Predicting the shock arrival time using 1D-HD solar wind model

Transcription

1 Article Geophyic April 1 Vol.55 No.11: doi: 1.17/ SPECIAL TOPICS: Predicting the hock arrival time uing 1D-HD olar wind model ZHANG Ying 1,*, CHEN JingYi & FENG XueShang 1 Intitute of Geology and Geophyic, Chinee Academy of Science, Beijing 19, China; State Key Laboratory of Space Weather, Center for Space Science and Applied Reearch, Chinee Academy of Science, Beijing 119, China Received April 11, 9; accepted Augut 11, 9 A 1D-HD hock propagation model i etablihed to predict the arrival time of interplanetary hock at 1 AU. Applying thi model to 68 olar event during the period of February 1997 to October, it i found that our model could be practically equivalent to the STOA, ISPM and HAFv. model in forecating the hock arrival time. The abolute error in the tranit time from our model i not larger than thoe of the other three model for the ame ample event. Alo, the prediction tet how that the relative error of our model i 1% for 31% of all event, 3% for 75%, and 5% for 84%, which i comparable to the relative error of the other model. Thee reult might demontrate a potential capability of our model in term of real-time forecating. interplanetary hock, hock propagation model, arrival time prediction Citation: Zhang Y, Chen J Y, Feng X S. Predicting the hock arrival time uing 1D-HD olar wind model. Chinee Sci Bull, 1, 55: , doi: 1.17/ Solar activitie are important driver of pace weather and play important role in leading to advere olar-terretrial environment. It i well known that variou kind of olar tranient activitie uch a olar flare, diappearing filament, and coronal ma ejection (CME) are reponible for trong interplanetary (IP) diturbance and correponding non-recurrent geomagnetic diturbance. The IP hock in the olar wind plama aociated with CME, olar flare, and tream-tream interaction herald the initiation of geomagnetic torm if ufficiently long and ufficiently largemagnitude outhward component of the interplanetary magnetic field exit following the hock. Therefore, predicting the arrival time of thee IP hock at the near Earth pace with enough lead time ha become a crucial apect in pace weather forecating. Several model aimed at forecating the arrival time of IP hock at 1 AU have been developed, to lit a few, uch a the hock time of arrival model (STOA), the interplanetary hock propagation model (ISPM) and the modified Hakamada-Akaofu-Fry/ verion- (HAFv.) model. Thee three model have been *Correponding author ( yzhang@paceweather.ac.cn) widely ued in real-time prediction of the arrival time. The STOA model i baed on imilarity theory of blat wave, modified by the piton-driven concept, which emanate from point exploion [1,]. The ISPM i baed on a.5d MHD parametric tudy of numerically imulated hock that how the organizing parameter to be the net energy input to the olar wind [3,4]. The HAFv. model i a modified kinematic olar wind model that calculate the olar wind peed, denity, magnetic field, and dynamic preure a a function of time and location [5,6]. The tatitical reult how that the performance of the above three model have been teted and the comparative tudy revealed that the performance of thee three model were practically identical in forecating the hock arrival time [68]. In thi paper, one interplanetary hock propagation model i built up baed on 1D-HD equation. The implified 1D-HD numerical model can better reflect the mot baic phyical image of the diturbance propagation in interplanetary pace. A et of 68 olar event during the period of February 1997 to October a teting data are ued to evaluate the performance of the 1D-HD model. The comparion of prediction reult between our model and the model of STOA, ISPM, and HAFv. are alo preented. Science China Pre and Springer-Verlag Berlin Heidelberg 1 cb.cichina.com

