# OSPREI: A Coupled Approach to Modeling CME-Driven Space Weather with
Automatically-Generated, User-Friendly Outputs

###### Abstract

Coronal Mass Ejections (CMEs) drive space weather activity at Earth and
throughout the solar system. Current CME-related space weather predictions
rely on information reconstructed from coronagraphs, sometimes from only a
single viewpoint, to drive a simple interplanetary propagation model, which
only gives the arrival time or limited additional information. We present the
coupling of three established models into OSPREI (Open Solar Physics Rapid
Ensemble Information), a new tool that describes Sun-to-Earth CME behavior,
including the location, orientation, size, shape, speed, arrival time, and
internal thermal and magnetic properties, on the timescale needed for
forecasts. First, ForeCAT describes the trajectory that a CME takes through
the solar corona. Second, ANTEATR simulates the propagation, including
expansion and deformation, of a CME in interplanetary space and determines the
evolution of internal properties via conservation laws. Finally, FIDO produces
in situ profiles for a CME’s interaction with a synthetic spacecraft. OSPREI
includes ensemble modeling by varying each input parameter to probe any
uncertainty in their values, yielding probabilities for all outputs.
Standardized visualizations are automatically generated, providing easily-
accessible, essential information for space weather forecasting. We show
OSPREI results for a CME observed in the corona on 2021 April 22 and at Earth
on 2021 April 25. We approach this CME as a forecasting proof-of-concept,
using information analogous to what would be available in real time rather
than fine-tuning input parameters to achieve a best fit for a detailed
scientific study. The OSPREI “prediction” shows good agreement with the
arrival time and in situ properties.

Space Weather

Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt,
MD, USA Dept. of Physics, The Catholic University of America, Washington DC,
USA

Christina<EMAIL_ADDRESS>
OSPREI performs ensemble simulations of the Sun-to-Earth behavior of CMEs on
time scales relevant for future forecasting

A standardized set of automatically-generated visualizations can provide
essential information for forecasters in an intuitive manner

Mimicking a forecasting approach, we apply OSPREI to the 22 April 2021 CME to
illustrate its capabilities

## Plain Language Summary

Coronal mass ejections (CMEs) are large plasma structures that erupt from the
Sun. These eruptions occur frequently but, depending on their exact properties
(such as speed and magnetic field strength and orientation), can have negative
effects on human technologies both in space or on the surface of the Earth. It
is important to know where a CME is going, when it will arrive, and its
properties upon impact. Currently, most CME forecasts are limited to the time
of arrival, and potentially the speed at that time, but have little to no
additional information. We present OSPREI, which couples existing models to
simulate the full Sun-to-Earth evolution of a CME. OSPREI simulates the change
in the path of a CME near the Sun, a range of effects during it’s transit to
Earth, and what it would look like as it passes over a spacecraft. OSPREI runs
very quickly so we can see how results change as the inputs change. To
facilitate forecasts, we have developed a set of standardized figures that
present OSPREI results (including CME location, time of arrival, and internal
properties) in an easily accessible format displaying the most likely values
and the range of possibilities.

##  1 Introduction

Forecasting space weather has gained increased importance in the public eye
with recent emphasis from NASA’s Moon to Mars initiative and the US
government’s National Space Weather Strategy and Action Plan in 2019 and the
Promoting Research and Observations of Space Weather to Improve the
Forecasting of Tomorrow (PROSWIFT) Act in 2020. As CMEs are key drivers of
space weather, both near the Earth and throughout the rest of the solar
system, understanding and forecasting their behavior should be a part of any
space weather predictions. Currently, most predictions focus simply on the
arrival time of a CME. The severity of CME-driven space weather effects
depends on the actual properties of the CME, such as its magnetic field
strength and orientation, but currently these are not routinely included in
the forecasts.

The first step to determining the potential impact of a CME is to determine
where it exists in three-dimensional space. Many eruptions have a visible
source on the solar disk, but some are back-sided or even “stealth” CMEs with
no obvious signatures on disk or in the low corona [<]e.g.¿Rob09,Oka19. As the
CME erupts and begins propagating through the corona it may deflect or rotate,
changing its position or orientation from those initial values
[<]e.g.¿Byr10,Gui11. Typically, a CME’s position is reconstructed by visually
fitting a geometric shape to one or more coronagraph images
[<]e.g.¿Xie04,The06. This yields information about a CME’s position and size,
and potentially its orientation. While relatively easy to routinely apply to
observations, there can be significant uncertainties in the reconstructed
values [<]e.g.¿Mie10. The technique, however, allows for a quick estimate on
whether a CME’s path will cause an impact at the Earth or at another location
of interest.

