Modeling geomagnetically induced electric field and currents by combining a global MHD model with a local one-dimensional method

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1 SPACE WEATHER, VOL. 10,, doi: /2012sw000772, 2012 Modeling geomagnetically induced electric field and currents by combining a global MHD model with a local one-dimensional method J. J. Zhang, 1,2 C. Wang, 1 and B. B. Tang 1 Received 31 January 2012; revised 10 April 2012; accepted 15 April 2012; published 30 May [1] Geomagnetically induced currents (GIC) flowing in long conductor systems on the ground are a well-known space weather hazard. We develop a new approach to simulating GICs by combining a global MHD model with a local one-dimensional method. As an example, we apply this approach to model the GIC at the Pirttikoski 400 kv transformer of the Finnish high-voltage power system during the space weather event of September The modeled results can capture the main observational features, and the model performances is better than two GIC persistence models, which demonstrates this promising new approach in GIC forecasting. Citation: Zhang, J. J., C. Wang, and B. B. Tang (2012), Modeling geomagnetically induced electric field and currents by combining a global MHD model with a local one-dimensional method, Space Weather, 10,, doi: /2012sw Introduction [2] Induced by temporal variation of the external magnetic field, the geoelectric field occurs at the Earth s surface producing geomagnetically induced currents (GIC) in technological facilities. It may bring about severe electric blackout, communication outage, and corrosion of oil and gas pipelines [Boteler and Pirjola, 1998], leading to economic losses in the society. It is always of interest to model the geomagnetically induced electric field and currents both in basic understanding of the the solar wind-magnetosphereionosphere-earth interaction chain [Viljanen et al., 2004] and in practical application to mitigate or avoid economic losses. [3] Generally speaking, the calculation of GIC in a conductor system is performed in two independent steps. The first step is referred to as geophysical step, which is to determine the geoelectric field in the area of the conductor system under study; the second step is the engineering step, which obtains the induced currents due to the given electric field. Once the induced electric field is obtained, GIC in technological systems can be easily computed. The geophysical part is much more difficult to solve, since the geoelectric field not only is affected by spatially and temporally varying ionospheric currents, but also depends on 1 State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, China. 2 Also at Graduate University of the Chinese Academy of Sciences, Beijing, China. Corresponding author: J. J. Zhang, State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing , China. (jjzhang@spaceweather.ac.cn) the Earth s conductivity. Theoretical modeling of the geomagnetically induced electric field have been carried out since 1980s. Häkkinen and Pirjola [1986] derived exact formulas for getting the electromagnetic field at the surface of a layered Earth produced by a three-dimensional auroral current system. But the calculations of the method are computationally demanding and thus impractical. The calculation of the surface fields is greatly simplified and accelerated when the complex image method (CIM) is applied [Boteler and Pirjola, 1998; Pirjola and Viljanen, 1998]. It considers an image of the primary ionospheric source at a complex depth to represent the induced telluric current when the Earth has a layered conductivity structure. Viljanen et al. [2004] pointed out that although CIM is a convenient tool for theoretical modeling purposes, it is not the most optimal choice for more operational applications. They showed that the CIM can be replaced by a more convenient local 1-D method. In the local 1-D method, the geoelectric field is determined from ground-based geomagnetic recording based on the plane wave relation between the horizontal electric and magnetic fields at the Earth s surface, a local 1-D Earth s conductivity model with no lateral variations is assumed in the method. Based on the local 1-D method, nowcast research of GIC has been carried out in some high latitude countries to monitor the impact of the geomagnetic perturbation on manmade technological systems. The GIC Now! server in Finland ( has been providing nowcast estimates of GIC in the Finnish natural gas pipeline system since June 2003 [Viljanen et al., 2006]. Boteler et al. [2007] developed a system named Real- Time GIC Simulator to simulate the GIC flowing in a power system in Canada. Copyright 2012 by the American Geophysical Union 1of11