2 154 ZHANG Ying, et al. Chinee Sci Bull April (1) Vol.55 No.11 1 Model decription 1.1 1D-HD equation The time-dependent equation governing a ingle fluid, pherically ymmetric, adiabatic olar wind are given by [9]. v v v, t r r r v v 1 p GM v, t r r r p p v v v a t r r r ( ) ( ). Here, a uual, denote denity, v the radial peed, p the thermal preure, a the ound peed( a p, the polytropic index), G the gravitational contant, and M the olar ma. In Heliophere Equator Coordinate, V and B are both zero. According to the conervation of magnetic flux, radial magnetic filed atifie Br 1 r. Phyical parameter, v, B, p, t, r will be non-dimenionalized by critical point value, v, B, p, A, R. We can obtain ( v) v, t r r v v p ( ), t r r r p p v pv v p, t r r r where 8p B i the ratio of plama thermal preure to magnetic preure, i the gravity accelera- gr VA tion dimenionle value, A R VA and VA B 4 are the characteritic Alfvén time and peed, R i the olar radiu. 1. Numerical grid Due to the large cale of the computational domain from 1 R to 15 R, during which the olar wind velocity change from ubonic to uperonic, we divide the computational domain into two domain. One domain i 1 R R (called domain 1), the other i R 16 R (called domain ). For domain 1, we chooe non-uniform grid ri () (1.5) i1 ; while for domain, we chooe uniform grid (1) () ri () ri ( 1).5. Thi diviion complete grid ytem of the computational domain [1 R, 15 R ]. The time increment i limited by the o-called Courant-Friedrich-Levy condition (CFL condition) with the Courant number.8, t.8* r Cf, where C f i the maximum of the local ound peed. 1.3 Boundary condition In order to obtain the initial ambient olar wind condition, the olar wind velocity, denity and preure in computational boundary hould be obtained. Then we can obtain the correponding value in the whole calculation domain by uing the iteration method for difference equation. We can chooe inner boundary (on olar urface) condition and outer boundary (at 1 AU) condition. In thi model, we chooe outer boundary condition. For implicitly, we only ue the oberved background olar wind velocity at 1 AU V w. In order to increae the tability of the procedure, if the background olar wind velocity i le than 5 km/, the number denity at 1 AU i aumed to be 18 cm 3, otherwie, it aumed to be 9 cm 3. The temperature at 1 AU i aumed to be T au. According to 1D-HD eq. (1), for teady tate, Tau andv w atify the contraint relation 4( 1) ( 1) au 4 Uau H ( ) ( ) U, 1 1 H GM auvw where H, U RRT au, 5 3. If the olar au pau wind velocity at 1 AU i given, the temperature at 1 AU can be determined uniquely by uing Newtonian iteration method to olve eq. (3). 1.4 Initial condition Before olving eq. (), Parker olar wind olution hould be obtained and thi will be the initial value condition. We aumed the background olar wind to be teady-tate olution of eq. (). The ytem doe not depend on the time, thu t. We ubtitute it into eq. (), 1D teady-tate olar wind model in dimenionle form can be obtained a dv 1 dp v, dr dr r vr cont C1, p cont C. According to eq. (4), we can obtain (3) (4) dv a a v (1 ), (5) dr v r r

3 ZHANG Ying, et al. Chinee Sci Bull April (1) Vol.55 No where a p i the local ound peed. From eq. (5), the critical point for dv dr are located at v r rc a c c, c pc a, where the olar wind change from ubonic to uperonic tate. Now we can write eq. (5) a a dv r r, dr a v(1 ) v p where 1 1 a CC1 ( vr ). Taking the critical point into account, and uing the iteration method for eq. (6), we can obtain the ditribution of the background olar wind velocity depending on r in the whole calculation domain. 1.5 Simulated diturbance model After obtaining the teady-tate olar wind olution, a time-dependent pule uperimpoed on the olar urface map i ued to introduce the coronal exploion event uch a flare and CME. Following the method of the HAF model [5,1], a high peed tream i introduced into the background olar wind tream, which propagate into the interplanetary region and caue the interplanetary hock. The temporal profile of the hock peed at the Sun i conidered to be governed by a time contant ( ) that appear in the exponential expreion: Vt () V ( t/ )exp(1 t/ ), where the value i determined from the integrated X-ray flux in the 1 8 Angtrom GOES channel a a proxy diagnotic. It i etimated, on the uual logarithmic flux cale, by the time duration meaured at one-half the ditance from the pre-event background level to the peak. The hock peed rie exponentially to an aumed maximum ( V, the Type II drift peed) and fall to a final decayed value of the background olar wind peed. After olving the ordinary differential eq. (5), the teadytate Parker olution can be obtained. The teady background olar wind will be the initial value of eq. (). We chooe appropriate