Study of Variation of Polar Cap Potential During Geomagnetic Storm Events of 24 November 2001 and 24 August 2005 as Observed From LFM and BATS‐R‐US Simulation

Abstract

In this paper we examine variation of polar cap potential (PCP) during two storm events that occurred on 24 November 2001 and 24 August 2005 using Lyon‐Fedder‐Mobarry (LFM) and Block‐Adaptive‐Tree‐Solarwind_Roe‐Upwind‐Scheme (BATS‐R‐US) simulations and compare it to Weimer model. These events were simulated for zero, pure B_y, pure B_z, and full IMF conditions separately, and the PCP obtained were compared with the zero IMF PCP value as a baseline (viscous) potential. For southward IMF, PCP is defined as sum of reconnection and viscous, whereas for northward IMF, it is peak to peak potential, which either will be viscous potential or reconnection potential, whichever is larger. Both events were simulated for a constant ionospheric conductivity of 5 mhos and the variation of PCP was found to be consistent with previous literatures. Furthermore, we found that BATS‐R‐US PCP fluctuated similar to LFM PCP for most parts although their PCP values did not exactly match. We observed that BATS‐R‐US PCP also goes below viscous value for northward IMF condition, something which was observed previously in LFM simulation only. We also found that BATS‐R‐US PCP is more sensitive to smaller fluctuation of IMF compared to LFM. For 24 August 2005 event, we found the PCP reach up to 550 and 440 kV and the viscous potential reached up to 120 and 110 kV for BATS‐R‐US and LFM, respectively. Similarly, for 24 November 2001 event PCP reached up to 800 and 400 kV and viscous potential reached up to 300 and 200 kV, respectively, for BATS‐R‐US and LFM.

Introduction

Solar wind flowing outward from the Sun can vary in its speed, density, and the orientation of interplanetary magnetic field (IMF) associated with it and interacts with geomagnetic field in two different ways: magnetic reconnection and viscous interaction. The amount of energy deposited on the geomagnetic system is dependent on solar wind speed, density, and orientation of IMF and is measured in terms of polar cap potential (PCP). PCP is defined as the difference between the maximum and minimum potential present in the dawnside/duskside of a given hemisphere.

Viscous interaction occurs due to velocity shear between magnetosheath and magnetopause plasma which gets mapped to the polar cap via magnetic field lines, thus creating viscous potential. Various authors have studied variation of viscous potential using in situ measurements as well as simulations (Axford & Hines, ; Boyle et al., ; Bruntz, Lopez, Bhattarai, et al., ; Reiff et al., ; Sonnerup et al., ). Bruntz, Lopez, Wiltberger, et al., () performed Lyon‐Fedder‐Mobarry (LFM) simulation (Lyon et al., ) to study viscous potential and derived a quasi‐empirical formula to calculate viscous potential for various solar parameters during steady states for a constant ionospheric conductivity of 10 mhos: ∅_V = (0.00431)n^0.439V^1.33(kV), where “n” is the solar wind density (/cm³) and “V” is the solar wind velocity (km/s). Bhattarai and Lopez () used LFM simulation to show that the viscous potential decreases significantly during periods of strong northward IMF due to the lack of tailward return flow in the magnetosphere. However, variation of viscous potential with respect to southward IMF and East‐West IMF is still not fully understood due to overlapping of viscous and reconnection cells.

Magnetic reconnection is the most significant contributor to PCP. During periods with strongly southward IMF a two‐cell convection pattern is formed in the ionosphere and the sum of the reconnection potential and the viscous potential contributes to PCP (Hill, ). Whereas for northward IMF, Bhattarai and Lopez (), Figure 2 therein) have shown that due to the formation of four‐cell convection pattern, PCP measured across will measure the crest to crest potential, which will either be equal to the viscous or reconnection potential, whichever is larger. During periods with purely East‐West IMF, a three‐cell convection pattern has been observed (Mitchell et al., ).

