Modeling the Impact of Geomagnetically Induced Currents on Electrified Railway Signaling Systems in the United Kingdom

Studies of space weather impacts on ground‐based infrastructure have been largely focused on power networks and pipelines, but railway signaling systems are also affected, with misoperations observed in several countries. This paper advances recent theoretical work on geomagnetically induced currents in railway signaling systems by modeling realistic railway lines with parameters from current industrial standards. Focusing on two example lines in the United Kingdom with different locations and orientation, a range of uniform electric fields are simulated along each modeled line. The results show that misoperations could be caused by geomagnetic interference at disturbance levels expected to recur over timescales of several decades. We also demonstrate that the UK estimate for the geoelectric field induced by a 1 in 100‐year extreme storm would be strong enough to cause widespread signal misoperations in both lines studied.

circuit interference, finding that "Signaling assets such as signaling and track circuits are potentially vulnerable to CMEs, and many assets are potentially vulnerable to Single Event Effects" (p. 20). It also identified signaling systems as a potential area of vulnerability, stating "The relative vulnerability of different types of systems (e.g., track-based train detection) is not clear at this stage" (p. 20). In 2015, the "Space Weather and Rail" workshop jointly organized by the European Commission's Joint Research Centre, the Swedish Civil Contingencies Agency, the UK Department for Transport and the US National Oceanic and Atmospheric Administration worked toward furthering understanding of space weather's impacts on railways and raising awareness among operators (Krausmann et al., 2015).
In Section 2 of this paper, we provide an overview of track circuit railway signaling systems and the mechanisms via which they can be impacted by space weather. This work builds upon the theoretical modeling of geomagnetic induction in track circuits presented in Boteler (2021), and in Section 3 we describe the model we have developed for this study. We also provide details on the electrical characteristics of the rails and the track circuit parameters that are included in our model, based on specifications from current United Kingdom industry standards. In Section 4, we introduce the two sections of the UK railway network being studied in this paper. In Section 4.1 we discuss factors that must be considered depending on whether an entire railway line, or only a portion of the line, is being modeled. We also examine which aspects of a railway line's design contribute the most to space weather susceptibility. Finally, in Section 4.2, uniform electric fields are applied to both railway lines included in our investigation and the results discussed, first for a range of realistic values based on geoelectric fields that have led to misoperations in the recent past, then for a 1 in 100-year extreme event.

Track Circuits
Track circuits are one of the main signaling systems designed to detect trains along a railway line. Figure 1 shows the operational principles of a track circuit on an AC-electrified railway line. Insulated rail joints (IRJs) are spaced along one of the rails (the signaling rail) which separates it into blocks; the other rail (the traction rail) is not broken into sections as it provides the return path for the traction current used to power the train. A voltage source is placed at the start of the block which drives a current through the signaling rail and into a relay at the end of the block, and this current energizes the relay which causes a green signal to be displayed, indicating there is no train present, as shown in (a). However, if a train is occupying the block, the wheels and axle redirect the current before it can reach the end, and the relay is not energized leading to a red signal that indicates a train is present, as shown in (b). The lengths of track circuit blocks and the traction rail can vary depending on if the section is located in a rural or an urban area. The two lines investigated in this study had a range of track circuit block lengths from 0.4 to 1.9 km and traction rail lengths of around 34 and 76 km; for comparison, values for the Swedish railway studied by Alm (1956) and Lejdström and Svensson (1956) were 1 and 4 km for track circuit blocks and 100 km for the traction rail.
By design, the normal operation of a track circuit relay requires it to energize or de-energize at specific current thresholds. This balance can be offset by geomagnetically induced currents which can either work to de-energize a relay in a block with no train present causing a "right side failure" (a mode of failure that does not compromise the safety of trains) or energize a relay in a block with a train present causing a "wrong side failure" (one which does compromise the safety of trains).

