PUBLICATIONS Space Weather RESEARCH ARTICLE 10.1002/2016SW001385 Key Points: • Six models were compared in prediction of geosynchronous magnetopause crossings • The effects of IMF Bz influence saturation and dawn-dusk asymmetry were found to be important • The best prediction was demonstrated by Lin et al.’s (2010) model
Correspondence to: A. V. Dmitriev,
[email protected]
Citation: Dmitriev, A. V., R. L. Lin, S. Q. Liu, and A. V. Suvorova (2016), Model prediction of geosynchronous magnetopause crossings, Space Weather, 14, 530–543, doi:10.1002/2016SW001385. Received 17 MAR 2016 Accepted 16 JUL 2016 Accepted article online 21 JUL 2016 Published online 4 AUG 2016
Model prediction of geosynchronous magnetopause crossings A. V. Dmitriev1,2, R. L. Lin3, S. Q. Liu3, and A. V. Suvorova1,2 1
Institute of Space Science National Central University, Chung-Li, Taiwan, 2Institute of Nuclear Physics, Moscow State University, Moscow, Russia, 3National Space Science Center, Chinese Academy of Sciences, Beijing, China
Abstract
An extended data set of magnetopause crossings observed at geosynchronous orbit was collected for nine major magnetic storms that occurred from 2000 to 2005. The new set of geosynchronous magnetopause crossings (GMCs) was used for comparative analysis of several magnetopause models during severe, strong, and extremely strong magnetic storms. The analysis allowed verification of specific effects such as saturation of an influence of interplanetary magnetic field Bz and dawn-dusk asymmetry. It was shown that the effects of saturation and duskward magnetopause skewing were important on the main phase of magnetic storms. Among the models considered, the most accurate prediction of GMCs was found for three models: Kuznetsov and Suvorova (1998a), Lin et al. (2010), and Dmitriev et al. (2011). The model by Lin et al. (2010) demonstrated the best capability of GMC prediction in a wide range of geomagnetic disturbances from severe to extremely strong magnetic storms.
1. Introduction A geosynchronous orbit, located at geocentric distance of ~6.6 Earth’s radii (RE), is populated by numerous satellites. During strong solar wind and/or geomagnetic disturbances, the dayside magnetosphere can shrink such that geosynchronous satellites cross the magnetopause and encounter the magnetosheath or even upstream solar wind [e.g., Russell, 1976; Suvorova et al., 2005; Dmitriev et al., 2014]. Fast streams of dense plasma from the magnetosheath or solar wind as well as energetic particles of solar and magnetospheric origin might result in a damage or even loss of geosynchronous satellites [e.g., Lanzerotti et al., 1998; Wrenn et al., 2002; Odenwald and Green, 2007; Choi et al., 2011]. Hence, prediction of the geosynchronous magnetopause crossings (GMCs) is important for safe operation of the satellites. Recently, a number of comparative studies were conducted on the base of new data sets of magnetopause crossings [Lin et al., 2010; Dmitriev et al., 2011; Case and Wild, 2013; Suvorova and Dmitriev, 2015]. It was shown that some magnetopause models are characterized by large standard deviation of up to ~2 Earth’s radii (RE) while others have an offset of up to ~2 RE. Most of these studies were mainly dealing with the magnetopause location under quiet and moderately disturbed solar wind conditions, under which GMCs cannot occur. Strong solar wind and magnetospheric disturbances, proper for GMCs, are characterized by such nonlinear effects as saturation of influence of Bz component of interplanetary magnetic field (IMF) and dawn-dusk asymmetry. However, the relative importance of these two effects under different solar wind and geomagnetic conditions is still an open question. The effect of saturation appears at geosynchronous orbit under very strong southward IMF, when the magnetopause stops shrinking after the magnitude of negative Bz exceeds a certain threshold [Kuznetsov and Suvorova, 1998a, 1998b; Shue et al., 1998; Dmitriev and Suvorova, 2000; Yang et al., 2003; Suvorova et al., 2005; Dmitriev et al., 2011]. It was shown that the threshold for saturation was about 20 nT and the solar wind pressure for saturation decreased with Dst variation.
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Experimentally, the effect of saturation can be revealed when a geosynchronous satellite stays inside the magnetosphere under very strong southward IMF and a certain solar wind pressure Psw. Apparently, there should be a threshold Psw, above which a satellite encounters the magnetosheath. Different authors reported different threshold pressures from 3 to 7 nPa [e.g., Suvorova et al., 2005]. Dmitriev et al. [2011] found that the threshold pressure decreased with the storm-time Dst variation. It was assumed that the decrease resulted from an increasing negative magnetic contribution of the cross-tail current strengthening during strong magnetic storms. However, the full understanding of the saturation effect is still not complete.