2 [4] Some works have been done to estimate the level of the GIC fluctuations by using the information of the upstream solar wind as input. Weigel et al. [2003] and Wintoft [2005] have reproduced some features of proxies of GIC relatively successfully by means of empirical models. On the basis of elementary physical principles, global magnetohydrodynamics (MHD) models have played a significant role in space weather studies in recent decades. And the ability of the models are being extended to modeling GIC. Directly related to the induced electric field and further to GIC that affect power transmission systems and pipelines, the time derivative of the geomagnetic field has been modeled by using MHD models by Raeder et al. [2001] and Yu and Ridley [2008]. Instead of simulating proxies of GIC, Pulkkinen et al. [2007] took the first attempt to modeling GIC directly based on MHD model, although the GIC sites in their study are fictitious. In their work, they computed the induced electric field on ground from the output of the threedimensional global MHD code BATS-R-US [Powell et al., 1999] by using the complex image method (CIM). The GIC at more than thirty magnetometer stations of IMAGE [Lühr, 1994] and Greenland [Friis-Christensen et al., 1985] magnetometer arrays were simulated during the geomagnetically active period of October The magnetometer stations were considered as GIC sites. Due to lack of the real measured GIC data, they calculated measured GIC from the measured geomagnetic recording at each magnetometer station. At last, comparison between simulated GIC and measured GIC at the geomagnetic stations was made. They found that for the studied event the model captures some central features of the measured GIC, although the modeled peak values are smaller. The GIC modeling approach they proposed has been used to the Solar Shield project, which is launched to establish an experimental system for forecasting and mitigating space weather effects on high-voltage power transmission systems [Pulkkinen et al., 2010a]. [5] As Viljanen et al. [2004] pointed out that the application of the local 1-D method is more convenient than the CIM method which has been used in Pulkkinen et al. s GIC modeling approach [Pulkkinen et al., 2007] in determination of the geoelectric field, we introduce a new approach to model the GIC flowing in long conductor systems on ground by combining a global MHD model with the local 1-D method. This will provide a new modeling process to extend the framework of the MHD-based space weather modeling down to the surface of the Earth and enable us test the capabilities of the MHD model to simulating space weather events from the GIC viewpoint. Moreover, rather than model GIC fluctuations at some fictitious GIC sites as what Pulkkinen et al. [2007] did, we will simulate GIC flowing in a real power system in this study and compare the modeled GIC with the GIC recording both qualitatively and quantitatively. [6] To satisfy the requirement of this study, a specific space weather event and power system are selected. During September 1999, the Solar Terrestrial Energy Program- Research, Applications and Modeling Phase(S-RAMP) Group of the Scientific Committee for Solar Terrestrial Physics (SCOSTEP) coordinated a Space Weather Month campaign to follow the progress of space weather events from their initiation on the Sun to their impacts at the Earth, including their effects on space-based and groundbased technological systems and the assessment of the accuracy of specification and forecasting techniques. GIC measured at two 400 kv transformers of the Finnish highvoltage power system are publicly available for the period of the campaign. The transformers are located at Pirttikoski (PIR) and Rauma (RAU), respectively. It provides us with an opportunity to make comparison between modeled and real measured GIC. Taking the space weather event during September 1999 as an example, we will carry out the modeling process to simulate the GIC flowing along the neutral lead of the PIR 400 kv transformer to the Earth during the event. [7] In the remainder of this paper we will first describe the methodology of the modeling in section 2. In section 3, we present the simulation results of GIC at the PIR 400 kv transformer during the space weather event of September 1999, and make comparison of the simulated and the measured GIC qualitatively. In section 4, two kinds of metrics will