Review On The Calculation Of Surface Electric And Magnetic Fields And Of Geomagnetically Induced Currents In Ground-Based Technological Systems

Space weather is a popular and important research topic today. Its origin isin the Sun. Space weather effects extend to the surface of the Earth where theyare usually called GIC referring to geomagnetically induced currents intechnological systems such as electric power transmission grids, oil and gaspipelines, telecommunication cables and railway equipment. GIC are a possiblesource of problems within such systems, and observations have been made sincethe first telegraph systems in the 1800's. This paper is a summary and reviewof present knowledge and of possibilities of modelling GIC in a system.Modelling efforts require a determination of the electric field occurring inconnection with a magnetic storm at the Earth's surface and a calculation ofthe resulting GIC. Different modelling techniques of the electric and magneticfields are evaluated in this paper, and special attention is paid to thecomplex image method (CIM) which is suitable for time-critical purposes likeforecasting of GIC. A discretely-earthed power system and a buried pipelineneed different calculation methods of GIC. The former can be treated by amatrix formalism while the distributed-source transmission line (DSTL) theoryis applicable to the latter.     

Fundamentals about the flow of geomagnetically induced currents in a power system applicable to estimating space weather risks and designing remedies

Geomagnetically induced currents (GIC) in technological systems, like electric power transmission grids, at the Earth's surface are caused by space weather processes, whose origin is in the Sun. In power systems, transformers may be saturated due to GIC leading to different problems extending from an increase of harmonics to a blackout of the system and damage of transformers. To design reasonable measures against impending problems, GIC magnitudes in the network should be estimated in different circumstances. This paper tackles basic features of GIC flow in a fictitious five-transformer/four-line power system, which is simple enough to make the equations easily manageable but complex enough to yield real and usable information. It is shown that the direction of the geoelectric field affects GIC at different sites but the dependence is not straightforward since GIC produced in one part of the system flows to others. Generally, transmission lines experience much larger GIC than transformers. Series capacitors in transmission lines prevent the flow of dc-like GIC but, without a careful analysis, their installation may result in larger GIC at some transformers of the system thus increasing the risk of problems.     

地磁感应电流（GIC）的作用与评估

地磁感应电流（GIC）可能对各种人工长距离导电体造成影响与危害.地磁扰动产生的感应电场的强度与地磁场强度、地下电阻率结构相关，在导电系统内生成的GIC的强度则同时与导电系统的内在结构有关.计算了加拿大Manitoba省三个典型地区在2000年7月15日的一个强烈磁暴期间产生的感应电场.通过对地磁活动性的统计分析，估计加拿大魁北克电网可能经受的最大GIC达每相78A（一年一次）和234A（每十年一次）.     

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with M being a positive integer for regular grids are discussed and illustrated by constructing the second order (M = 1) and the fourth order (M = 2) recursion formulas.     

Recordings and occurrence of geomagnetically induced currents in the Finnish natural gas pipeline network

A project implemented to study the effects of space weather on the Finnish natural gas pipeline was started in August 1998. The aims of the project were (1) to derive a model for calculating geomagnetically induced currents (GIC) and pipe-to-soil (P/S) voltages in the Finnish natural gas pipeline, (2) to perform measurements of GIC and P/S voltages in the pipeline and (3) to derive statistical predictions for the occurrences of GIC and P/S voltages at different locations in the pipeline network.GIC and P/S voltage were recorded at a compressor station. The GIC measurement was made with two magnetometers, one right above the pipe, and another at the Nurmijärvi Geophysical Observatory about 30 km southwest. The largest GIC since November 1998 has been 30 A. The P/S voltage recording was stopped in May 1999, but GIC is still measured.GIC statistics were derived based on the recordings of the geomagnetic field at Nurmijärvi. The geoelectric field was calculated by using the plane wave model. This field was input to the general pipeline model resulting in the distribution of currents and P/S voltages at selected points in the pipeline. As could be expected, the largest P/S voltage variations occur at the ends of the pipeline network, while the largest GIC flow in the middle parts.     

Geomagnetically induced currents in the Finnish high-voltage power system

We consider geomagnetically induced currents (GICs) in power systems from the viewpoint of a geophysicist. Special attention is paid to the Finnish high-voltage power system, in which exact theoretical model calculations together with recordings have been performed for several years. We present several examples of theoretically computed GICs using different geophysical models for estimating the geoelectric field driving GICs. Statistical prediction of GICs is outlined referring to studies made in Finland. We show that a combination of GIC recordings at few sites with theoretical modelling of ionospheric currents and the earth's conductivity, and data of geomagnetic activity makes it possible to derive GIC statistics of the entire power system. Finally, we discuss requirements for a long-range prediction of GICs, which will obviously be a widely-studied topic in future.     