It is a widely accepted idea that southward IMF is the key parameter in determining onset of a geomagnetic storm (e.g.Feldstein et al., , Russell et al., ). One of the key ways of measuring effect of storms is the Dst index. Dst index measures the perturbation in horizontal component of Earth's magnetic field along equatorial line due to variation in ring current intensity. Based on the Dst index, storms can be classified into four categories: (i) weak/small (30–50 nT) sustained for about an hour, (ii) moderate (−50 to −100 nT) sustained for about 2 hr, (iii) intense (−100 to −250 nT), and very intense (−250 and above) sustained for about 3 hr (Gonzalez et al., ). Based on this classification, both events discussed here can be categorized as intense storm.

Measuring PCP in situ is not always feasible due to positioning of the satellites. Thus, comparing simulated PCP value with actual PCP value is always a challenge. In order to establish a baseline, we are using PCP obtained from empirical Weimer model (Weimer, ). Weimer model is a statistical electric potential model developed using past satellite measurements of ionospheric electric fields and simultaneous measurement of solar wind IMF conditions. Since a satellite may not always pass through the region of largest potential, Weimer model only estimates the lower limit of PCP. LFM PCP values have been previously compared with empirical Weimer model and PCP thus obtained is found to be in very good agreement during periods of southward IMF if appropriate scaling factor was applied in order to adjust ionospheric conductance (Bruntz et al., ; Lopez et al., ).

In this paper we will be discussing variation of PCP during two storm events: (i) 24 August 2005 and (ii) 24 November 2001 using LFM and BATS‐R‐US simulation for a constant ionospheric conductivity value of 5 mhos compared to Weimer potential. We will also be performing both simulations with one or more of the IMF components turned off and compare those with PCP during zero IMF condition (i.e., viscous potential). Furthermore, we will be comparing LFM and BATS‐R‐US PCP values during full IMF condition with PCP obtained from Weimer model (will be referred to as Weimer potential here on) for identical solar wind condition and analyze their overall behavior.

Both simulation models used here ignored ring current as we wished to compare the PCP between these two models with as many fewer variables as possible. However, ring current is a significant contributor to magnetosphere‐ionosphere coupling. The azimuthal pressure gradient in the inner magnetosphere is considered as the main driver of region 2 current (Vasyliunas, ). Pembroke et al. () coupled LFM with Rice Convection Model in order to study the impact of presence of ring current, and they found a substantial increase in ring current pressure with stronger region 2 currents; however, they did not observe a significant change in PCP. Zheng et al. () performed simulation using Comprehensive Ring Current Model to determine change in region 2 field aligned current for different values of PCP using data from real storm events and found that it depended on overall strength and instantaneous values of PCP. They showed a stronger and equatorward expansion of region 2 current for higher PCP as well as a stronger ring current due to more ring current particles able to penetrate deeper into inner magnetosphere. Ebihara et al. () looked at DMSP‐F13 satellite data and also found an increase in PCP when a strong CME hit Earth's magnetosphere. They also found an increase in intensity and equatorward expansion of region 2 current in Comprehensive Ring Current Model simulation.

BATS‐R‐US PCP has also been compared with Weimer model in Kalafatoglu Eyiguler et al. () (Figure ) for a real solar wind event and they found that Weimer potential were seen to match BATS‐R‐US PCP with Rice Convection Model or Comprehensive Ring Current Model turned on, but at times, it is seen to vary significantly. They also attributed some part of this variation to change in ionospheric conductance during the storm period.

Thus, presence of ring current in these simulations is expected to increase the PCP value, although their relationship and dynamics is not at all linear and is yet to be understood fully.

Introduction to LFM and BATS‐R‐US Simulation

The LFM simulation model (Lyon et al., ) uses spherically distorted grid to solve three‐dimensional time‐dependent single‐fluid magnetohydrodynamic equations. Simulation boundary extends from +25 to −300 R_E along x direction and ±100 R_E along y and z direction. The inner boundary of this simulation is spherical and terminates at 3 R_E. Below this surface, the Birkeland current is mapped along the magnetic field line into the ionosphere in order to calculate PCP. For this research, we used LFM model with grid resolution of 50 × 24 × 32 and all simulation results present here are performed without dipole tilt. In the x‐z plane, the resolution is about 0.35 R_E along inner boundary; at magnetopause it is about 0.32 R_E and along the tail it is about 0.88 R_E at about x = −10 R_E and 1.3 R_E at x = −20 R_E. In other planes the grids are radially and azimuthally distributed. Generally, x axis point toward the center of the Sun from center of the Earth, z axis points toward the Earth's north pole, and y axis completes the right‐hand rule for both of these simulation models. However, there are specific coordinates systems like Geocentric Solar Ecliptic and Geocentric Solar Magnetospheric that are chosen while running these simulation models and the definition of x, y, and z axes may vary slightly.

