The present understanding is that the coupling of the solar wind and the Earth's magnetosphere occurs via magnetic reconnection and viscous processes such as the Kelvin–Helmholtz instability (e.g., ) and diffusion . Although viscous processes may play a strong role, particularly when the interplanetary magnetic field (IMF) is northward (IMF BZ>0 nT) (e.g., ), magnetic reconnection on the dayside magnetopause is responsible for the majority of plasma transport across the magnetopause during southward interplanetary magnetic field IMF (IMF BZ<0 nT), allowing the solar wind to drive activity in the Earth's space environment . The intervals of extended periods of strongly southward IMF typically arise when the Earth encounters an interplanetary coronal mass ejection (ICME) (see, e.g., ). ICMEs are interplanetary counterparts of coronal mass ejections (CMEs), large eruptions of plasma and magnetic field from the Sun, driving the strongest geomagnetic disturbances (e.g., ). The signatures of ICMEs at 1 AU include high helium abundance , high magnetic field magnitude and low plasma beta , low ion temperatures , and smooth rotation of the magnetic field . While there have been attempts to form a universal set of signatures to describe ICMEs , they vary significantly such that no single set of criteria is able to describe all the ICME events, and none of them is unique to ICMEs. For example, only one-third to one-half of all the ICMEs have a magnetic flux rope (or a magnetic cloud) e.g.,, whose signatures combine enhanced magnetic field, reduced proton temperature, and the smooth rotation of the magnetic field over an interval of a day . While magnetic clouds are the most studied part of ICMEs due to their significant potential to cause large space storms, their relationship with the entire ICME sequence still poses many questions (e.g., ). Moreover, if the ICME is sufficiently faster than the ambient solar wind plasma, a shock is formed ahead of the ICME , with a region of compressed solar wind plasma between the leading shock front and the magnetic cloud, referred to as the sheath region.

The sheath and ejecta are the most distinctive parts of ICMEs (see, e.g., ), and both can drive intense magnetic storms (e.g., ). However, they have clear differences in their solar wind conditions and, consequently, their coupling to the magnetosphere is different . ICME sheaths typically include high solar wind dynamic pressure and fluctuating IMF, including both northward and southward orientations within a short time period . The duration of the sheath is also typically shorter than the following cloud: for example. obtained the average values of 10.6 and 30.6 h for sheaths and clouds, respectively. Sheaths are known to enhance high-latitude ionospheric currents and they are found to have higher coupling efficiency than clouds . The clouds typically enhance the equatorial ring current .

Due to the potential for strongly southward IMF orientation, ICME magnetic clouds drive enhanced magnetospheric activity. Moreover, during cloud events, due to the combination of generally high magnetic fields and low plasma densities, the solar wind Alfvén–Mach number MA can reach quite low values and even be close to unity. The role of MA in solar wind–magnetosphere coupling has been highlighted in recent studies . In particular, the role of low MA conditions typical for ICME magnetic cloud in the saturation of the ionospheric cross-polar cap potential (CPCP) has been a subject of several studies e.g.,.

Global MHD models have been used to study the effects of ICMEs on the magnetospheric and ionospheric dynamics. used the H3DMHD model (e.g., ) to examine a CME event on 15 March 2013. They found that the high-energy solar energetic proton time–intensity profile can be explained by the interaction of a CME-driven shock with the heliospheric current sheet embedded within nonuniform solar wind. A recent paper by studied the Bastille Day geomagnetic storm event (15 July 2000) driven by a halo CME. They found that the inclusion of auroral conductivity in the ionospheric part of the global MHD model by led to saturation of the CPCP without any effect on the field-aligned currents, thus suggesting a current system with a dynamo in the magnetosphere and a load in the ionosphere. The difficulty in assessing these studies is that they often do not include uncertainty estimate of the model results, while the methods are different for each study. Moreover, while the different MHD simulations are based on the same plasma theory, the approaches are different in terms of the exact form of the equations, the numerical solutions, and the initial and boundary conditions, thus making comparisons of different models difficult. Nonetheless, understanding of the performance limits of the simulations is essential for meaningful comparisons to in situ measurements.

