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Comparative analyses of current three-dimensional numerical solar wind models

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Abstract

We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories: (I) theoretical, empirical and numerically based models and (II) self-consistent multi-dimensional numerical magnetohydrodynamic (MHD) models. The models of Category I are used to separately describe the solar wind solution in two plasma flows regions: transonic/trans-Alfvénic and supersonic/super-Alfvénic, respectively. Models of Category II construct a complete, single, numerical solar wind solution through subsonic/sub-Alfvénic region into supersonic/super-Alfvénic region. The Wang-Sheeley-Arge (WSA)/ENLIL in CISM is the most successful space weather model that belongs to Category I, and the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme (BATS-R-US) code in SWMF (Space Weather Modeling Framework) and the solar-interplanetary conservative element solution element MHD (SIP-CESE MHD) model in SWIM (Space Weather Integrated Model) are the most commonly-used models that belong to Category II. We review the structures of their frameworks, the main results for solar wind background studies that are essential for solar transient event studies, and discuss the common features and differences between these two categories of solar wind models. Finally, we conclude that the transition of these two categories of models to operational use depends on the availability of computational resources at reasonable cost and point out that the models’ prediction capabilities may be improved by employing finer computational grids, incorporating more observational data and by adding more physical constraints to the models.

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References

  • Arge C N, Pizzo V J. 2000. Improvement in the prediction of solar wind conditions using near-real time solar magnetic field updates. J Geophys Res-Atmos, 105: 10465–10480

    Google Scholar 

  • Arge C N, Henney C J, Koller J, et al. 2010. Air Force Data Assimilative Photospheric Flux Transport (ADAPT) Model. The Twelfth International Solar Wind Conference. AIP Conf Proc, 1216: 343–346

    Google Scholar 

  • Arge C N, Henney C J, Koller J, et al. 2011. Improving data drivers for coronal and solar wind models. Astronomical Society of the Pacific Conference Series. 444: 99–104

    Google Scholar 

  • Brackbill, J U, Barnes D C. 1980. The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations. J Comput Phys, 35: 426–430

    Google Scholar 

  • Chang S. 1995. The method of space-time conservation element and solution element—A new approach for solving the Navier-Stokes and Euler equations. J Comput Phys, 119: 295–324

    Google Scholar 

  • Chang S C, Wang X Y, To W M. 2000. Application of the spacectime conservation element and solution element method to one-dimensional convection-diffusion problems. J Comput Phys, 165: 189–215

    Google Scholar 

  • Cohen O, Sokolov I V, Roussev I I, et al. 2007. A semiempirical magnetohydrodynamical model of the solar wind. Astrophys J, 654: L163–L166

    Google Scholar 

  • Cohen O, Sokolov I V, Roussev I I, et al. 2008. Validation of a synoptic solar wind model. J Geophys Res-Atmos, 113: A03104

    Google Scholar 

  • de Toma G, Arge C N. 2010. The Sun’s magnetic field during the past two minima. The Twelfth International Solar Wind Conference. AIP Conf Proc, 1216: 679–681

    Google Scholar 

  • Dedner A, Kemm F, Kröner D, et al. 2002. Hyperbolic divergence cleaning for the MHD equations. J Comput Phys, 175: 645–673

    Google Scholar 

  • Detman T R, Intriligator D S, Dryer M, et al. 2011. The influence of pickup protons, from interstellar neutral hydrogen, on the propagation of interplanetary shocks from the Halloween 2003 solar events to ACE and Ulysses: A 3-D MHD modeling study. J Geophys Res, 116: A03105

    Google Scholar 

  • Detman T, Smith Z, Dryer M, et al. 2006. A hybrid heliospheric modeling system: Background solar wind. J Geophys Res, 111: A07102

    Google Scholar 

  • Evans C R, Hawley J F. 1988. Simulation of magnetohydrodynamic flows—A constrained transport method. Astrophys J, 332: 659–677

    Google Scholar 

  • Fedder J A, Slinker S P, Lyon J G, et al. 1995a. Global numerical simulation of the growth phase and the expansion onset for a substorm observed by Viking. J Geophys Res, 100: 19083–19094