BATS‐R‐US (Block‐Adaptive‐Tree‐Solarwind_Roe‐Upwind‐Scheme) is a model developed by Center for Space Environment Modeling at the University of Michigan. This model is designed using Message passing Interface and Fortran90 standard and executes on a massively parallel computer system. It solves three‐dimensional magnetohydrodynamic equations in finite volume form and uses an adaptive grid composed of rectangular blocks arranged in varying degrees of spatial refinement levels (Gombosi et al., ; Powell et al., ; Ridley et al., ). All BATS‐R‐US simulation analyzed here have been performed using Community Coordinated Modeling Center resource and contains 755,136 cells. In the x‐z plane, it has a resolution of ¼ R_E around the Earth and 0.5 R_E resolution in near‐tail and magnetopause region and has fairly similar resolution in other planes too. In terms of number of grids in BATS‐R‐US, it is about 19 times denser compared to LFM version used in this research (https://ccmc.gsfc.nasa.gov/requests/grid_BATSRUS.php).

Result and Discussion

Event 1–24 August 2005

Figure  shows a solar wind storm event that occurred on 24 August 2005 from 05:00 to 12:00 hours. All hours here correspond to universal time (UT). In the second panel, the x component of velocity (V_x) increased from 450 to 550 km/s between 05:00 to 09:00 hours and then further increased up to 650 km/s between 09:00 and 12:00 hours. In the first panel, the solar wind density fluctuated multiple times to values higher than 40/cm³. The nominal density during quiet period is around 4–5 particles per cc. The variation of SYM‐H in the bottom panel shows strong perturbation in equatorial geomagnetic field by about 170 nT at around 11:45 hours. Although the actual event lasted longer, we did not simulate periods after 12:00 hours due to unreliable solar wind data.

Fig. 1. Solar wind profile during 24 August 2005 from 5:00 to 12:00 hours. All units are in GSM coordinate system. From top to bottom panels show the proton density ρ in cm−3), solar wind plasma speed (Vx in km/s), x component of IMF (Bx in nT), y component of IMF (By in nT), z component of IMF (Bz in nT), and SYM‐H index (nT), respectively.

Figure  shows variation of PCP during the storm event described in Figure . We see a reasonably well correlation in PCP (bottom panel) obtained from LFM, BATS‐R‐US, and Weimer model during nominal solar wind condition (5:00–6:30 hours). However, once solar wind density and velocity starts to increase, the values start to differ but the variation pattern between these all these models are still similar. For this event LFM and BATS‐R‐US PCP are seen to be in better agreement than Weimer.

Fig. 2. Comparison of polar cap potential (PCP) obtained from LFM and BATS‐R‐US simulation and Weimer model for the storm event.

The PCP obtained from Weimer model is seen to be lower than LFM and BATS‐R‐US for southward IMF conditions. Since Weimer model used potentials obtained from satellite data and satellite may not always pass through the region of highest potential, it only provides the lower bound of the PCP values and this phenomenon can also be observed in Figure  as well during periods of southward IMF. However, during periods of northward IMF, LFM, and BATS‐R‐US PCP drops below Weimer potential value because Weimer model does not incorporate reduction of viscous potential value during northward IMF.

In figures below, we will be discussing in detail the cause of PCP fluctuation in LFM simulation by analyzing how individual components of IMF affect overall PCP and compare it with PCP obtained from BATS‐R‐US. In order to do so, let us start by evaluating the contribution to PCP when IMF is turned off.

Figure  shows variation of PCP when we turned all the IMF components to zero. Thus, the PCP obtained in this case is purely mechanical in nature, that is, solely due to dragging of magnetopause plasma due to velocity difference between the magnetopause and magnetosheath plasma, thus forming a convection pattern inside the magnetosphere which gets mapped to the ionosphere along magnetic field lines producing viscous potential (Bruntz et al., ). The value of viscous potential is seen to increase with increase in solar wind speed and density which has also been confirmed by various authors by analyzing in situ observation data (Boyle et al., ; Newell et al., ) as well as simulation models (Bruntz, Lopez, Bhattarai, et al., ; Sonnerup et al., ). BATS‐R‐US is seen to be more sensitive to density fluctuation compared to LFM, although PCP obtained from both of them are very close, which might be due to better resolution and/or different numerical solving schemes.

