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Methodology for time-domain estimation of storm time geoelectric fields using the 3-D magnetotelluric response tensors

Geoelectric fields at the Earth's surface caused by magnetic storms constitute a hazard to the operation of electric power grids and related infrastructure. The ability to estimate these geoelectric fields in close to real time and provide local predictions would better equip the industry to mitigate negative impacts on their operations. Here we report progress toward this goal: development of robust algorithms that convolve a magnetic storm time series with a frequency domain impedance for a realistic three-dimensional (3-D) Earth, to estimate the local, storm time geoelectric field. Both frequency domain and time domain approaches are presented and validated against storm time geoelectric field data measured in Japan. The methods are then compared in the context of a real-time application.

Space Weather

Down to Earth with an electric hazard from space

In reaching across traditional disciplinary boundaries, solid-Earth geophysicists and space physicists are forging new collaborations to map magnetic-storm hazards for electric-power grids. Future progress in evaluation storm time geoelectric hazards will come primarily through monitoring, surveys, and modeling of related data.

Space Weather

Calculation of voltages in electric power transmission lines during historic geomagnetic storms: An investigation using realistic earth impedances

Commonly, one-dimensional (1-D) Earth impedances have been used to calculate the voltages induced across electric power transmission lines during geomagnetic storms under the assumption that much of the three-dimensional structure of the Earth gets smoothed when integrating along power transmission lines. We calculate the voltage across power transmission lines in the mid-Atlantic region with both regional 1-D impedances and 64 empirical 3-D impedances obtained from a magnetotelluric survey. The use of 3-D impedances produces substantially more spatial variance in the calculated voltages, with the voltages being more than an order of magnitude different, both higher and lower, than the voltages calculated utilizing regional 1-D impedances. During the March 1989 geomagnetic storm 62 transmission lines exceed 100 V when utilizing empirical 3-D impedances, whereas 16 transmission lines exceed 100 V when utilizing regional 1-D impedances. This demonstrates the importance of using realistic impedances to understand and quantify the impact that a geomagnetic storm has on power grids.

Space Weather

The electric storm of November 1882

In November 1882, an intense magnetic storm related to a large sunspot group caused widespread interference to telegraph and telephone systems and provided spectacular and unusual auroral displays. The (ring current) storm time disturbance index for this storm reached maximum − Dst ≈ 386 nT, comparable to Halloween storm of 29–31 October 2003, but from 17 to 20 November the aa midlatitude geomagnetic disturbance index averaged 214.25 nT, the highest 4 day level of disturbance since the beginning of aa index in 1868. This storm contributed to scientists' understanding of the reality of solar‐terrestrial interaction. Past occurrences of magnetic storms, like that of November 1882, can inform modern evaluations of the deleterious effects that a magnetic superstorm might have on technological systems of importance to society.

Space Weather

Geospace environment modeling 2008--2009 challenge: D st index

This paper reports the metrics-based results of the D st index part of the 2008–2009 GEM Metrics Challenge. The 2008–2009 GEM Metrics Challenge asked modelers to submit results for four geomagnetic storm events and five different types of observations that can be modeled by statistical, climatological or physics-based models of the magnetosphere-ionosphere system. We present the results of 30 model settings that were run at the Community Coordinated Modeling Center and at the institutions of various modelers for these events. To measure the performance of each of the models against the observations, we use comparisons of 1 hour averaged model data with the D st index issued by the World Data Center for Geomagnetism, Kyoto, Japan, and direct comparison of 1 minute model data with the 1 minute D st index calculated by the United States Geological Survey. The latter index can be used to calculate spectral variability of model outputs in comparison to the index. We find that model rankings vary widely by skill score used. None of the models consistently perform best for all events. We find that empirical models perform well in general. Magnetohydrodynamics-based models of the global magnetosphere with inner magnetosphere physics (ring current model) included and stand-alone ring current models with properly defined boundary conditions perform well and are able to match or surpass results from empirical models. Unlike in similar studies, the statistical models used in this study found their challenge in the weakest events rather than the strongest events.