    Google Scholar 

  • Fedder J A, Lyon J G, Slinker S P, et al. 1995b. Topological structure of the magnetotail as a function of interplanetary magnetic field direction. J Geophys Res, 100: 3613–3621

    Google Scholar 

  • Feldman W C, Barraclough B L, Gosling J T, et al. 1998. Ion energy equation for the high-speed solar wind: Ulysses observations. J Geophys Res, 103: 14547–14558

    Google Scholar 

  • Feng X S, Xiang C Q, Zhong D K, et al. 2005. A comparative study on 3-D solar wind structure observed by Ulysses and MHD simulation. Chin Sci Bull, 50: 672–676

    Google Scholar 

  • Feng X S, Hu Y Q, Wei F S. 2006. Modeling the resistive MHD by the CESE method. Sol Phys, 235: 235–257

    Google Scholar 

  • Feng X S, Zhou Y F, Wu S T. 2007. A novel numerical implementation for solar wind modeling by the modified conservation element/solution element method. Astrophys J, 655: 1110–1126

    Google Scholar 

  • Feng X S, Zhang Y, Yang L P, et al. 2009. An operational method for shock arrival time prediction by one-dimensional CESE-HD solar wind model. J Geophys Res, 114: A10103

    Google Scholar 

  • Feng X S, Yang L P, Xiang C Q, et al. 2010. Three-dimensional solar wind modeling from the Sun to Earth by a SIP-CESE MHD model with a six-component grid. Astrophys J, 723: 300–319

    Google Scholar 

  • Feng X S, Zhang S H, Xiang C Q, et al. 2011. A hybrid solar wind model of the CESE+HLL method with a Yin-Yang overset grid and an AMR grid. Astrophys J, 734: 50, doi:10.1088/0004-637X/734/1/50

    Google Scholar 

  • Feng X S, Yang L P, Xiang C Q, et al. 2012a. Validation of the 3D AMR SIP-CESE solar wind model for four Carrington rotations. Sol Phys, 279: 207–229

    Google Scholar 

  • Feng X S, Jiang C W, Xiang C Q, et al. 2012b. A data-driven model for the global coronal evolution. Astrophys J, 758: 62

    Google Scholar 

  • Feng X S, Xiang C Q, Zhong D K. 2013a. Numerical Study of Interplanetary solar storms (in Chinese). Sci Sin Terrae, 43: 912–933

    Google Scholar 

  • Feng X S, Zhong D K, Xiang C Q, et al. 2013b. GPU computing in space weather modeling. Numerical Modeling of Space Plasma Flows: ASTRONUM-2012, ASP Conference Series, 474: 131–139

    Google Scholar 

  • Feng X S, Zhong D K, Xiang C Q, et al. 2013c. GPU-accelerated computing of three-dimensional solar wind background. Sci China Earth Sci, 56: 1864–1880

    Google Scholar 

  • Feng X S, Xiang C Q, Zhong D K, et al. 2014. SIP-CESE MHD model of solar wind with adaptive mesh refinement of hexahedral meshes. Comput Phys Commun, 185: 1965–1980

    Google Scholar 

  • Fry C D, Sun W, Deehr C S, et al. 2001. Improvements to the HAF solar wind model for space weather predictions. J Geophys Res, 106: 20985–21001

    Google Scholar 

  • Gibson S E, Kozyra J U, de Toma G, et al. 2009. If the Sun is so quiet, why is the Earth ringing? A comparison of two solar minimum intervals. J Geophys Res, 114: A09105

    Google Scholar 

  • Gombosi T I, Powell K G, De Zeeuw, et al. 2004. Solution-adaptive magnetohydrodynamics for space plasmas: Sun-to-earth simulations. Comput Sci Engineer, 6: 14–35

    Google Scholar 

  • Goodrich C C, Sussman A L, Lyon J G, et al. 2004. The CISM code coupling strategy. J Atmos Solar Terr Phys, 66: 1469–1479

    Google Scholar 

  • Gressl C, Veronig A M, Temmer M, et al. 2014. Comparative study of MHD modeling of the background solar wind. Sol Phys, 289: 1783–1801

    Google Scholar 

  • Han S M, Wu S T, Dryer M. 1988. A three-dimensional, time-dependent numerical modeling of super-sonic, super-Alfvénic MHD flow. Comput Fluids, 16: 81–103