Fig. 3. PCP obtained using LFM and BATS‐R‐US simulation for a zero‐IMF condition.

The value of viscous potential obtained from LFM has been used in previous research as a baseline to determine merging potential during southward and east/westward IMF condition (Lopez et al., ). In the case of purely northward IMF, Bhattarai and Lopez () have shown that merging potential cannot be obtained by subtracting viscous potential from PCP due to a four‐cell convection pattern forming in the ionosphere which decouples viscous and reconnection potential. They also found that the viscous potential weakens significantly as the magnitude of northward IMF increases.

For the event discussed in this part, the viscous potential reaches up to about 125 kV for BATS‐R‐US and about 100 kV for LFM simulation during period when solar wind speed and density are around 600 km/s and 30 per cc.

Figure  shows variation of PCP due to purely y component of IMF. In the figure, we see LFM that PCP reaches up to about 300 kV. PCP obtained from BATS‐R‐US is seen to be always lower than that obtained by LFM once the storm arrives, but the fluctuation pattern is seen to be strikingly similar to that of LFM.

Fig. 4. Variation of PCP as obtained from LFM simulation due to purely y component of IMF.

Figure  shows variation of PCP due to the presence of only z component of IMF. LFM PCP stays around 100 kV from 6:40 to 8:30 hour, although IMF changes from weakly southward to weakly northward. This higher value (nominally it is around 20–40 kV (Boyle et al., ; Doyle & Burke, )) is due to the increase in viscous potential because of higher velocity and density solar wind values. Once the IMF gets strongly northward (between 8:30 and 9:10 hours), the PCP decreases to about 60 kV. However, we see a viscous potential of about 90 kV during the same time period from Figure . Although it looks contradictory, Bhattarai and Lopez () have studied in detail about the decrease in PCP during purely northward IMF and found that the viscous potential decreases below zero‐IMF viscous value due to absence of return flow inside the magnetopause.

Fig. 5. Variation of PCP during purely z component of IMF.

In Figure , IMF B_z turns southward around 9:15 hours and gets stronger until 10:20 hours during which we see PCP increasing significantly as expected due to increased reconnection rate, after which it starts decreasing due to the weakening of southward B_z. This variation of PCP as seen in LFM simulation is consistent with previous studies performed using LFM simulation for steady as well as real solar wind condition (Bhattarai et al., ; Bhattarai & Lopez, ; Bruntz, Lopez, Wiltberger, & Lyon, ; Lopez et al., ). PCP obtained from BATS‐R‐US is seen to match well with LFM until B_z starts turning strong southward after which BATS‐R‐US is showing higher values of PCP. We also observe that BATS‐R‐US consistently responds more to minor fluctuation of IMF components compared to LFM PCP. This might be either due to better grid resolution of BATS‐R‐US or different numerical schemes used to solve the magnetohydrodynamic equations or combination of both.

Figure  compares PCP obtained from LFM simulation driven by different IMF conditions. The green curve here denotes PCP when all IMF component is turned off, that is, viscous potential. We observe from the graph that PCP decreases below the viscous value during purely B_z condition only as observed by Bhattarai and Lopez () during steady state LFM simulation. We also see that during period of southward IMF from 9:00 to 11:00 hour, PCP due to full IMF (red) and pure B_z IMF (blue) have similar trend.

Fig. 6. Comparison of PCP obtained from LFM simulation for different IMF conditions.

Lopez et al. () found that one can reproduce PCP with a complex input by using PCP values obtained from LFM simulation to generate partial responses to individual IMF components using simple linear superposition. In Figure , since full IMF is always higher than purely B_z and B_y IMF during periods of southward IMF (9:00–11:00 hours), the linear superposition hypothesis seems to work well. However, in Figure  where we are comparing PCP during different IMF condition in BATS‐R‐US simulation, during periods of southward IMF and between 9:00 and 10:00 hours we see that PCP due to purely B_z component (blue line) gets higher than PCP due to full IMF (red line), suggesting that BATS‐R‐US might not obey linear superposition of orthogonal merging concept introduced by Lopez et al. ().

