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1、JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ?, XXXX, DOI:10.1029/,A Data-drivenSolarWindMHDModel:From 1Rsto1AUD RA F TSeptember 30,2014, 11:21amD R A FTX - 2FENG ET AL.: SHORT TITLEAbstract.We present here a time-dependent three-dimensional magne-tohydrodynamics (MHD) solar wind simulation driven by time-

2、varying line-of-sight solar magnetic eld data. The simulation is based on the 3 dimen-sional (3D) Solar-Interplanetary (SIP) adaptive mesh renement (AMR) space-time conservation element and solution element (CESE) MHD (SIP-AMR-CESE MHD) model. In this simulation, we rst achieve the initial solar win

3、dbackground with time-relaxation method by inputting a potential eld ob-tained from the synoptic photospheric magnetic eld, and then generate thetime-evolving solar wind by advancing the initial 3D solar wind backgroundwith continuously varying photospheric magnetic eld. The model updatesthe inner b

4、oundary conditions by using the projected normal characteristic(PNC) method, inputting the high-cadence photospheric magnetic eld da-ta corrected by solar dierential rotation, and limiting the mass ux escap-ing from the the solar photosphere. We employ the model to investigate thesolar wind evolutio

5、n from July 1st to August 11th in 2008 using the synop-tic maps provided by Global Oscillation Network Group (GONG). We com-pare the numerical results with the solar coronal observations fromthe Extreme ultraviolet Imaging Telescope (EIT) board on Solarand Heliospheric Observatory (SOHO) and the mea

6、surements fromOMNI at 1 astronomical unit (AU). The model results are validat-ed by comparisons with the standard potential eld source surface(PFSS) model, and the MHD simulation with a monthly synopticmagnetogram (MHD-MSM). Comparisons show that the presentD R A F TSeptember 30, 2014, 11:21amD R A

7、F TX - 3FENG ET AL.: SHORT TITLEMHD results have good overall agreement with coronal andinter-planetary structures, including the sizes and distributions of coro-nal holes, the positions and shapes of the streamer belts, and thetransitions of the solar wind speeds and magnetic eld polarities.D R A F

8、 TSeptember 30, 2014, 11:21amD R A F TX - 4FENG ET AL.: SHORT TITLE1. IntroductionNumerical space weather modeling plays an important role in space weather study.Three-dimensional numerical MHD modeling can achieve a rst approximation to morecomplete physics by providing a simplied description of na

9、tural phenomena in spaceplasmas. MHD models enable us to reproduce space weather conditions and help us tounderstand some of theirrelated physical processesDryer, 2007; Aschwandenetal., 2008;Watermann et al., 2009; Feng et al., 2011b, 2013. For such purpose, some MHD modelshave been developed(e.g.,

10、Usmanov and Goldstein 2006; Tothet al. 2012; Riley et al.2011; Nakamizo et al. 2009; Hayashi 2013b; Feng et al. 2010). The study on steadysolar wind is an essential part of space weather predictions. On the one hand, some large-scale structures in the solar wind may cause adverse eects in the geospa

11、ce Gonzalezet al., 1989; Tsurutani et al., 2006. On the other hand, in modelling the evolution ofcoronal mass ejection (CME), the quasi-steady solar wind serves as the initial state, onwhich modelers inpose various mimicked eruption models, such as ux rope models Wuet al., 1999; Toth et al., 2007; L

12、ugaz et al., 2011; Manchester et al., 2008; Lionello et al.,2013, the cone model Zhao et al., 2002, and the shock jump conditions van der Holstet al.,2005.Physically speaking, photospheric magnetic eld dominates solar coronal states, andthus controls the heliospheric large-scale solar wind structure

13、s Mikic et al., 1999; Neuge-bauer et al., 1998; Mackay and van Ballegooijen, 2006. Global estimates of the solarphotospheric magnetic eld distribution are critical for numerical solar wind modelling.Commonly used solar wind models usually initialize the MHD codes by using potentialD R A F TSeptember

14、 30, 2014, 11:21amD R A F TX - 5FENG ET AL.: SHORT TITLEmagnetic eld based on the synoptic charts of the photospheric magnetic eld and Parkersolar wind solution to run with time-relaxation method until a steady-state equilibriumis achieved (e.g., Usmanov and Goldstein 2006; Feng et al. 2014; van der