be introduced to estimate the performance of the model quantitatively. Finally, we will give discussion and summary in section Methodology 2.1. Numerical Model [8] Many three-dimensional (3-D) MHD codes have been developed to simulate the global behavior of the solar wind-magnetosphere-ionosphere system in literature, for instance, the Lyon-Fedder-Mobarry (LFM) code [Lyon et al., 1998], the BATS-R-US code of the Michigan group [Powell et al., 1999], the European GUMICS code [Janhunen, 1996], and so on. The global MHD code utilized in this study is the so-called piecewise parabolic method with a Lagrangian remap (PPMLR)-MHD code which is developed by Hu et al. [2005, 2007]. The code is an extension of the Lagrangian version of the piecewise parabolic method (PPMLR) [Colella and Woodward, 1984] to MHD. It possesses a formal accuracy of the third order in space and the second order in time, and a low numerical dissipation. [9] The PPMLR-MHD code solves ideal MHD equations for the solar wind-magnetosphere-ionosphere coupling system. The coupling process between magnetosphere and ionosphere has been described in detail by Wang et al. [2011]; here we just give a brief description. An inner magnetosphere boundary is set at r =3R E, and an electrostatic ionosphere is set at r = R E. A magnetosphereionosphere electrostatic coupling model is imbedded between inner boundary and ionosphere to drive the inner boundary convection. From the inner boundary the fieldaligned currents (FAC) are mapped along the Earth s dipole magnetic field lines to the ionosphere where they are used as source term of a two-dimensional Poisson equation for electric potential. Once the potential is 2of11

3 obtained, they are mapped back to the inner boundary to calculate convection velocity. To calculate the conductance tensor of the ionosphere, two models are applied together. For the contribution from the solar EUV radiation, we use a model in which the conductance depends on the solar flux F 10.7 and solar zenith angle c [Moen and Brekke, 1993]. For the auroral region, the model developed by Ahn et al. [1998] is used, in which the conductance is empirically derived from the geomagnetic disturbance. The Hall and Pedersen conductance over the dark polar cap region and subauroral region are given to be constants 2.0 S and 1.0 S, respectively, regardless of the magnetic perturbation level Calculation of Geomagnetic Variation [10] To calculate the geomagnetic disturbance, we derive the equivalent current system (ECS) first, detailed description of the method to obtain the ECS in simulation can be found in Raeder et al. [2001] and Wang et al. [2011]. The total height-integrated horizontal ionospheric current can be generally split into two parts: the poloidal current J P and toroidal current J T [Kamide et al., 1981;Raeder et al., 2001]. Fukushima [1976] pointed out that the geomagnetic disturbance produced by poloidal ionospheric current and fieldaligned current (FAC) cancel under the assumption of radial field lines. And the contribution from the magnetospheric currents could be ignored compared with the ionospheric currents for the high latitude region we concerned, so the ionospheric toroidal current J T could be considered as the equivalent current. Thus we can simply obtain the geomagnetic perturbations on ground by using Biot-Savart s law with J T dbðrþ ¼ m Z 0 R r J T ðr Þ 4p s jr r j 3 d2 r ; ð1þ where r denotes the position of the current source, R is the location of the point of interest on ground. The integration domain is limited to about 1000 km both in latitudinal and longitudinal directions overhead, which is enough to produce most fraction of horizontal perturbation approximately in auroral region [Yu and Ridley, 2008]. The effect of the induced (telluric) current on the geomagnetic variations at the Earth s surface is difficult to quantify for its effect is depend on the ground conductivity and the frequency of the external magnetic field. For simplicity, we neglect the effect of it. This is reasonable since the ratio of telluric current contribution to total horizontal magnetic variations close to strong currents is typically 10 20% [Tanskanen et al., 2001], though the ratio can reach to 40% during very rapid changes such as substorm onsets with the duration of a few minutes, the magnetic field variations on ground are still mainly of ionospheric origin [Pulkkinen et al., 2003]. Neglecting the effect of telluric current means here that the amplitude of the geomagnetic field on ground is slightly underestimated. Further this can cause slightly