Fig. 7. Comparison of PCP obtained from BATS‐R‐US simulation for different IMF conditions.

Gordeev et al. (), Figure 2 therein) performed BATS‐R‐US simulation for ideal solar wind condition with purely B_z component that switch from northward to southward at regular time interval. In that research when the B_z was northward, the PCP decreased down to 15 kV for +5 nT B_z and to 10 kV for +10 nT B_z which hints to reduction of viscous potential in BATS‐R‐US simulation as well. In the same paper they simulated a real solar wind event, and during periods with strong northward IMF (Figure ), PCP is seen to be reduced to about 15 kV suggesting reduction of viscous potential during northward IMF.

In Figure , we also see that PCP due to purely B_z IMF (blue line) decreases below the viscous value (green line) during periods of northward IMF, implying a reduction of viscous potential during periods of northward IMF in BATS‐R‐US similar to that observed by Bhattarai and Lopez () in LFM simulation.

Event 2–24 November 2001

In this section we will be presenting results obtained for 24 November 2001 storm event. Both LFM and BATS‐R‐US PCP will be analyzed here too. Since we have explained in detail trend lines of PCP and the reason for such variation on the basis of previous published research, for Event 2 we will only discuss phenomenon that are unique to this particular event.

Figure  shows solar wind profile from 6:00 to 14:00 hours. Although the actual storm lasted much longer, we only chose data that were usable from OMNI database. During this period, the solar wind speed stayed high compared to nominal value of about 400 km/s but had relatively smaller fluctuation compared to Event 1. Thus, most of the changes in PCP values for Event 2 can be attributed to change in solar wind density and IMF components.

Fig. 8. Solar wind profile during 24 November 2001 from 6:00 to 14:00 hours. (top to bottom) Proton density (ρ in cm−3, solar wind plasma speed (Vx in km/s), x component of IMF (Bx in nT), y component of IMF (By in nT), z component of IMF (Bz in nT), and SYM‐H index (nT), respectively.

The bottom panel of Figure  shows variation of PCP for full solar wind condition obtained from LFM and BATS‐R‐US simulations. During time interval of 6:15–6:40 hours when B_y is getting stronger whereas B_z is fluctuating, BATS‐R‐US is found to yield PCP much higher than LFM and Weimer. BATS‐R‐US PCP responds similarly between time interval 10:40–11:30 hours. For this event, Weimer PCP variation pattern is not seen to match well with other two simulation PCP during southward IMF periods. This might be due to PCP obtained from simulation being sensitive to faster fluctuation of solar wind parameters and not having enough time to attain steady state PCP value.

Fig. 9. Comparison of PCP obtained from LFM and BATS‐R‐US simulation and Weimer model for the storm event.

During periods of northward IMF between 8:00 and 10:30 hours, LFM and BATS‐R‐US PCP are seen to be higher during some interval than Weimer, although the viscous potential is supposed to reduce. Newell et al. () used fit of 10 magnetospheric parameters to determine an empirical formula and found that $n^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{v}^2$ provides best match for viscous potential, where “n” is the density (/cc) and “v” is the velocity of solar wind (km/s). Thus, the higher simulation PCP is due to higher of solar wind density, velocity, and B_y component compensating for this reduction due to northward IMF value and keeping simulation PCP values higher than Weimer PCP.

If we look at the variation of PCP during zero IMF condition between these two simulations, we do not see significant difference (Figure ). In both of these events, BATS‐R‐US PCP is seen to be consistently higher than LFM PCP for zero IMF runs (compare Figures  and ).

Fig. 10. PCP obtained using LFM and BATS‐R‐US simulation for a zero‐IMF condition.

During Event 2, PCP obtained for purely B_y condition from LFM and BATS‐R‐US seem to match reasonably well (Figure ). We also observed that, for Event 1 PCP, due to pure B_y IMF obtained from BATS‐R‐US, is smaller than that from LFM simulation; however, the opposite is seen in Figure . This should have been caused by difference in fluctuation pattern of solar wind density and velocity between Events 1 and 2. The B_y dependence of PCP on solar wind speed and density in BATS‐R‐US will be an interesting phenomenon to explore in future research.