15、 Holst et al.2010; Toth et al. 2012; Hayashi 2005).Synoptic mapsof solar photospheric magneticeld are constructed bycombiningallthevalues for each Carrington longitude from line-of-sight (LOS) photospheric magnetogramsduring the specied Carrington rotations (CRs). For each magnetogram, the data with

16、ina certain longitudinal range of the central meridian are used to create the synoptic maps.Theindividual valuesfor each Carrington longitude are weighted for the central meridiandistance Ulrich et al., 2002; Liu et al., 2012. It should be noted that the number ofsource data points for each Carringt

17、on longitude variessignicantly from dierent instru-ments. Due to the LOS measurements only available from the the ground stations or theinstruments board on spacecraft orbiting in the ecliptic plane, there are data gaps in thepolar regions of the synoptic maps, because the projection eect on the LOS

18、 measure-ments leads to higher noises of the data in both polar regions and the Suns tilt anglecauses data missing periodically. Svalgaard et al. 1978 analyzed the magnetograms atWilcox Solar Observatory (WSO) and concluded that poleward 55 latitude, the eld wasnearly radial and of the form 11.5cos8

19、 (where is colatitude) during 1976-1977. Wangand Sheeley 1992 developed potential models of solar corona by using similar formulaeto extrapolate the polar eld. Arge and Pizzo 2000 lled the polar eld by tting asecond-order polynomial to the most reliable observations, which were made when the ab-solu

20、te valuesof solar b angles were greater than 5. Using the data from SOHO/MichelsonDoppler Imager (MDI), Liu et al. 2007 compared the performances of the following sevenD R A F TSeptember 30, 2014, 11:21amD R A F TX - 6FENG ET AL.: SHORT TITLEmethodsofinterpolating the polar elds: one dimensional (1D

21、) cubic spline interpolationmethod, the potential eld method, the smoothed 1D cubic spline interpolation method,the method of Svalgaard et al. 1978, the two dimensional (2D) temporal interpolationmethod, the 2D spatial interpolation method, and the ux-transportation model basedmethod Schrijver et al

22、., 2002. Sun et al. 2011 developed a new technique by com-bining a two-dimensional spatial/temporal interpolation and a simple version of the uxtransport model.When the full-rotation synoptic maps of photospheric eld are used to constrain thesolar wind model, the solar magnetic eld is assumed to cha

23、nge very littile during a CR.This assumption is rather reasonable during solar minimum phases. However, the solarmagnetic eld varies dramatically especially near solar maxima and in ascending phasesSmith et al., 2001; Burlaga et al., 2002; Goelzer et al., 2013. The steady solar wind pre-scribed by t

24、he full-rotation synoptic maps can basically capture some global structures,but they can hardly reproduce the dynamic features in the solar corona and heliosphere(e.g., Usmanov and Goldstein 2006; van der Holst et al. 2010; Feng et al. 2011a; Tothet al. 2012). In order to remedy this defect, researc

25、hers drove their models using daily-updated synoptic maps of the photospheric magnetic eld instead of the full-rotationsynoptic maps. The advantage of a daily-updated map (over a full-rotation map) lies inthat the part of the map directed towards Earth consists of the most recent magnetic ob-servati

26、ons available, especially east of the Suns central meridian. Arge and Pizzo 2000input the daily-updated synoptic maps into the Wang-Sheele-Arge (WSA) model, andimproved the prediction of the solar wind conditions with a continuous empirical func-tion. Hayashi 2013a applied the daily-updated data to

27、the solar wind MHD model andD R A F TSeptember 30, 2014, 11:21amD R A F TX - 7FENG ET AL.: SHORT TITLEobtained several coronal features that a xed boundary condition cannot yield. Intriliga-tor et al. 2012 combined the WSA model and the daily-updated synoptic maps to drivethe inner boundary at 0.1AU

28、 for the model of hybrid heliospheric modeling system withpickup protons (HHMS-PI). In addition, Hernndez et al. 2007a incorporated the dataof far-side active regions derived from helioseismology into the daily-updated data. Argeet al. 2013 produced nearly-realistic estimates of the instantaneous gl

29、obal photosphericmagnetic eld distribution by using the Air Force Data Assimilative Photospheric uxTransport (ADAPT) model, which can assimilate helioseismic far-side active region dataand the evolved magnetic ux according to the observation for no measurements.It is well known that dierent parts of