underestimation of the ground electric field and GIC according to the relations between ground magnetic field and electric field and between the electric field and GIC, which will be introduced later Local 1-D Method [11] Based on the plane wave method [Cagniard, 1953] and the Earth s local 1-D conductivity assumption, i.e., the conductivity depends only on depth, the induced electric field is related to the magnetic field in spectral domain as follows [Viljanen et al., 2004]: Z ~E x ðwþ ¼ ~ 0 ðwþ By ~ ðwþ; E ~ Z y ðwþ ¼ ~ 0 ðwþ Bx ~ ðwþ; m 0 where m 0 is the vacuum permeability, ~ Z 0 (w) is the surface impedance dependent of the thicknesses and conductivities of the layered Earth. The subscripts x and y denote the north and the east in geographic coordinates, respectively. This is the so-called local 1-D method. [12] The time series of geomagnetic variations at the concerned point on ground derived from the MHD model first are transformed from geomagnetic coordinates to geographic coordinates. The computations of the local 1-D method are carried out in the spectral domain, transformations between the temporal and the spectral domain are conducted using Fourier transformation. With the information about the Earth s 1-D local conductivity model and simulated geomagnetic variations, the geoelectric field is thus obtained Calculation of GIC From Electric Field [13] The calculation of GIC in a power system is a straightforward task after the electric field is given. If we take the simplest assumption that the electric field is spatially uniform over the region of the whole system, GIC can obtained from m 0 GICðÞ¼aE t x ðþþbe t y ðþ; t where E x, E y are the modeled values close to or at the GIC site; a and b are constant coefficients, which are determined by the topology and electrical properties of the system of interest. They can be obtained theoretically when knowing the power grid information including the network topology, station coordinates, transformer resistances, transmission line resistances, and station earthing resistances [Lehtinen and Pirjola, 1985]. If the electric field and the corresponding GIC are known they also can be deduced empirically [Pulkkinen et al., 2006; Wik et al., 2008]. But it should be noted that the empirical a and b are only valid for the network configuration during the period when the coefficients are determined. If changes occur in the network, new empirical coefficients a and b need be determined. Equation (3) can also be applied for continuously earthed systems like buried pipelines. Figure 1 gives the whole modeling process schematically. 3. Example of the Usage of the Method 3.1. The September 1999 Event [14] During the Space Weather Month campaign of September 1999, an interplanetary magnetic cloud (IMC) ð2þ ð3þ 3of11

4 3.2. Finnish High-Voltage Power System [15] We obtained GIC data during the event of September 1999 at the PIR and RAU 400 kv transformers of the Finnish high-voltage power system (Figure 4). The locations of the two transformers PIR and RAU, geomagnetic station SGO (Sodankylä Geophysical Observatory) which is the nearest magnetometer station from PIR, Figure 1. Schematic diagram of the modeling process. extending from 22 to 23 September triggered a large storm. It is considered that the source of this event was a faint but complete halo coronal mass ejection (CME) event observed at 0606 UT on 20 September [Lam et al., 2002], it reached Earth 63 hours later with a required travel speed of 660 km/s. Figure 2 shows the solar wind and interplanetary magnetic field (IMF) conditions at the Earth s bow shock nose for 33 hours from 0100 UT on 22 September to 1000 UT on 23 September, including the three components of IMF and solar wind velocity, solar wind temperature and plasma density. Following a forward shock at about 1200 UT on 22 September, an IMC event extends from 2000 UT on 22 September to 0700 UT on 23 September with maximum southward IMF of 22 nt, and the IMF rotated from southward to northward during the passage of the IMC. The minimum SYM H index of the triggered storm is 166 nt, and the minimum AL index is 1465 nt during the period. The indices are plotted in Figure 3. The data presented in Figure 2 and Figure 3 are 1 min High Resolution OMNI (HRO) data from NASA OMNI database ( Figure 2. The solar wind and interplanetary magnetic field (IMF) conditions at the Earth s bow shock nose from 0100 UT on 22 September to 1000 UT on 23 September From top to bottom, plots show the three components of the IMF and solar wind velocity, the solar wind plasma density, and the temperature. 4of11