Regardless of the different approaches used in global codes, the performances of the models have been assessed in several studies. Usually such assessments are done through comparisons of the simulation results with in situ or remote observations of dynamic events or plasma processes . This is often not easy, as even small errors in the simulation configuration may create large differences with respect to the observations locally at a single point , even if the simulation would reproduce the large-scale dynamic sequence correctly. Moreover, recent studies have shown that none of the codes emerges as clearly superior to the others, each having their strengths and weaknesses. In the absence of uniform code performance testing methodology, validating the results individually is important.

In this study we use the GUMICS-4 and global MHD simulation and consider two ICME events, one with a significantly stronger solar wind driver than the other. To compare the two events, we use variables that are both particularly sensitive to upstream changes and used extensively in previous studies, and examine how those variables are affected by the two events. The comparisons include the subsolar magnetopause position, the amount of energy transferred from the solar wind into the magnetosphere, the CPCP, and the magnetic field magnitude within the inner part of the magnetosphere, thus including both global and local variables. We especially focus on periods within the magnetic clouds within the ICMEs, by using two different spatial resolutions. We provide an uncertainty estimate (standard deviation and in some cases also relative difference) for each quantity by comparing simulation results to well-established references, which include the Shue model (magnetopause location), the epsilon parameter (energy transferred through the magnetopause), the polar cap index (PCI) (CPCP), and in situ measurements by the Geotail and Cluster spacecraft (magnetic field magnitude). Both uncertainty estimate methods are assessed and they are used if the method is valid for the chosen quantity.

This paper is structured in a following way: Sect.  describes GUMICS-4 global MHD code and the simulation setup, Sect.  describes characteristics of the two ICME events and the executed simulations, Sect.  presents the main results and Sect.  includes the discussion followed by conclusions.

We use the solar wind data from the NASA OMNIWeb service (http://omniweb.gsfc.nasa.gov, last access: 30 January 2018) and the solar energetic particle data from the NOAA NCEI Space Weather data access (https://www.ngdc.noaa.gov/stp/satellite/goes/index.html, last access: 22 March 2018). Onset times for the ICME sheath (i.e., the shock time) and the magnetic cloud boundary times are retrieved from the Wind spacecraft ICME catalog (https://wind.nasa.gov/ICMEindex.php, last access: 30 January 2018). Figures  and show the upstream parameters during both events. For both figures, IMF X,Y,Z components and the IMF magnitude are shown in panel (a), upstream plasma flow velocity X,Y,Z components in panel (b), the upstream plasma number density in panel (c), upstream Alfvén–Mach number (in logarithmic scale) in panel (d), energetic proton fluxes for three GOES-15 energy channels between 8 and 80 MeV in panel (e), and the cross-polar cap potential from the GUMICS-4 simulation in panel (f). Figure  includes the time range from 09:00 UT, 14 July to 15:00 UT, 17 July 2012, while Fig.  shows the period from 19:00 UT, 28 April to 17:00 UT, 1 May 2014. The time of the ICME shock and the start and end times of the ICME are marked with vertical red lines in both figures. The grey-shaded regions indicate the time periods simulated with the maximal 0.25 RE spatial resolution. Both IMF and plasma flow velocity components are given in the GSE coordinate system, which is also the coordinate system used by the GUMICS-4 simulation.