30、 the Sun spin at dierent rates by measuringthe motions of structures on the photosphere, which is called the dierential rotation.However, the synoptic mapsof photospheric magnetic eld generated above are based onthe premise that the photosphere rotates rigidly at dierent latitudes, so they contain n

31、oinformation on the solar dierential rotation. Recent studies began to take into accountof the solar dierential rotation when studying the solar corona. Lionello et al. 2005used a global 3D MHD model to study the eects of dierential rotation on the coronalmagnetic eld by introducing an articial dier

32、ential rotation into a steady corona solu-tion obtained from the time relaxation method. They identied examples of interchangereconnection and found other changes of topology of the magnetic eld due to the dif-ferential rotation. Yeates et al. 2007 corrected the synoptic maps with solar dierentialro

33、tation, and employed the corrected data to initialize the surface ux transport (SFT)model Wang et al., 1989, 2002. Using the same method, Fenget al. 2012b produced theglobal time-varying and self-consistent synchronic snapshots of the photospheric magneticD R A F TSeptember 30, 2014, 11:21amD R A F

34、TX - 8FENG ET AL.: SHORT TITLEeld to advance their 3D numerical global coronal SIP-AMR-CESE-MHD model. Zhaoet al. 2004 proposed amodiedversionof synoptic charts, nameda ”synchronic frame”,in which the positions of the synoptic data are longitudinally shifted in accordance withthe solar dierential ro

35、tation. The synchronic frame data of photospheric magnetic eldhave been used by Hayashi et al. 2008 in simulating the global solar corona around theHalloween event in 2003.Global simulation of dynamic solar wind is one of the challenging problems in spaceweather modelling. Solar wind is rather than

36、of steady state, but physically dynamiccorresponding to the solar rotation, solar mass ow and solar magnetic eld evolution,especially during solar eruptions Tu and Marsch, 1995; Zurbuchen and Richardson, 2006;McComasetal., 2008. Recently, some solar wind simulations are performed to reproducethe tim

37、e-varying structures of solar wind. It is a critical issue to utilize the daily-updatedor higher-cadence synoptic maps to drive the solar wind models. These synoptic map-s contain too much noise and very strong magnetic eld in active regions. A propersmoothing procedure is usually applied to make th

38、em friendly to MHD models. In ad-dtion, the synoptic maps can serve as the near-realistic inner boundary conditions forthe radial magnetic eld of solar corona. However, updating the radial magnetic eldusing the synoptic maps without special care probably leads to the physical inconsistencyand the un

39、physical vibrations near the sub-Alfvenic solar surface boundary Nakagawa,1980, 1981a. In order to minimize these eects, researchers Wu et al., 2006; Wang et al.,2011; Hayashi, 2012, 2013a; Feng et al., 2012d prescribed the inner boundary conditionsusing the PNC method developed by Nakagawa 1980, 19

40、81a, b and Nakagawa et al.1987. Inspired by Mikic et al. 1999, Yang et al. 2012 and Feng et al. 2012c solved aD R A F TSeptember 30, 2014, 11:21amD R A F TX - 9FENG ET AL.: SHORT TITLEPoisson equation on a sphere at 1 solar radius (Rs) to deal with the nonzero tangentialelectric eld due to the varyi

41、ng radial magnetic eld so that the photospheric synopticmaps can be self-consistently combined with the PNC method at the inner boundary.Based on the considerations mentioned above, we devote our data-driven SIP-CESE-MHD model to simulating the temporal solar wind evolution from July 1st to July 14t

42、h in2008 by using 6-hour-cadence synoptic maps provided by GONG. The code rst achievesa steady-state equilibrium of solar wind using the leading preprocessed synoptic map onJuly 1st. Based on the simulated background solar wind, we then advance our model withthe changing the bottom boundary, which i

43、s determined from the PNC method and thecontinuously time-varying solar observations. Finally, we achieve the temporally varyingsolar wind structures inresponse to the changing photospheric magneticeld. This paperis organized as follows. In Section 2, we briey describe some aspects of the SIP-CESE-M

44、HD model. Section 3 lists the processing methods of synoptic maps and the treatmentsof boundary conditions. In Section 4, we present the simulation results, and compare themwith the SOHO/EIT observations and the OMNI data at 1AU. Finally, some concludingremarks and discussions are made in the last s

