Differences in the arrival-time error
As shown in Fig. 2, the simulated solar wind speed shows a smooth change compared to the actual shocks. The simulation can capture a shock structure with about 3 grid points. If the simulation has a sufficiently high spatial resolution, the shock location could converge to the center of the gradient of the apparent width. However, we set the spatial resolution of the simulation to be as low as possible to execute multiple simulation cases within a reasonable lead time from the arrival of the CME by using a general workstation. Because the grid intervals in the radial direction of around 1 AU are approximately 2.3 Rs, the width of a radially propagating shock in the simulation becomes about 7 Rs. It takes approximately 2 h for the shock of a typical speed 680 km/s to pass through the Earth’s position. If a shock structure inclines in the non-radial direction, the apparent shock width will be larger than the width observed for a shock structure that is perpendicular to the radial direction. In the case shown in Fig. 2a, the shock plane was oriented about 40–50° from the Sun–Earth line, and therefore, the shock width along the Sun–Earth line becomes about 5 grid points (see 0.95–1.0 AU).
This study used the IPS data to optimize the simulations. The IPS observation detects the density enhancement in front of the CMEs. As described in the previous paragraph, because of the coarse spatial resolution, the simulated CMEs have density distributions that are gradual compared to the actual ones. This study would select the most realistic case by comparing the observed IPS data with the simulated IPS calculated from the gradual density distribution. This means that the front part of the density enhancement of the selected simulation should be the most reliable location for the CME front. Therefore, the onset time of the shock should be defined as the arrival time regardless of the origin of the shock width of the simulations.
IPS data improved the arrival time forecast of the SUSANOO MHD simulation compared to that derived from the SUSANOO simulation without IPS data by 1.7 h (25%). The error bar of the arrival time in each simulation run is mainly given by the intervals of initial CME speed (100 km/s), which corresponds to about 1-h difference in the arrival time as shown in Fig. 2b. Therefore, we can distinguish a difference of arrival times only larger than 1 h. In 10 of the 12 events, IPS-based SUSANOO provided a better or similar (i.e., the difference is less than 1 h) arrival time compared to the SUSANOO without IPS, and the arrival time of IPS-based SUSANOO is worse than that of SUSANOO without IPS in only two of the 12 cases as shown in Fig. 3b. Therefore, we consider that this improvement from SUSANOO without IPS to IPS-based SUSANOO is encouraging although we need for further study with a much larger sample.
Another point is that the IPS-based SUSANOO significantly improved the arrival-time forecast compared to the SUSANOO without IPS in three CME events (No. 3, 8, and 9, i.e. 2014-04-02, 2015-06-22, and 2015-06-25), which resulted in large arrival-time errors when forecast by the SUSANOO simulation without IPS (i.e., with either CACTus or LASCO). For example, for the CME event observed on June 25, 2015, the LASCO based simulation produced an arrival-time error of approximately 10 h, while the IPS based forecast selected a different simulation run that produced an arrival-time error of only 3 h approximately. From the perspective of space weather forecasting, a large arrival-time error can have serious consequences, which suggests that IPS data play a crucial role in the forecasting system.
The approach employed in this study provided better arrival-time forecasts than the real-time operated WSA-ENLIL-cone model, even without IPS data, probably because only a limited number of CME events were tested, and this result might not be maintained for a larger data set. However, the probability of our simulation providing a reliable forecast is high. Our simulation used a spheromak instead of a cone as the CME model, resulting in a more realistic reconstruction of CME propagation. Moreover, the magnetic flux, radial width, and longitudinal width of the spheromak were assumed to be proportional to the X-ray flux of the corresponding flare (see ”Methods“ section). If a fixed magnetic flux, radial width, and longitudinal width for all spheromak had been set, the average arrival time would have been worse. Therefore, this assumption can improve the estimated arrival-time error. This study based on a full 3D simulation that includes the polar regions of the heliosphere that can provide a better reconstruction of the interaction between CMEs and solar wind.
Our simulation approach resulted in earlier arrival-time predictions, which is consistent with previous MHD simulations (Wold et al. 2018). If the magnetic field flux of the spheromak is too strong, acceleration and expansion of the CME can be overestimated, which may result in an earlier prediction. If the size of the CME is too small, the drag force from the background solar wind can be underestimated, which can also result in an earlier prediction. Furthermore, a radio scattering region may exist in front of the CME (Gothoskar and Rao 1999), which could result in early prediction even when using IPS data.
Causes of the arrival-time error
The simulations that best fit the IPS data still exhibited arrival-time errors. In this study, we only optimized the initial speed of the CME; the other parameters were approximately assumed from GOES and LASCO observations. These assumptions should be optimized in future studies. Some CME parameters assumed in this study can be derived from LASCO white-light images by fitting the CME geometry using models such as the graduated cylindrical shell model (e.g., Thernisien et al. 2006). CMEs propagating in interplanetary space can be derived from the Heliospheric Imager onboard STEREO satellites (Möstl et al 2014; Howard 2015). White-light coronagraph data can also be estimated from our MHD simulations by calculating the Thomson scattering along the line of sight. Therefore, we may be able to optimize the CME parameters other than the initial speed by combining IPS observations, white-light observations, and MHD simulations. In addition, the CME model can be improved from the spheromak to some other more realistic models.
The velocity, density, and temperature of background solar wind in our simulation were obtained from empirical models. These models have ambiguities and result in CME arrival-time errors because the interactions between background solar wind and CMEs can affect the propagation of CMEs (e.g., Chen 1996; Vršnak and Gopalswamy 2002). Background solar wind velocity can also be derived from IPS observations using the tomography technique (Kojima et al. 1998; Jackson et al 1998), and the derived velocity distribution can be adopted as the inner boundary of the global MHD simulation (Jackson et al. 2015). In future modeling efforts, we may first derive background solar wind velocity distribution from IPS data using the tomography technique, in which transient phenomena such as CMEs are less prominent because the tomography of the background solar wind requires at least several days of IPS data. Then, we can simulate and fit CMEs using IPS data acquired just before forecasting in which CMEs are more prominent.
Application to the space weather forecasting system
The approach employed in this study has been partially installed in the space weather forecasting system of the National Institute of Information and Communications Technology (NICT), which is the Japanese space weather forecasting center. During daily operation, CME arrival times should be forecasted as soon as possible after a CME is observed and the initial forecast should be given automatically or semi-automatically by human forecasters with a large error range. IPS data can be made available approximately 1–2 days after the onset of CMEs exhibiting typical speeds. IPS data cannot be used for the initial forecast itself but can be used to limit the range of the initial forecast, which is similar to data assimilation forecasts of typhoon trajectories. It takes about 2–4 days for the typical CMEs to reach the Earth from their onset. Therefore, our IPS-based forecast will work for most CMEs. The IPS-based forecast may not be able to record the signature of the fastest CME, which is generally the most significant and which arrives at the Earth within 1 day. Coordinated observations of several IPS stations on different longitudes will improve the observation cadence of the IPS, which may lead to further improvement in the accuracy of forecasting the arrival of extremely fast CMEs.