A Computationally Efficient, Time-Dependent Model of the Solar Wind for Use as a Surrogate to Three-Dimensional Numerical Magnetohydrodynamic Simulations

Abstract

Near-Earth solar-wind conditions, including disturbances generated by coronal mass ejections (CMEs), are routinely forecast using three-dimensional, numerical magnetohydrodynamic (MHD) models of the heliosphere. The resulting forecast errors are largely the result of uncertainty in the near-Sun boundary conditions, rather than heliospheric model physics or numerics. Thus ensembles of heliospheric model runs with perturbed initial conditions are used to estimate forecast uncertainty. MHD heliospheric models are relatively cheap in computational terms, requiring tens of minutes to an hour to simulate CME propagation from the Sun to Earth. Thus such ensembles can be run operationally. However, ensemble size is typically limited to 10 1 to 10 2 members, which may be inadequate to sample the relevant high-dimensional parameter space. Here, we describe a simplified solarwind model that can estimate CME arrival time in approximately 0.01 seconds on a modest desktop computer and thus enables significantly larger ensembles. It is a one-dimensional, incompressible, hydrodynamic model, which has previously been used for the steady-state solar wind, but it is here used in time-dependent form. This approach is shown to adequately emulate the MHD solutions to the same boundary conditions for both steady-state solar wind and CME-like disturbances. We suggest it could serve as a "surrogate" model for the full three-dimensional MHD models. For example, ensembles of 10 5 to 10 6 members can be used to identify regions of parameter space for more detailed investigation by the MHD models. Similarly, the simplicity of the model means it can be rewritten as an adjoint model, enabling variational data assimilation with MHD models without the need to alter their code. The model code is available as an Open Source download in the Python language. B M. Owens 5 Met Office, Exeter, UK 43 Page 2 of 17 M. Owens et al.Figure 1 An example of a three-dimensional numerical MHD solution of the solar wind, using the MAS coronal model and the HelioMAS heliospheric model. The photospheric magnetic field for Carrington Rotation 1833 (spanning September 1990) was used, as it results in both fast and slow wind in the equatorial plane. (a) Latitude-time plot at Earth longitude of V r at the corona-heliosphere interface (30 R ) from MAS. (Note if the solar-wind structure is time stationary, this is an exact mirror image of a Carrington map.) The white line shows the Heliographic Equator. (b) The associated time series of V r at the sub-Earth point. (c) Latitude-time plot at Earth longitude of V r at Earth orbit (215 R ) from HelioMAS. (d) The associated time series of V r at Earth from HelioMAS (black) and HUXt (red). See text for details of the HelioMAS and HUXt models.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a lin...

Ensemble CME Modeling Constrained by Heliospheric Imager Observations

“…HUXt (Owens, Lang, et al, 2020) is a numerical model of the solar wind that uses a reduced physics approach, treating the solar wind as a 1‐D incompressible hydrodynamic flow. This allows very efficient computational solutions, being ∼1,000 times faster than comparable 3‐D MHD solar wind models.…”

“…Here we report case studies of four CMEs that highlight the potential utility of such an approach, enabled through computationally efficient solar wind modeling. Using the HUXt solar wind model (Owens, Lang, et al, 2020; Riley & Lionello, 2011), we consider the evolution of the CMEs launched on 31 August, 28 September, 10 October, and 20 November in 2012. With HUXt, we produce an ensemble hindcast of these events and demonstrate that HI observations of these CMEs can be used to appropriately weight the ensemble members.…”

Domain of Influence Analysis: Implications for Data Assimilation in Space Weather Forecasting

“…Finally, a more realistic model for the background magnetic field should be used, rather than a simple static dipole. We focused mainly on calculating the DOI at different times and locations, but a similar approach can be used to estimate the arrival time of the CME, as described in Owens et al (2020).…”

A Comparison Study of Extrapolation Models and Empirical Relations in Forecasting Solar Wind

“…A state-of-the-art solar wind forecasting framework combines the coronal model described above with the innerheliospheric model to estimate wind parameters at L1. Kinematic extrapolation methods that rely on 1D stream propagation like Heliospheric Upwind eXtrapolation (Reiss et al, 2019) and its time dependent variant HUXt (Owens et al, 2020) provides a computationally efficient solution without providing physical insight as done by the 3D MHD physics based models like ENLIL (Odstrcil et al, 2004), SWMF (Tóth et al, 2012), EUHFORIA (Pomoell and Poedts, 2018). The different approaches adopted for forecasting solar wind along with their quality assessment are presented in a review by MacNeice et al (2018).…”