45、ection.2. Model DescriptionThe three-dimensional MHD equations governing solar wind plasma used in this workare written as:Ut+ F= S(1)whereU = (, v, e1, B1)T ,D R A F TSeptember 30, 2014, 11:21amD R A F TX - 10FENG ET AL.: SHORT TITLEvvv + I(p +1B 2+ B 1B ) 0 B1B1 B 1B0 B 0B 12 1 1 2F =,v(e1 + p + 2

46、 B1 + B1 B0) (v B1)(B1 + B0)vB BuandTTS = 0, F0, v F0, 0 B(0, B, v B, v) + SH,with e1 = p + 1 v2 + 1 B2. He1 re, , v, p and B are the mass density, plasma velocity,122gas pressure and magnetic eld, respectively. The external force exerted on the plasmaGMF0 = rr2v is the sum of solar gravity force an

47、dinertial force in the co-sr3rotating frame with the Sun. G = 6.67384 1011 m3kg1s2, Ms = 1.989 1030 kg, =13.2 deg/day, which stand for the gravity constant, the mass of the sun, and the angularspeed of solar rotation, respectively.In the MHD model, the Powells source terms B(0, B, vB, v)T are added

48、to advectthe divergence of magnetic eld B with the velocity of the plasma ow Powell et al.,1999; Toth et al., 2006. Besides, the magnetic eld is split into two parts B = B0 + B1Tanaka, 1994; Gombosi et al., 2003; Nakamizo et al., 2009; Feng et al., 2010, whereB0 represents the time-independent poten

49、tial magnetic eld calculated from theinitialsynoptic maps, and B1 is the time-dependent part updated by the MHD solver. Thistechnique can make the MHD solver numerically less challenging to maintain positivepressure Janhunen et al., 2012; Toth et al., 2012; van der Holst et al., 2010.In solar wind s

50、imulation, coronal heating/solar acceleration plays an important rolein producing realistic solar wind solution.Various heating terms Mikic et al., 1999;Usmanov et al., 2000; Roussev et al., 2003; Cohen et al., 2008; Nakamizo et al., 2009; Fenget al., 2010; van der Holst et al., 2010; Riley et al.,

51、2011 are usually added to the MHDequations to achieve the observed pattern of fast and slow solar wind. As in Feng et al.D R A F TSeptember 30, 2014, 11:21amD R A F TX - 11FENG ET AL.: SHORT TITLE2010, the volume heating source terms adopted in this work which read SH =( r 1) exp( r ) and SE = Q1Ca

52、exp( r ) +(0, SM er, SE, 0)T , where SM = QMCaRsLMLQ1Q2Ca (r 1) exp( r ). Here, LM , LQ and LQ are heating heights and are 1Rs,LQ2120.8Rs and 1Rs. Such volume heating source terms can be further specied bythe coecients QM , Q1 and Q2, which are 7.91014Nm3, 1.18107Jm3s1, 1.5109Jm3s1, respectively. Be

53、sides, Ca = C a/ max(C ) is a normalized proleafactor closely related to the Wang-Sheeley-Arge (WSA) model Wang et al.,1997; Arge and Pizzo, 2000; Arge et al., 2003; Arge et al., 2003, 2004; Owens3(5.81.6e1(b/8.)(1+fs)2/75) 3.5. f , the magnetic expansion factor,et al., 2005, with Ca =sreads fs = (1

54、 )2BRs , where BR and BR are the magnetic eld strength at theRBRssolar surface and at the heliocentric distance R=2.5 Rs. b is the minimumangular separation between an open magnetic eld foot point and its nearestcoronal hole boundary.In solving the MHD equations, if the magnetic eld is very strong,

55、the total energyis dominated by magnetic energy, and it may result in negative thermal pressures whensubtracting the magnetic energy from the total energy. In order to avoid this, it is betterto solve the pressure equation,p + (vp) = ( 1)p v + ( 1)SEtdirectly instead of the energy equation. Conseque

56、ntly, we employ the switch designedby Balsara and Spicer 1999 to detect the grid points where the negative pressures mayoccur, and solve the pressure equation only on these points. If negative pressures stilloccur, we either replace them with the positive ones of the previous time step or calculatethem according to the local density and a low temperature of 104K.D R A F TSeptember 30, 2014, 11:21amD R A F TX - 12FENG ET AL.: SHORT TITLETheMHDequatio