Once the trajectory and CME speed, which can be calculated from a height-time
profile, are known then the transit time can be determined. At the simplest
level this is distance divided by the speed, but most forecasting models
incorporated some form of drag with the background solar wind. Analytical
models can be as simple as a one-dimensional [<]e.g¿Vrs07DBM, or incorporate
the geometry and size of the CME [<]e.g.¿Zic15. More sophisticated models
embed a CME pulse in a fluid solar wind background, yielding not only the
arrival time but the evolution of the CME itself
[<]e.g.¿Ods99,Ril12,Shi16,Poe17EGU. While more computationally expensive than
the analytic models, these fluid models can be used for forecasts, but real-
time results tend to be restricted to individual runs rather than ensemble
studies (see discussion of real-time ensembles in May15AT), limiting any
information on the probabilities of specific outcomes. Wol18 found a mean
absolute error of 10 hours for the real-time forecasts of 273 CMEs from the
Community Coordinated Modeling Center using the WSA-ENLIL+Cone model. This
value tends to be representative of the error for most current arrival time
models [<]e.g.¿Ril18.

Addressing the severity of the impact requires knowing the CME properties.
Most arrival time models also produce the speed of a CME as it is
intrinsically related to any physics-based calculation of transit time. The
fluid models include predictions of the density of the CME, but typically the
CME is treated as a pressure pulse and does not have an internal magnetic
structure. Very sophisticated, fully-magnetohydrodynamic simulations are
possible [<]e.g¿Tor18, but most cannot be done in real time. Several analytic
models exist that include some evolution of internal CME properties at either
coronal or interplanetary distances [Kumar Rust (1996), Durand-Manterola .
(2017), Mishra Wang (2018)], but these have not yet been incorporated into
forecasts.

Alternatively, the magnetic structure of a CME can be forward modeled by
combining the observed position of a CME with a flux rope model, allowing for
the generation of synthetic in situ profiles [<]e.g.¿Kun10,Sav15. This method
allows for rapid results but does rely on many simplifying assumptions and can
only produce the general trends and not any smaller-scale variation. Despite
the relative simplicity of this method it is not yet routinely used in
forecasts.

Kay1745 and Kay18 begun working toward a unified Sun-to-Earth CME forecasting
model, which led to the Open Solar Physics Rapid Ensemble Information (OSPREI)
model presented in this paper. Kay1745 combined a coronal CME model with an in
situ magnetic field model and showed results for 45 CMEs observed by the
STEREO spacecraft. Kay18 showed how ensembles could be used to explore the
sensitivity to input parameters for both these models and a simple arrival
time model. In Kay18, the three models functioned independently and were not
directly linked. Now, for the first time, we present a fully-coupled suite
using the most recent versions of the individual model components and have
developed a set of visualizations designed to facilitate space weather
forecasting. We apply OSPREI to an observed CME as if it were being forecast,
and describe the resulting “predictions.”

##  2 OSPREI Suite

OSPREI combines three established models into a fully-coupled tool to
facilitate potential forecasts. Each of these models has been thoroughly
described in their individual papers so here we only provide a brief summary
and focus on the flow of information between them. Figure 1 contains a
schematic showing the three components of OSPREI, the connections between
them, and their individual inputs and outputs, as well as a cartoon of an
OSPREI CME.

Figure 1: Schematic showing the three components of OSPREI and the connections
between their inputs and outputs (top). Cartoon showing the CME shape from the
side and through the cross section.

The first model in the OSPREI chain is Forecasting a CME’s Altered Trajectory
[<]ForeCAT,¿Kay15, which simulates the deflection and rotation of a CME
through the corona. ForeCAT relies on a Potential Field Source Surface model
[<]PFSS, e.g.¿Alt69 of the background coronal magnetic field, which we
initialize using a synchronic magnetogram corresponding to the date of the
eruption. Magnetic tension and pressure gradients from the background cause
the CME to deflect in latitude and longitude. Any torque from these forces
cause a rotation in the CME’s tilt. The radial velocity profile and expansion
of the CME are set using empirical models. Therefore, in ForeCAT, the final
coronal speed and size should be treated as inputs rather than outputs like
the latitude, longitude, and tilt.

The second component is ANother Type of Ensemble Arrival Time Results
[<]ANTEATR,¿KayAP1, an interplanetary CME model. ANTEATR includes drag,
analogous to most other arrival time models, but also includes internal
magnetic and thermal forces that determine a CME’s expansion and deformation.
The expansion changes both the full angular width and perpendicular angular
width ($AW$ and $AW_{\perp}$ in Fig. 1, analogous to face-on and edge-on
angular widths). The deformation changes the aspect ratio of the CME’s central
axis (ratio of $L_{r}$ to $L_{\perp}$ in Fig. 1) and the cross section
($r_{r}$ to $r_{\perp}$). Typically, we find that the angular widths remain
constant or slowly decrease and that the CME pancakes, or flattens in the
radial direction relative to the perpendicular direction. ANTEATR uses the
simulated position and orientation from ForeCAT (as well as the input coronal
speed and size) and determines the arrival time, as well as the CME
propagation and expansion speeds, size, and shape upon arrival. It also
provides the internal properties (density, temperature, and magnetic field
strength), which evolve according to conservation laws.