Figure shows the arrival of the leading shock at 18:53 UT on 14 July 2012 as the simultaneous abrupt jump in the plasma and magnetic field parameters and the following ICME sheath as irregular directional changes in the IMF and compressed plasma and field. The energetic particle fluxes for the two lower-energy channels increase until after the shock passage, which suggests continual particle acceleration in the shock driven by the ICME. At 06:54 UT on 15 July, the onset of the ICME magnetic cloud is identified by strong southward turning of the IMF. There is significant reduction in the number density and the clear decrease in the variability of the interplanetary magnetic field. During the next 45 h, the IMF direction stayed strongly southward while slowly rotating towards a less southward orientation. We note that in the trailing part of the ICME, the field changes rather sharply to northward, thereafter continuing to rotate southward again. We cannot rule out that this end part is not another small ICME, but as our study focuses on the strong southward magnetic fields in the main part of the ICME we do not consider the origin of this end part further here.

The ICME on April 2014 was slower than the July 2012 ICME, and its speed was very close to the ambient solar wind speed. Hence, no shock nor clear sheath developed ahead of this ICME. The onset of the ICME-related disturbance is marked by the increased plasma number density followed by a rapid decrease and a clear southward turning of the IMF at 20:38 UT on 29 April (Fig. ). The weaker activity is also evident in the lack of energetic particle fluxes above the background in the magnetosphere. The very early phase of this cloud may contain some disturbed solar wind (the region of higher density and fluctuating field), but we do not identify it as a sheath and focus our study on the effects of the cloud proper.

Both magnetic clouds are characterized by a low Alfvén–Mach number. In the 2012 case, MA drops even below unity and is 1.9 on average during the cloud structure, while during the 2014 magnetic cloud, the minimum MA was 3.8 and the average was 5.8.

The 2012 event features generally larger CPCP, with values above 40 kV and reaching 70 kV (Fig. f). On the other hand, during the 2014 event the CPCP peaks early at 50 kV and subsequently reduces to 20 kV (Fig. f). GUMICS-4 CPCP values depend on grid resolution, and while lower grid resolution may result in substantially lower CPCP values than the observed values , higher resolution leads to higher CPCP values e.g., and thus better agreement with the observations.

The 2012 ICME event is considerably longer than the 2014 event, with 57 h 26 min total duration, of which 12 h 1 min are sheath and 45 h 25 min part of the magnetic cloud passage. The 2014 event lasted 21 h 13 min in total. The 2012 ICME had larger effects on magnetospheric activity, as the solar wind driving was considerably stronger, with the average IMF magnitude and solar wind speed of 14 nT and 490 kms-1, respectively, compared with 8.5 nT and 303 kms-1 of the 2014 event. The maximum IMF magnitude and upstream solar wind speed were also larger during the 2012 event, with 21 (10) nT and 660 (321) kms-1 maximum values measured during the 2012 (2014) cloud. However, while maximum number density was higher during the 2012 magnetic cloud (36 vs. 30 cm-3), the average number density was considerably higher during the 2014 event (2012: 2 cm-3 vs. 2014: 12 cm-3).

During the two ICME events, data from the Cluster 1 (hereafter Cluster) and Geotail satellites were available from the CDAWeb service (https://cdaweb.sci.gsfc.nasa.gov/index.html/, last access: 8 October 2018). Figure  shows the orbits of Cluster (blue) and Geotail (green) along with the magnetopause location (black) from the empirical Shue model on the XY plane (Fig. a and c) and on the XZ plane (Fig. b and d) for both events. The magnetopause position is computed for the most earthward magnetopause location during the events, while the orbit tracks include intervals of nominal upstream conditions before and after the ICME events. Start and end points of the time intervals are marked with a cross and a triangle, respectively. Dots mark the points where satellite orbits intersect (located visually) the innermost position of the magnetopause. The variability of the magnetopause position means that between those orbit tracks the S/C may cross to outside the magnetosphere. The used coordinate system is GSE. Based on Fig. , the Cluster spacecraft orbits inside of the magnetosphere throughout the 2012 event and for most of the 2014 event. On the other hand, Geotail is outside the magnetosphere an extended period during 16–17 July 2012 as well as during several periods in April–May 2014.

