Ward B. Manchester

Space Weather Modeling Framework: A new tool for the space science community

[1] The Space Weather Modeling Framework (SWMF) provides a high-performance flexible framework for physics-based space weather simulations, as well as for various space physics applications. The SWMF integrates numerical models of the Solar Corona, Eruptive Event Generator, Inner Heliosphere, Solar Energetic Particles, Global Magnetosphere, Inner Magnetosphere, Radiation Belt, Ionosphere Electrodynamics, and Upper Atmosphere into a high-performance coupled model. The components can be represented with alternative physics models, and any physically meaningful subset of the components can be used. The components are coupled to the control module via standardized interfaces, and an efficient parallel coupling toolkit is used for the pairwise coupling of the components. The execution and parallel layout of the components is controlled by the SWMF. Both sequential and concurrent execution models are supported. The SWMF enables simulations that were not possible with the individual physics models. Using reasonably high spatial and temporal resolutions in all of the coupled components, the SWMF runs significantly faster than real time on massively parallel supercomputers. This paper presents the design and implementation of the SWMF and some demonstrative tests. Future papers will describe validation (comparison of model results with measurements) and applications to challenging space weather events. The SWMF is publicly available to the scientific community for doing geophysical research. We also intend to expand the SWMF in collaboration with other model developers.

Adaptive numerical algorithms in space weather modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics-based space weather modeling and even short-term forecasting.

ERUPTION OF A BUOYANTLY EMERGING MAGNETIC FLUX ROPE

We present a three-dimensional numerical magnetohydrodynamic simulation designed to model the emergence of a magnetic flux rope passing from below the photosphere into the corona. For the initial state, we prescribe a plane-parallel atmosphere that comprises a polytropic convection zone, photosphere, transition region, and corona. Embedded in this system is an isolated horizontal magnetic flux rope located 10 photospheric pressure scale heights below the photosphere. The flux rope is uniformly twisted, with the plasma temperature inside the rope reduced to compensate for the magnetic pressure. Density is reduced in the middle of the rope, so that this section buoyantly rises. The early evolution proceeds with the middle of the rope rising to the photosphere and expanding into the corona. Just as it seems the system might approach equilibrium, the upper part of the flux rope begins to separate from the lower, mass-laden part. The separation occurs through stretching of the field, which forms a current sheet, where reconnection severs the field lines to form a new system of closed flux. This flux then erupts into the corona. Essential to the eruption process are shearing motions driven by the Lorentz force, which naturally occur as the rope expands in the pressure-stratified atmosphere. The shearing motions transport axial flux and energy to the expanding portion of the magnetic field, driving the eruption.

A Semiempirical Magnetohydrodynamical Model of the Solar Wind

We present a new MHD model for simulating the large-scale structure of the solar corona and solar wind under “steady state” conditions stemming from the Wang-Sheeley-Arge empirical model. The processes of turbulent heating in the solar wind are parameterized using a phenomenological, thermodynamical model with a varied polytropic index. We employ the Bernoulli integral to bridge the asymptotic solar wind speed with the assumed distribution of the polytropic index on the solar surface. We successfully reproduce the mass flux from Sun to Earth, the temperature structure, and the large-scale structure of the magnetic field. We reproduce the solar wind speed bimodal structure in the inner heliosphere. However, the solar wind speed is in a quantitative agreement with observations at 1 AU for solar maximum conditions only. The magnetic field comparison demonstrates that the input magnetogram needs to be multiplied by a scaling factor in order to obtain the correct magnitude at 1 AU.