The final component is the ForeCAT In situ Data Observer [<]FIDO,¿Kay17FIDO,
which creates synthetic in situ profiles. FIDO takes the position and
orientation from ForeCAT and the evolved CME properties and arrival time from
ANTEATR. FIDO determines the relative position of the spacecraft to the CME
and calculates the magnetic field vector and velocity for that specific
location. It also estimates the Kp index from the speed and magnetic field as
done in Kay20SIT. Within FIDO, the CME continues to expand as it passes over
the spacecraft according to the speeds provided by ANTEATR. FIDO can also
forecast the shock and sheath ahead of a CME using the Rankine-Hugoniot shock
conditions with the CME and solar wind properties [Kay . (2020)]. This is a
simple analytic shock model for the average sheath and cannot produce the
stochastic fluctuations that are commonly observed.

Within OSPREI these components are fully coupled so that a single call to the
model runs the full Sun-to-Earth simulation. OSPREI can also be set to run an
ensemble where the user specifies the number of individual runs, the input
parameters to randomly vary, and their ranges. Standardized data files are
created, which can then be immediately processed into user-friendly figures
using a separate routine. We also note that combinations of the various
components of OSPREI can be run instead of the full set. For example, one can
specify the coronal position and orientation from a coronal reconstruction and
use those values to drive ANTEATR and FIDO instead of the ForeCAT simulation.
OSPREI has begun the model onboarding process at CCMC so that it will become
available for the community to run via runs on request and instant runs.

##  3 Observed CME

To illustrate its capabilities, we apply OSPREI to the 2021 April 22 CME. This
CME was chosen for no particular reason other than it is a relatively recent
CME that is more dynamic than merely a small blob convecting out with the
background solar wind. To mimic the approach that would be used for a real-
time prediction we use as much information as possible from the Community
Coordinated Modeling Center’s (CCMC’s) Space Weather Database Of
Notifications, Knowledge, Information (DONKI), which catalogs the forecast
information from the Moon to Mars Space Weather Analysis Office.

DONKI lists this CME as erupting from Active Region 12814 at S24W08
(Stonyhurst longitude) and that the eruption is first visible in STEREO A EUVI
195 Å and SDO AIA 171/193 Å starting at 04:21 UT on April 21. The CME then
undergoes a northeastern deflection and is reconstructed at S13E08 in the
corona with a reported speed of 803 km/s and angular width of 30∘.

Figure 2 shows observations of the 2021 April 22 CME. Fig. 2(a) shows a
composite image of SDO AIA channels (171 Å blue, 193 Å green, and 211 Å red)
around 04:47 UT. The red rectangle shows the location of the active region and
the post eruption arcades, which we zoom in on in the highlight panel. Fig
2(b) shows an image from STEREO COR2A at 08:23 UT with the right panel
including our own Graduated Cylindrical Shell reconstruction [<]GCS, ¿The06,
which has a latitude of -10∘, longitude of -1∘ Stonyhurst, and tilt of 20∘.

Figure 2: (a) Composite EUV image of the solar disk highlighting the CME
source region. (b) Coronagraph images of the CME with and without the GCS
reconstruction. (c) In situ observations near the time of CME arrival with the
sheath (dark gray) and flux rope portions (light gray) highlighted.

In DONKI, this CME was predicted to arrive at 17:27 UT on April 24 but was
linked to an in situ shock arrival at 22:24 UT on April 24. Fig. 2(c) shows
OMNI in situ data around this time span with the top panel showing magnetic
field (black is total B, purple, red, and blue are $B_{x}$, $B_{y}$, and
$B_{z}$ in GSE coordinates), the second panel showing the temperature, the
third panel showing the number density, the fourth panel showing the velocity,
and the bottom panel showing the Kp index. The shaded region corresponds to
our CME boundaries with the dark gray in front designated as the sheath and
the light gray the CME (or flux-rope-like component) itself. We set the
internal boundary at 07:00 UT on April 25 and the end boundary at 5:00 UT on
April 26 based on sharp changes in the in situ measurements. These two
boundaries are estimates and one could potentially argue for different values
but these regions are only used for illustrative purposes and not any
quantitative analysis. To mimic a real time forecast we do not use any in situ
information about the CME when setting the initial parameters as it would not
be available. We do use the upstream in situ solar wind information, which is
used for the interplanetary drag and expansion and the sheath calculation, as
our focus is not on forecasting the solar wind itself and OSPREI can be
coupled with any model designed for that.

##  4 OSPREI Inputs

We now address how we determine OSPREI inputs from the information that would
be available for a real-time forecast. Table 1 lists all 34 parameters that
can be varied for an OSPREI simulation. All three components of OSPREI are
fully-determined by these numbers and the PFSS background driven by the
synchronic magnetogram. The table shows the parameter name, the value used for
our test case, and the source for that value. If a parameter is varied within
our ensemble then we also include the range considered. Parameters are grouped
by OSPREI component, background solar wind, or satellite properties.