Geomagnetic Induction Modeling
The analysis in this paper builds upon modeling techniques for geomagnetic induction in track circuits developed by Boteler (2021) and references therein. Each rail is considered to be a transmission line with series impedances and parallel admittances equivalent to the resistance of the rails and the leakages to the ground respectively. The transmission line model for each rail is then converted to an equivalent-pi circuit constructed with admittances and current sources (Boteler, 2013), and the circuits for both rails are combined with the track circuit relay components to form a nodal admittance network, as shown in Figure 2. By design, the traction rail is also periodically connected to the earth to avoid hazardous voltage build-ups, and these grounding points are also included at this stage.
The power supply current sources, I power , are calculated using Equation 1, where V power is the power supply voltage and r power is the power supply resistance.

=
(1) The current sources induced as a result of the electric field are calculated with Equation 2, where E ‖ is the electric field component parallel to the rail and Z is the series impedance of the rail.
= ‖ (2) Figure 1. Circuit diagram of a railway signaling track circuit for a single block along a network in the cases of (a) the absence of a train in the block and (b) a train occupying the block. Insulated rail joints separate each block from its neighbors, while the continuous rail is connected across all blocks. A power supply is connected to the side of the circuit from which the train enters (left in this case) and an accompanying resistor to protect it from short-circuiting; the relay is on the far end of the block (right in this case), formed of resistors and an electromagnet which in (a) is energized by the power supply, causing the switch to be in the configuration to display a green light, indicating the section is clear. When a train enters the block, as in (b), the wheels and axle short circuit the power supply causing the electromagnet to be de-energized, and the switch falls to the configuration that displays a red light, indicating the section is occupied.

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The sum of current sources directed into each node is combined to form [J] (a matrix of nodal current sources).

Rail and Track Circuit Properties
Obtaining realistic values for the electrical characteristics of an AC railway network is crucial to analyzing the impacts of GICs in DC signaling systems to the best degree of accuracy. The sections of track considered in this paper are 2-track with single-rail return and no earth wires, where 2-track means that there are two pairs of rails side-by-side, one for each direction of travel.

Rail Resistance
The railway lines being modeled use UIC 60 (60 kg m −1 ) rail (NR/GN/ELP/27312, 2006), the dimensions are provided by British steel: Rail product range (2020) from which a cross-section area of 7,600 mm 2 was calculated. We have used a value of 220 nΩ m for the resistivity of British Steel Grade 700 steel giving a resistance per unit length of the rail as 0.0289 Ω km −1 . Mariscotti (2020) and sources therein provide the same value for the per unit length resistance of UIC 60 rail.

Earthing and Bonding
The traction rail itself is not entirely continuous since track geometry or safety design features will call for occasional gaps or side switching. In such cases, both sides of each break in the rail are bonded together to ensure a continuous path for traction return current to flow. Figure 3 illustrates some of the cases where bonding is needed. These include, but are not limited to, continuity bonds used to bridge expansion joints (designed to account for the thermal expansion that rails experience with seasonal temperature changes), cross bonds (used to connect all traction rails on a line together with a path to ground to ensure low impedance is maintained throughout the line) and transposition bonds (used when the traction rail switches sides). The latter requirement can arise in numerous circumstances, including at turnouts (junctions) where they are needed to avoid the short-circuiting of adjacent track circuits. The traction rail is also bonded to all of the overhead line equipment (OLE) structures, in particular the masts located approximately every 60 m along the rail. The mast foundations connect the whole system to Earth, contributing significantly to the leakage to ground from the traction rail (Keenor, 2021). The components making up the network are the current source and admittance of the power supply (j power and y power respectively), the admittance of the relay (y relay ), the admittance to the ground at each node (e.g., y 1 , y 2 ), the admittance due to the rail between nodes, (e.g., y 12 , y 23 ), and the currents induced in the rails due to the geoelectric field between nodes (e.g., j 12 , j 23 ).

