Non-linear optimal multivariate spatial design using spatial vine copulas

A multivariate spatial sampling design that uses spatial vine copulas is presented that aims to simultaneously reduce the prediction uncertainty of multiple variables by selecting additional sampling locations based on the multivariate relationship between variables, the spatial configuration of existing locations and the values of the observations at those locations. Novel aspects of the methodology include the development of optimal designs that use spatial vine copulas to estimate prediction uncertainty and, additionally, use transformation methods for dimension reduction to model multivariate spatial dependence. Spatial vine copulas capture non-linear spatial dependence within variables, whilst a chained transformation that uses non-linear principal component analysis captures the non-linear multivariate dependence between variables. The proposed design methodology is applied to two environmental case studies. Performance of the proposed methodology is evaluated through partial redesigns of the original spatial designs. The first application is a soil contamination example that demonstrates the ability of the proposed methodology to address spatial non-linearity in the data. The second application is a forest biomass study that highlights the strength of the methodology in incorporating non-linear multivariate dependence into the design.     

Assessment of change in design flood frequency under climate change using a multivariate downscaling model and a precipitation-runoff model

Precipitation and runoff are key elements in the hydrologic cycle because of their important roles in water supply, flood prevention, river restoration, and ecosystem management. Global climate change, widely accepted to be happening, is anticipated to have enormous consequences on future hydrologic patterns. Studies on the potential changes in global, regional, and local hydrologic patterns under global climate change scenarios have been an intense area of research in recent years. The present study contributes to this research topic through evaluation of design flood under climate change. The study utilizes a weather state-based, stochastic multivariate model as a conditional probability model for simulating the precipitation field. An important premise of this study is that large-scale climatic patterns serve as a major driver of persistent year-to-year changes in precipitation probabilities. Since uncertainty estimation in the study of climate change is needed to examine the reliability of the outcomes, this study also applies a Bayesian Markov chain Monte Carlo scheme to the widely used SAC-SMA (Sacramento soil moisture accounting) precipitation-runoff model. A case study is also performed with the Soyang Dam watershed in South Korea as the study basin. Finally, a comprehensive discussion on design flood under climate change is made.     

Aeolian sediment fingerprinting using a Bayesian mixing model

Identifying sand provenance in depositional aeolian environments (e.g. dunefields) can elucidate sediment pathways and fluxes, and inform potential land management strategies where windblown sand and dust is a hazard to health and infrastructure. However, the complexity of these pathways typically makes this a challenging proposition, and uncertainties on the composition of mixed‐source sediments are often not reported. This study demonstrates that a quantitative fingerprinting method within the Bayesian Markov Chain Monte Carlo (MCMC) framework offers great potential for exploring the provenance and uncertainties associated with aeolian sands. Eight samples were taken from dunes of the small (~58 km²) Ashkzar erg, central Iran, and 49 from three distinct potential sediment sources in the surrounding area. These were analyzed for 61 tracers including 53 geochemical elements (trace, major and rare earth elements (REE)) and eight REE ratios. Kruskal–Wallis H‐tests and stepwise discriminant function analysis (DFA) allowed the identification of an optimum composite fingerprint based on six tracers (Rb, Sr, ⁸⁷Sr, (La/Yb)_n, Ga and δCe), and a Bayesian mixing model was applied to derive the source apportionment estimates within an uncertainty framework. There is substantial variation in the uncertainties in the fingerprinting results, with some samples yielding clear discrimination of components, and some with less clear fingerprints. Quaternary terraces and fans contribute the largest component to the dunes, but they are also the most extensive surrounding unit; clay flats and marls, however, contribute out of proportion to their small outcrop extent. The successful application of these methods to aeolian sediment deposits demonstrates their potential for providing quantitative estimates of aeolian sediment provenances in other mixed‐source arid settings, and may prove especially beneficial where sediment is derived from multiple sources, or where other methods of provenance (e.g. detrital zircon U–Pb dating) are not possible due to mineralogical constraints. Copyright © 2017 John Wiley & Sons, Ltd.     