Figures and show time series of the magnetic field magnitude |B| along the Geotail (panel a) and Cluster (panel b) orbits during the 2012 and 2014 events. Green (Geotail) and blue (Cluster) curves show the observations, while the black (magenta) curve shows the magnetic field magnitude along the spacecraft orbits in GUMICS-4 simulation using 0.5 (0.25) RE maximum spatial resolution. The yellow-shaded regions in panels (a) and (b) indicate times when the spacecraft may encounter magnetopause crossings. Note that a logarithmic scale is used for the Cluster data. Panel (c) in both figures shows the radial distance of the spacecraft from the center of the Earth. Note that satellite measurements have been interpolated over long (several hours) data gaps, most notably on 16 July, 12:15–18:45 UT.

At the start of the 2012 event, Geotail resides in the plasma sheet but quickly moves to the boundary layer (roughly 14 July, 16:00 UT to 15 July, 06:00 UT), after which it enters the lobe as the cloud proper hits the magnetosphere. At around the end of the data gap at the end of 16 July, the spacecraft moves to the low-latitude boundary layer and the magnetosheath (identified from plasma data not shown here).

At the start of the 2012 event, Cluster is near perigee, recording field values dominated by the dipole contribution. Cluster exits the ring current region around 16:00 UT on 14 July and enters the plasma sheet. A brief encounter in the lobe is recorded between roughly 18:00 UT 15 July and 06:00 UT 16 July. A second period in the inner magnetosphere commences around 12:00 UT on 16 July, with exit to the lobe after 00:00 UT 17 July (identified from plasma and energetic particle data not shown here).

In this paper we study (1) how the magnetosphere responds to two ICME events with different characteristics by means of using the GUMICS-4 global MHD simulation and (2) how accurately GUMICS-4 reproduces the effects of the two events. The 2012 event was stronger in terms of solar wind driver, the 2014 event being significantly weaker in terms of both solar wind speed and IMF magnitude. We considered both global and local parameters, including magnetopause nose position along the Sun–Earth line, total energy transferred from the solar wind into the magnetosphere, and the ionospheric cross-polar cap potential (CPCP). Local measures include response of the magnetic field magnitude along the orbits of Cluster and Geotail spacecraft. The two ICME events were simulated using 0.5 RE maximum spatial resolution. To test the effect of grid-resolution enhancement on global dynamics, we simulated 6 h subsets of both CME cloud periods with 0.25 RE maximum spatial resolution. As uncertainty metrics we use both relative difference magnitude δ and SD.

Due to stronger solar wind driving, the 2012 event causes the magnetosphere to compress more than during the 2014 event, with the magnetopause moving earthward at the onset of the 2012 ICME sheath and reaching 7 RE distance from Earth, until moving sunward at the onset of ICME magnetic cloud (see Fig. c). Both ICMEs are preceded by low IMF BZ and solar wind dynamic pressure, with 2014 missing high-amplitude fluctuations before ICME cloud due to the absence of a separate ICME sheath. Despite this, the movement of the magnetopause is similarly earthward prior to the cloud, reaching 9.5 RE just before the onset of the cloud (see Fig. c). During the cloud, however, the orientation of the IMF slowly rotates from southward to northward and the magnetopause is in constant sunward (earthward) motion in 2012 (2014). While the polarity of the IMF changes before the end of the ICME in 2012, it changes from southward to northward only after the end of the ICME in 2014.

The magnetopause nose location in GUMICS-4 is identified as a single grid point from the maximum value of JY along the Sun–Earth line. Location deviations in response to solar wind driving in the GUMICS-4 results are dependent on the driver intensity: stronger driving during the 2012 CME magnetic cloud leads to a larger relative difference magnitude δ (2012: 8.0 % δ on average) as compared to the model, whereas the agreement between the simulation and the empirical model is quite good (3.3 % δ on average) during weaker driving during the 2014 event (Figs.  and ). This view is further supported by SDs: for the full simulation time range, the SD is 0.661 (0.321) in 2012 (2014). Average δ during nominal solar wind conditions is almost identical for both events: 2.5 % for the 2012 event and 2.4 % for the 2014 event.