Leakage Admittance
The leakage admittance of a rail is determined by the rail fastenings, sleepers (crossties) and the ballast, and varies over a wide range due to environmental conditions and underlying ground. NR/GN/ELP/27312 (2006) gives the conventional figure for leakage admittance used by Network Rail to be 0.125 S km −1 , however, the configuration of the rails means that the signaling and traction rails have different leakage admittance. The signaling rails have insulating pads that reduce leakage, giving a leakage admittance of 0.1 S km −1 ; the traction rails are bonded to OLE structures, this results in a much larger leakage admittance of 1.6 S km −1 . Another factor considered in this study is the additional leakage from earth mats bonded to the traction return circuit at traction feeder stations, these structures increase the leakage by 10 S for each feeder station (NR/SP/SIG/50004, 2006). In the lines examined in this study, a feeder station is located between Preston and Lancaster.

Track Circuits
Track circuit parameters, including power supply and relay components, vary across the world and even within a specific country, with many different types of equipment and configurations being used. For the UK lines, we obtained the relevant data from the Network Rail Standards Portal. In this study, we have used the combination of "BR867 AC Immune DC Track Feed Unit" (NR/BR/867, 1990) and the "BR939A Miniature Tractive Armature AC Immune DC Neutral Track Relay" (NR/BR/939A, 1971). This represents the preferred design according to the most recent Network Rail standards (NR/PS/SIG/11755, 2000). The side of the track circuit from where the train enters consists of a 10 V power supply in series with a 7.2 Ω resistor to limit the current when short-circuited by the locomotive, the far end consists of the relay coil with a resistance of 20 Ω. The pickup current of the relay is 0.081 A with the dropout current being 68% of that value at 0.055 A, this means when the current flowing through an energized relay drops below 0.055 A, the relay will be de-energized and for it to be energized again, the current will need to exceed 0.081 A.

Railway Line Modeling
The geographical data for the railway lines studied, that is, the longitudes and latitudes of points along the line were obtained from OpenStreetMap. The lengths of track circuit blocks and hence their start and end points were estimated using Network Rail Sectional Appendices and the railway tracking website Traksy (https://traksy.uk/ live). Once the lines were separated into blocks, the orientation of each block in the line was calculated and used to determine the parallel electric field component along each line segment.
The sections of the railway network chosen for this study are introduced in Figure 4: the 76 km Glasgow to Edinburgh via Falkirk line and a 34 km portion of the West Coast Main Line from Preston to Lancaster. Both lines are Figure 3. A schematic diagram showing the usage of the various bonds required to ensure a continuous path for the current is provided in the traction rail. Along the top traction rail, a continuity bond is used to bridge the gap over an expansion joint designed to protect rails from the effects of thermal expansion during seasonal temperature changes; along the bottom traction rail, transposition bonds are used to temporarily switch the sides of the traction rail due to a turnout (junction) to avoid short-circuiting the track circuit in the branch; connecting both traction rails is a cross bond, designed to ensure voltages are evenly spread across all rails in a line to decrease the hazard of unsafe voltages building up along a rail.
electrified with 50 Hz AC at 25 kV. The two sections were selected for their different orientation (east-west for Glasgow to Edinburgh and north-south for Preston to Lancaster) and different geological terrane. For the following analyses, we will consider only the track in one direction of travel, eastwards for Glasgow to Edinburgh and northwards for Preston to Lancaster. Each track circuit is assumed to consist of one power supply at the start of the block (relative to the direction of travel) and one relay at the end of the block.

Modeling a Section of a Line
When modeling track circuits within a section of traction rail that extends beyond the area of study such as the Preston to Lancaster segment of the WCML, the entire length of the rail must be represented in the model to provide a valid voltage profile along the traction rail section and accurate current values across the relays. To more accurately model the geomagnetic interference on the Preston to Lancaster section, 310 × 1 km blocks before the section and 230 × 1 km blocks after the section have been included in the model, with orientation representative of the general line geometry of the WCML. The Preston to Lancaster section of the line still uses the original estimated block lengths, which range from 0.6 to 1.8 km. Figure 5 compares the voltage profiles along the section of traction rail between Preston and Lancaster when (a) the ends of the traction rail are set at Preston and Lancaster and (b) the ends of the traction rail are extended to encompass the entire WCML using the method detailed above. It can be seen that the voltage profile is significantly different if the entire length of the traction rail is not considered. If detailed information about the adjacent rail sections is not available, but the adjacent rails are uniform and nearly straight, they can be represented by an equivalent "active termination" (Boteler, 1997) where the external portion of the rail is a single voltage source and series resistance connected to ground. Calculations with active terminations to represent the northern and southern sections of the WCML give almost identical results to those from calculations including the additional representative sections beyond the area of study.