Simulation of broadband seismic ground motions at dam canyons by using a deterministic numerical approach

As a deterministic numerical approach for simulation of earthquake ground motions, the spectral element method (SEM) is applied to generate a broadband acceleration array for dam-canyons instead of the traditional empirical or stochastic methods. Specifically, the SEM analysis model with an extra fine mesh is used for the Pacoima Canyon to simulate the entire path starting from earthquake source rupture via the propagation medium to the local site. The source and the 3D earth model (velocity structure) are validated through the modeling of the Newhall earthquake on 28 October 2012 at a frequency of up to 8 Hz. Subsequently, the San Fernando earthquake records on 13 January 2001 are further used to study the effects of propagation path in simulation. Finally, the spatially varying ground motions at the Pacoima Canyon are obtained for different source mechanisms. The results show that the source mechanism and the local site topography significantly affect the distribution of the peak accelerations along the canyon.     

A simple model of a phreatic surface through an earth dam

A simple numerical model for estimating a phreatic surface in an earthen dam is presented. The numerical approach is based upon the Complex Variable Boundary Element Method (CVBEM). By expanding the CVBEM approximation geometric functions into a first order Taylor series, the unknown phreatic surface location geometrics can be approximated without iteration by solving a single matrix system. The developed technique provides for the numerical solution of the inverse problem of locating the phreatic surface coordinates. A comparison of results produced from this simple approach to results produced from a finite element analog and an iterative CVBEM analog for an example problem is presented.     

Prediction efficiency in an avalanche model for different target events

The avalanche formation model has much in common with the formation of earthquakes [Bak and Tang, 1989]. A well-known modification of this model is studied and predictability of the strongest events is demonstrated. The prediction efficiency increases with the size of target events. In particular, 75% of strong events are predicted for a fixed size if an alarm lasts for one-third of the observation time.     

有缝重力坝动力非线性数值计算模型及其应用

对于有缝重力坝的分析，基于连续介质力学的界面单元-有限元方法难于比较精确地模拟缝间的接触应力，从而无法合理地估算坝体应力与变形。作者对于多体系统和分区连续介质所发展的非连续变形计算力学模型能够根据接触界面的本构特性及其力学和运动学约束条件精确地再现受力过程中界面相互作用力的传递与非连续变形状态，本文将其应用于有缝重力坝的动力分析。实例数值分析表明该模型的计算结果从定性上讲是合理的，并且为判断坝体缝隙的工作状态与界面应力提供了有力的依据。     

Mercury dynamic simulation of Minamata Bay by using a three-dimensional numerical model

Ocean Dynamics - Residual mercury dynamic has been the research emphasis since mercury contamination was publicly recognized in Minamata Bay. Simulation of mercury distribution and transport...     

Optimization of the Sefid-Roud Dam desiltation process using a sophisticated one-dimensional numerical model

Although water and soil conservation activities reduce reservoir sedimentation, it is inevitable that reservoirs fed by rivers transporting high amounts of sediment will experience sedimentation. The Ghezel-Ozan and Shah-Roud rivers, which flow to the Sefld-Roud reservoir dam, are both highly sediment-laden and transport significant amounts of sediment in both bed load and suspended load forms to the reservoir. Hence, it seems that the only practical way to remove the sediment from the reservoir is to flush it out using the Chasse method. In the present paper, field measurements of Chasse operation characteristics taken in previous years are presented, and a numerical model that simulates this process is introduced. After calibrating the model using field measured data, the calculated results （for reservoir pressure flushing and released sediment volume） of the numerical model were compared with other measured data for the same Chasse operation and the results agree well. Finally, using the numerical simulation results, the best approaches to ensure highly effective flushing while conserving reservoir water are presented （at least for the Sefid-Roud dam）. The operation of the bottom outlet gates, the shape of the output hydrograph, and the reservoir water level variation during flushing were optimized. In addition, the numerical model and related parameters, which need to be calibrated, are discussed.     

A numerical study of the string function using a primitive equation ocean model

Abstract

We use results from a primitive-equation ocean numerical model (SCRUM) to test a theoretical 'string function' formulation put forward by Tyler and Käse in another article in this issue. The string function acts as a stream function for the large-scale potential energy flow under the combined beta and topographic effects. The model results verify that large-scale anomalies propagate along the string function contours with a speed correctly given by the cross-string gradient. For anomalies having a scale similar to the Rossby radius, material rates of change in the layer mass following the string velocity are balanced by material rates of change in relative vorticity following the flow velocity. It is shown that large-amplitude anomalies can be generated when wind stress is resonant with the string function configuration.     