numerical cheme (here we chooe Roe cheme [11]), and the partial differential equation () can be olved. The evolution of eq. () hould be teady tate if no diturbance i introduced. We can obtain the 1D evolution of the diturbance propagation in interplanetary pace if a diturbance i introduced on the olar urface. c (6) 1.6 Criteria for judging arrival of IP hock at Earth Here, following the method ued by the HAF model, a threhold of hock earch index (SSI) i introduced to judge arrival of IP hock at Earth. In HAF model, the hock arrival time (SAT) i determined by computing predicted olar wind peed, denity, and dynamic preure at L1 pacecraft poition for everal day into the future [5,6]. The predicted SAT are extracted from automatic can of the temporal profile of the dynamic preure imulated at L1 uing a SSI: SSI log( PPmin ), where P i either the dynamic preure or momentum flux; P i the difference in P during conecutive 1-h time tep, and P min i the minimum P value for thee time tep. Shock arrival time wa identified a the time of maximum SSI a long a SSI exceed the threhold. For our preent method, the threhold of SSI i aumed to be.4. Prediction reult and comparion For the 1D-HD model, the input parameter are the initial hock peed V, the duration of the olar event, and the background olar wind peed V w. Figure 1 how the dependence of the tranit time to 1 AU predicted by the 1D-HD model on the initial hock peed for different and different V w. It can be een from Figure 1(a) that tranit time decreae with the increae of the initial hock peed. And the background olar wind peed i lower; the trend of the change i more obviou. Decreaing the background olar wind peed can weaken the dependence of the tranit time on the initial hock peed, particularly at the latter lower value. Figure 1(b) give the hock tranit time T veru the initial hock peed for different. We alo found that the tranit time decreae with the increae of the initial hock peed. And the tranit time decreae with the hock driving time for an initial hock peed. For teting purpoe, we elected 68 olar tranient event during the period from February 1997 to October [6]. In thi paper, we only concern on forecating the hock arrival time, therefore, the event without a correponding IP hock arrival at 1 AU and thoe with an ambiguou relationhip between the olar event and the hock at 1 AU are not included here. For the 68 event, the required input parameter are: initial hock peed ( V ), hock driving time ( ), background olar wind peed ( V w ) and the correponding hock arrival time. By applying the 1D-HD model to the data et of 68 event, we obtained the original reult on the prediction of the hock arrival time. The prediction error i defined by T HD T HD T o, where T o i the oberved tranit time and T HD i the predicted tranit time by 1D-HD model.

4 156 ZHANG Ying, et al. Chinee Sci Bull April (1) Vol.55 No.11 Figure 1 (a) The hock tranit time T veru the initial hock peed V for different background olar wind peed V w. (b) The hock tranit time T veru the initial hock peed for different duration time of olar event. Figure give the oberved tranit time T o plotted againt the original predicted tranit time T HD. The olid line denote the linear fitting of T o with T HD, T o = T HD. Thi linear fitting doe not fit the realit one (dotted line). The prediction error of 1D-HD model are probably induced by many factor. One i that the 1-D model doe not take into account the location of the tranient event, which contribute to the hock arrival time. Another i that the initial hock peed would affect hock arrival time. Alo, the background olar wind peed ha an important effect on the hock arrival time [1,13]. The model i pherically ymmetric; thu, it cannot reflect the realitic inhomogeneou olar wind. However, the background olar wind for every event cannot be given by the preent model. Heinemann preented that the prediction error would be within 915 h if the inhomogeneitie of background olar wind wa not conidered [14]. Taking all of thee argument into account, we revie the reult for predicting the tranit time a follow: T HD T HD, where T HD tand for the modified tranit time. The reult how that, for the 68 event, the original mean error T of the 1D-HD model i h, while the mean error i 1.75 h after our modification of the firt