5 Table 1. Coordinates of GIC Sites PIR and RAU and Geomagnetic Observatories SGO and NGO Station Geographic Latitude Geographic Longitude Geomagnetic Latitude Geomagnetic Longitude PIR SGO RAU NGO Figure 3. AL/AU index and SYM H index from 0100 UT on 22 September to 1000 UT on 23 September and NGO (Nurmijärvi Geophysical Observatory) which is the nearest geomagnetic observatory from RAU are marked in Figure 4. The coordinates of the transformers and geomagnetic observatories are shown in Table 1. In this study we simulate the GIC at the PIR 400 kv transformer only, because the magnetic latitude of the RAU 400 kv transformer is beyond the lowest boundary of the ionosphere that can be included in the MHD-based model. This limitation of the model will be discussed later. [16] In order to calculate GIC, the parameters a and b in equation (3) should be determined for the PIR 400 kv transformer. Without the power grid data, we determine the two parameters empirically. The geomagnetic variations recorded at SGO and a 1-D conductivity model (Table 2) [Viljanen et al., 1999] are used to determine the electric field at PIR by using local 1-D method. The chosen ground conductivity model is a resistive conductivity model which is the typical model for the ground of central Finland. We crudely assume the model is appropriate for the whole power grid in this study. The distance between the PIR 400 kv transformer and SGO is about 100 km and it is sufficiently short to determine the electric field at the GIC site by using the magnetic recordings at SGO, in Finnish GIC studies sufficiently close has been found to be of the order of 200 km [Pulkkinen et al., 2006]. On the basis of equation (3), we obtain a and b by a least squares fit using measured GIC at PIR and the calculated geoelectric field. We choose the most disturbed 4 hours from 2000 UT to 2400 UT on 22 September for the fitting process, and get a = 9.6 Akm/V, b = 5.9 Akm/V, the cross-correlation coefficient between measured and fitted GIC is The fitted GIC and measured GIC during the entire period of 33 hours are shown in Figure 5. Good agreement between the fitted and measured GIC indicates the chosen ground conductivity model is reasonable. Same ground conductivity model and coefficients a, b are applied in the simulation part, the key point of the whole simulation process lies in whether or not the MHD model can reproduce realistic geomagnetic variations at the site of interest, from which the GIC is derived at last. Thus the approach to obtain a and b and the crude assumption of the ground conductivity model in this section can be considered acceptable. [17] The geomagnetic data at SGO is obtained from the IMAGE magnetometer website ( reqform/dataform.html). The time resolution of magnetic field data and GIC data are 10 s originally and then they are averaged to 1 min in order to keep accord with the 1 min resolution of the simulation result. Table 2. Ground Conductivity Model Figure 4. Finnish high-voltage power system. The Pirttikoski (PIR) 400 kv transformer, the Rauma (RAU) 400 kv transformer, and the geomagnetic observatories SGO and NGO are marked on the map. Depth (km) Resistivity (Wm) , , , ,000 > of11

6 Figure 5. Measured (grey) and fitted (black) geomagnetically induced current (GIC) at the PIR 400 kv transformer for the investigated period from 0100 UT on 22 September to 1000 UT on 23 September Simulation Results [18] We simulate the GIC at the PIR 400 kv transformer when the IMC swept across the Earth using the modeling process introduced in section 2. The 1 min solar wind and IMF data which are shown in Figure 2 drive the global PPMLR-MHD model at the inflow boundary without the correction of the time difference for the solar wind propagation from 30 R E to the bow shock nose, which is about 3 min here. While the IMF B x is fixed to keep divergencefree condition in the simulation. First, the geomagnetic variations at SGO are modeled to compute further the induced geoelectric field by using the local 1-D method. One should note that in practical GIC simulation, the geomagnetic variations at the GIC site under study can be calculated directly from the output of the MHD model to obtain the modeled geoelectric field. Here we calculate the ground magnetic disturbance at SGO rather than PIR in order to make the comparison of the measured and simulated magnetic field fluctuations. Moreover, the distance between SGO and PIR is short enough, the magnetic field variations at SGO can be used to determine the geoelectric field at the GIC site as mentioned in section 3.2. [19] In