Modeling the Entire Line
The methodology described above is suitable for analyzing portions of lines that do not include either or both ends of the traction rail. But additional considerations have to be made when modeling the entire traction rail due to the effects of the ends of the line. To demonstrate this, a simplified track circuit model has been produced, consisting of 70 × 1 km blocks all orientated directly eastwards. The track circuit voltage has been set to zero, allowing us to examine the effects of only the induced currents. Figure 6 shows the voltage profiles and nodal voltages along the traction rail and each of the signaling rails when eastward electric fields of −2 V km −1 and −4 V km −1 were applied. The short thin lines illustrate how rail voltage is neither constant from node-to-node nor continuous across nodes. The potential differences across the relays in each track circuit block are shown in a separate panel. The voltage profiles along the traction rail and signaling rails agree with the characteristic electrically long and electrically short profiles as shown in Boteler (2021), respectively. It can be seen that with a constant uniform electric field applied, the nodal voltages of the traction rail and signaling rails, although having different minima and maxima, decrease along the line, following a sideways S-shaped curve. At the beginning of the line, the voltages start at their maximum point, decreasing to a central plateau. At a point near the termination of the line, the nodal voltages of both rails converge, causing the potential difference across the relay to be zero.
Closer to the termination of the line the polarity of the potential difference is reversed. It can also be seen that the location of the crossover point where the potential difference reverses remains constant regardless of the electric field strength applied. In Figure 7, the crossover point can be seen at track circuit block 64, and beyond that point the polarity of the currents is reversed.   [J ] is proportional to E and inversely proportional to the rail impedance. However, as the impedances of the signaling rails and traction rail are equal, changing E scales the currents induced in all rails by the same factor. As [Y ] −1 is constant and [J ] has been scaled by a certain factor, the result of the matrix multiplication is that [V ] would be scaled by the same factor. The current across the relays is determined by the relay resistance, which is constant, and the potential difference across the rail, which is the difference between two voltage nodes within [V ]. This means that the potential difference is again scaled by that same factor. Consequently, when the potential difference is zero, scaling it by any factor would still result in zero, leading to a common crossover point that is independent of the electric field strength.

Susceptibility to Geomagnetic Interference
In this section, we investigate the factors which contribute to the susceptibility of a track circuit relay to induced currents. For the Glasgow to Edinburgh line, the model was run for eastwards electric field values of 0 to −4 V km −1 in increments of 0.1, recording the current across the relay in each block for every E-field value. The blocks were then sorted by length and the range of currents across each relay was plotted to determine if there was a dependence on block length. To examine the effects of the angle between a block's rails and the geoelectric field, a second set of modeled data was taken with the E-field in each block orientated along the rail. The results of this modeling are shown in Figure 8. Due to the effects of the ends of the traction rail on the voltage profiles, we split the blocks near the ends from those in the center. When compared with blocks of similar length in the center of the line, the range of current values across relays toward the ends of the line is larger near the start and smaller and oppositely directed near the termination. The angle between the E-field and the rails has a definite impact, the currents induced in the section will be largest when the E-field is parallel to the rail and zero when the E-field is perpendicular to the rail. Most of the rails in blocks between Glasgow and Edinburgh are closely aligned with the direction of the E-field so the currents through most of the relays experience only minor variation, the exceptions we see are mainly due to the northwards orientation of the track leaving Glasgow before turning east toward Edinburgh. If we consider only blocks at the center of the line, the length of the blocks is a first-order indicator of the current through the relay. Considering the case when the E-field is aligned with the rails (shown by blue dashed lines in Figure 8), relay misoperations occur where the blocks are the longest. Other subtle effects can also be noted, that is, the length of surrounding blocks, which affects the current across the relay of a block in between. This analysis was repeated for Preston to Lancaster with a northwards electric field without the need to filter blocks near the ends due to it being a central segment of the WCML. The results, as shown in Figure 9, agree with those for Glasgow to Edinburgh, that is, the longer blocks are more susceptible to geomagnetic interference than shorter ones.