Comparison of the magnetopause location between the 0.25 RE (0.5 RE) resolution run and the Shue model shows that the relative difference between the two is below 10 % for 92 % (89 %) of the 6 h subset in 2012 (Fig. c), while corresponding analysis of the 6 h subset in 2014 (Fig. c) yielded differences below 10 % for 100 % of the time regardless of the resolution. It should be noted that, despite the relative difference in magnitude being slightly lower for the 0.5 RE resolution run than for the 0.25 RE resolution run for both the 2012 (4.9 % and 5.6 %) and 2014 (3.2 % and 4.5 %) events, the 0.25 RE run reaches better agreement with the Shue model, especially when the magnetopause is moving during high solar wind driving in 16 July, 01:00 UT (Fig. c).

When spatial resolution is increased, gradient quantities such as JY have sharper profiles and therefore larger values . As it is the maximum value of JY that we use to locate the magnetopause nose, the nose position evaluation in the lower-resolution runs is more ambiguous due to the larger spread of the current and due to the larger grid cell size. This may lead to changes in the maximum value of up to several RE over short time periods in response to upstream fluctuations. In the finer-resolution runs, JY distribution is sharper, which leads to lesser fluctuations in the maximum value determination. However, the differences between the two grid resolutions occur only under rapidly varying solar wind or very low solar wind density conditions.

The empirical models developed by are based on statistical analysis of a large number of spacecraft measurements of plasma and magnetic field during magnetopause crossings. While the model is optimized for moderate upstream conditions, the model targets especially stronger driving periods. However, we computed the difference in the magnetopause position between the two models and found that it is mostly less than 0.1 RE with a maximum difference of 0.4 RE, with the model predicting more sunward magnetopause nose. Because of the small difference at the magnetopause nose, we have only used the model in our study. Our results agree with previous papers , with the latter reporting a 3.4 % average relative difference between the Shue model and GUMICS-4. Moreover, according to , global MHD models are very close to each other in terms of predicting magnetopause standoff distance.

Differences in the magnetopause location do not necessarily translate into differences in global measures, as can be seen from Figs. d and d, which show the time evolution of the energy transferred from the solar wind through the magnetopause surface. The response of the total energy Etot during both ICME cloud periods is quite similar regardless of the used grid resolution. As an integrated quantity, energy entry is a better indicator of the true physical processes of the GUMICS-4 solution and does not suffer from dependence on grid resolution like the maximum JY . Therefore, in analyses of simulation results, it would be better to consider such global integrated quantities, even if they have no direct observational counterparts. This can be seen in Figs. d and d, with large differences between GUMICS-4 and the ϵ parameter in energy transferred from the solar wind into the magnetosphere in both 2012 and 2014. However, standard deviations show that GUMICS-4 reproduces the temporal evolution of the ϵ parameter better during low solar wind driving (2014) than during high driving (2012), as the respective SD values are 0.725 and 2.263. Moreover, our results are mostly on the same order of magnitude compared to what was obtained by by using plasma flow streamlines for computing the magnetopause surface from GUMICS-4 results.

In the ionosphere, the cross-polar cap potential value is dependent on the grid resolution, with higher resolution yielding higher polar cap potential values (see Figs. e and e). In comparison with the PCI , standard deviation is considerably lower for the 2014 event (5.107) than for the 2012 event (15.838). Thus, at least two factors contribute to the ionospheric coupling: grid resolution and intensity of solar wind driving. Considering that the SD values are clearly higher than, e.g., the corresponding energy transfer values and that the PCI considers only the Northern Hemisphere, the PCI may not provide the most accurate reference for GUMICS-4. However, both considerable difference between GUMICS-4 and the PCI and the dependence on grid resolution agree with previous studies e.g.,. Generally, global MHD codes differ from each other in terms of the CPCP values . It is not easy to reproduce realistic CPCP values in a global MHD code, since they are generally prone to close excessive amounts of electric current through the polar cap and thus the CPCP values are either unrealistically large (e.g., LFM model, ), with reasonable auroral electrojet currents, or reasonable accompanied by low auroral electrojet currents (e.g., GUMICS-4 and BATS-R-US model; ).