Space Weather

Surface electric fields for North America during historical geomagnetic storms

To better understand the impact of geomagnetic disturbances on the electric grid, we recreate surface electric fields from two historical geomagnetic storms—the 1989 “Quebec” storm and the 2003 “Halloween” storms. Using the Spherical Elementary Current Systems method, we interpolate sparsely distributed magnetometer data across North America. We find good agreement between the measured and interpolated data, with larger RMS deviations at higher latitudes corresponding to larger magnetic field variations. The interpolated magnetic field data are combined with surface impedances for 25 unique physiographic regions from the United States Geological Survey and literature to estimate the horizontal, orthogonal surface electric fields in 1 min time steps. The induced horizontal electric field strongly depends on the local surface impedance, resulting in surprisingly strong electric field amplitudes along the Atlantic and Gulf Coast. The relative peak electric field amplitude of each physiographic region, normalized to the value in the Interior Plains region, varies by a factor of 2 for different input magnetic field time series. The order of peak electric field amplitudes (largest to smallest), however, does not depend much on the input. These results suggest that regions at lower magnetic latitudes with high ground resistivities are also at risk from the effect of geomagnetically induced currents. The historical electric field time series are useful for estimating the flow of the induced currents through long transmission lines to study power flow and grid stability during geomagnetic disturbances.

Space Weather

Statistical modeling of storm level Kp occurrences: Solar cycle modulation

We consider the nonstationary, statistical modeling of the occurrence in time of large Kp geomagnetic storms over the course of multiple solar cycles. Previous work showed that wait times between storms can be represented by an exponential density function, consistent with the realization of a Poisson process. Here we also assume a Poisson process, but to account for solar cycle modulation of storm likelihood, we assume an occurrence rate given by a parametric constant plus a simple sinusoidal function of time. Parameter estimation is accomplished using maximum likelihood, yielding good fits to the Kp data. We find that the relative phase between storms and sunspots depends on storm size. We quantify previous observations that small storms tend to occur during the declining phase of the solar cycle, while large storms tend to occur very close to solar maximum. We predict average wait time between storms and the storm occurrence rate up through the year 2018.

Space Weather

Movie‐maps of low‐latitude magnetic storm disturbance

We present 29 movie‐maps of low‐latitude horizontal‐intensity magnetic disturbance for the years 1999–2006: 28 recording magnetic storms and 1 magnetically quiescent period. The movie‐maps are derived from magnetic vector time series data collected at up to 25 ground‐based observatories. Using a technique similar to that used in the calculation of Dst , a quiet time baseline is subtracted from the time series from each observatory. The remaining disturbance time series are shown in a polar coordinate system that accommodates both Earth rotation and the universal time dependence of magnetospheric disturbance. Each magnetic storm recorded in the movie‐maps is different. While some standard interpretations about the storm time equatorial ring current appear to apply to certain moments and certain phases of some storms, the movie‐maps also show substantial variety in the local time distribution of low‐latitude magnetic disturbance, especially during storm commencements and storm main phases. All movie‐maps are available at the U.S. Geological Survey Geomagnetism Program Web site ( http://geomag.usgs.gov ).

Space Weather

Assessing the validity of station location assumptions made in the calculation of the geomagnetic disturbance index, Dst

In this paper, the effects of the assumptions made in the calculation of the Dst index with regard to longitude sampling, hemisphere bias, and latitude correction are explored. The insights gained from this study will allow operational users to better understand the local implications of the Dst index and will lead to future index formulations that are more physically motivated. We recompute the index using 12 longitudinally spaced low-latitude stations, including the traditional 4 (in Honolulu, Kakioka, San Juan, and Hermanus), and compare it to the standard United States Geological Survey definitive Dst. We look at the hemisphere balance by comparing stations at equal geomagnetic latitudes in the Northern and Southern hemispheres. We further separate the 12-station time series into two hemispheric indices and find that there are measurable differences in the traditional Dst formulation due to the undersampling of the Southern Hemisphere in comparison with the Northern Hemisphere. To analyze the effect of latitude correction, we plot latitudinal variation in a disturbance observed during the year 2005 using two separate longitudinal observatory chains. We separate these by activity level and find that while the traditional cosine form fits the latitudinal distributions well for low levels of activity, at higher levels of disturbance the cosine form does not fit the observed variation. This suggests that the traditional latitude scaling is insufficient during active times. The effect of the Northern Hemisphere bias and the inadequate latitude scaling is such that the standard correction underestimates the true disturbance by 10–30 nT for storms of main phase magnitude deviation greater than 150 nT in the traditional Dst index.

