Matthew Lang

The solar wind is a continuous outflow of plasma and magnetic flux which fills the heliosphere. Variations in the solar wind can lead to many problematic effects (Hapgood, 2011), such as disruption to power and communications systems and health hazards for astronauts and aircrew on flights over the poles. Therefore, it is vital that we forecast the solar wind accurately, however, forecasting ahead by more than one hour requires accurate prediction of the solar wind conditions near the Sun.
Data assimilation (DA) has been used to improve initial conditions for weather forecasting, leading to a reduction in the `butterfly effect' and hence improvements in forecasting skill. Improvements in numerical weather predictions have gone hand-in-hand improvements in the implementation of data assimilation methods into the models. This can be seen by the increase in skill observed in the late 90’s/early 2000’s when ECMWF updated their DA methodology and started assimilating satellite observations.
DA optimally merges observations with prior information (eg. from a previous forecast) to produce, what we call, the posterior. This posterior is our best estimate of the truth, given the observations we have. It is generated by minimising a cost function (see slide 2) that is, in essence, the sum of all the errors present in the system. These errors are weighted by their uncertainties to ensure that the posterior is drawn towards observations with high certainty and remains nearer the prior information if there is lower certainty.
We have developed a new DA scheme based upon the HUXt solar wind model, a lightweight, temporal solar wind model. The advantage of this DA scheme is that it no longer assumes that the Sun is steady over 27 days and can incorporate fast-moving observation sources (eg. Parker Probe), the disadvantage is that it takes longer to run. A prior initial state (and uncertainty) is generated from an ensemble of solar coronal model runs that estimates the solar wind speed at 30 solar radii (rS), and a 27-day forecast is generated using the HUXt model. The posterior is generated by assimilating observations into the HUXt forecast sequentially in 27 1-day ‘chunks’ (i.e. Day 1’s observations are assimilated to update the prior forecast, Day 1’s analysis is used to forecast Day 2 and Day 2’s observations are assimilated; this repeats until all observations are processed). In the polar plots, we show the DA (the right images) updating the solar wind in the domain between 30-240rS as we move through the 27-day window, when we assimilate STEREO A and B’s observations. We can see that the solar wind speed is updated in the region around the Parker Spiral from STEREO A/B to the Sun and this update is then corotated by the HUXt model towards Earth. This increases the structure in the solar wind between the Sun and Earth, which may yield improved solar wind condition to propagate Coronal Mass Ejections through, morphing them and potentially improving CME arrival times.
Finally, we show the data assimilation results at each satellite location. We can see that the posterior at STEREO A and B are very close to the observations (as expected) and yield and improvement of ~83% RMSE reduction. At ACE, where we have not assimilated data, we can see that the posterior has managed to reconstruct the fast wind band at the end of August and led to an RMSE reduction of 28%. These results show that DA has huge potential and that this system can accurately reconstruct solar wind features at Earth from in-situ observations that are far from the Earth.