Modelling of space weather effects on pipelines

The interaction between the solar wind and the Earth's magnetic field produces time varying currents in the ionosphere and magnetosphere. The currents cause variations of the geomagnetic field at the surface of the earth and induce an electric field which drives currents in oil and gas pipelines and other long conductors. Geomagnetically induced currents (GIC) interfere with electrical surveys of pipelines and possibly contribute to pipeline corrosion.In this paper, we introduce a general method which can be used to determine voltage and current profiles for buried pipelines, when the external geoelectric field and the geometry and electromagnetic properties of the pipeline are known. The method is based on the analogy between pipelines and transmission lines, which makes it possible to use the distributed source transmission line (DSTL) theory. The general equations derived for the current and voltage profiles are applied in special cases. A particular attention is paid to the Finnish natural gas pipeline network.This paper, related to a project about GIC in the Finnish pipeline, thus provides a tool for understanding space weather effects on pipelines. Combined with methods of calculating the geoelectric field during magnetic storms, the results are applicable to forecasting of geomagnetically induced currents and voltages on pipelines in the future.     

华北地区地电暴时GIC及涡旋电流响应分析

通过地电场台址近地表介质电阻率和地电场值计算大地电流,从大地电流场中分离出涡旋电流;根据平面波理论和水平导电层模型,使用地磁暴观测数据在频率域计算地磁感应电场(GIE),由GIE计算地磁暴感应电流(GIC).计算结果与实测值对比分析表明:GIE计算结果与实测地电暴具有很好的相位一致性;GIC涡旋中心相对地电暴涡旋中心存在向SE漂移约3°的现象;磁暴时地磁场Z分量的幅值分布图中极大值区域与涡旋中心重合,可能是GIC涡旋中心偏移的原因.另外,根据电磁感应原理提出的等效环电流模型,在一定程度上解释了涡旋大地电流的形成机制.本项工作可应用于地磁观测与地电观测的相互校正,同时有助于认识地电暴对大地电流分布的影响.     

中国广东电网的几次强磁暴影响事件

2001年以来,随着我国阳\|淮系统等多条500 kV长距离线路的相继建成投运,江苏上河、广东岭澳等地变压器多次发现不明原因的强烈振动和噪声增大事件.本文通过对2004年11月以来、十几次磁暴地磁数据与变压器中性点实测电流数据的比较,证明了干扰事件是磁暴在电网产生的地磁感应电流（GIC）所为;其中,2004年11月7日和10日磁暴在岭澳核电站引发的GIC最大值为47A和55.8A,大于直流输电单极运行时变压器中性点的直流电流水平,因此磁暴对岭澳核电站的瞬时影响比直流输电的影响大;监测数据表明广东电网的GIC水平高于阳淮输电系统的水平,初步分析认为与电网结构和海岸效应等因素有关.目前,举世瞩目的1000 kV特高压工程已开工建设,特高压线路的单位电阻最多是500 kV的二分之一,并且线路更长、规划规模大、且变压器采用单相变压器组结构,磁暴影响问题迫切需要研究.     

电网磁暴灾害风险影响因素研究综述

磁暴是源自太阳磁场剧烈变化的地球空间效应,随着电网规模的增大和电压等级的增高,磁暴灾害已经成为诱发电网故障风险的威胁之一.研究电力系统磁暴灾害风险的影响因素可为预防与控制其引发的电网事故提供重要参考.在分析历史典型磁暴事件的基础上,剖析了磁暴诱发电力系统故障的机理,阐述了故障传播与电力系统响应的过程,总结了近年来关于影响电力系统的地磁感应电流水平及其产生的变压器无功损耗方面的研究成果,从磁暴本身的特点和电力系统的参数与结构两方面将影响因素分类.以GIC标准模型,通过改变磁暴扰动环境和电力系统参数,说明了各因素对电网磁暴灾害风险的影响程度,并比较了不同因素影响后果的差异,最后指出了尚未解决的问题和可能的研究方向.     

大地电导率横向突变处磁暴感应地电场的邻近效应

大地电性结构的横向变化会对磁暴时的感应地电流和地面电磁场产生影响.本文假设扰动地磁场变化的源为地面以上一定高度的面电流,以某一典型层状大地电导率结构为基础,构造含有电导率横向突变的地电模型.针对感应电流的方向与横向分界面平行的情形,采用伽辽金有限元法对电导率横向突变处的感应地电场进行了分析,揭示了电导率横向差异产生的趋肤效应和邻近效应的机理,针对与电性结构分界面平行的输电线路,从评估地磁感应电流的角度讨论了影响的严重程度和范围.     

Using the pseudospectral technique on curved grids for 2D acoustic forward modelling1

The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non-physical diffractions by using curved grids that generally follow the interfaces. A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled. One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so-called multiblock strategy). The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space. The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods.     