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It is believed that the IMF Bz influence saturation is a manifestation of a general saturation effect. The effect is that under certain conditions the ionospheric convection and the Region 1 current system become saturated. Further increases in the solar wind electric field do not produce corresponding increases in ionospheric convection or Region 1 currents because the dayside merging rate is limited, in contrast to “normal” times when the dayside merging rate is proportional to the solar wind electric field [e.g., Russell et al., 2001]. This happens generally under conditions of large southward IMF, but really, what produces the effect is low Mach number solar wind [e.g., Borovsky and Denton, 2006; Lavraud and Borovsky, 2008; Lopez et al., 2010]. Even though convection saturates, the ring current does not [Russell et al., 2001; Lopez et al., 2009], so larger VBz will still produce increased Dst effect, even if the effects of Region 1 on the dayside magnetopause boundary do not change [e.g., Sibeck et al., 1991; Wiltberger et al., 2003]. The nonlinear effect of saturation becomes important when the Alfven Mach number is below 3. The effect of dawn-dusk asymmetry consists in a duskward skewing of the magnetopause on the main phase of magnetic storms during strong southward IMF [Kuznetsov and Suvorova, 1998b; Dmitriev et al., 2004, 2005a, 2011]. The skewing can be represented by a rotation of the magnetopause nose point toward dawn by an angle of ~15° [Dmitriev et al., 2004] or by a duskward shifting of the magnetopause by few tenths to 2 RE [Kuznetsov and Suvorova, 1998a, 1998b; Dmitriev et al., 2005a]. The dawn-dusk asymmetry increases with southward IMF and with geomagnetic storm strength. It is attributed to storm-time intensification of the asymmetrical ring current peaking in the dusk sector. The numerical description of the dawn-dusk asymmetry is still incomplete because of insufficient statistics of GMCs. Among the models considered in previous studies, the following models demonstrated high capabilities in prediction of magnetopause crossings: Kuznetsov and Suvorova’s [1998a] model (hereafter KS98), Shue et al.’s [1998] model (hereafter Sh98), Dmitriev and Suvorova’s [2000] model (hereafter DS00), Chao model modified by Yang et al. [2003] (hereafter Ch03), Lin et al.’s [2010] model (hereafter Li10), and Dmitriev et al.’s [2011] predictive model (hereafter PM11). All the models can predict, to a certain extent, GMCs under strongly disturbed solar wind and geomagnetic conditions. They also take into account the effect of Bz influence saturation under strong southward IMF. The KS98, Sh98, and Ch03 models are axially symmetric. In addition, the KS98 model predicts ~0.5 to 2 RE duskward shifting of the magnetopause under strong southward IMF. The Li10 model is a 3-D model, which enables to describe magnetopause indentation in the cusp regions and tilt angle effect. The DS00 model is also a 3-D model, which represents the magnetopause dawn-dusk asymmetry but does not depend on the tilt angle. The model computer code is available at http://arxiv.org/ftp/arxiv/papers/1302/ 1302.1704.pdf. The PM11 model was especially designed to predict GMCs. The model allows calculating the solar wind pressure required for GMC at a given angular location and under given IMF Bz and Dst variation. The duskward skewing of the model magnetopause is controlled by the IMF Bz. The Dst variation influences the Bz saturation effect. The model code is presented at http://arxiv.org/ftp/arxiv/papers/1305/ 1305.6707.pdf. In the present study, we conduct a comparative analysis of six magnetopause models mentioned above. The analysis is based on an extended data set of GMCs accumulated during magnetic storms occurred from 2000 to 2005. It is important to note that comparison of those six models in prediction of a new independent data set was not yet performed. The methods of GMC identification and model comparison are described in section 2. The results of comparative analysis are presented in section 3. Section 4 is devoted to discussion of the results. Section 5 is conclusions.
