Xing Meng

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.

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.

Classical and semirelativistic magnetohydrodynamics with anisotropic ion pressure

We study the magnetohydrodynamics (MHD) equations with anisotropic ion pressure and isotropic electron pressure under both the classical and semirelativistic approximations in order to develop a numerical model. The dispersion relation as well as the characteristic wave speeds are derived. In addition to the exact wave speed solutions, we also provide efficient approximate formulas for the semirelativistic magnetosonic speeds. The equations are discretized with the Rusanov and Harten-Lax-van Leer numerical schemes and implemented into the BATS-R-US MHD code. We perform a set of verification tests.

Medium Range Thermosphere-Ionosphere Storm Forecasts

The development of quantitative models that describe physical processes from the solar corona to the Earth’s upper atmosphere creates the possibility of numerical space weather forecasting with a lead time of a few days [Merkin et al., 2007; Toth et al., 2007]. Developing such a capability for the thermosphere and ionosphere is the objective of an effort described here sponsored by the NASA/National Science Foundation (NSF) Partnership for Collaborative Space Weather Modeling [Schunk, 2014]. Despite significant scientific progress in Sun-to-Earth modeling over the last few years, there is currently no system in place that relies on the physics-based model development of the past 10 years, to forecast moderate to intense upper atmosphere storms caused by solar wind disturbances. Mannucci [2012] suggests that a physics-based approach to forecasting upper atmospheric space weather has scientific as well as practical benefits.

Predicting the time derivative of local magnetic perturbations

Some of the potentially most destructive effects of severe space weather storms are caused by the geomagnetically induced currents. Geomagnetically induced currents (GICs) can cause failures of electric transformers and result in widespread blackouts. GICs are induced by the time variability of the magnetic field and are closely related to the time derivative of the local magnetic field perturbation. Predicting dB/dt is rather challenging, since the local magnetic perturbations and their time derivatives are both highly fluctuating quantities, especially during geomagnetic storms. The currently available first principles-based and empirical models cannot predict the detailed minute-scale or even faster time variation of the local magnetic field. On the other hand, Pulkkinen et al. (2013) demonstrated recently that several models can predict with positive skill scores whether the horizontal component of dB/dt at a given magnetometer station will exceed some threshold value in a 20 min time interval. In this paper we investigate if one can improve the efficiency of the prediction further. We find that the Space Weather Modeling Framework, the best performing among the five models compared by Pulkkinen et al. (2013), shows significantly better skill scores in predicting the magnetic perturbation than predicting its time derivative, especially for large deviations. We also find that there is a strong correlation between the magnitude of dB/dt and the magnitude of the horizontal magnetic perturbation itself. Combining these two results one can devise an algorithm that gives better skill scores for predicting dB/dt exceeding various thresholds in 20 min time intervals than the direct approach.