While at first glance this may appear an unwieldy number of parameters to set
for predictions, we feel it can be managed and that it is the minimum
necessary to describe a CME’s full behavior from the Sun to the Earth. First,
we emphasize that this is a completely explicit list of every free parameter
that could potentially be changed. For our test case we leave 15 parameters at
default values, which would likely be done for actual forecasts. Of the 19
parameters remaining, 4 of them correspond to the location of the Earth or
satellite of interest, 3 define the background solar wind properties, and 6
can be reconstructed or estimated from coronal observations (either reported
in DONKI or our own GCS fit).

This leaves 6 “difficult” parameters, or ones for which default values are not
well-constrained. First is the initial tilt of the CME, which we can visually
estimate from EUV imagery and make sure this estimate aligns with any polarity
inversion lines in the PFSS model. We also have a measure of the tilt in the
corona from our GCS reconstruction and would expect the initial value to be
similar unless extreme rotations are observed. Next, the perpendicular angular
width of the CME can technically be estimated from the $\kappa$ parameter in
the GCS fit but we find that this parameter is rarely accurately adjusted for
scientific reconstructions, let alone real-time predictions, so this is
essentially unconstrained beyond what seems like a “reasonable” guess.
Similarly, the mass of a CME can be reconstructed from white-light images
[<]e.g.¿Plu19 but with large uncertainty [Vourlidas . (2010), de Koning
(2017)] and this is not commonly done for reconstructions. We again pick a
reasonable value, assuming mass tends to scale with CME speed and size.

The initial magnetic field strength of the flux rope and internal CME
temperature are completely unconstrained. These are two critical parameters
for determining the interplanetary behavior and not having a good measure of
them for real-time predictions is a major limitation, as it will be for any
model sophisticated enough to include forecasts of these internal properties.
We hope that continued research will provide a better option in the future,
such as scaling to flare, active region, or dimming properties [Qiu . (2007),
Gopalswamy . (2017), Dissauer . (2019)], but for now we pick reasonable values
assuming that the scaling parameters tend to increase with CME size/speed. The
final uncertain parameter is the handedness of the flux rope. We use the
Bothmer-Schwenn relationship, which links the handedness to the hemisphere
from which the CME erupts. This relationship is generally true over a large
number of CMEs but may not hold for a specific individual CME. Detailed
studies can provide a more accurate guess at this handedness [<]e.g.¿Pal17 but
may not be feasible on forecasting timescales.

Table 1: Full List of OSPREI Free Parameters Parameter | Value | Source
---|---|---
Start time | 2021/04/21 22:00 | GCS timing
Starting nose height | 1.1 $R_{s}$ | Default
ForeCAT CME Properties |  |
Initial latitude | -24$\pm$1∘ | DONKI
Initial longitude | 260$\pm$1∘ | DONKI
Initial tilt | 25$\pm$1∘ | EUV estimate
Max coronal velocity | 800$\pm$50 km/s | DONKI
Max coronal AW | 30$\pm$5∘ | DONKI
Max coronal AW⟂ | 12$\pm$1∘ | Unconstrained
Maximum mass | 3$\pm$0.5$\times$1015 g | Unconstrained
Coronal axis shape $\delta_{Ax}$ | 0.75$\pm$0.1 | Default
Coronal cross section shape $\delta_{CS}$ | 1$\pm$0.1 | Default
ForeCAT empirical models |  |
Initial slow rise velocity | 50 km/s | Default
Start of rapid acceleration | 2.5 $R_{s}$ | GCS timing
Height of max coronal velocity | 10 $R_{s}$ | Default
Expansion model AW0 | 5∘ | Default
Expansion model length scale | 1 $R_{s}$ | Default
Height of max mass | 10 $R_{s}$ | Default
ANTEATR CME Properties |  |
Flux rope magnetic scaling | 3$\pm$0.25 | Unconstrained
Elliptical flux rope model [m,n] | [0,1] | Default
Elliptical flux rope model $\tau$ | 1 | Default/Lundquist-like
Elliptical flux rope model $C$ | 1.927 | Default/Lundquist-like
Flux rope temperature scaling | 2$\pm$0.25 | Unconstrained
Adiabatic index $\gamma$ | 1.33$\pm$0.1 | Default
Interplanetary expansion factor f | 0.5$\pm$0.1 | Default
FIDO CME Properties |  |
Flux rope handedness | Right | Bothmer-Schwenn
Solar Wind Properties |  |
Solar wind 1 AU velocity | 430$\pm$25 km/s | OMNI
Solar wind 1 AU density | 4$\pm$1 cm-3 | OMNI
Solar wind 1 AU magnetic field | 3.5$\pm$1 nT | OMNI
Solar wind 1 AU temperature | 6.2$\times$104 K | Default
Drag coefficient | 1 | Default
Satellite Parameters |  |
Latitude | -5.033∘ | Earth location
Longitude | 258.374∘ | Earth location
Distance | 213 $R_{s}$ | L1
Orbital Speed | 2.8$\times$10-6 rad/s | Earth’s orbit
All longitudes in Carrington coordinates at the start time.