Fig. 11. PCP obtained using LFM and BATS‐R‐US simulation for a purely By IMF condition.

Figure  shows variation of BATS‐R‐US and LFM PCP for purely B_z IMF. Here we see that BATS‐R‐US is yielding consistently higher PCP compared to LFM when the IMF turns southward, which we did not observe during Event 1. PCP during intervals 6:15–6:40 and 10:40–11:30 hours are seen to be significantly higher than LFM for this event. A closer observation during these intervals show a sharp increase in velocity from 6:15 to 6:40 hours (25‐min interval) and sudden change in density between 10:40 and 11:30 hours (50‐min interval); whereas for Event 1 both velocity and density remained fairly constant when B_z switched to negative value and started getting stronger (9:20–10:00 hours, 40‐min interval). Thus, we believe that BATS‐R‐US overpredicts PCP values compared to LFM when fluctuations/strengthening/weakening of solar wind parameter is sudden. Again, this might be due to difference in grid resolution or numerical scheme implemented to solve the system or combination of both.

Fig. 12. PCP obtained using LFM and BATS‐R‐US for a purely Bz IMF condition.

Figure  shows how PCP varies for Event 2 during different IMF conditions in LFM simulation. We again see reduction in viscous potential during periods of northward IMF (8:00–10:40 hours) as expected. During 9:20–9:50 hours, we see full IMF PCP (red line) values lower than viscous potential values (green line) as the B_z is strongly northward during this period. Even if PCP due to B_y has been added to full IMF, an increasing B_y potential value (black line) is not strong enough to compensate loss of viscous potential due to stronger northward IMF resulting in the red line decrease below viscous value during those hours.

Fig. 13. Comparison of PCP during different IMF condition obtained from LFM simulation.

Figure  shows variation of PCP during different IMF conditions as obtained from BATS‐R‐US simulation. Just like LFM, the full IMF as well as purely B_z IMF PCP are seen to go below viscous potential value suggesting decrease in viscous potential during purely northward IMF condition.

Fig. 14. Comparison of PCP during different IMF condition from BATS‐R‐US simulation.

Conclusions

We have examined the behavior of PCP in LFM and BATS‐R‐US simulation and Weimer model for two different storm events that occurred on 24 August 2005 and 24 November 2001. Both events were simulated for a constant ionospheric conductivity of 5 mhos. During both events we found that variation pattern of PCP was consistent with behavior of PCP observed in previous research by Bhattarai et al. (), Lopez et al. ( and ), Bruntz, Lopez, Bhattarai, et al., and Bruntz, Lopez, Wiltberger, & Lyon, ), and Mitchell et al. (), although most of these previous works dealt with steady state IMF conditions.

Weimer model PCP was used as a baseline to compare the simulation PCP values for both events. We found that during the first event, the PCP variation trends were similar for all three models. Simulation PCP values were seen to decrease below Weimer PCP value during northward IMF during this event which is consistent with previously observed results (Bhattarai & Lopez, ; Lopez et al., ).

For the second event BATS‐R‐US PCP was found to fluctuate more compared to Weimer and LFM PCP. Since the fluctuation of solar wind parameters is more frequent in second event, higher fluctuation in BATS‐R‐US PCP might be due to better resolution of BATS‐R‐US or due to different numerical schemes used to solve the magnetohydrodynamics equations or combination of both. The PCP values from simulation were observed to be higher than Weimer during periods of northward IMF during this event. This was due to higher values of solar wind parameters which compensated for any decrease in viscous potential values due to northward IMF. Although the PCP values from all three models did not match in both events for most periods, the overall response to fluctuation of solar wind parameter had similar trend for most part.

We also observed that the PCP obtained from BATS‐R‐US simulation decreases below the viscous value as predicted by Bhattarai and Lopez () for LFM simulation. We also observed that PCP during pure B_y condition for BATS‐R‐US and LFM simulation matches better than B_z or zero condition.

Acknowledgments

This work used global MHD simulation code available at CCMC (Community Coordinated Modeling Center), operating at NASA GSFC (http://ccmc.gsfc.nasa.gov) to perform BATS‐R‐US simulation and Weimer model.