    Google Scholar 

  • Harvey K L, Recely F. 2002. Polar coronal holes during cycles 22 and 23. Solar Phys, 211: 31–52

    Google Scholar 

  • Hayashi K. 2005. Magnetohydrodynamic simulations of the solar corona and solar wind using a boundary treatment to limit solar wind mass flux. Astrophys J Suppl Ser, 161: 480–494

    Google Scholar 

  • Hayashi K, Zhao X P, Li, Y. 2008. MHD simulations of the global solar corona around the Halloween event in 2003 using the synchronic frame format of the solar photospheric magnetic field. J Geophys Res, 113: A07104

    Google Scholar 

  • Hayashi K. 2012. An MHD simulation model of time-dependent co-rotating solar wind. J Geophys Res, 117: A08105

    Google Scholar 

  • Harten A, Lax P, Leer B. 1983. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev, 25: 35–61

    Google Scholar 

  • Hu Y Q, Feng X S, Wu S T, et al. 2008. Three-dimensional MHD modeling of the global corona throughout solar cycle 23. J Geophys Res, 113: A03106

    Google Scholar 

  • Intriligator D S, Detman T, Gloecker G, et al. 2012. Pickup protons: Comparisons using the three-dimensional MHD HHMS-PI model and Ulysses SWICS measurements. J Geophys Res, 117: A06104

    Google Scholar 

  • Jacobs C, Poedts S. 2012. A numerical study of the response of the coronal magnetic field to flux emergence. Sol Phys, 280: 389–405

    Google Scholar 

  • Jiang C W, Feng X S. 2013. Extrapolation of the solar coronal magnetic field from SDO/HMI magnetogram by a CESE-MHD-NLFFF code. Astrophys J, 769: 144

    Google Scholar 

  • Jiang C W, Wu S T, Feng X S, et al. 2014. Formation and eruption of an active region sigmoid. I. A study by nonlinear force-free field modeling. Astrophys J, 780: 55

    Google Scholar 

  • Jin M, Manchester W B, van der Holst B, et al. 2013. Numerical simulations of coronal mass ejection on 2011 march 7: One-temperature and two-temperature model comparison. Astrophys J, 773: 50

    Google Scholar 

  • Kissmann R, Kleimann J, Fichtner H, et al. 2008. Local turbulence simulations for the multiphase ISM. Mon Not R Astron, 391: 1577–1588

    Google Scholar 

  • Kleimann J, Kopp A, Fichtner H, et al. 2004. Three-dimensional MHD high-resolution computations with CWENO employing adaptive mesh refinement. Comput Phys Commun, 158: 47–56

    Google Scholar 

  • Kleimann J, Kopp A, Fichtner H, et al. 2009. A novel code for numerical 3-D MHD studies of CME expansion. Annales Geophys, 27: 989–1004

    Google Scholar 

  • Koren B. 1993. A robust upwind discretisation method for advection, diffusion and source terms. In: Vreugdenhil C B, Koren B, eds, Notes on Numerical Fluid Mechanics. Vieweg-Braunschweig: Springer. 117–138

    Google Scholar 

  • Lapenta G, Pierrard V, Keppens R, et al. 2013. SWIFF: Space weather integrated forecasting framework. J Space Weather Space Clim. 3: A05

    Google Scholar 

  • Lee J Y, Sussman A. 2005. High performance communication between parallel programs. Proc 19th IEEE Inter Paral Distr Proces Sympos, 5: 177

    Google Scholar 

  • Linker J A. 2011. A next-generation model of the corona and solar wind. Technical Report AFRL-OSR-VA-TR-2012-0199, Air Force Force of Scientific Research, Arlington VA

    Google Scholar 

  • Linker J A, Lionello R, Mikić Z, et al. 2001. Magnetohydrodynamic modeling of prominence formation within a helmet streamer. J Geophys Res-Space Phys, 106: 25165–25176

    Google Scholar 

  • Linker J A, Mikić Z, Biesecker D A, et al. 1999. Magnetohydrodynamic modeling of the solar corona during Whole Sun Month. J Geophys Res-Space Phys, 104: 9809–9830