##  5 OSPREI Results

The following subsections show our OSPREI results for the 2021 April 22 CME.
We emphasize that our focus is on presenting OSPREI as a tool used in a real-
time fashion and the outputs available for predictions, not the details of
this specific CME. We have not fine-tuned any parameters to achieve a perfect
fit. It is possible that the results could be improved for a detailed
scientific study of this event, but our “forecast” approach still yields very
encouraging results.

We run an ensemble of 100 members and allow for variations in 15 different
initial parameters. The range of the ensemble variations is meant to represent
the uncertainty in reconstructed values or our best guesses for plausible
values. The full ensemble requires about an hour to run on an average laptop.
Any forecasting center would likely have computers with more sophisticated
processing power, potentially reducing the run time to tens of minutes.

###  5.1 Coronal Predictions

We begin with the coronal predictions. Figure 3 shows the change in latitude
(top panel), longitude (middle), and tilt (bottom) versus distance from
ForeCAT. In the left panels, the black line shows the ensemble seed, the dark
gray shows the core of the ensemble (one standard deviation about the mean),
and the light gray shows the full range. The numbers in the bottom right
display the mean and standard deviation for each value at the end of the
ForeCAT simulation. The histograms in the right panels show the distribution
of the ensemble values at the end of this component.

Figure 3: ForeCAT results showing the latitude (top), longitude (middle), and
orientation (bottom) versus distance. Each panel includes the ensemble seed
profile (black), the full range of the ensemble (light gray), and one standard
deviation about the mean (dark gray). The histograms on the right show the
distribution of the final values for each parameter.

Fig. 3 shows the expected northeastern deflection for the majority of ensemble
members. The CME longitude is shown with respect to the Earth location at the
time of the GCS measurement, which is almost 4∘ lower in Carrington longitude
than the start time due to the rotation of the Carrington coordinate system
with the solar surface. The majority of CMEs show a slight clockwise rotation,
though the full range exhibits more significant rotations in both directions.
We typically interpret this spread in rotations as consistent with a
background magnetic field causing little to no rotations and that they instead
result from slight imbalances in our chosen initial position. The ForeCAT
results yield a position and orientation consistent with the DONKI and GCS
reconstructions but additionally provide a range of probabilities based on a
physics-driven simulation.

###  5.2 Interplanetary Predictions

The next set of figures show results for the ANTEATR interplanetary
predictions. Figure 4 shows the evolution of parameters at interplanetary
distances, the shading is a similar format to Fig. 3 but all panels include a
second parameter in blue. ANTEATR does generate additional results not shown
here, such as the speed of the central axis in both the radial and
perpendicular directions, but we limit this figure to the values most relevant
to provide a clear picture for forecasting. The mean value and standard
deviation at the end of the simulation are displayed for each parameter.

Figure 4: Interplanetary evolution of the CME in the same format as Fig. 3.
The top left shows the angular width (black) and perpendicular angular width
(blue). The top right shows the axial (black) and cross section (blue) aspect
ratios. The bottom left shows the front velocity (black) and the expansion
velocity (blue). The bottom right shows the magnetic field strength (black)
and temperature (blue).

The top left shows the evolution of the angular widths, $AW$ and $AW_{\perp}$.
Both widths show a small increase in the first 20 $R_{s}$ due to the magnetic
and thermal forces. Beyond 50 $R_{s}$, the ensemble seed shows a slight
decrease in both parameters. The full ensemble ranges between slight increases
and slight decreases depending on the exact initial parameters but in general
is consistent with nearly constant angular widths. The top right shows the
change in the axis and cross section aspect ratios, $\delta_{Ax}$ and
$\delta_{CS}$. Both decrease, which corresponds to a pancaking effect where
the radial direction becomes relatively shortened due to the combined effects
of drag and axial magnetic forces. Both ratios show a sharp decrease early on
but a continued decrease at farther distances, though a few outliers show a
secondary increase in $\delta_{Ax}$.

The bottom left panel shows the speed of the CME front, $v_{F}$, and the
expansion speed, $v_{Exp}$. Technically, we show the rate at which the radial
cross section length, $r_{r}$ in Fig. 1, increases, but this is analogous to
the in situ expansion speed that would be observed for a direct hit at the CME
nose. $v_{Exp}$ shows an initial increase due to an overpressure relative to
the background, which causes the increase in $AW_{\perp}$, but then decreases
as the external pressure becomes larger than that inside. $v_{F}$ shows an
initial increase, which is driven by the expansion of the cross section
pushing the nose forward, but quickly begins decreasing as both the drag and
axial magnetic forces act to slow down the forward motion.

