Ensemble Modeling of Coronal Mass Ejections - A Superior Means Of Prediction? The Jury Is Still Out

 

CME captured by the Solar Dynamics and Heliospheric Observatory in February, 2013.

CMEs or coronal mass ejections, are intensely energetic eruptions of magnetized plasma from the solar corona. They are not to be treated lightly,  given they are the primary driver of what we call space weather. Powerful CMEs  are of such magnitude that they merit the name "Carrington events" and originate at the solar central meridian (relative to Earth observers) are events we wish to avoid.

The "ultimate" CME then is that which smacks us broadside, knocking down power grids like tenpins, and can disrupt other critical services, (communications, GPS) dependent on spacecraft. Hence, it is of interest to attempt to forecast these plasma monsters.  

One method has been to detect microwave bursts, which tend to fluctuate about 5-15 minutes before CME ejection. The problem is that this affords only limited time for preparation and is still under review. Another theoretical method has sought to double down on the rate of increase of the poloidal magnetic field, i.e. 

 d Φp(t )/dt

associated with the emerging flux rope that presumably spawns the magnetic instability triggering the CME.  For an actual (practical) forecast basis one would require the relevant function to be adjusted for each CME because each would exhibit a different poloidal component and hence magnetic flux,  Φp(t ).   Such a function in terms of the electromotive force might be written:

E(t ) ≡ −(1/c)dΦp(t )/dt 

The technique, for obvious reasons,  is called a "theoretical forecast."  Research already done by James Chen and Valbona Kunkel (The Astrophysical Journal, Vol. 717, p. 1105) show the best fit solutions to the preceding equation match actual CME trajectories to within 1-2 % of the CME height data and temporal profile, i.e. of the predicted derivative for Φp(t ).  

By contrast, the current "state of the art" forecasting of CME arrivals  uses 3‐D magnetohydrodynamic (3‐D MHD) models of the heliosphere.   However, one review of CME forecasting techniques based on 3‐D MHD models concluded (Riley et al. 2018)  that the mean absolute arrival time error is still   20% to 50%  (+ 10 hrs)  of the expected Sun‐Earth transit time and that the accuracy of arrival time forecasts had not measurably improved since 2012. 

 Uncertainty in arrival times is important, make no mistake. At Earth, CMEs are the main driver of space weather, which energizes Earth's space environment and disrupts critical services provided by spacecraft, power grids, and aircraft navigation. Consequently, understanding the propagation of CMEs through the solar wind, and being able to estimate their expected arrival at Earth, are key research questions and objectives for space weather forecasting centers.

Since the launch of the National Aeronautics and Space Administration's (NASA's) STEREO mission in 2007  solar physicists have been able to routinely observe the propagation of CMEs from the solar corona, out through the inner heliosphere to Earth orbit, using the white‐light coronagraph and heliospheric imager (HI) instruments in the Sun‐Earth‐Connection‐Heliospheric‐Investigation instrument package. Before this, CMEs could only be routinely observed close to the Sun (typically within 30 solar radii) in the white‐light Large Angle and Spectrometric Coronagraph (LASCO) on NASA's SOHO mission (Brueckner et al., 1995), and measured with in situ solar wind plasma monitors, typically in near‐Earth space.

Cumulative observations reveal that CMEs undergo many different dynamical processes during their propagation through the corona and heliosphere. Coronagraphs show that CMEs are accelerated and can be deflected and deformed by structures in the solar corona. This is due largely to gradients in magnetic pressure between features like coronal holes, active regions, and the heliospheric current sheet   Furthermore, interactions with the solar wind are important in determining a CME's evolution.

These models  require an inner boundary condition only for determining the state of the solar wind. However, the inner boundary conditions cannot be observed directly, and must be estimated from observations of the Sun's photosphere and extrapolated using models of the Sun's corona.  To be sure,  heliospheric models are currently driven by the output of coronal models that are empirically tuned to match in situ observations near Earth.  CMEs are typically introduced to these 3‐D MHD models as time‐dependent perturbations of the solar wind speed and plasma parameters at the model's inner boundary.  So there is great latitude for introducing uncertainty especially given the models are aimed at improved forecasting.

Not surprisingly, initial condition-based ensembles are being increasingly investigated as a way to better estimate the uncertainty in 3D MHD simulations of CME propagation Such modeling permits a probabilistic interpretation of the forecast, which can be more valuable than a single deterministic forecast.  However, 3D MHD simulations are computationally expensive.  Hence,  it is challenging to accurately sample the relevant parameter space of CME and solar wind properties, particularly for a large number of events or for multiple interacting CMEs.

In recent publications, there is growing interest in using HI observations to weight ensemble members as a means of providing improved estimates of solar wind‐CME interactions and CME arrival times at Earth. It is instructive to briefly summarize recent studies of four CMEs that highlight the potential utility of such an approach, enabled through computationally efficient solar wind modeling.

In this case, four CMEs that were previously analyzed by Barnard et al. (2017) are shown in Table 1 below. For each event, NOAA's SWPC produced a forecast of the CME using the standard (WSA‐ENLIL)  Cone modeling system. Using the available coronagraph data, SWPC calculated estimates of the required cone CME parameters, specifically the CME source longitude and latitude, width, speed, and the time at a height of 21.5r⊙.  Verification of the forecasts using in situ solar wind plasma observations from the ACE spacecraft at the L1 point subsequently established their arrival times. 

Table of CME Properties from Barnard et al,  Ensemble CME Modeling Constrained by Heliospheric Imager Observations  (AGU  Advances)

Barnard et al. (op. cit.) also developed a procedure to produce a statistical consensus estimate of the CME front location for each HI1A and HI1B image, which allows the time‐elongation profile of the CME front to be computed at any position angle spanned by the CME. Examples of these consensus profiles are presented in Figure 1, for CME #1 and CME #4. They also demonstrated that the resulting time‐elongation profiles had better uncertainty estimates and more stable feature tracking than those obtained through the more commonly used J‐map technique (Davies et al., 2009).

                                       Image for CME #1 

                                   Image for CME #4

The authors write:

"For these four events, there is some agreement between the observed and modeled time elongation profiles. We note that the agreement is typically better for the HI1B SSW observations, rather than HI1A, especially for CME‐2, CME‐3, and CME‐4; these SSW profiles are within the ensemble spread and track closely to the deterministic run and other ensemble members.

This is less the case for the HI1A SSW profiles, which are typically closer to the edge of the ensemble distribution and in some cases outside it, particularly for CME‐2 and CME‐4. For CME‐2 the HI1A SSW profile follows an obviously different trajectory from the deterministic HUXt run and is outside of the spread of all ensemble members. "

This is concerning given they note: "the cause of the disagreement in HI1A is not immediately clear. Both the SSW tracking of the CME in HI1A images, and the representation of the CMEs evolution within HUXt could be factors. "

Also:  "Consequently, there is no unique mapping of a CMEs parameters to the observed time elongation profiles, and many profiles are degenerate for different combinations of CME parameters, both modeled and observed."

It is also possible that the best estimates of the CME parameters were far from the truth, or that the ensemble spread was not appropriate for this event.   In any case an arrival time uncertainty of +  10 hours is simply too much to be of genuine practical utility  - though it does improve on some of the existing models used.   

One takeaway from this recent work is that much more CME observation and research needs to be done.  On the plus side, at least solar physicists have finally resolved the question of which comes first, solar flares or CMEs!