Space Weather

Operational nowcasting of electron flux levels in the outer zone of Earth's radiation belt

We describe a lightweight, accurate nowcasting model for electron flux levels measured by the Van Allen probes. Largely motivated by Rigler et al. ( 2004 , https://doi.org/10.1029/2003SW000036 ), we turn to a time‐varying linear filter of previous flux levels and K p . We train and test this model on data gathered from the 2.10 MeV channel of the Relativistic Electron‐Proton Telescope sensor onboard the Van Allen probes. Dynamic linear models are a specific case of state space models and can be made flexible enough to emulate the nonlinear behavior of particle fluxes within the radiation belts. Real‐time estimation of the parameters of the model is done using a Kalman filter, where the state of the model is exactly the parameters. Nowcast performance is assessed against several baseline interpolation schemes. Our model demonstrates significant improvements in performance over persistence nowcasting. In particular, during times of high geomagnetic activity, our model is able to attain performance substantially better than a persistence model. In addition, residual analysis is conducted in order to assess model fit and to suggest future improvements to the model.

Space Weather

Geoelectric hazard maps for the Pacific Northwest

Maps of extreme value, horizontal component geoelectric field amplitude are constructed for the Pacific Northwest United States (and parts of neighboring Canada). Multidecade long geoelectric field time series are calculated by convolving Earth surface impedance tensors from 71 discrete magnetotelluric survey sites across the region with historical 1‐min (2‐min Nyquist) geomagnetic variation time series obtained from two nearby observatories. After fitting statistical models to 1‐min geoelectric amplitudes realized during magnetic storms, extrapolations are made to estimate threshold amplitudes that are only exceeded, on average, once per century. One hundred‐year geoelectric exceedance amplitudes range from 0.06 V/km at a survey site in western Washington State to 9.47 V/km at a site in southeast British Columbia; 100‐year geoelectric exceedance amplitudes equal 7.10 V/km at a site north of Seattle and 2.28 V/km at a site north of Portland. Systematic and random errors are estimated to be less than 20%, much less than site‐to‐site differences in geoelectric amplitude that arise from site‐to‐site differences in surface impedance. Maps of 100‐year exceedance amplitudes are compared with the peak geoelectric amplitudes realized during the March 1989 magnetic superstorm; it is noted that some storms of relatively modest intensity can generate localized geoelectric fields of relatively high amplitude. The geography of geoelectric hazard across the Pacific Northwest is closely related to known geologic and tectonic structures.

Pacific Northwest

Extreme‐value geoelectric amplitude and polarization across the northeast United States

Maps are presented of extreme‐value geoelectric field amplitude and horizontal polarization for the Northeast United States. These maps are derived from geoelectric time series calculated for sites across the Northeast by frequency‐domain multiplication (time‐domain convolution) of 172 magnetotelluric impedance tensors, acquired during a survey, with decades‐long, 1‐min resolution time series of geomagnetic variation, acquired at three magnetic observatories. The maps show that, during intense magnetic storms, high geoelectric amplitude hazards are realized across electrically resistive, igneous and metamorphic rock of the Appalachian Mountains and the New England Highlands, while low geoelectric hazards are realized across electrically conductive, sedimentary rock of the Appalachian Plateau and the Mid‐Atlantic Coastal Plain. From statistical extrapolation, once‐per‐century (100‐year) geoelectric amplitudes are highest at a site in Virginia at 25.44 V/km (followed by a site in Maine at 21.75 V/km and a site in Connecticut at 19.39 V/km); 100‐year geoelectric amplitude exceeds 10 V/km at 12 sites across the northeast; geoelectric amplitude is lowest at a site in Virginia at 0.05 V/km. Average errors for these values are estimated to be about 38%, or much less than the more than 2 orders of magnitude range seen in geoelectric amplitudes from one survey site to another across the northeast. It is noteworthy that geoelectric fields tend to be most (least) polarized at locations with high (low) geoelectric hazard. Furthermore, geoelectric fields over the Appalachians tend to be polarized southeast‐to‐northwest, or generally in a direction orthogonal to the southwest‐to‐northeast geological strike. Results reported here inform utility companies in projects for evaluating and managing the response of power grid systems to the deleterious effects of geomagnetic disturbance.