2. Methods Geosynchronous magnetopause crossings were identified by using magnetic field and plasma data acquired from geosynchronous satellites GOES 8, 10, and 12 and LANL 1989-046, 1990-095, 1991-080, 1994-084, and LANL-1997A, respectively. The location of satellites at geographic equatorial plane is shown in Figure 1. The distribution of satellites is not uniform. The longitudinal sector from 0° to 90° is not covered by geosynchronous satellites. The method of GMC identification and determination of corresponding solar wind conditions is described in detail by Suvorova et al. [2005]. Here we briefly introduce basic principles of the method. We used
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high-resolution (~1 min) International Solar Terrestrial Physics (ISTP) data (http://cdaweb.gsfc.nasa.gov/cdaweb/ ist_public/) from geosynchronous satellites GOES and LANL and upstream monitors Geotail, Wind, and ACE. We identified so-called magnetospheric intervals (hereafter MS intervals), when a geosynchronous satellite was located in the magnetosphere, and magnetosheath intervals (hereafter MSh intervals), when a geosynchronous satellite was located in the magnetosheath. In the dayside magnetosphere, the geomagnetic field at geosynchronous orbit is regular, strong (>100 nT), and has a dominant northward component. The magnetospheric plasma has very low density ( 10 nPa. These conditions should be sufficient for GMCs in a wide local time range as predicted by the models. Note that neither saturation nor dawn-dusk asymmetry effects can help to avoid the false alarm. The PM11 model predicted that even large southward IMF and high pressure were not sufficient for GMCs when the negative Dst was not strong enough. As a result, the PM11 model provided the best score (Er = 18.3 and OUR = 0.01) in this storm. Good prediction capabilTable 2. Comparison of Models for Extremely Strong Magnetic Storms ities were also demonstrated by the Model Er (%) OUR Li10 and Ch03 models. KS98 Sh98 DS00 Ch03 Li10 PM11
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18.6 27.3 30. 21.2 16.0 20.2
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0.03 0.82 0.09 0.67 0.22 0.41
On the main phase of the 6 April 2000 magnetic storm, the effect of IMF Bz influence saturation can be clearly seen within ~20 min interval around 22 UT. At that time, IMF Bz was negative and 535
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Figure 4. The same as in Figure 2 but for strong geomagnetic storms on (a) 6–7 April 2000, (b) 15 May 2005, (c) 11 April 2001, and (d) 9–10 November 2004.
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Table 3. Comparison of Models for Strong Magnetic Storms Model
Er (%)
OUR
KS98 Sh98 DS00 Ch03 Li10 PM11
26.9 21.5 35.5 21.6 20.9 18.5
0.39 0.55 0.11 0.42 0.26 0.33
strong Bz ~ 30 nT, Ma was close to 3, and solar wind pressure decreased to Psw ~ 8 nPa that resulted in MS interval observed by GOES 10 in the postnoon sector at ~1330 MLT. All the models, excepting Sh98, predicted false MSh interval.
The storm on 15 May 2005 is characterized by a long-lasting (almost 4 h) initial phase and a short (less than 2 h) main phase (see Figure 4b). The initial phase was accompanied by northward IMF and high Psw varying around 30 nPa. At that time, LANL 1994 and 1997 observed MSh intervals in the noon and postnoon sectors. The MSh intervals were predicted by the KS98, Li10, and PM11 models. The other models overestimated the solar wind pressure required for GMCs under northward IMF. The Li10 model underestimated the magnetopause distance and predicted several false GMCs. From 0600 to 0645 UT on 15 May 2005, GMCs were observed by LANL 1997 in dusk sector. They were caused by a high Psw of up to ~60 nPa and/or strong southward IMF (Bz ~ 40 nT). The MSh interval was well predicted by the DS00 and Li10 models and partially by the Ch03 and PM11 models. The KS98 and Sh98 models overestimated the magnetopause size in the dusk sector. In contrast, the DS00 model underestimated the magnetopause distance and predicted numerous false GMCs. The large number of false GMCs and overestimations resulted in a large percentage of errors (>30%) for all the models (see Figure 3). Among of them, the PM11, Li10, and DS00 models demonstrated the smallest error of ~34%. Figure 4c demonstrates GMC prediction during a storm on 11 April 2001. The storm has a long-lasting main phase accompanied by a high solar wind pressure varying between 20 and 30 nPa and strong variations of IMF Bz. Most of models provide a reasonable prediction of