SURF: A Fast New Solar Wind Model Could Sharpen Space-Weather Forecasts

When a coronal mass ejection erupts from the Sun, forecasters race to predict when the billion-tonne cloud of plasma will slam into Earth’s magnetic field. The stakes are enormous: geomagnetic storms can knock out power grids, disable satellites, disrupt GPS navigation and endanger astronauts. Yet the models that underpin operational space-weather forecasting face a stubborn trade-off between physical realism and computational speed. A new open-source modelling framework called SURF, short for Space-weather Utilities for Research and Forecasting, promises to ease that trade-off, offering a compressible hydrodynamic solver that is thousands of times faster than full three-dimensional magnetohydrodynamic simulations while capturing key physics that simpler models miss.

SURF was developed by Mathew J. Owens and Luke A. Barnard of the University of Reading and described in the journal Solar Physics. The framework packages together two modelling options. The first is HUXt, a well-established reduced-physics model that treats the solar wind as a one-dimensional advection problem and has already found use in both forecasting and a diverse range of scientific applications, from planetary studies to comet-tail analysis. The second, and the centrepiece of the new work, is a newly developed one-dimensional compressible hydrodynamic solver called hydro, which adds physically consistent compression effects while retaining the computational efficiency needed for ensemble forecasting, uncertainty quantification and large parametric studies.

The distinction matters because the solar wind is a compressible fluid. Fast streams emitted from coronal holes eventually catch up with slower wind ahead of them, piling plasma into compressed stream interaction regions bounded by shock-like fronts. HUXt, which lacks physics-based compressibility, agrees with full three-dimensional magnetohydrodynamic models to within about five percent for the same boundary conditions, but its largest deviations appear precisely at those compression fronts. SURF-hydro addresses this weakness by solving the one-dimensional Euler equations of mass, momentum and energy conservation in spherical geometry, using finite-volume methods with Riemann solvers and second-order spatial reconstruction.

The numerical machinery is sophisticated but conceptually standard in computational fluid dynamics. The model discretises the radial domain into spherical shell cells and computes fluxes across cell interfaces using a Harten-Lax-van Leer-Contact solver, which handles the discontinuities that arise at shocks. Two reconstruction schemes are available: a first-order piecewise constant method for maximum speed, and a default second-order piecewise linear method with a monotonized central limiter that keeps sharp features like shocks intact without introducing spurious oscillations. Because the flow is radial in spherical geometry, the model includes a geometric source term in the momentum equation, reflecting the fact that the surface area of a sphere grows as the square of distance from the Sun.

Validation against an analytical benchmark is impressive. The team compared SURF-hydro with an exact solution for steady-state, pressure-driven expansion of a uniform spherical wind, treating the solar wind as isentropic flow through a nozzle whose cross-sectional area grows with distance squared. The second-order solution reproduced the analytical solar wind speed with an error of just 0.04 percent, with density and temperature errors below one percent, and conserved mass to within one percent across the whole domain. Speed matters too: a five-day simulation for a single longitude takes about 0.1 seconds on a standard desktop processor, roughly ten thousand times cheaper than a full three-dimensional magnetohydrodynamic run.

Perhaps the most consequential contribution is a new way of setting the model’s inner boundary conditions. Solar wind models typically start at 0.1 astronomical units, about a fifth of Mercury’s orbital distance, where the flow is already super-magnetosonic. Coronal models supply speed and magnetic field at that boundary, but density and temperature must be inferred from the speed, usually by assuming some form of equilibrium such as constant mass, momentum or kinetic energy flux. Owens and Barnard instead mined thirty years of near-Earth OMNI observations, removed all periods contaminated by coronal mass ejections, and derived empirical relations between solar wind speed, density and temperature at 1 astronomical unit. They then back-mapped those relations to 0.1 astronomical units using the analytical nozzle solution, producing a non-equilibrium look-up table that can be interpolated for any inner-boundary speed.