A hybrid absorbing boundary condition for elastic staggered‐grid modelling

We recently proposed an efficient hybrid scheme to absorb boundary reflections for acoustic wave modelling that could attain nearly perfect absorptions. This scheme uses weighted averaging of wavefields in a transition area, between the inner area and the model boundaries. In this paper we report on the extension of this scheme to 2D elastic wave modelling with displacement‐stress formulations on staggered grids using explicit finite‐difference, pseudo‐implicit finite‐difference and pseudo‐spectral methods. Numerical modelling results of elastic wave equations with hybrid absorbing boundary conditions show great improvement for modelling stability and significant absorption for boundary reflections, compared with the conventional Higdon absorbing boundary conditions, demonstrating the effectiveness of this scheme for elastic wave modelling. The modelling results also show that the hybrid scheme works well in 2D rotated staggered‐grid modelling for isotropic medium, 2D staggered‐grid modelling for vertically transversely isotropic medium and 2D rotated staggered‐grid modelling for tilted transversely isotropic medium.     

The problem of scaling in grid-related hydrological process modelling

This article shows some important scaling aspects that exist in hydrological process grid modelling with GIS, with respect to selecting the optimal grid width. Hydrologically relevant space parameter fields should often be regarded as self-similar fractals for which certain invariance characteristics are applied. These characteristics are especially important if there is an extensive change in the model grid width. The self-similarity generates simple scaling laws, which can be used for rescaling procedures. © 1997 John Wiley & Sons, Ltd.     

Estimating reference evapotranspiration using numerical weather modelling

Evapotranspiration is an important hydrological process and its estimation usually needs measurements of many weather variables such as atmospheric pressure, wind speed, air temperature, net radiation and relative humidity. Those weather variables are not easily obtainable from in situ measurements in practical water resources projects. This study explored a potential application of downscaled global reanalysis weather data using mesoscale modelling system 5 (MM5). The MM5 is able to downscale the global data down to much finer resolutions in space and time for use in hydrological investigations. In this study, the ERA‐40 reanalysis data are downscaled to the Brue catchment in southwest England. The results are compared with the observation data. Among the studied weather variables, atmospheric pressure could be derived very accurately with less than 0·2% error. On the other hand, the error in wind speed is about 200–400%. The errors in other weather variables are air temperature (<10%), relative humidity (5–21%) and net radiation (4–23%). The downscaling process generally improves the data quality (except wind speed) and provides higher data resolution in comparison with the original reanalysis data. The evapotranspiration values estimated from the downscaled data are significantly overestimated across all the seasons (27–46%) based on the FAO Penman–Monteith equation. The dominant weather variables are net radiation (during the warm period) and relative humidity (during the cold period). There are clear patterns among some weather variables and they could be used to correct the biases in the downscaled data from either short‐term in situ measurements or through regionalization from surrounding weather stations. Artificial intelligence tools could be used to map the downscaled data directly into evapotranspiration or even river runoff if rainfall data are available. This study provides hydrologists with valuable information on downscaled weather variables and further exploration of this potentially valuable data source by the hydrological community should be encouraged. Copyright © 2010 John Wiley & Sons, Ltd.     

开展空间天气业务对广东社会经济的影响

通过对空间天气和空间天气学的描述,介绍空间天气学的研究内容、方法、监测手段以及空间天气灾害的危害;分析了在广东开展空间天气业务的必要性,并对如何开展广东空间天气业务提出建议。     

基于非规则双重网格的三维声波方程模拟

三维声波方程相比二维声波方程能够更好的模拟三维空间的地震波传播,模拟标量近似下的弹性波在三维复杂介质的传播过程.基于非规则网格的正演模拟方法的格子法可以处理很好的刻画起伏地表、速度间断面等复杂构造,但是这类方法需要大量的几何描述来描述网格.本文提出了三维六面体双重网格的格子法来模拟声波方程,一方面该方法继承了格子法能够灵活处理自由表面和速度间断面的特性.另一方面,该方法通过双重网格的实现极大的减少了几何描述文件的大小,可以最大的实现GPU加速,实现粗粒度并行,在节省了几何描述空间的同时达到了很高的加速比.     

2D finite-difference viscoelastic wave modelling including surface topography

We have pursued two-dimensional (2D) finite-difference (FD) modelling of seismic scattering from free-surface topography. Exact free-surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity–stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free-surface topography. The wave equations are numerically discretized by an eighth-order FD method on a staggered grid in space, and a leap-frog technique and the Crank–Nicholson method in time.
In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back-scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter-crust heterogeneities.     

Uncertainty estimation of a complex water quality model: The influence of Box–Cox transformation on Bayesian approaches and comparison with a non-Bayesian method

In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box–Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box–Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the residuals distribution. If residuals are not normally distributed, the uncertainty is over-estimated if Box–Cox transformation is not applied or non-calibrated parameter is used.