The polar cap structure and the distribution of the FAC do not change much in either of the simulations, thus suggesting that the coupling of the magnetosphere and the ionosphere remains relatively constant. As is shown in Fig. a–b, the region 1 currents are clearly visible, while the region 2 currents get stronger only by enhancing the grid resolution in the MHD region . However, the upstream conditions change considerably from 01:00 to 03:00, with the upstream Alfvén–Mach number decreasing from 1.9 to 0.6, suggesting that polar cap potential saturation mechanisms are likely to take place . Considering that GUMICS-4 reproduces saturation with both 0.5 RE (this paper) and 0.25 RE resolutions , it is apparent that the FAC influence on the dayside magnetospheric magnetic field does not contribute to the saturation effect. However, to actually prove it is beyond the scope of the current paper. We therefore conclude that the increase in the CPCP during the 0.5 RE simulation run is caused by processes outside of the magnetosphere, likely in the magnetosheath, and that GUMICS-4 responds differently to low Alfvén–Mach number solar wind depending on grid resolution.

Figures and illustrate the CPCP as a function of the solar wind EY component. Color-coded are the IMF magnitude in Figs. a and a, the solar wind speed in Figs. b and b, and the upstream Alfvén–Mach number in Figs. c and c. Nominal solar wind conditions before and after the actual ICME events as well as the ICME sheath and cloud periods are considered separately. We note that only results from the lower spatial resolution (0.5 RE) runs are included in the figures. Consistent with earlier studies, Fig.  shows saturation of the CPCP during high solar wind driving (see, e.g., ): with nominal solar wind conditions or during the ICME sheath period the response of the CPCP to the upstream EY is rather linear, while for the ICME cloud period the CPCP saturates when EY>5 mVm-1. From Fig. a it can be seen that the saturation occurs when B>12 nT and Fig. b shows that the increase in the CPCP in the linear regime depends on the upstream velocity in such a way that the increase is clearly higher for lower velocity values (cloud event) than for higher velocity values (sheath event and nominal conditions), as suggested by previous statistical and numerical studies. The latter study proposes that this is because of the more rapid diversion of the solar wind flow in the pressure-gradient-dominated magnetosheath under faster solar wind, which leaves a smaller amount of plasma at the magnetic reconnection site.

The saturation of the CPCP is absent in Fig.  due to the significantly weaker solar wind driving during the 2014 event (the upstream EY is below 4 mVm-1). This in turn leads to the upstream Alfvén–Mach number being on average 5.8 during the ICME cloud event. suggest that when the Alfvén–Mach number decreases below 4 and the overall magnetosheath plasma beta (p/pB, where p is the plasma pressure and pB the magnetic pressure) below 1, the magnetosheath force balance changes such that plasma flow streamlines are diverted away from the magnetic reconnection merging region in the dayside magnetopause , which causes the CPCP saturation. However, the CPCP saturation limit of MA=4 is not necessarily the only governing parameter, as there is both observational evidence with large MA values (up to 7.3) and simulation results indicating saturation at low but above MA=1 values (this study). Nonetheless, our results suggest that the saturation of the CPCP is dependent on the upstream MA in such a way that MA needs to be below 4 for the saturation to occur.

