WSA Model and Forecasts
Nick Arge
Space Vehicles Directorate
Air Force Research Laboratory
1
WSA Coronal & Solar Wind Model
Schatten Current
Sheet Model
PFSS
Model
5-30 Rs
2.5 Rs
Solar Wind
Model
(e.g., 1D
Kinematic
model, ENLIL,
HAF)
(5-30Rs to 1AU)
Source Surface
Plot courtesy Sarah McGregor (BU/CISM)
2
WSA Model Coronal Output
Predicted Solar Wind Speed at 5.0 R
(New Empirical Relationship )
Coronal Field (5.0R)
Coronal Holes
PFSS+SCS MODEL (R = 5.0 R)
3.5
V  f s , θ b   265 
1.5
1  f s 1/ 3
3
 θ
  

 1 b
 

7
.
5

 
-1
 
5.8  1.6e
 km s




Where:
fs = Magnetic field expansion factor.
θb = Minimum angular distance that an open field
footpoint lies from nearest coronal hole boundary
(i.e., Angular depth inside a coronal hole)
3
Solar Wind Speed and IMF Polarity in the Ecliptic
Driven by Daily Updated Photospheric Field Maps
IMF directed radially
away from Sun.
IMF directed radially
toward from Sun.
4
Predictions & Observations:Near Solar Maximum
Solar Wind Speed Predictions & Observations
IMF Polarity Predictions & Observations
5
Predictions & Observations
Solar Wind Speed Predictions & Observations
Solar Wind Speed Predictions & Observations
6
Boston University Validation of WSA Event-Based
Approach: (High Speed Events)
Contingency Tables
Observed
Model
Observed
Missed
Model
False
HSE
No HSE
HSE
166
36
No HSE
64
-
( Owens et al., JGR 2005)