Uniform Electric Fields
For the following analysis, a range of uniform electric field values between ±4 V km −1 have been applied. They are based on the lower limit of geoelectric field values observed in Sweden during the storm of July 1982, where  interference on railway signaling was observed (Wik et al., 2009). Each block is assumed to be absent of any trains meaning all signals should displaying a green light, with the current flowing through the relay at a value above the relay dropout threshold. Figure 10 shows the current through the relay of each track circuit block along the two sections assuming no external electric field is applied, the line below each main panel is a schematic representation of all the signals along the section where a green outline with no fill indicates normal operation and black outline with red fill indicates a false signal. It can be seen that all relays are operating normally, with the differences in current arising from network design factors such as the length of blocks and the inclusion of traction feeder stations.
Assuming the field is uniform across the entire area of the section, electric fields ranging from 4 to −4 V km −1 increasing in intervals of 0.1 V km −1 were applied. For the "east-west" orientated Glasgow to Edinburgh line, the electric field was aligned to geographic east (E y ). For the "north-south" orientated Preston to Lancaster section, a geographic north direction (E x ) was chosen.
For Glasgow to Edinburgh, the threshold westward electric field value at which signal misoperations begin to occur is E y = −2.8 V km −1 . At the most negative electric field (E y = −4 V km −1 ) of the range we have applied, the currents induced in the track circuits are sufficiently strong to cause 14 of the relays to de-energize, displaying false signals as seen in Figure 11. With Glasgow to Edinburgh, as we are modeling the entire line, it is also important to look at the case of positive (eastward) electric fields due to the reversed potential difference beyond the crossover point. At E y = 4 V km −1 , the de-energization of the blocks beyond the crossover can be seen in Figure 12 when compared with the profiles of the negative electric fields. However, no signal misoperations occur due to the short length of the blocks toward the termination of the line.
For Preston to Lancaster, the threshold southward electric field value at which signal misoperations begin to occur is E x = −2.5 V km −1 . At E x = −4 V km −1 , the currents induced in the track circuits cause 17 of the relays Figure 11. In the absence of a train, for each of the geoelectric fields applied: the current through each of the 75 track circuit relays between Glasgow and Edinburgh. The blue dots indicate the current of each relay, the red (solid) line shows the threshold below which the track circuit would de-energize and display an incorrect signal, and the green (dashed) line shows the threshold the current would need to rise above to re-energize if de-energized. Below each plot is a schematic view of each signal and whether it is operating correctly, an unfilled green dot means normal operation and a filled red dot indicates a misoperation. In this case, there are signal misoperations at E y = −2.8 V km −1 (1 misoperation) and E y = −4 V km −1 (14 misoperations).
to be de-energized, as seen in Figure 13. As Preston to Lancaster is a central segment of the WCML, positive (northward) electric field values are not considered.

1 in 100 Year Extreme
An estimate for a 1 in 100-year extreme geoelectric field for the UK is estimated by Beggan et al. (2013) to be approximately 5 V km −1 . As we are considering an extreme case, we set the value to be negative (opposite to the direction of travel) for both lines being modeled. The currents across the relays for sections A and B are shown in Figures 14 and 15 respectively, with nearly all of the relays being de-energized between Preston to Lancaster and almost half of all relays being de-energized between Glasgow and Edinburgh. This suggests that a 1 in 100-year extreme geoelectric field value applied to the two railway sections would result in significant signal misoperations.