Figure 6 we present the x-component (geographic north) and y-component (geographic east) of the measured and simulated geomagnetic field perturbation at SGO. The simulation generally reproduces the intense magnetic fluctuation caused by the IMC. The measured and simulated time derivative of B x and B y are also presented in the figure. The timing of main activities and the basic fluctuation from the simulation are similar to the observation. The geoelectric field computed from the simulated and measured geomagnetic field at SGO are presented in Figure 7, the 1-D ground conductivity model of Table 1 is adopted in calculation. Similar fluctuation of the main active period between the two results can be seen. The modeled and real measured GIC are shown in Figure 8. We can see that the modeled GIC curve is very similar to the measured GIC curve though the amplitudes of the modeled peak values are lower than those of the measured peak values, and the timing of the major activities between simulation and observation is very close. 4. Estimation of the Model Performance [20] In order to estimate the performance of the model during the investigated event quantitatively, two metrics are used in this section Log-Spectral Distance [21] The spectral power determines the level of disturbance in various frequency ranges that can be generated by the model compared with the observed level of fluctuations. In order to quantify the models capability to reproduce the GIC-related features of the magnetic field power spectra, the metric which is called log-spectral distance was developed by Pulkkinen et al. [2010b], and this part of the study builds on the work of them. The logspectral distance M s is a single number measuring the discrepancy between the observed spectral distribution and that obtained by a model in a given spectral range. The derivation of the M s is described as follows. [22] In spectral domain, equation (3) can be written as G ~ ICðwÞ ¼ a E ~ x þ b E ~ y ¼ a Z0 ~ By ~ b Z0 ~ Bx ~ : m 0 m 0 The relation (4) takes the form of a triangle inequality for power spectra G ~ ICðwÞ a j jj Z m ~ 0 jj B ~ y jþj b jj Z 0 m ~ 0 jj B ~ x j: 0 To calculate the log-spectral distance, the logarithm of the ratio of the right-hand side of equation (5) between observed and simulated variables is defined as m s " jaj Bx ~ m s ðwþ ¼ log obs þjbj B ~ # y obs jaj B ~ x sim þjbj B ~ : ð6þ y sim ð4þ ð5þ 6of11

7 Figure 6. The x-component, y-component, and time derivative of the measured (grey) and the simulated (black) geomagnetic field fluctuation at SGO from 0100 UT on 22 September to 1000 UT on 23 September Here, rather than assume a = b as what Pulkkinen et al. [2010b] did originally, we put a = 9.6 Akm/V and b = 5.9 Akm/V derived in section 3.2 into equation (6). Finally, log-spectral distance M s is computed sffiffiffiffiffiffiffiffiffiffiffiffi 1 X M s ¼ m 2 s N ; ð7þ where N is the number of frequencies. As a dimensionless quantity, M s can be equal or larger than zero, M s = 0 denotes the perfect model performance. To carry out spectral analysis, first we divide the time series of measured and simulated magnetic fluctuations of the whole period we investigated into 2 hours long segments with w 50% overlap between adjacent segments. After being multiplied with the Hann window function, data within each segment are transformed to the spectral domain by Fourier transformation. Spectra from all segments are averaged to form the spectra of measured and simulated magnetic variation in equation (6), and the sum in equation (7) is conducted over the periods min. Finally we get M s = 6.18, the value indicates the performance of the model is not bad according to the work of Pulkkinen et al. [2011], which provided a benchmark for monitoring the performance of space weather models Utility Metric [23] From the user s perspective, they prefer metrics that is helpful for them to make decision to maximize the 7of11