The bottom right shows the internal magnetic field strength (taken at the
central axis) and the logarithm of the temperature. Both parameters decrease
as the CME expands, as expected, but this gives a most probable value and the
range for these internal properties upon impact, which is uncommon for a
simple analytic prediction.

Instead of looking at full profiles, forecasters may prefer to simply see the
range of possibilities at the time of impact. Figure 3(a) shows histograms of
different values from ANTEATR. ANTEATR does not simulate the full path of the
satellite through the CME, that is only performed in FIDO, so properties such
as the duration are estimated from the geometry. The histograms include
$v_{F}$ and $v_{Exp}$ as in Fig. 4 and are global properties of the CME rather
than what one may observe in situ for that specific impact location. As such,
if available, outputs from FIDO (shown in Fig. 5(b)) should be prioritized
over analogous ANTEATR outputs.

Figure 5: Histograms of the outputs from ANTEATR (a) and FIDO (b). Where
possible, comparable values between ANTEATR and FIDO are presented in
analogous panels (i.e. the front velocity in both center panels).

The top left panel shows the transit time. ANTEATR only simulates the flux
rope, the sheath is not included until FIDO, so this corresponds to the
arrival of the front of the flux rope. The text displays the mean arrival time
of 02:18 on April 25, which is within 5 hours of the boundary we estimated
from observations. The top middle panel shows an average duration of 29 hours,
which is a bit longer than the observed duration. The top right panel shows an
average density of 5.7$\pm$1.1cm-3 and the middle left shows a temperature of
$\log(T)=$4.4$\pm$0.1K. We find average propagation and expansion speeds of
500 km/s and 40 km/s (middle row, center and right panels), but again, these
correspond to the general CME properties, not what may be measured in situ at
a specific point of impact. The bottom row shows $B_{F}$ (left), the magnetic
field at the front of the CME, which is equivalent to the poloidal field at
the edge of the cross section, and $B_{C}$ (middle), taken at the center of
the flux rope and equivalent to the toroidal field at the axis. ANTEATR does
not require the handedness of the internal magnetic field so these magnetic
field values are unsigned. Finally, we estimate $Kp$ at the front of the CME
using $v_{F}$ and $B_{F}$.

###  5.3 In Situ Predictions

The next figures correspond to FIDO results for the synthetic in situ magnetic
and velocity profiles. Fig. 5(b) shows histograms of various parameters,
analogous to the ANTEATR results in Fig. 5(a) but for a more accurate
simulation of the CME-satellite interaction and including the CME-driven
sheath. Where possible, we include analogous properties in the same location
in both figures, but not all panels are directly comparable.

Figure 6: (a) Individual in situ profiles for each ensemble member (gray) with
the ensemble seed (blue) and OMNI observations (red). (b) Contours of the
probability of specific in situ values over time derived from the density of
the individual profiles.

The top row shows the transit time, sheath duration, and CME duration (left to
right). The mean CME duration is the same as seen an ANTEATR, suggesting our
geometric estimate is fairly accurate, but we do see a slightly larger range
from the ensemble members that interact at more oblique angles. The sheath has
an average duration of 5 hours and the predicted arrival time is 5 hours
earlier than the sheath-free ANTEATR time. The predicted start at 21:25 UT on
April 24 is only an hour different than our measured start at 22:24 UT.

The middle row shows the speed in the sheath, at the front of the flux rope,
and the expansion speed. The expansion speed is calculated as is done for
observations as one half of the difference between the speed at front and end
of the flux rope portion. These histograms show a higher front speed (590
km/s) but lower expansion speed (33 km/s) for the in situ values at the actual
impact location as compared to the ANTEATR values given for the nose.

The bottom row shows the maximum magnetic field (11$\pm$1nT) and the most
negative $B_{z}$ (-6$\pm$2 nT) within each ensemble profile (left and center
panels). The bottom right panel shows the maximum Kp, which is largest value
calculated over the full profile from the velocity and magnetic field. We find
a mean maximum Kp of 5.4 with a standard deviation of 0.4, which we find
occurs in the sheath and is slightly higher than that estimated from ANTEATR
alone.

Figure 6 shows the full in situ profiles in two different formats, which
provide more details than the histograms, but may not be as easy to quickly
interpret. Both panels show the total magnetic field strength ($B$), three
components in GSE coordinates ($B_{x}$, $B_{y}$, $B_{z}$), the estimated Kp,
and the in situ velocity profiles, from top to bottom. Both panels show the
observed in situ profiles in red and the seed profile in blue. Panel (a) shows
the individual profiles for each ensemble member (gray line) whereas panel (b)
shows the percentage chance for different values of each parameter. The values
are weighted by the total number of CMEs that impact the spacecraft so that in
many time cells the total percentage of any value is less than 100 as not all
CMEs were present at that time.

