以有效去除强噪声干扰,抑制中高频段的近场源效应,同时保留了微弱的有效信号,保证了处理结果的正确性.最后针对方差比方法无法识别的方波噪声,提出了一种简单的平移方法,成功去除了持续时间大于窗口长度的方波噪声;将该方法与远参考技术结合,可以有效抑制近场源噪声干扰,获得光滑连续并且可信的测深资料.     

Transmissivity and storage coefficient estimation by coupling the Cooper–Jacob method and modified fuzzy least-squares regression

Traditionally the Cooper–Jacob equation is used to determine the transmissivity and the storage coefficient for an aquifer using pump test results. This model, however, is a simplified version of the actual subsurface and does not allow for analysis of the uncertainty that comes from a lack of knowledge about the heterogeneity of the environment under investigation. In this paper, a modified fuzzy least-squares regression (MFLSR) method is developed that uses imprecise pump test data to obtain fuzzy intercept and slope values which are then used in the Cooper–Jacob method. Fuzzy membership functions for the transmissivity and the storage coefficient are then calculated using the extension principle. The supports of the fuzzy membership functions incorporate the transmissivity and storage coefficient values that would be obtained using ordinary least-squares regression and the Cooper–Jacob method. The MFLSR coupled with the Cooper–Jacob method allows the analyst to ascertain the uncertainty that is inherent in the estimated parameters obtained using the simplified Cooper–Jacob method and data that are uncertain due to lack of knowledge regarding the heterogeneity of the aquifer.     

基于概率统计的地震岩相识别不确定性定量评价方法

地震岩相识别能够提供具有不同储层特征的岩相分布信息,对岩相识别的不确定性开展定量评价分析可降低后期油藏建模与储层评价的风险.考虑了地震岩相识别中测井岩相定义、岩石物理建模、井震尺度匹配及地震反演等环节的不确定性对岩相识别的影响,基于概率统计方法,引入熵函数实现了地震岩相识别不确定性定量评价,并结合岩相概率、重建率等多角度综合定量分析不确定性的构成及传递特征,系统地实现了地震岩相识别不确定性评价流程的整体连通.提出了结合属性交绘特征约束反演参数空间,提高地震岩相识别运算效率.模拟数据分析表明利用熵函数可精确实现岩相识别不确定性地定量表征,利用属性交绘特征约束参数空间既大幅度减少运算量,也可降低地震岩相识别的不确定性.     

Assessing underwater noise levels during pile-driving at an offshore windfarm and its potential effects on marine mammals

Marine renewable developments have raised concerns over impacts of underwater noise on marine species, particularly from pile-driving for wind turbines. Environmental assessments typically use generic sound propagation models, but empirical tests of these models are lacking. In 2006, two 5 MW wind turbines were installed off NE Scotland. The turbines were in deep (>40 m) water, 25 km from the Moray Firth Special Area of Conservation (SAC), potentially affecting a protected population of bottlenose dolphins. We measured pile-driving noise at distances of 0.1 (maximum broadband peak to peak sound level 205 dB re 1 μPa) to 80 km (no longer distinguishable above background noise). These sound levels were related to noise exposure criteria for marine mammals to assess possible effects. For bottlenose dolphins, auditory injury would only have occurred within 100 m of the pile-driving and behavioural disturbance, defined as modifications in behaviour, could have occurred up to 50 km away.     

Assessing the impact of interannual variability of precipitation and potential evaporation on evapotranspiration

The impact of interannual variability of precipitation and potential evaporation on the long-term mean annual evapotranspiration as well as on the interannual variability of evapotranspiration is studied using a stochastic soil moisture model within the Budyko framework. Results indicate that given the same long-term mean annual precipitation and potential evaporation, including interannual variability of precipitation and potential evaporation reduces the long-term mean annual evapotranspiration. This reduction effect is mostly prominent when the dryness index (i.e., the ratio of potential evaporation to precipitation) is within the range from 0.5 to 2. The maximum reductions in the evaporation ratio (i.e., the ratio of evapotranspiration to precipitation) can reach 8–10% for a range of coefficient of variation (CV) values for precipitation and potential evaporation. The relations between the maximum reductions and the CV values of precipitation and potential evaporation follow power laws. Hence the larger the interannual variability of precipitation and potential evaporation becomes, the larger the reductions in the evaporation ratio will be. The inclusion of interannual variability of precipitation and potential evaporation also increases the interannual variability of evapotranspiration. It is found that the interannual variability of daily rainfall depth and that of the frequency of daily rainfall events have quantitatively different impacts on the interannual variability of evapotranspiration; and they also interact differently with the interannual variability of potential evaporation. The results presented in this study demonstrate the importance of understanding the role of interannual variability of precipitation and potential evaporation in land surface hydrology under a warming climate.     