Validated 8 years of WSA predictions
Event-based approach: high speed enhancements (HSE):
 Captures more than 72% of the observed HSE events
 Most of the false HSEs are small
 Missed HSEs: are small events or transients
 Timing of HSEs shows no offset. Slight underestimation of
magnitude of fastest events – probably due to transients
7
Solar Wind Model Driver:
Photospheric Field Synoptic Maps
Corrections that often need to be applied to photospheric field maps
(depending on the observatory):
• Line-of-sight fields need to be converted to radial orientation (including
effects due to the Solar b angle).
• Observational evidence suggests this is generally true except in
strong active regions!
• Monopole moment needs to be removed.
• Polar fields need to be corrected and filled (when necessary).
• Can use historical data for retrospective studies.
• Field corrected (when necessary) for magnetic field saturation effects.
• Flux transport processes (differential rotation, meridional flow, diffusion,
etc.)
8
Modeling Results With & Without Polar Field
Corrections Applied
Polar Fields Corrected
Derived Coronal Holes
Derived Coronal Holes
Polar Fields Not Corrected
Solar Wind Speed Predictions (WSA Model) and Observations
Poles NOT Corrected
Poles Corrected
9
Monopole Moments in Synoptic Maps
Split bi-polar
Region
Corresponding
Negative
polarity
missing
10
Time Evolution of Photospheric &
Coronal Features
11
Solar Wind Sources Near & Far From Active Regions
WSA Model Predictions & Observations: CR2027
Coronal Field (5.0R)
NSO/SOLIS
Observed & Predicted IMF Polarity
Coronal Holes
Observed & Predicted Solar Wind Speed
+ / — = Outward/(Inward) Footpoint Field Polarity
12
Solar Wind Sources Near & Far From Active Regions
WSA Model Predictions & Observations: CR2028
Coronal Field (5.0R)
NSO/SOLIS
Observed & Predicted IMF Polarity
Coronal Holes
Observed & Predicted Solar Wind Speed
+ / — = Outward/(Inward) Footpoint Field Polarity
13
Solar Wind Sources Near & Far From Active Regions
WSA Model Predictions & Observations: CR2029
Coronal Field (5.0R)
NSO/SOLIS
Observed & Predicted IMF Polarity
Coronal Holes
Observed & Predicted Solar Wind Speed
+ / — = Outward/(Inward) Footpoint Field Polarity
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Summary
1) The WSA model predicts ambient solar wind speed and IMF polarity 1-7 days in advance at L1.
Model validated using 8 years (~1 solar cycle) of predictions & the results are VERY encouraging.
2) Careful handing of the input photospheric magnetic field data is essential for improving the predictive
success of the model. In particular,
• Monopole moments.
• Polar fields.
• Radial field Assumption.
• Flux transport processes.
3) The ability of the WSA model to successfully predict solar wind speed appears to be a function of the
proximity of its source regions to strong active regions. That is
If the source region is close to (far from) a strong active region, then the model’s speed
predictions are generally poor (good).
Possible reasons why the model performs less well when the solar wind source lies near an active region.
- Fields near active regions are not potential, as the WSA model assumes.
(MHD and/or Force Free coronal model could help here).
- The model assumes that the photospheric field is radial everywhere.
Observational evidence suggests this is generally true except in strong active regions!
(Direct measurement of radial fields needed in active regions).
- A different empirical solar wind speed relationship is required near active regions.
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WSA Coronal - ENLIL MHD Solar Wind
Model Coupling (A Joint AFRL-CISM Effort)
Output of WSA MODEL
ENLIL 3D MHD Solar Wind Model
(R = 21.5 R)
Coronal Field Strength
Solar Wind Speed
Output of ENLIL MODEL at 1AU
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Coupled Model: PFSS+SCS
Schatten Current Sheet Model (SCS): 2.5 – 21.5 R
Potential Field
Source Surface
Model (PFSS):
1.0 – 2.5 R
21.5 R
2.5 R
Solar
Wind
Model
(e.g., 1D
Kinematic
model, ENLIL,
HAF)
Schatten, 1971; Wang and Sheeley 1995
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Model Input
Magnetic Field Measurements at the Photosphere
LOS Disk Image: Magnetograms
LOS B Field Remapped to
Heliographic Coordinates
LOS B Field Remapped to
Heliographic Coordinates
& Converted to Radial
Courtesy Mount Wilson Solar Observatory
18
Boston University Validation of WSA
( Owens et al., JGR 2005)
•
•
Validated 8 years of WSA predictions
Mean Squared Error (MSE)
• 3 day old magnetograms give optimal prediction
• No systematic time lag
• Skill scores low on average (<10%)
Hypothetical Example
MSE(A) < MSE(B)
(Same for correlation coefficients)
Courtesy Matt Owens (BU/CISM)
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Validating Coronal Models Using Coronal Holes
Solar Minimum
Solar Maximum
Short After Solar Maximum
de Toma, Arge, and Riley (2005)
MAS/SAIC
20
Photospheric Field Synoptic Map Types
21
Predictions & Observations:Near Solar Minimum
Solar Wind Speed Predictions & Observations
IMF Polarity Predictions & Observations
22
A Technique For Filling Missing Polar Regions
Weighted mean
of boundary
values used to fill
the poles. The
weighting is
function of
inverse distance
raised to some
power.
Boundary
Values used
to Fill Poles
•Pole
• Pole
Equator
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Daily-Updated Synoptic Map With Poles Filled
Pole filled using a
“noisy” boundary.*
Pole filled using a
“trimmed” boundary.*
*Note,
the synoptic maps
shown here are NOT from
CR1921 or 1922 but
illustrate well why filling
the poles needs to be done
very carefully!
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Synoptic Map Types
Weighting
Functions
New
Magnetogram
~13º
+90º
(a)
Latitude
-90º
347º
0º
347º 360º
Longitude
DAILY UPDATED MAP
Merged Field
Data
Unmerged Field Data
From Latest
Magnetogram
+90º
(b)
Zhao
Frame
Method
Latitude
-90º
347º 0º
347º 360º
Longitude
DAILY UPDATED FRAME MAP
FULL CARRINGTON MAP
+90º
(c)
250º
0º
Longitude
DAILY UPDATED MAP
Latitude
250º
360º
Cut from
Previous
Map
-90º
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Solar Wind Predictions Using Photospheric Field Maps
With Different Grid Resolutions
5 Degree
2.5 Degree
Solar Wind Speed Predictions & Observations
ICME
IMF Polarity Predictions & Observations
Solar Wind Speed Predictions & Observations
ICME
IMF Polarity Predictions & Observations
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Arge et al. 2004
Arge et al. 2005
WSA Model Predictions & Observations: CR2018
Coronal Field (5.0R)
NSO/SOLIS
Observed & Predicted IMF Polarity
Coronal Holes
Observed & Predicted Solar Wind Speed
+ / — = Outward/(Inward) Footpoint Field Polarity
27