Bayesian stochastic modelling for avalanche predetermination: from a general system framework to return period computations

Stochastic models are recent but unavoidable tools for snow avalanche hazard mapping that can be described in a general system framework. For the computation of design return periods, magnitude and frequency have to be evaluated. The magnitude model consists of a set of physical equations for avalanche propagation associated with a statistical formalism adapted to the input–output data structure. The friction law includes at least one latent friction coefficient. The Bayesian paradigm and the associated simulation techniques assist considerably in performing the inference and taking estimation errors into account for prediction. Starting from the general case, simplifying hypotheses allows computing the predictive distribution of high return periods on a case-study. Only release and runout altitudes are considered so that the model can use the French database. An inversible propagation model makes it possible to work with the latent friction coefficient as if it is observed. Prior knowledge is borrowed from an avalanche path with similar topographical characteristics. Justifications for the working hypotheses and further developments are discussed. In particular, the whole approach is positioned with respect to both deterministic and stochastic hydrology.     

A depth-averaged tidal numerical model using non-orthogonal curvilinear co-ordinates

The two-dimensional shallow-water equations are developed for non-orthogonal curvilinear co-ordinates, in terms of the local deviations of the mesh from east and north. The equations are discretised and applied to a numerical model of tides in the Menai Strait in north Wales. The mesh is designed partially to fit the coastline and deep channels in the domain. After calibration, the model produces results which correspond well with measurements. This research was carried out while on sabbatical leave from University of Plymouth.     

Response of an arch dam to non-uniform excitation generated by a seismic wave scattering model

Non-uniform ground motions are generated based on a single record available at a site and seismic wave scattering analysis. The Chino Hills 2008 earthquake records at the Pacoima Dam site are used to indicate the accuracy of the method. Dynamic analysis of the Pacoima dam-reservoir-foundation under uniform and non-uniform ground motions is carried out using the EACD-3D2008 software, and the results are compared to recorded responses at different locations on the dam. There is good agreement between computed and recorded displacements of the dam for non-uniform excitation. For uniform excitation, the displacements are underestimated in comparison with those obtained from recorded excitation. Significant intensification of stresses, especially near the foundation, and different patterns of stress distribution are observed for non-uniform excitation in comparison with uniform excitation. For uniform excitation maximum stresses occur in the crown cantilever near the crest, but for non-uniform excitation the maximum stresses occur along the sides and near the foundation.     

Likelihood-free simulation-based optimal design with an application to spatial extremes

In this paper we employ a novel method to find the optimal design for problems where the likelihood is not available analytically, but simulation from the likelihood is feasible. To approximate the expected utility we make use of approximate Bayesian computation methods. We detail the approach for a model on spatial extremes, where the goal is to find the optimal design for efficiently estimating the parameters determining the dependence structure. The method is applied to determine the optimal design of weather stations for modeling maximum annual summer temperatures.     

Analysis of the positive ionospheric response to a moderate geomagnetic storm using a global numerical model

Current theories of F-layer storms are discussed using numerical simulations with the Upper Atmosphere Model, a global self-consistent, time dependent numerical model of the thermosphere-ionosphere-plasmasphere-magnetosphere system including electrodynamical coupling effects. A case study of a moderate geomagnetic storm at low solar activity during the northern winter solstice exemplifies the complex storm phenomena. The study focuses on positive ionospheric storm effects in relation to thermospheric disturbances in general and thermospheric composition changes in particular. It investigates the dynamical effects of both neutral meridional winds and electric fields caused by the disturbance dynamo effect. The penetration of short-time electric fields of magnetospheric origin during storm intensification phases is shown for the first time in this model study. Comparisons of the calculated thermospheric composition changes with satellite observations of AE-C and ESRO-4 during storm time show a good agreement. The empirical MSISE90 model, however, is less consistent with the simulations. It does not show the equatorward propagation of the disturbances and predicts that they have a gentler latitudinal gradient. Both theoretical and experimental data reveal that although the ratio of [O]/[N₂] at high latitudes decreases significantly during the magnetic storm compared with the quiet time level, at mid to low latitudes it does not increase (at fixed altitudes) above the quiet reference level. Meanwhile, the ionospheric storm is positive there. We conclude that the positive phase of the ionospheric storm is mainly due to uplifting of ionospheric F2-region plasma at mid latitudes and its equatorward movement at low latitudes along geomagnetic field lines caused by large-scale neutral wind circulation and the passage of travelling atmospheric disturbances (TADs). The calculated zonal electric field disturbances also help to create the positive ionospheric disturbances both at middle and low latitudes. Minor contributions arise from the general density enhancement of all constituents during geomagnetic storms, which favours ion production processes above ion losses at fixed height under day-light conditions.     