GMCs during the storm, excepting the KS98 model. Namely, the model predicted a false MSh interval from 1515 to 1545 UT because of a strong duskward skewing of the magnetopause such that the model magnetopause distance decreases substantially in the prenoon and noon sectors. The false alarms cause negative OUR (underestimation). This example demonstrates that the duskward skewing of ~2 RE is too large at the beginning of magnetic storms. For the 11 April 2001 storm, the best score was found for the PM11 model (see Figure 3). The Li10 and Sh98 models also demonstrated quite high capabilities of GMC prediction. The 9–10 November 2004 storm (Figure 4d) followed the extremely strong magnetic storm on 7–8 November 2004 (see Figure 2b). It was preceded by an interval of large negative Dst of about 100 nT, which was supported by a long-lasting (from 13 to 18 UT) negative Bz and Psw of ~10 nPa. At 1330–1400 UT on 9 November 2004, a short MSh interval was observed in the prenoon sector by LANL 1990 and GOES 12. The interval was successfully predicted by the asymmetrical models KS98 and PM11, while the other models overestimated the magnetopause distance. This fact indicates a prominent duskward skewing of the magnetopause at that time. From 1900 to 2300 UT on 9 November 2004, MSh intervals were caused by very high solar wind pressure and or strong southward IMF. All the models predicted GMCs very well. Significant difference between the observations and predictions can be found from 0100 to 0530 UT on 10 November 2004. At that time, LANL 1991 and 1997 observed several brief magnetosheath encounters in the noon sector. They were caused mainly by strong Psw pulses of up to 50 nPa. Most of the models predicted the MSh intervals very well. However, the models also predicted numerous false GMCs (strong underestimation), which were related to large southward IMF. For example, a false MSh interval of ~1 h duration was predicted by the models from 0420 to 0520 UT on 10 November 2004. At that time, IMF Bz was varying around 20 nT, Psw ~ 10 nPa, and Ma ~3 that corresponded to the regime of Bz influence saturation. The saturation resulted in a MS interval, which was observed at that time by LANL 1997 in postnoon sector (14–15 MLT). Note that the KS98, Sh98, and PM11 models predicted only the first half of the false MSh interval. The successful rejection of the second half can be explained by a duskward skewing of the magnetopause in the KS98 and PM11 models and by overestimation of the Psw required for GMC in the Sh98 model, as we mentioned above. For the entire storm, the best capability of prediction was found for the Sh98 and Ch03 models (see Figure 3).
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Figure 5. The same as in Figure 2 but for severe geomagnetic storms on (a) 21–22 October 2001, (b) 26–27 July 2004, and (c) on 24 August 2005.
Table 3 shows common performance of the models in prediction of GMCs during the strong magnetic storms. The best score with Er = 18.5% and OUR = 0.33 is demonstrated by the PM11 model. Then the Li10 model is going with Er = 20.9% and OUR = 0.26. The Sh98 and Ch03 models also demonstrate low percentage of errors ~21.5% despite of high OUR indicating to systematical overestimation of the magnetopause distance as one can see in Figure 3. Figure 5 presents a comparison of GMC predictions during severe (Dstmin ~ 200 nT) magnetic storms on 21–22 October 2001, 26–27 July 2004, and 24 August 2005. The storms are characterized by high variability of the IMF Bz and Psw that causes a complex dynamics of the Dst variation on the main phase and maximum DMITRIEV ET AL.
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Table 4. Comparison of Models for Severe Magnetic Storms
of the storms. The high variability makes the prediction difficult because of the evolution of the solar wind and KS98 29.3 0.00 IMF irregularities propagating through Sh98 29.0 0.66 DS00 37.7 0.47 the interplanetary medium and the Ch03 30.4 0.74 magnetosheath [Collier et al., 1998; Li10 26.9 0.06 Richardson and Paularena, 2001; PM11 25.6 0.12 Weimer et al., 2002]. Under such circumstances, accurate determination of the solar wind conditions, affecting the magnetopause, was difficult that might result in a decrease in the accuracy of prediction (see Figure 3 and Table 4). Model
Er (%)
OUR
