Estimating uncertainty associated with water stages from a single SAR image

It is the goal of remote sensing to infer information about objects or a natural process from a remote location. This invokes that uncertainty in measurement should be viewed as central to remote sensing. In this study, the uncertainty associated with water stages derived from a single SAR image for the Alzette (G.D. of Luxembourg) 2003 flood is assessed using a stepped GLUE procedure. Main uncertain input factors to the SAR processing chain for estimating water stages include geolocation accuracy, spatial filter window size, image thresholding value, DEM vertical precision and the number of river cross sections at which water stages are estimated. Initial results show that even with plausible parameter values uncertainty in water stages over the entire river reach is 2.8 m on average. Adding spatially distributed field water stages to the GLUE analysis following a one-at-a-time approach helps to considerably reduce SAR water stage uncertainty (0.6 m on average) thereby identifying appropriate value ranges for each uncertain SAR water stage processing factor. For the GLUE analysis a Nash-like efficiency criterion adapted to spatial data is proposed whereby acceptable SAR model simulations are required to outperform a simpler regression model based on the field-surveyed average river bed gradient. Weighted CDFs for all factors based on the proposed efficiency criterion allow the generation of reliable uncertainty quantile ranges and 2D maps that show the uncertainty associated with SAR-derived water stages. The stepped GLUE procedure demonstrated that not all field data collected are necessary to achieve maximum constraining. A possible efficient way to decide on relevant locations at which to sample in the field is proposed. It is also suggested that the resulting uncertainty ranges and flood extent or depth maps may be used to evaluate 1D or 2D flood inundation models in terms of water stages, depths or extents. For this, the extended GLUE approach, which copes with the presence of uncertainty in the observed data, may be adopted.     

Issues in characterizing heterogeneity and connectivity in non-multiGaussian media

The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.     

Truncation of the distribution of ground-motion residuals

Recent studies to assess very long-term seismic hazard in the USA and in Europe have highlighted the importance of the upper tail of the ground-motion distribution at the very low annual frequencies of exceedance required by these projects. In particular, the use of an unbounded lognormal distribution to represent the aleatory variability of ground motions leads to very high and potentially unphysical estimates of the expected level of shaking. Current practice in seismic hazard analysis consists of truncating the ground-motion distribution at a fixed number (ε _max) of standard deviations (σ). However, there is a general lack of consensus regarding the truncation level to adopt. This paper investigates whether a physical basis for choosing ε _max can be found, by examining records with large positive residuals from the dataset used to derive one of the ground-motion models of the Next Generation Attenuation (NGA) project. In particular, interpretations of the selected records in terms of causative physical mechanisms are reviewed. This leads to the conclusion that even in well-documented cases, it is not possible to establish a robust correlation between specific physical mechanisms and large values of the residuals, and thus obtain direct physical constraints on ε _max. Alternative approaches based on absolute levels of ground motion and numerical simulations are discussed. However, the choice of ε _max is likely to remain a matter of judgment for the foreseeable future, in view of the large epistemic uncertainties associated with these alternatives. Additional issues arise from the coupling between ε _max and σ, which causes the truncation level in terms of absolute ground motion to be dependent on the predictive equation used. Furthermore, the absolute truncation level implied by ε _max will also be affected if σ is reduced significantly. These factors contribute to rendering a truncation scheme based on a single ε _max value impractical.     

Assessment of long-term variation in displacement for a GPS site adjacent to a transition zone between collision and subduction

A transition and subduction zone adjacent to the Ryukyu Arc, Ryukyu Trench, and Okinawa Trough, extends between southern Japan and northeastern Taiwan. It is generated during the northwestward subduction of the Philippine Sea Plate, which lies the Eurasian Plate along the Ryukyu Trench. The movement of the Philippine Sea Plate is hindered at the northeastern corner of Taiwan, which causes complicated structure of the Philippine Sea Plate at the western end of the Ryukyu subduction zone. Development of the active subduction and transition boundary near the western Ryukyu Arc is evaluated statistically by using displacements derived from GPS site data. The statistical model shows that the absolute displacement derived from GPS measurements of nearly 8 years indicates a maximum spatial variation of 0.625 m. Three trends are observed for such long-term progress, and use of linear regression also reveals quite good consistency between the data and statistic models. Such rate is also elevated following the trend development. Southeastern and nearly horizontal movement is suggested to the main development of for the site movements, it is likely related to the tensional activity adjacent to this boundary.     