8 Figure 7. The calculated geoelectric field (E x, E y ) from 0100 UT on 22 September to 1000 UT on 23 September The grey line and black line represent geoelectric field calculated from the measured and the simulated geomagnetic variations at SGO, respectively. economic gain. For the complex GIC signal, the basic metric based on data-model correlation can t satisfy the requirement of the users only interested in economic utility. The utility metric (for details, see Weigel et al. [2006] and Pulkkinen et al. [2007]) is more suitable for them. The metric was developed to evaluate a model on the basis of its ability to predict an event. An event is defined as follows: Within a forecast window 0 t T F, the absolute value of GIC exceeds event threshold GIC thres. The windows are moved over the time series in non-overlapping parts, events are recorded for both the measured and the simulated GIC for given T F and GIC thres [Pulkkinen et al., 2007]. The forecast model has utility if the monetary gain U F is greater than zero: U F BN H CN H > 0; ð8þ where N H is the number of correct forecasts, N H is the number of false alarms, C is the cost of taking mitigating action and B is the benefit from having taken mitigating action when an event occurred. A few general assumptions are made to restrict the problem, which are (1) the user takes the same mitigating action following each forecast of an event, (2) an always mitigate strategy yields a net monetary loss for the user, and (3) the user seeks to maximize monetary gain U F. The missed events are not taken into account because here considering utility with respect to a system that was never mitigated, a missed event will cause the same monetary loss for both the reference system and the system taking mitigation actions based on the forecast. [24] In equation (8), B and C are both system dependent and are estimated by the user. Without the detailed Figure 8. Measured (grey) and simulated (black) GIC at the PIR 400 kv transformer from 0100 UT on 22 September to 1000 UT on 23 September of11

9 in Figure 9 are small compared with the values in practical engineering issues. Even so the test approach is considered acceptable, since our primary interest is to test the capability of the MHD-based model in predicting GIC events compared with the persistence models. Practical engineering problems can be taken into account in future work. Figure 9. Forecast ratio R F as a function of the event threshold GIC thres for the simulation result (asterisks) and two different persistence models, model 1 (triangles) and model 2 (crosses). knowledge of these two parameters, Weigel et al. [2006] suggested that the developer of the model can determine whether the model is potentially useful or not by reporting the forecast ratio which is defined as R F N H N H if the inequality R F > C/B is satisfied, then taking action following every forecast will yield U F > 0. The model with a higher R F will provide greater economic utility U F in model comparisons. [25] For the investigated period in this study, we choose the disturbed period from 1700 UT on September 22 to 0700 UT on September 23 to calculate the forecast ratio R F for the simulated GIC as a function of GIC thres. In Figure 9, we show the curve along with the curves for two different persistence models for T F = 60 min as what Pulkkinen et al. [2007] did. The two persistence models are (1) always an event forecast in which during disturbed periods the alarm is switched on, and (2) nearest neighbor forecast in which the forecast for the next forecast window is the same as the observation for current window. As seen from Figure 9, R F generated from the simulation is generally higher than that from the other two persistence models for the PIR 400 kv transformer during the period we examined for T F = 60 min. This means that the application of the MHD-based simulation is capable of producing superior economic benefit than the used persistence models. In the calculation, the GIC thresholds GIC thres are chosen arbitrarily; in reality the threshold should depend on the type of transformer since the sensitivity of different transformer types to the effects of GIC is different. Due to the transformer type used in Finland has a very low GIC sensitivity, large GICs have never caused problems in the Finnish power grid [Elovaara, 2007]. The GIC thres values included ð9þ 5. Discussion and Summary [26] In this paper we propose a new approach to combine the global MHD model with the local 1-D method to model GIC. On one hand it gives a method to extend the framework of space weather modeling which is based on MHD model down to the surface of the Earth; on the other hand it provides a way to predict GIC flowing in technology systems on ground. As an example, we utilizes the new approach to simulate the GIC flowing from the neutral lead of the PIR 400 kv transformer to the Earth in the Finnish high-voltage power grid when an IMC swept over the Earth during the Space Weather Month campaign of September The model captures the main features of the geomagnetic fluctuations which are associated with GIC. The curve of the modeled GIC signal presents similar shape as the measured one, and the timing of major activity is close