An interesting aspect is that the CPCP does not reach its maximum simultaneously with EY; i.e., the CPCP is largest with moderate EY (5–6 mVm-1) (see Fig. ). As EY increases to 11 mVm-1, the CPCP decreases from 70 to 40 kV. This is actually apparent in Fig. h as well: the absolute values of both BZ and VX reach their maximum values a few hours after the onset of the magnetic cloud, which is at 06:54 UT, 15 July. However, the CPCP is at that time quite moderate, about 40 kV, and does not reach its maximum until 16 July, when both BZ and VX have already reduced significantly. Thus the CPCP overshoots in Fig. , a feature that was not observed in a GUMICS-4 study by using artificial solar wind input consisting of relatively high-density and constant driving parameters.

The performance of GUMICS-4 was put to the test by means of comparing the magnetic field magnitude |B| to in situ data of the Cluster and Geotail satellites. GUMICS-4 values are mostly lower than those measured by either of the two spacecraft, with GUMICS-4 predictions being closer to Cluster than Geotail. Computed standard deviations reveal that, over the entire simulation periods, the temporal evolution of GUMICS-4 magnetic field magnitude predictions is closer to Geotail measurements (2012: SD = 5.476, 2014: SD = 6.564, equatorial orbit) than Cluster measurements (2012: SD = 25.054, 2014: SD = 24.795, polar orbit) for both events. It should be noted that the times when Cluster is closer than 3.7 RE to Earth are ignored when computing SD values due to the inner boundary of the GUMICS-4 MHD region, which is located at 3.7 RE.

During both events, |B| is increased during ICMEs, especially their magnetic cloud counterparts. During the 2012 ICME sheath both Cluster and Geotail record fluctuating |B| until the onset of the cloud. While missing a sheath in 2014, magnetic field magnitude measured by Cluster fluctuates as well prior to the cloud. At the same time (29 April, 15:00 UT) |B| measured by Geotail decreases sharply. The difference between Cluster/Geotail and GUMICS-4 is mostly on the order of 10 % but can reach above 50 % values, especially during the 2012 magnetic cloud event in both Cluster and Geotail orbit. Such a difference seems relatively large, especially since it was shown by that all the global MHD models available at the Community Coordinated Modeling Center (CCMC) are close to each other when comparing the ability to reproduce magnetic field components to in situ measurements. While the study used 662 simulation runs, it should be noted that GUMICS-4 was used in only 12 of them. However, GUMICS-4 should predict |B| closer to in situ measurements at least during moderate solar wind driving, as was shown by . In his work the difference in |B| was 10 % or lower on 20 February 2002, when no ICME events were recorded.

With such discrepancy between our results and previous results, we checked some of the simulation runs at CCMC, in which BATS-R-US code was used, and searched for runs of either of the two ICME events discussed in this paper, with magnetic field measurements along Geotail and/or Cluster orbit also available. BATS-R-US was chosen since it shares several features with GUMICS-4. We found one simulation run (CCMC run name Tom_Bridgeman_022415_1) in which the 2012 event was simulated, with results along Geotail orbit available. In addition, we simulated the 2014 event (CCMC run name Antti_Lakka_070918_2) to check the results along Cluster path. Consequently, we are able to compare GUMICS-4 and BATS-R-US in both 2012 (Geotail) and 2014 (Cluster), and the results are shown in Fig. . Panel (a) shows comparison between the two models during the 2012 event and panel (b) during the 2014 event. In situ measurements by Geotail and Cluster are shown in panels (a) and (b), respectively. Note that the 2012 BATS-R-US run was completed at around 17 July 00:00 UT. By looking at the figure it is apparent that the predictions of both GUMICS-4 and BATS-R-US are quite similar, especially during the magnetic cloud events at both Cluster and Geotail orbits. Actually, GUMICS-4 is mostly closer to Cluster measurements than BATS-R-US in 2014, when Cluster exits the magnetosphere and |B| measured by Cluster fluctuates between 10 and 40 nT, as was discussed in Sect. . In 2012 a large difference in |B| (up to 100 %) during ICME cloud applies to both models. During ICME sheath and nominal solar wind conditions |B| fluctuates more and the prediction accuracy of the models depends on the time interval under inspection. It is evident that both models are quite equal considering the ability to reproduce |B| during both 2012 and 2014 ICME events.