    Google Scholar 

  • Lionello R, Linker J A, Mikić Z. 2001. Including the transition region in models of the large-scale solar corona. Astrophys J, 546: 542–551

    Google Scholar 

  • Lionello R, Linker J A, Mikić Z. 2009. Multispectral emission of the Sun during the first Whole Sun Month: Magnetohydrodynamic simulations. Astrophys J, 690: 902–912

    Google Scholar 

  • Lionello R, Mikić Z, Linker J A. 1999. Stability of algorithms for waves with large flows. J Comput Phys, 152: 346–358

    Google Scholar 

  • Lionello R, Downs C, Linker J A, et al. 2013. Magnetohydrodynamic simulations of interplanetary coronal mass ejections. Astrophys J, 777: 76

    Google Scholar 

  • Manchester W B IV, van der Holst B, Tóth G, et al. 2012. The Coupled Evolution of Electrons and Ions in Coronal Mass Ejection-driven shocks. Astrophys J, 756: 81

    Google Scholar 

  • McGregor S L, Hughes W J, Arge C N, et al. 2011. The distribution of solar wind speeds during solar minimum: Calibration for numerical solar wind modeling constraints on the source of the slow solar wind. J Geophys Res-Space Phys, 116: A03101

    Google Scholar 

  • Merkin V G, Lyon J G, McGregor S L, et al. 2011. Disruption of a heliospheric current sheet fold. Geophys Res Lett, 38: L14107

    Google Scholar 

  • Mikić Z, Linker J A, Schnack D D, et al. 1999. Magnetohydrodynamic modeling of the global solar corona. Phys Plasmas, 6: 2217–2224

    Google Scholar 

  • Nakamizo A, Tanaka T, Kubo Y, et al. 2009. Development of the 3-D MHD model of the solar corona-solar wind combining system. J Geophys Res-Space Phys, 114: A07109

    Google Scholar 

  • Odstrčil D. 1994. Interactions of solar wind streams and related small structures. J Geophys Res-Space Phys, 99: 17653–17671

    Google Scholar 

  • Odstrčil D, Pizzo V J. 1999a. Distortion of the interplanetary magnetic field by three dimensional propagation of coronal mass ejections in a structured solar wind. J Geophys Res-Space Phys, 104: 28225–28240

    Google Scholar 

  • Odstrčil D, Pizzo V J. 1999b. Three-dimensional propagation of CMEs in a structured solar wind flow: 1. CME launched within the streamer belt. J Geophys Res-Space Phys, 104: 483–492

    Google Scholar 

  • Owens M J, Spence H E, McGregor S, et al. 2008. Metrics for solar wind prediction models: Comparison of empirical, hybrid, and physics-based schemes with 8 years of L1 observations. Space Weather, 6: S08001

    Google Scholar 

  • Pahud D M, Merkin V G, Arge C N, et al. 2012. An MHD simulation of the inner heliosphere during Carrington rotations 2060 and 2068: Comparison with MESSENGER and ACE spacecraft observations. J Atmos Solar Terr Phys, 83: 32

    Google Scholar 

  • Porth O, Xia C, Hendrix T, et al. 2014. MPI-AMRVAC for solar and astrophysics. Astrophys J Suppl Ser, 214: 4

    Google Scholar 

  • Powell K G. 1994. A Riemann solver for ideal MHD that works in more than one dimension. Technical Report. ICASE Report 94-24

    Google Scholar 

  • Powell K G, Roe P L, Linde T J, et al. 1999. A solution-adaptive upwind scheme for ideal magnetohydrodynamics. J Comput Phys, 154: 284–309

    Google Scholar 

  • Riley P, Linker J A, Mikić Z, et al. 2003. Using an MHD simulation to interpret the global context of a coronal mass ejection observed by two spacecraft. J Geophys Res-Space Phys, 108: 1272

    Google Scholar 

  • Riley P, Linker J A, Lionello R, et al. 2012. Corotating interaction regions during the recent solar minimum: The power and limitations of global MHD modeling. J Atmos Solar Terr Phys, 83: 1–10

    Google Scholar 

  • Riley P, Lionello R. 2011. Mapping solar wind streams from the Sun to 1 AU: A comparison of techniques. Sol Phys, 270: 575–592