Alfvén wave solar model (AWSoM): Coronal heating

We present a new version of the Alfven wave solar model, a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently. The physics include the following. (1) The model employs three different temperatures, namely the isotropic electron temperature and the parallel and perpendicular ion temperatures. The firehose, mirror, and ion-cyclotron instabilities due to the developing ion temperature anisotropy are accounted for. (2) The Alfven waves are partially reflected by the Alfven speed gradient and the vorticity along the field lines. The resulting counter-propagating waves are responsible for the nonlinear turbulent cascade. The balanced turbulence due to uncorrelated waves near the apex of the closed field lines and the resulting elevated temperatures are addressed. (3) To apportion the wave dissipation to the three temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating. (4) We have incorporated the collisional and collisionless electron heat conduction. We compare the simulated multi-wavelength extreme ultraviolet images of CR2107 with the observations from STEREO/EUVI and the Solar Dynamics Observatory/AIA instruments. We demonstrate that the reflection due to strong magnetic fields in the proximity of active regions sufficiently intensifies the dissipation and observable emission.

Three-dimensional MHD Simulation of the 2003 October 28 Coronal Mass Ejection: Comparison with LASCO Coronagraph Observations

We numerically model the coronal mass ejection (CME) event of 2003 October 28 that erupted from AR 10486 and propagated to Earth in less than 20 hr, causing severe geomagnetic storms. The magnetohydrodynamic (MHD) model is formulated by first arriving at a steady state corona and solar wind employing synoptic magnetograms. We initiate two CMEs from the same active region, one approximately a day earlier that preconditions the solar wind for the much faster CME on the 28th. This second CME travels through the corona at a rate of over 2500 km s−1, driving a strong forward shock. We clearly identify this shock in an image produced by the Large Angle Spectrometric Coronagraph (LASCO) C3 and reproduce the shock and its appearance in synthetic white-light images from the simulation. We find excellent agreement with both the general morphology and the quantitative brightness of the model CME with LASCO observations. These results demonstrate that the CME shape is largely determined by its interaction with the ambient solar wind and may not be sensitive to the initiation process. We then show how the CME would appear as observed by wide-angle coronagraphs on board the Solar Terrestrial Relations Observatory (STEREO) spacecraft. We find complex time evolution of the white-light images as a result of the way in which the density structures pass through the Thomson sphere. The simulation is performed with the Space Weather Modeling Framework (SWMF).

CORONAL MASS EJECTION SHOCK AND SHEATH STRUCTURES RELEVANT TO PARTICLE ACCELERATION

Most high-energy solar energetic particles are believed to be accelerated at shock waves driven by coronal mass ejections (CMEs). The acceleration process strongly depends on the shock geometry and the structure of the sheath that forms behind the shock. In an effort to understand the structure and time evolution of such CME-driven shocks andtheirrelevancetoparticleacceleration,weinvestigatetheinteractionofafastCMEwiththeambientsolarwind by means of a three-dimensional numerical ideal MHD model. Our global steady state coronal model possesses high-latitudecoronalholesandahelmetstreamerstructurewithacurrentsheetneartheequator,reminiscentofnear solar minimum conditions. Fast and slow solar winds flow at high and low latitude, respectively, and the Archimedean spiral geometry of the interplanetary magnetic field is reproduced by solar rotation. Within this model system, we drive a CME to erupt by introducing a Gibson-Low magnetic flux rope that is embedded in the helmet streamer in an initial state of force imbalance. The flux rope rapidly expands and is ejected from the corona with maximum speeds in excess of 1000 km s � 1 , driving a fast-mode shock from the inner corona to a distance of 1 AU. We find that the ambient solar wind structure strongly affects the evolution of the CME-driven shocks, causing deviations of the fast-mode shocks from their expected global configuration. These deflections lead to substantial compressions of the plasma and magnetic field in their associated sheath region. The sudden postshock increase in magneticfieldstrengthonlow-latitudefieldlinesisfoundtobeeffectiveforacceleratingparticlestotheGeVrange. Subject heading gs: acceleration of particles — MHD — shock waves — Sun: coronal mass ejections (CMEs)