The discrepancy between in situ measurements and the two models may not concern only GMHD models, since we computed the magnetic field during the 2012 event at Cluster orbit using the empirical Tsyganenko magnetic field model T89 e.g.,. For most parts GUMICS-4 is actually closer to Cluster observations, with the gap between the two models gradually decreasing as Cluster approaches the perigeum on 16 July (not shown). Therefore it is reasonable to assume that something in the ICME event, possibly unusually strong compression, leads to a larger field than predicted by the GMHD models or the Tsyganenko model, and that, e.g., increasing the spatial resolution of the GMHD models would not make a significant difference for the two reasonably similar codes . The negligible effect of enhanced spatial resolution is actually shown in Figs.  and for GUMICS-4.

It should be noted that the event is one of the strongest that occurred in 2012 by the mean magnetic field magnitude value during magnetic cloud. On the other hand, in some cases good agreement can be obtained when modeling strong ICMEs. Recently studied two events that occurred in 2015 and were the strongest events of solar cycle 24, and achieved reasonable agreement between measurements and different models, such as BATS-R-US with the Rice Convection Model and empirical models including the Tsyganenko T96 model. Mostly the error in the magnetic field magnitude was less than 15 nT, with the error increasing for a short while to more than 50 nT. The reason why some events cause greater errors than other events is however beyond the scope of the current paper and is left for future studies.

We conclude that for both events, |B| predicted by GUMICS-4 is closer to Cluster observations, which feature high magnetic field magnitude outside the plasma sheet. While the differences between GUMICS-4 and in situ measurements can be quite large, it was shown that the |B| predicted by GUMICS-4 agrees well with BATS-R-US predictions, and thus the large differences are not model-related but rather related to the upstream conditions during the ICME events. Thus the relative difference in |B| may not be a good metric when simulating ICME events and evaluating the performance of a global MHD model.

While the agreement between predicted and measured |B| may depend on the upstream conditions, the overall time evolutions seem to have a better match, and the SD values suggest that GUMICS-4 reproduces temporal evolution of |B| better at Geotail orbit, which is much further away from the Earth than Cluster and resides mostly in the lobe and on the boundary layer. We computed standard deviations for Cluster orbit when the S/C is both further and closer than 5 RE away from the center of the Earth. SD for further than 5 RE is 22.984 (19.666) for the 2012 (2014) event, while for closer than 5 RE the SD is 106.337 (104.605) for the 2012 (2014) event. If these calculations are repeated for 6 RE distance, the SD values are 14.390 (15.282) when the S/C is further in 2012 (2014) and 104.618 (88.423) when the S/C is closer in 2012 (2014). Thus, the temporal evolutions agree better when Cluster is further away from the Earth.

The differences are most likely not caused by grid cell size variations due to the adaptive grid of GUMICS-4, because the simulation runs over simulated 6 h stages produce quite similar results for both resolutions. Also, the two runs deviate most from each other during the first hours of the 6 h stage, during which the 0.25 RE run may not have fully eliminated the effects of simulation initialization, which can prevail for hours . Moreover, the adaptive grid of GUMICS-4 is enhanced the most near the dayside magnetopause. Both events show signs of increased deviation from the measurements near the dayside magnetopause (edges of yellow-shaded regions in Figs.  and ), further manifesting inaccuracies in determining the magnetopause in GUMICS-4.

The results of this paper can be summarized as follows.

Enhancing spatial resolution of the magnetosphere in GUMICS-4 affects the accuracy of the determination of the magnetopause subsolar point. Global measures, such as energy transferred from the solar wind into the magnetosphere, are not affected. The cross-polar cap potential can be affected significantly, with up to over a factor of 2 difference between simulations using different spatial resolutions for the magnetosphere.