prediction reult. The prediction reult i improved after thi modification. Table 1 give the mean abolute error of STOA, ISPM, HAFv., and 1D-HD model. The mean error of STOA, ISPM, and HAFv. model are 14.9 h, h, and 14.1 h, repectively. The mean abolute error of thee model are nearly identical, which how imilar capability of forecating the IP hock arrival time among thee model. Figure 3 give the hitogram of error in the predicted tranit time for the 1D-HD model. The hitogram how a Gauian ditribution with a peak around zero after modified the prediction reult. Thi property of approximate normal ditribution demontrate that the propagation of the interplanetary diturbance are mainly accounted for the model and may be influenced additionally by other factor. However, other error ource, uch a coronal denity ditribution, complex heliopheric environment, and olar wind inhomogeneitie [1517], can alo influence the propagation and arrival of IP hock and may lead to complicated ditribution of the predicted tranit time. And thee error ource can explain, at leat partly, the fact that the mean abolute error of the model are all above 1 h. Figure The oberved tranit time T o plotted veru the predicted tranit time T HD. The olid line denote a linear fitting. Table 1 model Averaged abolute error of STOA, ISPM, HAFv., and 1D-HD Model Averaged abolute error (h) STOA 14.9 ISPM HAFv D-HDoriginal D-HDmodified 1.75

5 ZHANG Ying, et al. Chinee Sci Bull April (1) Vol.55 No A for the relative error of prediction, i.e., T o T T The prediction tet for how that, for elected 68 event, 9% of all the event have the relative error le than 1%, 66% have relative error le than 3%, and 9% have the relative error le than 5% before modification of the prediction reult. But after modification, 31% of all the event have the relative error le than 1%, 75% have the relative error le than 3%, and 84% have the relative error le than 5%. It i found that the prediction reult i improved for the relative error le than 1% after modification. For the STOA model, 4%, 63%, and 78% of all the event have the relative error le than 1%, 3%, and 5%, repectively. For the ISPM model, 1%, 5%, and 59% of all the event have the relative error le than 1%, 3%, and 5%, repectively. For the HAFv. model, 31%, 7%, and 93% of all the event have the relative error le than 1%, 3%, and 5%, repectively. We can ee from Table that the performance of the four model in term of relative error are nearly identical a well. Figure 3 The hitogram of error in the predicted tranit time for the 1D-HD model. Table Comparion of prediction reult from STOA, ISPM, HAFv. and 1D-HD model Model Event percentage 1% 3% 5% TOA 4% 63% 78% ISPM 1% 5% 59% HAFv. 31% 7% 93% 1D-HD (original) 9% 66% 9% 1D-HD (modified) 31% 75% 84% o pred. 3 Concluion and dicuion In thi paper, one interplanetary hock propagation model i built up baed on 1D-HD equation by uing Roe cheme. Gonzalez et al. [18] ued a one-dimenional, hydrodynamic ingle-fluid model to imulate eight CME at two kind of ambient olar wind condition and obtained ome tatitical reult. Thee reult how that for thee cae the travel time depend not only on the CME initial peed, but on the ambient wind and other CME characteritic. However, the imulation how that the arrival time of very fat CME (V cme >1 km/) ha a maller diperion and therefore prediction can be made with reaonable accuracy [18]. Our model alo obtain the ame reult: the arrival time would be affected by initial hock peed and the background hock peed. The tranit time decreae with the increae of the initial hock peed. And the background olar wind peed i lower; the trend of the change i more obviou. Decreaing the background olar wind peed can weaken the dependence of the tranit time on the initial hock peed, particularly at the latter lower value. We ued 68 olar event during the period of February 1997 to October a tet event for 1D-HD model to predict the hock arrival time. The input parameter for thi model are initial hock peed, hock driving time and background olar wind peed. The prediction tet for elected 68 event tell u that 31% of all the event have the relative error le than 1%, 75% have the relative error le than 3%, and 84% have the relative error le than 5%. Thi how that our model could be practically equivalent to the