Connecticut, Delaware, Maine, Maryland, Massachuse

Intensity and impact of the New York Railroad superstorm of May 1921

Analysis is made of low‐latitude ground‐based magnetometer data recording the magnetic superstorm of May 1921. By inference, the storm was driven by a series of interplanetary coronal mass ejections, one of which produced a maximum pressure on the magnetopause of ~64.5 nPa, sufficient to compress the subsolar magnetopause radius to ~5.3 Earth radii. Over the course of the storm, low‐latitude geomagnetic disturbance exhibited extreme local time (longitude) asymmetry that can be attributed to substorm disturbance extending to low latitudes. The storm attained an estimated maximum − Dst on 15 May of 907 ± 132 nT, an intensity comparable to that of the Carrington event of 1859. The May 1921 storm brought spectacular aurorae to the nighttime sky. It also interfered with and damaged telephone and telegraph systems associated with railroad systems in New York City and State. These later effects were due to a combination of three factors: the localized details of geomagnetic vector disturbance, the geographic expression of the Earth's surface impedance tensor, and the configurations and physical parameters of the electrical networks of the day.

New York

A 100-year geoelectric hazard analysis for the U.S. high-voltage power grid

A once-per-century geoelectric hazard map is created for the United States high-voltage power grid. A statistical extrapolation from 31 years of magnetic field measurements is made by identifying 84 geomagnetic storms with the Kp and Dst indices. Data from 24 geomagnetic observatories, 1079 magnetotelluric survey sites, and 17,258 transmission lines are utilized to perform a geoelectric hazard analysis with the most comprehensive data publicly available. With this data we estimate once-per-century geoelectric fields at the magnetotelluric survey sites and calculate the theoretical voltages within transmission lines in the United States power grid. Once-per-century geoelectric field strengths span more than three orders of magnitude from a minimum of 0.02 V/km at a site in Idaho to a maximum of 26.8 V/km at a site in Maine, with nearly 30% of the surveyed land area ex- ceeding 1 V/km. We show the influence that geoelectric field polarization has on geoelec- tric hazards when viewed on a power transmission network. The calculated transmission line voltages can exceed 1000 V in some transmission lines. Four regions in the United States with particularly notable geoelectric hazards are identified and discussed: the East coast, Pacific Northwest, upper Midwest, and the Denver metropolitan area.

Space Weather

Modified GIC estimation using 3-D Earth conductivity

Geomagnetically induced currents (GICs) are quasi-direct current (DC) electric currents that flow in technological conductors during geomagnetic storms. Extreme GICs are hazardous to man-made infrastructure. GICs enter and exit the technological systems, such as the electric power grid, at grounding points, and their magnitudes depend on the currents that flow underground. They are, therefore, a function of the Earth's electrical conductivity, represented at ground level as Earth impedances, as well as the resistance parameters of the power network. Traditional GIC estimation practices are based on Earth impedances obtained from laterally homogeneous or piecewise layered-Earth models. We refer to these methods, collectively, as the 1-D approximation. However, GIC hazard mitigation can be improved with more accurate GIC modeling that takes the spatially heterogeneous Earth's conductivity into account. Here, we propose a modified approximation for GIC estimation that is very similar to the 1-D approximation but is instead derived from empirical 3-D Earth impedances. Our formulation sets up the computation of static, frequency-dependent power line telluric response functions, which, once computed, may be considered part of the power grid system model. These response functions may then be used for historical scenario analysis of GIC hazards and for simplified real-time, albeit approximate, GIC estimation in a power grid. This modest modification to the simpler local field formulation approach avoids real-time integration of geoelectric fields along power lines while taking the realistic 3-D Earth into account in a rigorous manner. Once implemented, the method provides a power grid operator with the benefits of convenience and computational speed for a first look real-time operational GIC hazard assessment. We estimate that the proposed modified 3-D GIC modeling approach produces GIC values that are well within 50% of those obtained with the full-scale power line integration of spatially variable geoelectric fields, for storms comparable in scale to the 2003 Halloween storm, all geological structures, and power lines located in the contiguous United States and other low- to middle-latitude regions.