Vibration tests and analysis of a model arch dam

Vibration tests were conducted on a 1/24-scale model of the North Fork Dam, a double-curvature arch dam, to determine natural frequencies, mode shapes and hydrodynamic pressures. The mode shapes and natural frequencies were determined from tests using two vibrators mounted on the crest of the dam. Hydrodynamic pressures at the dam/reservoir interface were determined from tests in which the vibrator was attached to the downstream foundation of the dam. The hydrodynamic pressures calculated using Westergaard's theory and a theory for arch dams developed by Perumalswami and Kar accurately predicted the measured pressure at frequencies below the first mode frequency of the dam. The differences in the two theories were insignificant. The Structural Analysis Program (SAP), a linear three-dimensional (3-D) finite element code, was used to compute mode shapes and frequencies for the dam with its base fixed and with a foundation. Numerical solution schemes used in the finite element analysis consisted of a Ritz analysis and a subspace iteration method. Calculations were conducted for both full and empty reservoir conditions. The accuracy of the Ritz analysis improved considerably as more nodes in flexible regions of the dam were loaded. However, the lowest eigenvalues were computed using the subspace iteration method. For the full reservoir, the natural frequencies decreased by 20-30 per cent when the foundation was included in the finite element model. The difference was less when the reservoir was empty. The calculations using the subspace iteration scheme and including the foundation agreed closely with experimental mode shapes and corresponding natural frequencies.     

Probabilistic reservoir operation using Bayesian stochastic model and support vector machine

Available water resources are often not sufficient or too polluted to satisfy the needs of all water users. Therefore, allocating water to meet water demands with better quality is a major challenge in reservoir operation. In this paper, a methodology to develop operating strategies for water release from a reservoir with acceptable quality and quantity is presented. The proposed model includes a genetic algorithm (GA)-based optimization model linked with a reservoir water quality simulation model. The objective function of the optimization model is based on the Nash bargaining theory to maximize the reliability of supplying the downstream demands with acceptable quality, maintaining a high reservoir storage level, and preventing quality degradation of the reservoir. In order to reduce the run time of the GA-based optimization model, the main optimization model is divided into a stochastic and a deterministic optimization model for reservoir operation considering water quality issues.The operating policies resulted from the reservoir operation model with the water quantity objective are used to determine the released water ranges (permissible lower and upper bounds of release policies) during the planning horizon. Then, certain values of release and the optimal releases from each reservoir outlet are determined utilizing the optimization model with water quality objectives. The support vector machine (SVM) model is used to generate the operating rules for the selective withdrawal from the reservoir for real-time operation. The results show that the SVM model can be effectively used in determining water release from the reservoir. Finally, the copula function was used to estimate the joint probability of supplying the water demand with desirable quality as an evaluation index of the system reliability. The proposed method was applied to the Satarkhan reservoir in the north-western part of Iran. The results of the proposed models are compared with the alternative models. The results show that the proposed models could be used as effective tools in reservoir operation.     

A multivariate gamma distribution arising from a Markov model

A Markov chain{X _t }, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX _t+1 givenX _t =x _t , which is assumed to be of the exponential formH()exp{-G()x _t }. For appropriate choice ofH andG the marginal distribution ofX _t is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX _t +1,...,X _t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables.     

Modeling parametric uncertainty in optimal open channel design using FORM-PGSL coupled approach

Optimal design of artificial open channels is essential for the planning and management of irrigation projects. In this paper a modified formulation is presented for the comprehensive design of open channels considering the seepage loss, evaporation loss and land acquisition cost along with the lining and excavation cost. The resulting formulation is solved using a recent meta-heuristic optimization technique namely probabilistic global search Lausanne (PGSL). The uncertainty associated with channel design parameter may lead to the failure of canals (channels). The parametric uncertainty in open channel design is modeled using first order reliability method (FORM). A bi-objective optimization model is presented in the study which minimizes the cost and minimizes the probability of overtopping considering a probabilistic cost function as the objective function. A new approach is proposed to solve the model in a meta-heuristic environment following PGSL as the solution method. Also a chance constrained optimization model which considers overtopping probability constraint and channel capacity constraint simultaneously along with the objective of minimization of cost is propounded and solved using PGSL. The solutions obtained using coupled FORM-PGSL approach is encouraging and the method can be used for optimal and reliable design of artificial open channels.