to perfect. The magnitude of the modeled peak GIC values are somewhat lower than the measured ones, which is expected since we neglect the effect of the telluric currents when calculating the geomagnetic variations on the Earth s surface. Two metrics are applied to estimate the performance of the model, one is the correlation-based metric and the other is user-relevant utility metric. Comparison of the utility metric for the simulation and two different persistence models shows that the global MHD-based modeling outperforms the persistence models. Although using different MHD codes and GIC modeling processes, Pulkkinen et al. [2007] obtained similar result. They found that the MHD-based model used in their work is capable of producing equal or even superior economic benefit to that of the two persistence models during the space weather event they investigated. [27] The main aim of this study is to propose a new MHD-based GIC modeling approach and carry out the approach by a real space weather event. So the specified space weather event and power station are selected because of the data availability of an entire space weather episode including the solar data, solar wind data, geomagnetic data and GIC data. The initial simulation result is encouraging when one power station and one event are considered. It indicates that the MHD-based GIC modeling at least has the potential to forecast the GIC flowing in ground facilities. To further validate the approach, a number of space weather events should be simulated to test its ability in the future work. [28] In spite of the success in reproducing some features of the GIC for the event we investigated, there is still large space to improve the current MHD model for simulating GIC accurately. For numerical consideration, there is a gap 9of11

10 region between the ionosphere model and inner boundary of the global MHD model. A coupling process carried out along the dipole magnetic field lines in that region. The inner boundary is usually set to 2.5R E 3.5R E, which implies that the lowest boundary of the ionosphere does not extend very low in magnetic latitude. This limit the ability of the model to simulate the GIC in technological systems only at region of very high latitude. As mentioned in section 3.2, due to the inner magnetospheric boundary of 3R E set in this study, the model cannot simulate GIC at the RAU 400 kv transformer because its location is beyond the lowest latitudinal boundary (59 in magnetic latitude) of the ionosphere in the MHD-based model. This may be improved by setting the inner magnetospheric boundary as close to the Earth as possible. Additionally, inclusion of model of ring current may promote the capability of the model to simulate the GIC events in middle and low latitude countries. Recently, the number of reports about the GIC-risks in power grids in mid- and low-latitude countries has increased [Gaunt and Coetzee, 2007; Liu et al., 2009]. Modeling GIC events which happen there becomes necessary. Moreover, the inclusion of the ring current model may be important for the development of the region 2 current system in MHD models. [29] To summarize, the focus of this study is to provide a new MHD-based GIC modeling approach. The good performance of the model for the studied space weather event makes us believe this new approach could be a promising way for GIC forecasting in the future. For application purpose, this approach should be tested, validated and improved by more space weather events in the future. [30] Acknowledgments. We thank the institutes who maintain the IMAGE Magnetometer Array for providing the geomagnetic data utilized in this study. We also thank A. Viljanen for providing the GIC data of the PIR 400 kv transformer of the Finnish high-voltage power grid and useful comments on the manuscript. Our acknowledgment also goes to X. J. Wang of Beihang University for helpful discussions. This work was supported by 973 program 2012CB825602, NNSFC grants , , and in part by the Specialized Research Fund for State Key Laboratories of China. References Ahn, B. H., A. D. Richmond, and Y. Kamide (1998), An ionospheric conductance model based on ground magnetic disturbance data, J. Geophys. Res., 103(A7), 14,769 14,780, doi: /97ja Boteler, D. H., and R. J. Pirjola (1998), The complex-image method for calculating the magnetic and electric fields produced at the surface of the Earth by the auroral electrojet, Geophys. J. Int., 132, Boteler, D., L. Trichtchenko, R. Pirjola, J. Parmelee, S. Souksaly, A. Foss, and L. 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