    Google Scholar 

  • Schatten K H, Wilcox J M, Ness N F. 1969. A model of interplanetary and coronal magnetic fields. Sol Phys, 6: 442–455

    Google Scholar 

  • Schrijver C J, Sandman A W, Aschwanden M J, et al. 2004. The Coronal Heating Mechanism as Identified by Full-Sun Visualizations. Astrophys J, 615: 512–525

    Google Scholar 

  • Schwadron N A, McComas D J, Elliott H A, et al. 2005. Solar wind from the coronal hole boundaries. J Geophys Res-Space Phys, 110: A04104

    Google Scholar 

  • Shen F, Feng X S, Wu S T, et al. 2011. Three-dimensional MHD simulation of the evolution of the April 2000 CME event and its induced shocks using a magnetized plasma blob model. J Geophys Res-Space Phys, 116: A04102

    Google Scholar 

  • Sokolov I V, Powell K G, Cohen O, et al. 2008. Computational magnetohydro dynamics, based on solution of the well-posed riemann problem. In: Pogorelov N V, Audit E, Zank G P, eds. Numerical Modeling of Space Plasma Flows: Astronomical Society of the Pacific Conference Series. 385: 291–298

    Google Scholar 

  • Sokolov I, Timofeev E V, Sakai J I, et al. 2002. Artificial wind—A new framework to construct simple and efficient upwind shock-capturing schemes. J Comput Phys, 181: 354–393

    Google Scholar 

  • Stevens M L, Linker J A, Riley P, et al. 2012. Underestimates of magnetic flux in coupled MHD model solar wind solutions. J Atmos Solar Terr Phys, 83: 22–31

    Google Scholar 

  • Stout Q F, De Zeeuw D L, Gombosi T I, et al. 1997. Adaptive blocks: A high performance data structure. Proc 1997 ACM/IEEE confer Supercomput. 1–10

    Google Scholar 

  • Sun X D, Liu Y, Hoeksema J T, Hayashi K, et al. 2011. A new method for polar field interpolation. Sol Phys, 270: 9–22

    Google Scholar 

  • Temmer M, Rollett T, Möstl C, et al. 2011. Influence of the ambient solar wind flow on the propagation behavior of interplanetary coronal mass ejections. Astrophys J, 743: 101

    Google Scholar 

  • Tóth G. 1996. A general code for modeling MHD flows on parallel computers: Versatile advection code. Astrophys Lett Communi, 34: 245–250

    Google Scholar 

  • Tóth G. 2006. Flexible, efficient and robust algorithm for parallel execution and coupling of components in a framework. Comput Phys Communi, 174: 793–802

    Google Scholar 

  • Tóth G, Odstrčil D. 1996. Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems. J Comput Phys, 128: 82–100

    Google Scholar 

  • Tóth G, Roe P L. 2002. Divergence- and curl-preserving prolongation and restriction formulas. J Comput Phys, 180: 736–750

    Google Scholar 

  • Tóth G, van der Holst B, Sokolov I V, et al. 2012. Adaptive numerical algorithms in space weather modeling. J Comput Phys, 231: 870–903

    Google Scholar 

  • Totten T L, Freeman J W, Arya S. 1996. Application of the empirically derived polytropic index for the solar wind to models of solar wind propagation. J Geophys Res-Space Phys, 101: 15629–15636

    Google Scholar 

  • Usmanov A V, Dryer M. 1995. A global 3-D simulation of interplanetary dynamics in June 1991. Sol Phys, 159: 347–370

    Google Scholar 

  • Usmanov A V, Goldstein M L. 2003. A tilted-dipole MHD model of the solar corona and solar wind. J Geophys Res-Space Phys, 108: 1354

    Google Scholar 

  • van der Holst B, Manchester W B IV, Frazin R A, et al. 2010. A data-driven, two-temperature solar wind model with Alfvén waves. Astrophys J, 725: 1373–1383

    Google Scholar 

  • Van der Holst B, Sokolov I V, Meng X, et al. 2014. Alfvén wave solar model (AWSoM): Coronal heating. Astrophys J, 782: 81