The payoff shows up in hindcast tests. For a representative 27-day interval of recurrent solar wind in 2019, a SURF-hydro hindcast driven by back-mapped in situ observations reproduced the observed base-level proton density of around five particles per cubic centimetre, along with the sharp density spikes of tens of particles per cubic centimetre at stream interaction regions, and temperatures ranging from about 50,000 kelvin in slow wind to 500,000 kelvin in compressed regions. By comparison, archived operational WSA-Enlil forecasts for the same period showed almost no density variation and temperatures systematically an order of magnitude too low. Crucially, the authors show this is not a flaw in Enlil’s physics but in its boundary conditions: when the same WSA coronal maps drove SURF-hydro with the new non-equilibrium relations, the variability in speed, density and temperature all improved markedly.

Extending the comparison across four years of observations reinforced the point. WSA-Enlil systematically under-dispersed solar wind speeds and produced far too little density variability, while its temperatures remained far too low even accounting for the reduced speed range, implicating the equilibrium assumption at the inner boundary. WSA-SURF-hydro, using the empirical relations, matched the observed ranges and trends much more closely, with the main discrepancy being somewhat elevated densities and temperatures at intermediate speeds, likely because the WSA coronal model produces too many fast streams. The authors suggest that operational systems could be significantly improved simply by adopting similar empirical density and temperature relations, an approach transferable to other solar wind models beyond SURF.

The framework also shines a light on an under-explored source of forecast uncertainty: the assumed properties of coronal mass ejections themselves. Operational systems insert CME perturbations at 0.1 astronomical units that are over-dense, typically four times the ambient density, partly to compensate for the neglected internal magnetic pressure of the cone-model representation. Yet observations at 1 astronomical unit show that interplanetary coronal mass ejections are actually cooler and more tenuous than the surrounding wind, partly from adiabatic expansion in transit and partly because significant expansion and cooling has already occurred close to the Sun. A super-posed epoch analysis of 45 fast magnetic clouds confirmed this picture, with the ejecta body characterised by declining speed and lower density and temperature than the ambient solar wind.

Because SURF-hydro can sample parameter space rapidly, the team ran sensitivity tests varying the initial density and temperature of a model CME launched into a structured ambient wind. Even without magnetic forces, the model reproduced the key observed features of CME evolution at 1 astronomical unit, including a hot, dense sheath ahead of the ejecta, an expanding body cooler and less dense than its surroundings, and durations of roughly 24 hours consistent with observations. The sensitivity results were striking: for one particular structured solar wind, varying the CME’s initial density and temperature at 0.1 astronomical units changed the transit time and arrival speed at Earth by 15 to 20 percent. Hotter, denser CMEs arrived sooner, faster and with stronger shocks. Since these parameters are observationally unconstrained and currently ignored in ensemble forecasting, the authors argue they merit systematic perturbation in future operational ensembles. With the SURF code freely available on GitHub and installable from PyPI and conda-forge, the framework offers researchers and forecasters alike an efficient bridge between idealised models and full three-dimensional simulations, and a practical tool for interrogating the assumptions that quietly shape every space-weather forecast.

Subject of Research: Compressible hydrodynamic modelling of the solar wind and coronal mass ejection propagation for space-weather research and forecasting

Article Title: Space-Weather Utilities for Research and Forecasting (SURF): A Tool for Investigating Hydrodynamic Aspects of Solar Wind and Coronal Mass Ejection Expansion and Evolution

Article References: Owens, M. J., & Barnard, L. A. (2026). Space-Weather Utilities for Research and Forecasting (SURF): A Tool for Investigating Hydrodynamic Aspects of Solar Wind and Coronal Mass Ejection Expansion and Evolution. Solar Physics, 301(9), Article 147. https://doi.org/10.1007/s11207-026-02738-7

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02738-7

Keywords: space weather, solar wind, coronal mass ejections, SURF, HUXt, hydrodynamic modelling, OMNI observations, WSA-Enlil, forecasting, heliospheric physics, boundary conditions, ensemble forecasting