Discussion
This study expands upon the theoretical work of Alm (1956), Lejdström and Svensson (1956), and Boteler (2021) by modeling realistic railway lines with parameters from current industrial standards. The electrical characteristics and parameters for the rails and track circuit components are specific to the UK 25 kV, 50 Hz AC railway lines, for example, the WCML and the Glasgow to Edinburgh via Falkirk line. These values can be replaced as necessary which allow the modeling to be used for any combination of rails, blocks and relay types, provided the data for those components are available. The main reason we chose a section of the WCML was because it is one of the UK's most important railway lines. It provides rail links to major cities, including an arterial connection between England and Scotland. With a pre-pandemic estimate of 35 million passengers annually (Department for Transport, 2015), the WCML provides crucial services including local and regional travel as well as freight. The Glasgow to Edinburgh via Falkirk line was chosen for its east-west orientation and due to it being a connection between two major cities.
The model showed that the potential difference across track circuit relays near to the ends of the line can vary greatly from those in the center even if they have identical properties and parameters. This means that the susceptibility of a track circuit block to induced currents cannot simply be determined from its length and orientation (i.e., alignment to the direction of the electric field). However, we have also shown that those assumptions are valid when studying sections of a longer line that are not near the ends of the traction rail.
The range of electric field values used in this analysis (±4 V km −1 ) is based on the electric field magnitude that caused signaling systems to misoperate in Sweden during a geomagnetic storm in July 1982 (Wik et al., 2009), where a value of 4-5 V km −1 was estimated. It was demonstrated that the two UK lines studied would have experienced signal misoperations if subjected to a geoelectric field of this magnitude. Comparing the electric field values at which signal misoperations begin to occur with estimates of electric fields across the UK for different timescales by Beggan et al. (2013), the value is equivalent to an event that could occur once every 30 years. Electric fields in the UK estimated for a 1 in 100-year extreme geomagnetic field by Beggan et al. (2013) were demonstrated to cause significant disruptions to the two lines studied, with a large number of signal misoperations occurring.
While the electrical characteristics of the rails used in this study are the conventional values given in Network Rail standards, there can be variation in these parameters. For example, the leakage from the rails to the ground is affected by the weather, increasing in wetter conditions and decreasing in drier conditions. The model was re-run using the range of leakage from the rails to the ground from Network Rail standard NR/GN/ELP/27312 (2006), and the results are as follows. It was found that when the leakage to the ground was maximized (0.4 S km −1 for the signaling rail and 2 S km −1 for the traction rail), the threshold electric field values at which signal misoperations begin to occur was lowered for both Glasgow to Edinburgh and Preston to Lancaster to −0.9 V km −1 and −0.7 V km −1 respectively. When the leakage to the ground was minimized (0.025 S km −1 for the signaling rail and 1.53 S km −1 for the traction rail), the threshold electric field values at which signal misoperations begin to occur was raised for both Glasgow to Edinburgh and Preston to Lancaster to −4.3 V km −1 and −4 V km −1 respectively. This means we are more likely to see signal misoperations on days that are wetter than average and vice versa. We also tested the impact of altering the rail resistance, but it was found that varying either or both of the rail's resistance values did not result in a significant change to the results.  It was shown that signal misoperations only occurred when the applied electric field was negative (i.e., opposite to the general direction of travel). This was due to the field being orientated such that the induced currents mostly contributed toward de-energizing the relays, flowing across the relay in a direction opposite to the current provided by the track circuit power supply. When the applied electric field was positive, the relays became more energized. This was the general case for most of the track circuit blocks, but if the model includes the entirety of the traction rail, the currents across the relays in blocks near a characteristic crossover point become less sensitive to the changes in the electric field. In blocks beyond the crossover point, the direction of current across the relays will be reversed, becoming increasingly energized with a more negative electric field. In the case of the Glasgow to Edinburgh line, the blocks beyond the crossover point do not de-energize sufficiently to cause a misoperation even when the electric field is at the maximum positive value of the range used in this study, this is mainly due to the length of those blocks, which happen to be the shortest ones on the line as they are approaching the terminal station in a large city. It is worth noting that this paper only considers one direction of each line studied, depending on the orientation and layout of the track circuits, positive electric fields could cause signal misoperations in other cases, for example, for the opposite direction of travel.
In this study, we have focused on geoelectric fields of constant direction and magnitude, when in reality they typically vary in intensity and direction over time. We note that the impact of time-varying fields will need to be considered in future work. For example, the duration over which geoelectric fields must maintain a given strength and/or orientation to cause a misoperation remains unclear. In such cases, the characteristic response times of various types of track circuits to current changes will also need to be examined. Furthermore, given the diverging/converging current flows shown in Figure 7, the possibility of charge build-up (that may work to oppose the geoelectric field) should be explored.
The impact of space weather on railway signaling is but one aspect of a multifaceted system that is intrinsically connected. Alongside signaling systems, the operation of a railway network also relies upon many interdependent systems such as power transmission, communication and Global Navigation Satellite Systems, all of which are susceptible to the effects of space weather (Hapgood et al., 2021). The UK report on rail resilience to space weather Darch et al. (2014) states: "Accidents are rarely caused by a single failure; compound effects from multiple impacts are likely to create a problem" (p. 5). Considering the delays that the railway network could be subjected to in the case of extensive signaling misoperations, passengers could potentially be trapped on a stationary train for extended periods. This is especially likely if other interdependent systems are also affected. The onboard air-conditioning and toilet systems are unable to continue operating for long periods without external power sources, subjecting passengers to uncomfortable and potentially harmful conditions. In this eventuality, if passengers were to take it upon themselves to leave the train unaided, then they would be subjected to severe risk due to currents flowing in the rails, trains on adjacent lines and a plethora of other hazards from walking unattended along a potentially remote section of track.
The simplification of not including trains in the model was necessary at this initial stage of model development. This also aided in getting an overview of the fundamental principles of how induced currents affect the rails and infrastructure without other sources of interference. While this setup was ideal for analyzing the "right side failures" that occur when trains are absent from track circuit blocks, a study into the more hazardous case of "wrong side failures" will be greatly beneficial to furthering our understanding of geomagnetic interference in railway signaling systems. We consider that to be a natural next step for this research.

