Data Assimilation Improves Space Weather Forecasting Skill

By: Matthew Lang

Over the past few years, I have been working on using data assimilation methodologies that are prevalent in meteorology to improve forecasts of space weather events (Lang et al. 2017; Lang and Owens 2019). Data assimilation does this by incorporating observations from spacecraft orbiting the Sun into numerical solar wind models, allowing for estimates of the solar wind to be updated. These updated solar wind conditions are then used to drive a solar wind model that produces forecasts of the solar wind at Earth. I have shown that over the lifetime of the STEREO-B spacecraft (2007-2014), data assimilation is able to reduce errors in solar wind forecasts by about 31% compared to forecasts performed without (Lang et al. 2020). Furthermore, these data assimilated forecasts can compensate for systematic errors in forecasts produced from in-situ observations alone.

Space weather is the study of the changing environmental conditions in near-Earth space and its impacts on humans and our technologies, both in space and on Earth. One of the major drivers of space weather events is the solar wind, the constant outflow of plasma (the fourth state of matter that can be thought of as a hot, highly magnetised gas) from the Sun’s surface. The solar wind fills the solar system with particles and magnetic field and is constantly bombarding the Earth’s magnetic field.

Coronal Mass Ejections (CMEs) are huge eruptions of plasma from the Sun’s atmosphere that can travel from the Sun to Earth, through the solar wind, in as little as 18 hours and can drive the most severe space weather events. These include depletion of a part of the ionosphere that is responsible for bouncing radio signals around the planet, hence hampering long-distance communication systems.

Figure 1: Transformer damage from a CME that caused a blackout in Quebec in 1989.

Another major impact on human technologies is that the solar wind and CMEs drive changes to the Earth’s magnetic field, inducing electrical currents in the Earth’s atmosphere that have the potential to overload power systems causing transformer fires and widespread blackouts (this occurred in Quebec in 1989 (see Figure 1) and Sweden in 2003). Most of the impacts of a severe space weather event can be mitigated against if accurate forecasts are available. And that’s where data assimilation comes in.

Data assimilation is the combination of information from forecasts and observations of a system to produce an optimal estimate for the true state of that system. It is an invaluable tool in many aspects of modern life, with applications ranging from course correction during the Apollo Moon landing missions, satellite navigation in areas of poor GPS coverage and oil reservoir modelling. The most notable application for this blog, however, is its use in numerical weather prediction where it is a necessary step for producing more accurate starting points for weather forecasts. This reduces the impact of the “butterfly effect”, where a small change can lead to a vastly different outcomes in the future (the famous hypothetical example being that the titular butterfly flaps it’s wings in Japan leading to a tornado forming in the USA). By ensuring that weather forecasts are started as close to the truth as possible, the resulting forecasts will be more accurate over longer periods.

For consecutive 27-day periods (the time taken for the Sun to rotate once at its equator, relative to the Earth) between 2007 and the end of 2014, an empirical solar wind model called MAS (Magnetospherics Around a Sphere) (Linker et al. 1999) was used to generate a prediction of the solar wind conditions, which I call the prior solar wind. Data assimilation is then performed using data from the STEREO-A, STEREO-B and ACE spacecraft to generate a new set of solar wind conditions which I shall refer to as the posterior solar wind. The STEREO spacecraft orbit the Sun at approximately the same radial distance as Earth, however STEREO-A orbits at a rate of 22⁰ faster and STEREO-B 22⁰ slower. The ACE spacecraft is in near-Earth space, between the Earth and the Sun. The prior and posterior solar winds are then input into the simplified solar wind model, HUXt (Owens et al. 2020), which was developed at the University of Reading to produce forecasts for the subsequent 27-days. Finally, the prior and posterior forecasts were compared with a forecast from the STEREO-B spacecraft (the closest in-situ observation of the solar wind behind the Earth during this time), generated by assuming that the solar wind speed observed at STEREO-B will occur at Earth with a time-lag defined by the distance of the spacecraft behind Earth and the rotational speed of the Sun.

Figure 2: Plot showing the Root Mean Squared Errors (± one standard error) of the prior (blue), posterior(red) and STEREO-B corotation (orange) mean 27-day forecast of the solar wind speed over the lifetime of STEREO-B.

The results of these forecasts are summarised in Figure 2, where the mean 27-day solar wind speed forecast from the prior, posterior and STEREO-B corotation forecast are shown over the lifetime of STEREO-B. The posterior and corotation forecasts have lower Root Mean Squared Errors (RMSEs) than the prior forecasts, showing that both are good improvements over the prior forecast at all lead-times. It is understandable that the STEREO-B corotation and posterior forecast are similar, as
both use the observations from the STEREO-B spacecraft in their forecast.

Figure 3:  Solar wind speed forecasts using the HUXt mode where the Sun is in the centre and Earth is in the same location as the ACE spacecraft (black circle). The left one is initialised from the MAS empirical model without data assimilation and the right one is initialised from a data assimilation analysis, where STEREO (black triangles) and ACE observations have been assimilated. A coronal mass ejection (CME) initialised with the same characteristics and released from the Sun at the same time and propagated through the two ambient solar winds yielding very different evolutions of the CME.

A major difference between the STEREO-B corotation and the posterior forecast, however, is that the corotation produces a forecast at a single point as opposed to the posterior forecast which produces a forecast at every point in the model domain (at all radii and longitudes of interest). This is an especially useful feature as accurate specification of the solar wind can influence how CMEs evolve on their way to Earth. Figure 3 shows two CMEs initialised with the same properties (obtained from (Barnard et al. 2020)); the left one is propagated through a ‘prior’ solar wind that has not had data assimilation performed on it, compared to the ‘posterior’ on the right which does include data assimilation. The CME evolution is changed greatly by the different ambient solar winds, with the CME arriving 19 minutes earlier than it was observed at Earth with a data assimilated solar wind, compared to 41 hours late in a solar wind without data assimilation. By comparison, for the same CME, the operational solar wind model used by the Met Office arrived at Earth 10 hours before it was observed (Barnard et al. 2020). This shows that there is great potential in this field for data assimilation to improve forecasts of not only the solar wind, but also the more hazardous coronal mass ejections.

References

Barnard, L., M. J. Owens, C. J. Scott, and C. A. Koning, 2020: Ensemble CME Modeling Constrained by Heliospheric Imager Observations. AGU Adv., 1, https://doi.org/10.1029/2020av000214

Lang, M., and M. J. Owens, 2019: A Variational Approach to Data Assimilation in the Solar Wind. Sp. Weather, 17, 59–83, https://doi.org/10.1029/2018SW001857.

——, P. Browne, P. J. van Leeuwen, and M. Owens, 2017: Data Assimilation in the Solar Wind: Challenges and First Results. Sp. Weather, 15, 1490–1510, https://doi.org/10.1002/2017SW001681.

——, J. Witherington, H. Turner, M. Owens, and P. Riley, 2020: Improving solar wind forecasting using Data Assimilation. http://arxiv.org/abs/2012.06362.

Linker, J. A., and Coauthors, 1999: Magnetohydrodynamic modeling of the solar corona during Whole Sun Month. J. Geophys. Res. Sp. Phys., 104, 9809–9830, https://doi.org/10.1029/1998JA900159.

Owens, M., and Coauthors, 2020: A Computationally Efficient, Time-Dependent Model of the Solar Wind for Use as a Surrogate to Three-Dimensional Numerical Magnetohydrodynamic Simulations. Sol. Phys., 295, 43, https://doi.org/10.1007/s11207-020-01605-3.

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