Strong motion uncertainty determined from observed records by dense network in Japan

The variation of ground motions at specific stations from events in six narrow areas was inspected by using K-NET and KiK-net records. A source-area factor for individual observation stations was calculated by averaging ratios between observed values for horizontal peak acceleration and velocity, as well as acceleration response spectra for 5% damping, and predicted values using a ground-motion model (usually known as an attenuation relation) by Kanno et al. (Bull Seismol Soc Am, 96:879–897, 2006). Standard deviations between observed and predicted amplitudes after the correction factor are less than 0.2 on the logarithmic scale and decrease down to around 0.15 in the short-period range. Intra-event standard deviation clearly increases with decreasing distance due to differing paths around near source area. Standard deviations may increase with amplitude or decrease with magnitude; however, both amplitude and magnitude of the data are strongly correlated with distance. The standard deviation calculated in this study is obviously much smaller than that of the original ground-motion model, as epistemic uncertainties are minimized by grouping ground motions at specific stations. This result indicates that the accuracy of strong ground motion prediction could be improved if ground-motion models for specified region are determined individually. For this to be possible, it is necessary to have dense strong-motion networks in high-seismicity regions, such as K-NET and KiK-net.     

Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models

This paper concerns efficient uncertainty quantification techniques in inverse problems for Richards’ equation which use coarse-scale simulation models. We consider the problem of determining saturated hydraulic conductivity fields conditioned to some integrated response. We use a stochastic parameterization of the saturated hydraulic conductivity and sample using Markov chain Monte Carlo methods (MCMC). The main advantage of the method presented in this paper is the use of multiscale methods within an MCMC method based on Langevin diffusion. Additionally, we discuss techniques to combine multiscale methods with stochastic solution techniques, specifically sparse grid collocation methods. We show that the proposed algorithms dramatically reduce the computational cost associated with traditional Langevin MCMC methods while providing similar sampling performance.     

2008年5月12日汶川地震谱震级及相关问题研究(英文)

基于P波和S波的谱震级特征对汶川地震进行了定量研究,可以看出P波和S波的最大谱震级出现在不同的周期上。对这一现象的构造物理意义进行了讨论,推测相对于P波而言,地震发生期间辐射的S波能量来自异常大的震源体积。选择部分全球地震的谱特征为背景,对汶川地震的体波谱震级特征进行了分析,结论是汶川地震的特征与其所处的周边环境是一致的。     

Uncertainty propagation of hydrodispersive transfer in an aquifer: an illustration of one-dimensional contaminant transport with slug injection

It is evident that the hydrodynamic dispersion coefficient and linear flow velocity dominate solute transport in aquifers. Both of them play important roles characterizing contaminant transport. However, by definition, the parameter of contaminant transport cannot be measured directly. For most problems of contaminant transport, a conceptual model for solute transport generally is established to fit the breakthrough curve obtained from field testing, and then suitable curve matching or the inverse solution of a theoretical model is used to determine the parameter. This study presents a one-dimensional solute transport problem for slug injection. Differential analysis is used to analyze uncertainty propagation, which is described by the variance and mean. The uncertainties of linear velocity and hydrodynamic dispersion coefficient are, respectively, characterized by the second-power and fourth-power of the length scale multiplied by a lumped relationship of variance and covariance of system parameters, i.e. the Peclet number and arrival time of maximum concentration. To validate the applicability for evaluating variance propagation in one-dimensional solute transport, two cases using field data are presented to demonstrate how parametric uncertainty can be caught depending on the manner of sampling.     

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.     

A naive uncertainty model for measuring operational risks faced by financial institutions

When insufficient data are available for measuring operational risk faced by a financial institute, most of the models depending on the probability theory are failure. Differing from that we use a probability distribution to depict random uncertainty, in this paper we use a number to represent the naive uncertainty in a phase serving for operational risk identification. The simplest form of the naive uncertainty model for measuring operational risk with multiple phases is the weighted mean with the uncertainties. It is also valid when we have a rough judgment for the uncertainties with intervals or fuzzy values. In this paper, we give a calculation case in lending operational risk to demonstrate the model validity.