Conclusion
This study presents the most realistic model of geomagnetic interference in DC signaling systems on AC-electrified railway lines to date. Built upon the techniques detailed in Boteler (2021) we have modeled two sections of the UK railway network, the north-south orientated Preston to Lancaster section of the WCML and the east-west orientated Glasgow to Edinburgh via Falkirk line.
Comparing these two sections, the model showed that the extent to which induced currents can affect track circuit relays depends heavily on whether the section studied includes the ends of the traction rail or whether it is part of a longer line. When considering the impact on relays in the center of a line it can be seen that block length is a first-order indicator of current across the relays. The angular difference between the rail orientation and the electric field direction is also a factor, with blocks aligned parallel to the electric field having the largest currents induced along them. There are also further subtle effects such as the lengths of blocks adjacent to a given track circuit block which can affect the overall voltage profile.
Uniform electric fields of magnitude comparable to those reported in Sweden (Wik et al., 2009) were applied to the track sections in our model. The threshold electric field that generated sufficiently strong GICs to cause relay de-energization in the Glasgow to Edinburgh line was −2.8 V km −1 . For the Preston to Lancaster section of the WCML, the threshold electric field that caused signal misoperations was −2.5 V km −1 . These values are equivalent to those generated by events that could occur approximately once every 30 years. When electric field was strengthened to −4 V km −1 , many misoperations occurred on both lines. For the Glasgow to Edinburgh line, in the blocks after the crossover point where the polarity of the potential difference is reversed, an electric field of 4 V km −1 was insufficient to cause any misoperations, mainly due to the short length of those blocks.
Applying a 1 in 100-year extreme geoelectric field, estimated to be −5 V km −1 , the GICs generated were strong enough to severely affect the signals in the Glasgow to Edinburgh and Preston to Lancaster lines. In this case, nearly all of the signals in both sections would misoperate, leading to significant operational impacts.