STOA, ISPM, HAFv. model in forecating the hock arrival time. However, like other imilar arrival time prediction model, thi preent 1D-HD model i jut a imple a well a ideal one with it own hortcoming. Firtly, coronal ma ejection i a complicated pace plama proce, and we only ue three kind of oberving data to imulate the diturbance coarely, neglecting the location of the CME. The prediction reult i not precie enough a being imagined. Secondly, we do not conider the forecating model for a pecific event, but only preent a method to predict the hock arrival time by inputting the oberving data. So there would be ome prediction error for a large number of event, which are only on a tatitic ene. For the imulation of ucceive event, there would be interaction among multi wave in interplanetary pace [1,13]. For thee event, the former event diturbance can be een a the background condition of the latter event. Thirdly, thi model i a 1-D model, which can only partly reflect the phyical picture of the diturbance propagation. The implified 1-D redial magnetic field make the evolution equation degenerate into HD equation. However, the occurrence of actual procee i controlled by MHD equation. If -D or 3-D imulation and the change of the normal magnetic field are conidered, the reliability of thi model would be improved. All

6 158 ZHANG Ying, et al. Chinee Sci Bull April (1) Vol.55 No.11 thee deerve future conideration. Thi work wa upported by the National Natural Science Foundation of China (Grant No , , and 4536), National Baic Reearch Program of China (Grant No. 6CB8634), Specialized Reearch Fund for State Key Laboratorie and Special Fund for Public Welfare Indutry (Meteorology) (Contract GYHY864). 1 Dryer M, Smart D F. Dynamical model of coronal tranient and interplanetary diturbance. Adv Space Re, 1984, 4: Smart D F, Shea M A. A implified model for timing the arrival of olar-flare-initiated hock. J Geophy Re, 1985, 9: Smith Z, Dryer M. MHD tudy of temporal and patial evolution of imulated interplanetary hock in the ecliptic plane within 1 AU. Solar Phy, 199, 19: Smith Z K, Dryer M. The Interplanetary Shock Propagation Model: A model for predicting olar-flare-caued geomagnetic udden impule baed on the -1/D MHD numerical imulation reult from the Interplanetary Global Model (DIGM), NOAA Technical Memorandum, ERL/SEL Fry C D, Sun W, Deehr C S, et al. Improvement to the HAF olar wind model for pace weather prediction. J Geophy Re, 1, 16: Fry C D, Dryer M, Smith Z, et al. Forecating olar wind tructure and hock arrival time uing an enemble of model. J Geophy Re, 3, 18, doi:1.19/ja Smith Z K, Dryer M, Ort E, et al. Performance of Interplanetary hock prediction model: STOA and ISPM. J Atmo Sol-Terr Phy,, 6: McKenna-Lawlor S, Dryer M, Kartalev M D, et al. Near real-time prediction of the arrival at the Earth of flare-generated hock during Solar Cycle 3. J Geophy Re, 6, 111, A1113, doi:1.19/ 5JA Nayagawa Y, Steinolfon R S. Dynamical repone of the olar corona. Atrophy J, 1976, 7: Hakamada K, Akaofu S I. Simulation of three-dimenional olar wind diturbance and reulting geomagnetic torm. Space Sci Rev, 198, 31: Cargo P, Gallice G. Roe matrice for ideal MHD and ytematic contruction of Roe matrice for ytem of conervation law. J Comput Phy, 1997, 136: Wu C C, Feng X S, Wu S T, et al. Effect of the interaction and evolution of interplanetary hock on background olar wind peed. J Geophy Re, 6, 111, A114, doi:1.19/6ja Xiong M, Zheng H N, Wang Y M, et al. A numerical imulation on the olar-terretrial tranit time of ucceive CME during November 4 5, 1998 (in Chinee). Chin J Geophy, 5, 48: Heinemann M. Effect of olar wind inhomogeneitie on tranit time of interplanetary hock wave. J Atmo Sol-Terr Phy,, 64: Moon Y J, Dryer M, Smith Z, et al. A revied hock time of arrival (STOA) model for interplanetary hock propagation: STOA-. Geophy Re Lett,, 9, 139, doi:1.19/gl Cho K S, Moon Y J, Dryer M, et al. A tatitical comparion of interplanetary hock and CME propagation model. J Geophy Re, 3, 18: Feng X S, Zhao X H. A new prediction method for the arrival time of interplanetary hock. Sol Phy, 6, 38: Gonzalez-Eparza J A, Lara A, Perez-Tijerina E, et al. A numerical tudy on the acceleration and tranit time of coronal ma ejection in the interplanetary medium. J Geophy Re, 3, 18, 139, doi: 1.19/1JA9186