We see that the majority of the profiles are in general agreement with the
observations. The gray lines tend to fall around the red observations,
similarly for the brightest contour regions. All ensemble members miss the
second increase in Kp around 00:00 UT on April 26, which results from a
fluctuation in $B_{z}$ not captured by the simple, analytic flux rope model.
It may be possible to improve the fit with a different flux rope model but no
ensemble members reproduce this bump, though some have profiles that remain
negative rather smoothly rotating to positive values. The majority of ensemble
members have a in situ velocity 50-100 km/s higher than the observations. This
may be improved by changing the interplanetary expansion factor, $f$, from its
default value. This determines whether the CME is initially expanding self-
similarly or convecting with the solar wind before the ANTEATR forces take
over. Again, our focus is presenting the OSPREI tool and the outputs that can
be generated for forecasts so we leave values at reasonable defaults that
would be used in real-time predictions rather than fine-tuning them for a best
fit.

These figures show the variety in the ensemble in more detail than the
histograms since they show the full profiles instead of reducing time-
variations to single values. For example, instead of just having a number for
the minimum $B_{z}$, the profiles show that for most cases this value occurs
several hours into the passage at the sheath/flux-rope boundary and it is a
quick dip into negative $B_{z}$, rather than an extended duration due to the
rotation in the flux rope magnetic field. The range in arrival times and
durations becomes more obvious. In Fig. 6(a) many of the individual starts and
ends of the simulations are visible. In Fig. 6(b) these variation cause there
to be a quite long time range where there is a small probability of CME
impact. A time range nearly twice as long as the duration of the ensemble seed
profile contains nonzero probabilities, though the strong probabilities cover
a much smaller range. Fig. 6(a) also shows a few outlier cases that behave
differently from the majority of the population. These have very low $B$ and
shorter sheath and flux rope durations. We also see a few very long duration
cases with weak magnetic field strength. We will briefly discuss these cases
in Section 6.2.

##  6 Further Analysis

###  6.1 Spatial Variations

FIDO yields the full in situ profile for a specific trajectory through the
CMEs, but it may be of use to see how things would change if the location of
the CME were spatially shifted. We use the CME geometries and internal
properties at the time of impact (from ANTEATR) to produce contour maps of
various properties, shown in Figure 7. We project the location of each
ensemble member onto a flattened map of latitude and longitude relative to the
Earth’s (or satellite’s) location (marked with a pale blue dot).

Figure 7: Spatial contours of different values using the location and internal
properties of the individual ensemble members. The pale blue dot indicates the
location of the Earth at the time of impact.

The top left panel shows the percentage chance of impact. This is simply the
sum of CMEs that impact that location divided by the total number of CMEs that
reach the satellite distance. The denominator is not necessarily the same as
the number in the ensemble, it is possible that the random variations lead to
input parameters than make the internal magnetic forces unstable (e.g.
combination of low mass with high magnetic field scaling and large $AW$). We
do not include these “failed” unstable CMEs in the percentage calculation but
we do include the misses that propagate the full distance and do not make
contact. For the example CME we find that the impact occurs toward the flank
of the CME and we are nearly at the boundary between the core where all CMEs
overlap and the region only reached by a few CMEs.

The bottom left panel shows the CME duration using the geometric estimate for
the flux rope duration from ANTEATR, rather than a full in situ simulation
value including the sheath, as from FIDO. Each location shows the average of
all CMEs that impact there. Most of the panel shows the duration decreasing as
one moves in latitude towards the edges of the cross section. The variations
become more unstructured toward the regions with a low chance of impact (such
as at low latitudes) since the average is then determined from a low number of
ensemble regions that impact that location.

The middle three panels on both rows show properties at the front and center
of the CME (top and bottom respectively). From left to right we show $B_{z}$,
the radial velocity $v_{r}$, and the estimated Kp. Both the RTN and GSE
coordinate systems depend on the latitude and longitude of the observer. The
values we show correspond to rotating these systems to each specific location
within the figure, rather than using fixed systems at the position indicated
by the pale blue dot. We note that we do include an estimate of the decrease
in $B$ due to CME expansion and flux conservation during the time between the
satellite interacting with the front and center of the CME. This CME is right-
handed with an axial field pointing toward positive longitude so we see a
stronger negative $B_{z}$ at the front than in the center. At the front, as
one moves in latitude away from the nose $B_{z}$ decreases due to the change
in the local poloidal direction rather than an actual decrease in the
magnitude of the poloidal field. The toroidal field predominantly points in an
east-west direction and the little bit of tilt only produces a small positive
$B_{z}$ near the central axis of the CME, as seen in the bottom panel.

The velocity contours combine the effects of different parts of the axis and
cross section expanding at different rates with the local orientation of the
radial vector. With a pancaked CME the edges tend to be moving faster but at a
more oblique angle to the radial. For the test case, this yields a faster
radial velocity near the edges than at the nose. We also consistently find a
larger speed at the front than at the center as this case is still expanding
at the time of impact.

