| Solar eruptive phenomena, such as flare, erupting prominence and corona mass ejection (CME).usually induce radiation storm, particle storm and fast ejection of plasma, which may be impact the Earth greatly and result in geomagnetic storm, ionospheric storm, the thermospheric storm and so on. Solar storms, the manifestation of hazard weather in space mentioned above, have a number of physical effects in the solar-terrestrial environment. As an important cause that can influence the performance and reliability of space-and ground-based technological systems and can endanger human life, solar storm plays a pivotal role in space weather research. On the basis of the observations of the solar-terrestrial environment, using the interplanetary scintilla (IPS) and fussy mathematics, the following aspects are studied observationally, theoretically.Using the close degree and membership function and comprehensive evaluation in fuzzy mathematics, in conjunction with the solar observation of CME and IPS observation for the interplanetary solar storms caused by CME, we present a close degree prediction method for geomagnetic disturbance events caused by coronal mass ejection (CME)--shock waves identified by IPS observation. Based on the analysis of 74 geomagnetic disturbance events caused by CME- shock waves identified by IPS observation during 1997-2003, five clustering indices and their weighted fuzzy sets are constructed. Typical fuzzy sets of small, moderate, intense geomagnetic disturbance events are built based on comprehensive evaluation. By constructing the respective fuzzy set of each event, based on the close degree between the fuzzy set and typical fuzzy sets, the prediction for geomagnetic disturbance magnitudes caused by the events can be obtained. Main results are as follows:For the 74 geomagnetic disturbance events, the prediction accuracy is 53.3% for small geomagnetic disturbance; 100% for moderate geomagnetic disturbances; and 90.20% for intense geomagnetic disturbances. The average precision of this method is 84%. This method is an effective application of fuzzy mathematics to studying the geomagnetic disturbance.The prediction for the arrival time of shocks always is the main topic. Based on the 73 geomagnetic disturbance events caused by coronal mass ejection (CME)—associated interplanetary shock waves and fuzzy mathematics, here is presented a prediction method for geomagnetic disturbances and the arrival time of shocks. According to the solar location of CME, the transit time of the interplanetary disturbance, the geomagnetic disturbance magnitude and the velocity jump observed by IPS at the disturbed front, five membership functions T (R),M,ΔV ,θ,φare constituted. Based on the five membership functions and fuzzy mathematics, prediction tests for the 73 CME-associated geomagnetic disturbance events during 1997- 2003 are made by considering the influence of CME velocity on the onset time of geomagnetic disturbances. Main results are : (1) before modified, prediction of the magnetic disturbance onset time—for 26.27% of all events, the relative error,ΔT / Tobs≤10%, and for 19.18%, 10% ?ΔT/Tobs≤20%, and for 19.18%, 20% ?ΔT/Tobs≤30%, and for 16.44%, 30% ?ΔT/Tobs≤40%, and for 9.58%, 40% ?ΔT/Tobs≤50%, and for 9.58%,ΔT /Tobs 50%; after modified, for 36.99% of all events, the relative error,ΔT / Tobs≤10%, and for 32.88%, 10% ?ΔT/Tobs≤20%, and for 17.81%, 20% ?ΔT/Tobs≤30%, and for 6.85, 30% ?ΔT/Tobs≤40%, and for 5.48, 40% ?ΔT/Tobs≤50%, and for 0%,ΔT /Tobs 50%; (2) prediction of the geomagnetic disturbance amplitudes—for 24.66% of all events, the relative error,Δ∑K∑Kobs≤10%; and for 60.27% ,Δ∑K∑Kobs≤30%; and only for 12.33%,Δ∑K∑Kobs≥50%. These results show that the prediction method has good feasibility for geomagnetic disturbance prediction. If the membership functions are established based on the various types of solar wind storm-geomagnetic disturbances, the prediction tests could improve. The characteristics of 32 accelerating coronal mass ejection (CME) and 32 decelerating CME happening during 1997-2003 are analyzed. Prediction tests are made for geomagnetic disturbance events caused by the gradually accelerating CME-associated interplanetary shock waves and the decelerating CME-associated interplanetary shock waves, which can be identified by interplanetary scintillation (IPS) observation during 1997-2003. New membership functions and new correctional item of onset time of geomagnetic disturbances are respectively constituted for two kinds of CME. Main results are: as for the accelerating CME, for the onset time of the geomagnetic disturbance, before classified, the relative error between the observation, To bs, and the prediction, T pre,ΔT Tobs≤10%for 6.25% of all events, 10% ?ΔTTobs≤30% for 40.63%, and 30% ?ΔTTobs≤50% for 31.26%, and 50% ?ΔTTobs for only 21.86% ,after classified ,ΔT Tobs≤10%for 21.86% of all events, 10% ?ΔTTobs≤30% for 56.27%, and 30% ?ΔTTobs≤50% for 12.51%, and 50% ?ΔTTobs for only 9.36% ; for the decelerating CME, before classified,ΔT Tobs≤10%for 31.25% of all events, 10% ?ΔTTobs≤30% for 37.50%, and 30% ?ΔTTobs≤50% for 28.12%, and 50% ?ΔTTobs for only 3.13% ,after classified ,ΔT Tobs≤10%for 25.00% of all events, 10% ?ΔTTobs≤30% for 59.37%, and 30% ?ΔTTobs≤50% for 12.50%, and 50% ?ΔTTobs for only 3.13% ;...
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