## 3 Simulations
### Significance of Spatiotemporal Interpolation in Space Weather Forecasting  
This paper compares credibilities of the sensors whether the spatiotemporal interpolation of the missing sensors is significant. The credibility is calculated from the time sequences of the simulation results after 72 h from the start. The time 72 h is minimum time that the faulted sensors are replaced with virtual ones by the neighbor sensors. The total number of the test sequences is 9907.  
Table 1 shows comparisons of the averaged credibility for each sensor for both the Case Study 1 (Section 3.2) and the Case Study 2 (Section 3.3). The sensor of ACE fails in Case Study 1. In Table 0(a), the credibilities with the spatiotemporal interpolation are larger than without it. The credibility with the spatiotemporal interpolation is 0.8 while without one is about 0.0. The faulted sensor is replaced with virtual one by the point of view of the credibility. In Table 0(b), on the other hand, the credibilities for both sensors of ACE and STEREO-A are larger than that ones without the interpolation. With the spatiotemporal interpolation, the credibilities of both sensors are 0.6, while about 0.0. In this case, the faulted sensors are also replaced with virtual ones by the point of view of the credibility. Therefore, generating virtual sensors by the spatiotemporal interpolation is significant in these two case studies.  
Table 2 shows a performance comparison of forecasting for the high-energy electron flux 24 h ahead. This paper compares a prediction success rate as a performance measure. This paper defines the prediction success rate as a fraction of warning alarm of the high-energy electron flux 24 h ahead. The sensor \(E_{24}\) alarms if its credibility is less than 0.5. The prediction performances for both cases of the single and the two sensors failed do not show any significant difference. For the case of the single sensor failed, the prediction success rates (used or unused) are almost equal in both cases. For the case of the two sensor failed, furthermore, the prediction success rates (used or unused) are equal in both cases. In these case studies, single or multiple faults of the sensors do not affect to the statistical performance for prediction of the high-energy electron flux 24 h ahead.  
In some test cases, however, the sensor faults are recovered by the mutual diagnosis and the sensor replacement. Moreover, the credibilities of the sensors with spatiotemporal interpolation are larger than without it. Therefore, the spatiotemporal interpolation for faulted sensors is a significant  
Figure 13: Network snapshot of the dynamic relational network for the test data shown in Figure 9. Figure (**a,b**) show the status of the nodes at 48 and 80 steps respectively. The circles and squares indicate the real and virtual sensor nodes respectively. The white (red) colored sensor nodes is normal (abnormal). The credibility for the normal status is larger than 0.5, otherwise abnormal. The rectangles indicate region of the satellite. The two sensors of GOES-10 is shown in the regions of the rectangles. The solid lines indicate the diagnosis flows of mutual diagnosis. The dashed line indicate diagnosis flows from real sensors to virtual sensors for prediction. The marks plus (minus) indicate diagnosis results as normal (abnormal) from the source nodes to the target nodes. (**a**) Step = 48 (After the real sensor for ACE failed); (**b**) Step = 80 (After the virtual sensor for ACE is created).  
approach to keep the system reliability, because the credibilities of some sensors are recovered as shown in Table 1.