The Kp contours combine the trends of the $B_{z}$ and $v_{r}$ panels. At the
front we see that the Kp would decrease if the impact moved in longitude
toward the nose, which has lower $v_{r}$, and decrease with northern movement
in latitude toward regions of more positive $B_{z}$. Near the axis of the CME,
the pattern is more complicated due to the individual components being more
complicated in the center, but in general the Kp remains below 2.

The right panels show the number density (top) and logarithm of the
temperature (bottom). Both of these parameters are treated as uniform within a
individual simulation so the spatial variations only result from the the
actual spatial distribution of the ensemble CMEs, not any internal structure.
We do not see as much variation in these parameters, with the exception of
some particularly hot CMEs in the low percentage chance of impact region.

###  6.2 Analyzing Trends

While the previous figures have shown the range of possibilities suggested by
the ensemble modeling, they have not provide much, if any, reason for those
variations. Figure 8 provides that information for when a forecaster wishes to
dive deeper. The horizontal axis shows each of the inputs varied within the
ensemble and the vertical axis shows significant outputs that can be
quantified by a single number, such as those shown in the histograms. Each
panel shows a scatter plot between an input and an output and are colored
according to their correlation coefficient to help illuminate any trends. Some
trends are expected, such as those between parameters that are both inputs and
outputs (e.g. large initial $AW$ correlated with large final $AW$). Others are
less direct but still expected (e.g. higher $B_{SW}$ leading to higher CME max
$B$ when the $B$ scaling is constant). In some cases we find that expected
trends may be washed out by the model physics (e.g. final T is only slightly
correlated with initial temperature scaling). Other times, unexpected trends
may occur (e.g. minimum $B_{z}$ with initial latitude or number density with
$B_{SW}$).

This figure also helps investigate outliers, such as seen in the in situ
figures. We see that for many of the final properties the ensemble members can
be separated into two distinct populations, the main group and a smaller group
of outliers. This is most visible in the two aspect ratios, $\delta_{Ax}$ and
$\delta_{CS}$, both velocities, $v_{F}$ and $v_{Exp}$, and $AW_{\perp}$. The
outlier cases all have a less pancaked shape, higher final propagation and
expansion velocities, and smaller perpendicular angular width. While we see a
clear separation in the final properties, the trends with initial properties,
or which specific inputs cause this behavior, are less obvious. These cases
tend to have smaller initial $AW$ and larger $\delta_{Ax}$, but are not that
dissimilar from the rest of the ensemble. Our interpretation is that the
smaller $AW$ creates a higher CME density and higher $\delta_{Ax}$ reduces the
internal magnetic forces, both of which weaken the pancaking and drag forces.
While this level of interpretation may not be necessary for routine
forecasting, it is essential to recognize while the majority of the ensemble
falls within the main group, making that the most probable forecast, there is
a small possibility of the observed behavior mirroring that of this subset
instead of the mean values.

Figure 8: Scatter plots showing the relation between variations in input
parameters (horizontal axes) and outputs (vertical axes). The data in each
panel is colored according to the correlation between that input-output pair.

##  7 Conclusion

We have presented the new CME forecasting suite OSPREI, which represents the
combination of previously established models and includes standardized, user-
friendly visualizations. To demonstrate OSPREI’s capabilities we have applied
it to the CME observed in the corona on 2021 April 22. We mimic a forecasting
approach, using the best information that would be available in a real-time
scenario, rather than fine-tuning inputs to optimize the output for a detailed
scientific study. OSPREI simulates the coronal deflection and rotation, the
interplanetary expansion, deformation, and arrival time, and the expected in
situ profiles, including an estimate of the Kp. From an ensemble of 100 runs
we have not only the most probability value for each output but a range of
possibilities and their likelihoods. Our visualizations provide this essential
information in an easily-accessible format. We also include more complex
visualization providing further details on expected spatial variations in the
CME properties and digging into the ensemble details by linking the inputs and
outputs and illuminating any trends that may be affecting different
populations within the ensemble.

###### Acknowledgements.

CK is supported by the National Aeronautics and Space Administration under
Grant 80NSSC19K0274 issued through the Heliophysics Guest Investigators
Program and by the National Aeronautics and Space Administration under Grant
80NSSC19K0909 issued through the Heliophysics Early Career Investigators
Program. The full OSPREI code is archived through Zenodo at
https://zenodo.org/badge/latestdoi/236822923 with DOI 10.5281/zenodo.5507441
and is available at GitHub at https://github.com/ckay314/OSPREI. The DONKI
entry for the 2021 April 22 CME is available at
https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CME/16772/1 and the shock arrival
at https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/IPS/16784/1. SDO composite
imagery is available from https://sdo.gsfc.nasa.gov/data/aiahmi/. The STEREO
coronagraph data is available at
https://secchi.nrl.navy.mil/secchi_flight/images. OMNI data are available at
https://omniweb.gsfc.nasa.gov/.

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