Multiple GMCs during the storm on 21 October 2001 were well predicted by the models (see Figure 5a). In particular, the effect of IMF Bz influence saturation was observed by the LANL 1991 in the noon sector (1130–1300 MLT) from 2130 to 2315 UT. At that time, the IMF Bz was mostly negative and strong with minimum of Bz ~ 25 nT, Alfven Mach number was varying around 3 with minimum Ma ~ 2.2, and the solar wind pressure was not very high (Psw = 5 to 10 nPa), but the subsolar magnetopause was located outside the geosynchronous orbit despite of strong southward IMF. The models correctly predicted this MS interval. In addition, during intervals of northward IMF from 2020 to 2120 UT and after 2320 UT, the models KS98, DS00, Li10, and PM11 predicted correctly MSh intervals produced by increases in the solar wind pressure, which did not exceed 30 nPa. As a result, PM11 model has the highest score of Er = 24 and OUR = 0.11. The Sh98 and KS98 models also demonstrated high capabilities of GMC prediction during the storm. Figure 5b shows comparison of GMC predictions during a long-lasting main phase of the 26–27 July 2004 magnetic storm. From 23 UT on 26 July to 5 UT on 27 July, several GMCs were observed by LANL 1994 in a wide range of local time from 9 to 15 LT. In the prenoon sector, GMCs were caused by negative Bz of ~ 10 nT and high Psw of ~10 nPa. They were successfully predicted by the KS98, Li10, and PM11 models. From 3 to 5 UT on 27 July, GMCs in the postnoon sector were caused by very high solar wind pressure enhanced up to 60 nPa. Only Li10 and PM11 models predicted those GMCs. From 13 to 15 UT on 27 July, GMCs were observed by GOES 12 in the prenoon sector. They were well predicted by the KS98 model and only partially by the Sh98, Li10, and PM11 models. Those models also predicted several false crossings caused mainly by a wide extent of the high-pressure pulses detected by the Wind upstream monitor. During the storm, the best OUR (almost zero) was demonstrated by KS98 (see Figure 3). The Sh98, DS00, and Ch03 models had small errors but very large OUR (almost 1) because they systematically overestimated the magnetopause distance and practically did not predict GMCs. A small error with low OUR can be found for the Li10 model. Figure 5c shows numerous GMCs and MSh intervals observed by LANL 1990 during the 24 August 2005 magnetic storm. The GMCs were mainly detected in the dawn and prenoon sectors and caused by high Psw of >20 nPa. From 09 to 11 UT, GMCs in the dawn sector were well predicted by the DS00, Ch03, Li10, and PM11 models though the DS00 model underestimated the magnetopause distance substantially and predicted numerous false GMCs. Note that time interval from 0940 to 1010 UT was accompanied by extremely strong southward IMF with Bz ~ 50 nT, solar wind pressure of ~10 nPa, and low Mach numbers with minimum of 1.6. Such conditions corresponded to IMF Bz influence saturation that prevented the magnetopause to move inside the geosynchronous orbit despite of extremely large negative Bz. From 11 to 14 UT, MSh intervals observed in the prenoon sector were well predicted by all the models, excepting Sh98 and Ch03, which overestimated the magnetopause distance and predicted false MS intervals quite often. From 1200 to 1215 UT, all the models predicted false GMCs that could be caused by the high variability of the solar wind such that a structure of northward IMF and lower Psw could actually affect the magnetopause. A MSh interval, observed from 14 to 15 UT in the noon sector, was accompanied by northward IMF and, hence, was caused by the high solar wind pressure of ~30 nPa. The Sh98 and Ch03 models did not predict the MSh interval because they require higher solar wind pressures for GMCs. As a result, the best capability
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Table 5. Comparison of the Models With Best Scores for Various Magnetic Storms Storm 20 Nov 2003 7–8 Nov 2004 a 6–7 Apr 2000 15 May 2005 a 11 Apr 2001 9–10 Nov 2004 a 21–22 Oct 2001 26–27 Jul 2004 24 Aug 2005 a
1
2
3
Dst
Li10 KS98 PM11 PM11 PM11 Sh98 PM11 Li10 Li10
PM11 Li10 Li10 Li10 Li10 Ch03 Sh98 KS98 PM11
KS98 PM11 Ch03 DS00 Sh98 PM11 KS98 PM11 KS98
480 400 300 300 280 270 220 200 180
Magnetic storms used in PM11 model.
of GMC prediction during the storm can be found for the Li10 model (Figure 3). The PM11 and KS98 models also predicted GMCs quite well. Overall, the severe magnetic storms are better predicted by the PM11 model with lowest Er = 25.6% and OUR = 0.12 as one can see from Table 4. The Li10 model also demonstrates very good performance. The Sh98 and KS98 models have similar percentage of errors of ~29%, but the KS98 model is very well balanced (OUR = 0.), while the Sh98 model suffers from systematical overestimation (OUR = 0.66).