Geophysical flows under location uncertainty,Part III SQG and frontal dynamics under strong turbulence conditions

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. This change can be consistently applied to all fluid dynamics evolution laws. This paper continues to explore benefits of this framework and consequences of specific scaling assumptions. Starting from a Boussinesq model under location uncertainty, a model is developed to describe a mesoscale flow subject to a strong underlying submesoscale activity. Specifically, turbulent diffusion and rotation effects have similar orders of magnitude. As obtained, the geostrophic balance is modified and the Quasi-Geostrophic assumptions remarkably lead to a zero Potential Vorticity. The ensuing Surface Quasi-Geostrophic model provides a simple diagnosis of warm frontolysis and cold frontogenesis.     

基于背景噪声研究云南地区面波速度非均匀性和方位各向异性

基于中国地震科学探测台阵项目一期在南北地震带南段架设的300多个地震台站,利用2011年10月至2012年9月的连续观测记录,采用基于背景噪声互相关函数的面波层析成像技术,研究了青藏高原东南缘的云南地区面波群速度和方位各向异性分布.结果显示,地壳的面波快波方向呈现近南北向,整体表现出围绕东喜马拉雅构造结顺时针旋转的趋势,和地表GPS速度场以及S波分裂的快波方位较为一致.小江断裂东西两侧的快波方位有一定差异.对反映深度大概在下地壳和上地幔顶部的长周期面波,快波方向从近南北向逐渐向北西向过渡,在菱形块体附近,26°N以南,快波方向和红河断裂的走向趋于一致;其他区域相比上地壳的快波方向也有较大变化,这种结果较为支持青藏高原东南缘的云南地区壳幔变形的解耦.在滇西南,澜沧江向东弧形展布区域,中下地壳快波方位呈现局部的圆周旋转趋势,结合该区地震分布规律和应力主轴方向,推测这种现象和块体挤压及旋转具有一定相关性.     

Weather noise impact on the uncertainty of simulated water balance components of river basins

Assessments of hydrological response to climatic changes are characterized by different types of uncertainties. Here, the uncertainty caused by weather noise associated with the chaotic character of atmospheric processes is considered. A technique for estimating such uncertainty in simulated water balance components based on application of the land surface model SWAP and the climate model ECHAM5 is described. The technique is applied for estimating the uncertainties in the simulated water balance components (precipitation, river runoff and evapotranspiration) of some northern river basins of Russia. It is shown that the larger the area of a basin the less the uncertainty. This dependency is smoothed by differences in natural conditions of the basins. Analysis of the spectral densities of water balance components shows that a river basin filters out high-frequency harmonics of spectral density of precipitation (corresponding to synoptic or sub-seasonal scale) during its transformation into evapotranspiration and especially into runoff.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR H. Kreibich     

Assessment of flood forecasting lead time based on generalized likelihood uncertainty estimation approach

Real time updating of rainfall-runoff (RR) models is traditionally performed by state-space formulation in the context of flood forecasting systems. In this paper, however, we examine applicability of generalized likelihood uncertainty estimation (GLUE) approach in real time modification of forecasts. Real time updating and parameter uncertainty analysis was conducted for Abmark catchment, a part of the great Karkheh basin in south west of Iran. A conceptual-distributed RR model, namely ModClark, was used for basin simulation, such that the basin’s hydrograph was determined by the superposition of runoff generated by individual cells in a raster-based discretization. In real time updating of RR model by GLUE method, prior and posterior likelihoods were computed using forecast errors that were obtained from the results of behavioral models and real time recorded discharges. Then, prior and posterior likelihoods were applied to modify forecast confidence limits in each time step. Calibration of parameters was performed using historical data while distribution of parameters was modified in real time based on new data records. Two scenarios of rainfall forecast including prefect-rainfall-forecast and no-rainfall-forecast were assumed in absence of a robust rainfall forecast model in the study catchment. The results demonstrated that GLUE application could offer an acceptable lead time for peak discharge forecast at the expense of high computational demand.     

Geophysical flows under location uncertainty,Part I Random transport and general models

A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction, an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.