    Google Scholar 

  • Van Leer B. 1979. Towards the ultimate conservative difference scheme. V. a second-order sequel to Godunov’s method. J Comput Phys, 32: 101–136

    Google Scholar 

  • Wang W, Killeen T L, Burns A G, et al. 1999. A high-resolution, three-dimensional, time dependent, nested grid model of the coupled thermosphere-ionosphere. J Atmos Solar Terr Phys, 61: 385–397

    Google Scholar 

  • Wiengarten T, Kleimann J, Fichtner H, et al. 2013. MHD simulation of the inner-heliospheric magnetic field. J Geophys Res-Space Phys, 118: 29–44

    Google Scholar 

  • Wood B E, Wu C C, Rouillard A P, et al. 2012. A coronal hole’s effects on coronal mass ejection shock morphology in the inner heliosphere. Astrophys J, 755: 43

    Google Scholar 

  • Worden J, Harvey J. 2000. An evolving synoptic magnetic flux map and implications for the distribution of photospheric magnetic flux. Sol Phys, 195: 247–268

    Google Scholar 

  • Wu S T, Guo W P. 1999. Generation and propagation of solar disturbances: A magnetohydrodynamic simulation. J Atmos Solar Terr Phys, 61: 109–117

    Google Scholar 

  • Wu C C, Fry C D, Berdichevsky D, et al. 2005. Predicting the arrival time of shock passages at Earth. Sol Phys, 227: 371–386

    Google Scholar 

  • Wu C C, Fry C D, Wu S T, et al. 2007. Three-dimensional global simulation of interplanetary coronal mass ejection propagation from the Sun to the heliosphere: Solar event of 12 May 1997. J Geophys Res-Space Phys, 112: A09104

    Google Scholar 

  • Wu C C, Dryer M, Wu S T, et al. 2011. Global three-dimensional simulation of the interplanetary evolution of the observed geoeffective coronal mass ejection during the epoch 1–4 August 2010. J Geophys Res-Atmos, 116: A12103

    Google Scholar 

  • Yang L P, Feng X S, Xiang C Q, et al. 2011. Simulation of the unusual solar minimum with 3D SIP-CESE MHD model by comparison with multi-satellite observations. Sol Phys, 271: 91–110

    Google Scholar 

  • Yang L P, Feng X S, Xiang C Q, et al. 2012. Time-dependent MHD modeling of the global solar corona for year 2007: Driven by daily-updated magnetic field synoptic data. J Geophys Res, 117: A08110

    Google Scholar 

  • Zhang Z C, John Yu S T, Chang S C. 2002. A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes. J Comput Phys, 175: 168–199

    Google Scholar 

  • Zhao X, Dryer M. 2014. Current status of CME/shock arrival time prediction. Space Weather Quart, 12: 14–35, doi:10.1002/2014SW001060

    Google Scholar 

  • Zhou Y F, Feng X S, Wu S T. 2008. Numerical simulation of the 12 May 1997 CME event. Chin Phys Lett, 25: 790–793

    Google Scholar 

  • Zhou Y F, Feng X S, Wu S T, et al. 2012. Using a 3-D spherical plasmoid to interpret the Sun-to-Earth propagation of the 4 November 1997 coronal mass ejection event. J Geophys Res-Space Phys, 117: A01102

    Google Scholar 

  • Zhou Y F, Feng X S. 2013. MHD numerical study of the latitudinal deflection. of coronal mass ejection. J Geophys Res-Space Phys, 118: 6007–6018

    Google Scholar 

  • Zuccarello F P, Bemporad A, Jacobs C M, et al. 2012. The role of streamers in the deflection of coronal mass ejections: Comparison between stereo three-dimensional reconstructions and numerical simulations. Astrophys J, 744: 66

    Google Scholar 

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  1. Center for Space Plasma and Aeronomic Research, the University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Shi Tsan Wu

  2. Space Weather Predictions Center, National Weather Service, National Oceanic and Atmospheric Administration, Boulder, Colorado, 80305, USA

    Murray Dryer

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Wu, S.T., Dryer, M. Comparative analyses of current three-dimensional numerical solar wind models. Sci. China Earth Sci. 58, 839–858 (2015). https://doi.org/10.1007/s11430-015-5062-1

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