A DATA-DRIVEN, TWO-TEMPERATURE SOLAR WIND MODEL WITH ALFVEN WAVES

We have developed a new three-dimensional magnetohydrodynamic (MHD) solar wind model coupled to the Space Weather Modeling Framework (SWMF) that solves for the different electron and proton temperatures. The collisions between the electrons and protons are taken into account as well as the anisotropic thermal heat conduction of the electrons. The solar wind is assumed to be accelerated by the Alfven waves. In this paper, we do not consider the heating of closed magnetic loops and helmet streamers but do address the heating of the protons by the Kolmogorov dissipation of the Alfven waves in open field-line regions. The inner boundary conditions for this solar wind model are obtained from observations and an empirical model. The Wang-Sheeley-Arge model is used to determine the Alfven wave energy density at the inner boundary. The electron density and temperature at the inner boundary are obtained from the differential emission measure tomography applied to the extreme-ultraviolet images of the STEREO A and B spacecraft. This new solar wind model is validated for solar minimum Carrington rotation 2077 (2008 November 20 through December 17). Due to the very low activity during this rotation, this time period is suitable for comparing the simulated corotating interaction regions (CIRs) with in situ ACE/WIND data. Although we do not capture all MHD variables perfectly, we do find that the time of occurrence and the density of CIRs are better predicted than by our previous semi-empirical wind model in the SWMF that was based on a spatially reduced adiabatic index to account for the plasma heating.

The Evolution of Coronal Mass Ejection Density Structures

We present a discussion of the time evolution of the mass and energy of a model coronal mass ejection (CME), analyzing both synthetic coronograph images and three-dimensional data of the numerical ideal magnetohydrodynamics (MHD) simulation. Our global steady state coronal model possesses high-latitude coronal holes and a helmet streamer structure with a current sheet near the equator, reminiscent of near solar minimum conditions. Within this model system, we drive a CME to erupt by the introduction of a Gibson-Low magnetic flux rope that is embedded in the helmet streamer in an initial state of force imbalance. The flux rope rapidly expands and is ejected from the corona with maximum speeds in excess of 1000 km s-1 driving a fast-mode shock that propagates from the inner corona to a distance of 1 AU. We study the mass and energetics of the CME inferred from the three-dimensional results of the simulation, as well as calculated from synthetic coronograph images produced at different times. The two-dimensional plane-of-sky density structure of a CME is discussed for wide-angle coronographs, such as the Heliospheric Imager (HI-2) on board STEREO (Solar Terrestrial Relations Observatory), and compared with the three-dimensional density structure. We found that the CME mass derived from the synthetic coronographic images is an underestimate by about 50% of the total mass of the CME according to the three-dimensional data. Two main reasons can be invoked: the poor assumption that all the mass of the CME is in the plane of the sky and the wrapping of the front shock around the density-depleted cavity, which leads to an apparent decrease in brightness of the front shock.

Numerical investigation of the homologous coronal mass ejection events from active region 9236

We present a three-dimensional compressible magneto-hydrodynamics (MHD) simulation of the three coronal mass ejections (CMEs) of 2000 November 24, originating from NOAA active region 9236. These three ejections, with velocities around 1200 km s-1 and associated with X-class flares, erupted from the Sun in a period of about 16.5 hr. In our simulation, the coronal magnetic field is reconstructed from MDI magnetogram data, the steady-state solar wind is based on a varying polytropic index model, and the ejections are initiated using out-of-equilibrium semicylindrical flux ropes with a size smaller than the active region. The simulations are carried out with the Space Weather Modeling Framework. We are able to reproduce the shape and velocity of the CMEs as observed by the LASCO C3 coronograph. The complex ejecta resulting from the interaction of the three CMEs is preceded at Earth by a single shock wave, which, in our simulation, arrives at Earth 10 hr later than the shock observed by the Wind spacecraft. This article discusses the three-dimensional aspects of the propagation, interaction, and merging of the forward shock waves associated with the three ejections. Synthetic images from the Heliospheric Imagers onboard the STEREO spacecraft are produced, and we predict that the large density jump associated with the interaction of the shocks should be observed by those coronographs in the near future.