4. Discussion Consideration of nine magnetic storms shows that best capability for GMC prediction is demonstrated by different models for different magnetic storms. For comparative analysis, we have selected three models with the best scores for each magnetic storm considered. They are listed in Table 5. Again, we distinguish three kinds of magnetic storms: extremely strong with Dstmin < 400 nT (first two lines), strong storms with Dstmin ~ 300 nT (next four lines), and severe storms with Dstmin ~ 200 nT (last three lines). From Tables 2 and 5, one can see that for the extremely strong magnetic storms, the best model is Li10, which took the first and second scores in Table 5. It is followed by the KS98 model, which has the first and third scores. Then PM11 model goes with the second and third scores. For the strong magnetic storms, the best model is PM11, which has three first and one third score in Table 5, then the model Li10, which takes three second scores, and the Sh98 model with one first and one third scores. During severe magnetic storms, GMCs are predicted most accurately by the PM11 as one can see in Table 4. Very good performance is also demonstrated by the Li10 model, which takes two first scores in Table 5. They are followed by the KS98 model with the one second and two third scores in Table 5. Note that GMCs occurred during two strong storms on 6–7 April 2000 and 11 April 2001 and one severe storm on 21–22 October 2001 were used in the development of PM11 model. Hence, in this sense, the capabilities of GMC prediction of Li10 model can be comparable with those of the PM11 model for the strong and severe magnetic storms. From analysis of Figure 3 and Tables 2 to 4, one can see that the DS00 model has very large percentage of errors and, thus, the purest capability in prediction of GMCs. The models Sh98 and Ch03 have largest OUR, and hence, they predominantly overestimate the magnetopause distance and the solar wind pressure required for GMCs. This results in very low false alarm rate, but the number of correct prediction of MSh intervals is also low. Finally, we have found three models: PM11, Li10, and KS98, which predict GMCs most accurately. The Li10 model provides well prediction in mostly wide range of geomagnetic activity from severe to extremely strong magnetic storms. The KS98 model suffers from too strong duskward shifting of the magnetopause under large southward IMF that results in the systematical underestimation of the magnetopause distance in the prenoon and noon sectors and overestimation in the postnoon sector. The PM11 model was developed on a database of severe to strong magnetic storms with the amplitude of Dstmin up to 300 nT. The model has some difficulties in extrapolation to the conditions of extremely strong magnetic storms with Dst < 400 nT. It is interesting to note that the KS98, Li10, and PM11 models were developed by using totally different methods. The KS98 model is more traditional. It is elaborated as a surface of rotation whose standoff distance and
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Table 6. Conditions for IMF Bz Influence Saturation at Geosynchronous Orbit Storm
Geosynchronous Satellites
MLT
Psw (nPa)
Bz (nT)
Ma
GOES-10 LANL 1991 GOES-12 LANL 1997 LANL 1997 LANL 1990
1330 ~12 11–12 ~12 ~14 ~8
8 10 6 8 10 10
30 25 50 45 25 50
3 2.8 1.1 2 3 1.6
6–7 Apr 2000 21–22 Oct 2001 a 20 Nov 2003 7–8 Nov 2004 9–10 Nov 2004 24 Aug 2005 a
Magnetosheath interval.
flaring are functions of Psw and Bz. The Li10 model is a sophisticated 3-D model, which describes the asymmetrical magnetopause surface as a function of the tilt angle, Psw, IMF strength, and Bz. Perhaps, the 3-D asymmetrical shape and dependence on the tilt angle result in the best performance of the Li10 model. In particular, introduction of the tilt angle effect significantly improves the predictability of magnetospheric models [e.g., O’Brien and McPherron, 2002]. The predictive PM11 model does not describe the magnetopause shape at all. The model predicts the solar wind pressure required for GMC at given GSM longitude and latitude as a function of Bz and Dst. The dependence for Psw is asymmetrical in longitudes in order to predict the duskward magnetopause skewing. The asymmetry depends slightly on Bz. The fact that three totally different models provide similar accuracy of GMC prediction is an important support of the validity of our results. We have shown that the KS98, DS00, and PM11 models cannot always correctly predict the duskward skewing of the magnetopause under strong southward IMF. The skewing is usually too large in the KS98 and DS00 models and sometimes too small in the PM11 model. It is reasonable to suggest that the dependence of skewing from the IMF Bz is ambiguous. The skewing is rather controlled by asymmetrical ring current developing on the main phase of magnetic storms, which is just related to southward IMF. But we do not know how the asymmetric ring current depends on the magnitude of IMF Bz. Hence, an additional study is required to find a more robust parameter controlling the duskward magnetopause skewing. We have also demonstrated an importance of the effect of IMF Bz influence saturation during several magnetic storms. Table 6 combines the conditions observed during saturation. We searched for intervals of very large southward IMF (