Space Weather

Numerical simulations of the geospace response to the arrival of an idealized perfect interplanetary coronal mass ejection

Previously, Tsurutani and Lakhina (2014, https://doi.org/10.1002/2013GL058825 ) created estimates for a “perfect” interplanetary coronal mass ejection and performed simple calculations for the response of geospace, including . In this study, these estimates are used to drive a coupled magnetohydrodynamic-ring current-ionosphere model of geospace to obtain more physically accurate estimates of the geospace response to such an event. The sudden impulse phase is examined and compared to the estimations of Tsurutani and Lakhina (2014, https://doi.org/10.1002/2013GL058825 ). The physics-based simulation yields similar estimates for Dst rise, magnetopause compression, and equatorial values as the previous study. However, results diverge away from the equator. values in excess of 30 nT/s are found as low as magnetic latitude. Under southward interplanetary magnetic field conditions, magnetopause erosion combines with strong region one Birkeland currents to intensify the response. Values obtained here surpass those found in historically recorded events and set the upper threshold of extreme geomagnetically induced current activity at Earth.

Space Weather

Extreme-event magnetic storm probabilities derived from rank statistics of historical Dst intensities for solar cycles 14-24

A compilation is made of the largest and second-largest magnetic-storm-maximum intensities, − Dst 1 and − Dst 2 , for solar cycles 14–24 (1902–2016) by sampling Oulu Dcx for cycles 19–24, using published − Dst m values for 4 intense storms in cycles 14, 15, and 18 (1903, 1909, 1921, 1946), and calculating 15 new storm-maximum − Dst m values (reported here) for cycles 14–18. Three different models are fitted to the cycle-ranked − Dst 1 and − Dst 2 values using a maximum-likelihood algorithm: A Gumbel model, an unconstrained Generalized-Extreme-Value model, and a Weibull model constrained to have a physically justified maximum storm intensity of − Dst m = 2500 nT. All three models are good descriptions of the data. Since the best model is not clearly revealed with standard statistical tests, inference is precluded of the source process giving rise to storm-maximum − Dst m values. Of the three candidate models, the constrained Weibull gives the lowest superstorm occurrence probabilities. Using the compiled data and the constrained Weibull model, a once-per-century storm intensity is estimated to be − Dst 1 = 663 nT, with a bootstrap 68% confidence interval of [497, 694] nT. Similarly, the probability that a future storm will have an intensity exceeding that of the March 1989 superstorm, − Dst m > 565 nT, is 0.246 per cycle with a 68% confidence interval of [0.140, 0.311] per cycle. Noting (possibly slight) ambiguity in the rankings of storm intensities, using the same methods, but storms more intense than those identified for cycles 14–16, would yield a higher once-per-century intensity and a higher probability for a − Dst m > 565 nT storm.

Space Weather

Magnetotelluric sampling and geoelectric hazard estimation: Are national-scale surveys sufficient?

At present, the most reliable information for inferring storm-time ground electric fields along electrical transmission lines comes from coarsely sampled, national-scale magnetotelluric (MT) data sets, such as that provided by the EarthScope USArray program. An underlying assumption in the use of such data is that they adequately sample the spatial heterogeneity of the surface relationship between geomagnetic and geoelectric fields. Here, we assess the degree to which the density of MT data sampling affects geoelectric hazard assessments. For electrical transmission networks in each of four focus regions across the contiguous United States, we perform two parallel band-limited (10 1 –10 3 s) hazard analyses: one using only USArray-style (∼70-km station spacing) MT data, and one incorporating denser (≪70-km station spacing) MT data. We find that the use of USArray-style MT sampling alone provides a useful first-order estimate of integrated geoelectric fields along electrical transmission lines. However, we also find that the use of higher density MT data can in some areas lead to order-of-magnitude differences in line-averaged electric field estimates at the level of individual transmission lines and can also yield significant differences in subregional hazard patterns. As we demonstrate using variogram plots, these differences reflect short-spatial-scale variability in Earth conductivity, which in turn reflects regional lithotectonic structure and history. We also provide a cautionary example in the use of electrical conductivity models to predict dense MT data; although valuable for hazard applications, models may only be able to reproduce surface geoelectric fields as captured by the MT data from which they were derived.

AGU Space Weather