1 WSA Model and Forecasts Nick Arge Space Vehicles Directorate Air Force Research Laboratory

2 Source Surface PFSS Model Schatten Current Sheet Model 5-30 Rs 2.5 Rs Plot courtesy Sarah McGregor (BU/CISM) Solar Wind Model (e.g., 1D Kinematic model, ENLIL, HAF) (5-30Rs to 1AU) WSA Coronal & Solar Wind Model

3 PFSS+SCS MODEL (R = 5.0 R  ) Predicted Solar Wind Speed at 5.0 R  (New Empirical Relationship ) km s -1 Where: f s = Magnetic field expansion factor. θ b = Minimum angular distance that an open field footpoint lies from nearest coronal hole boundary (i.e., Angular depth inside a coronal hole) WSA Model Coronal Output Coronal Holes Coronal Field (5.0R  )

4 IMF directed radially toward from Sun. IMF directed radially away from Sun. Solar Wind Speed and IMF Polarity in the Ecliptic Driven by Daily Updated Photospheric Field Maps

5 Solar Wind Speed Predictions & Observations IMF Polarity Predictions & Observations Predictions & Observations:Near Solar Maximum

6 Solar Wind Speed Predictions & Observations Predictions & Observations Solar Wind Speed Predictions & Observations

7 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 Observed HSENo HSE Model HSE16636 No HSE64- Contingency Tables Missed False Observed Model Boston University Validation of WSA Event-Based Approach: (High Speed Events) ( Owens et al., JGR 2005)

8 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.) Solar Wind Model Driver: Photospheric Field Synoptic Maps

9 Modeling Results With & Without Polar Field Corrections Applied Polar Fields Not CorrectedPolar Fields Corrected Derived Coronal Holes Solar Wind Speed Predictions (WSA Model) and Observations Poles NOT Corrected Poles Corrected

10 Monopole Moments in Synoptic Maps Split bi-polar Region Corresponding Negative polarity missing

11 Time Evolution of Photospheric & Coronal Features

12 Observed & Predicted IMF Polarity Observed & Predicted Solar Wind Speed Solar Wind Sources Near & Far From Active Regions WSA Model Predictions & Observations: CR / — = Outward/(Inward) Footpoint Field Polarity Coronal Holes Coronal Field (5.0R  ) Photospheric Field & Coronal Hole Boundaries NSO/SOLIS

13 Observed & Predicted IMF Polarity Observed & Predicted Solar Wind Speed Solar Wind Sources Near & Far From Active Regions WSA Model Predictions & Observations: CR / — = Outward/(Inward) Footpoint Field Polarity NSO/SOLIS Coronal Holes Coronal Field (5.0R  ) Photospheric Field & Coronal Hole Boundaries

14 Observed & Predicted IMF Polarity Observed & Predicted Solar Wind Speed + / — = Outward/(Inward) Footpoint Field Polarity NSO/SOLIS Coronal Holes Coronal Field (5.0R  ) Photospheric Field & Coronal Hole Boundaries Solar Wind Sources Near & Far From Active Regions WSA Model Predictions & Observations: CR2029

15 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.Summary

16 WSA Coronal - ENLIL MHD Solar Wind Model Coupling (A Joint AFRL-CISM Effort) Output of WSA MODEL (R = 21.5 R  ) Coronal Field Strength Solar Wind Speed ENLIL 3D MHD Solar Wind Model Output of ENLIL MODEL at 1AU

17 Schatten Current Sheet Model (SCS): 2.5 – 21.5 R  Potential Field Source Surface Model (PFSS): 1.0 – 2.5 R  Coupled Model: PFSS+SCS Schatten, 1971; Wang and Sheeley R  21.5 R  Solar Wind Model (e.g., 1D Kinematic model, ENLIL, HAF)

18 LOS B Field Remapped to Heliographic Coordinates Model Input Magnetic Field Measurements at the Photosphere Magnetic Field Measurements at the Photosphere Courtesy Mount Wilson Solar Observatory LOS Disk Image: Magnetograms LOS B Field Remapped to Heliographic Coordinates & Converted to Radial

19 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%) Boston University Validation of WSA ( Owens et al., JGR 2005) MSE(A) < MSE(B) (Same for correlation coefficients) Hypothetical Example Courtesy Matt Owens (BU/CISM)

20 Validating Coronal Models Using Coronal Holes Solar Minimum Solar Maximum Short After Solar Maximum MAS/SAIC de Toma, Arge, and Riley (2005)

21 Photospheric Field Synoptic Map Types

22 Solar Wind Speed Predictions & Observations IMF Polarity Predictions & Observations Predictions & Observations:Near Solar Minimum

23 A Technique For Filling Missing Polar Regions Boundary Values used to Fill Poles Pole Equator Pole Weighted mean of boundary values used to fill the poles. The weighting is function of inverse distance raised to some power.

24 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!

25 Synoptic Map Types DAILY UPDATED MAP Longitude Latitude +90 º 360º 250º FULL CARRINGTON MAP - 90º Cut from Previous Map 0º 347º DAILY UPDATED MAP New Magnetogram Weighting Functions ~13º Latitude - 90º Longitude +90º 347º360º Latitude 0º Longitude +90º 360º - 90º 347º DAILY UPDATED FRAME MAP Merged Field Data Unmerged Field Data From Latest Magnetogram 347º Zhao Frame Method (a) (b) (c)

26 Solar Wind Speed Predictions & Observations IMF Polarity Predictions & Observations Solar Wind Speed Predictions & Observations IMF Polarity Predictions & Observations ICME Solar Wind Predictions Using Photospheric Field Maps With Different Grid Resolutions 5 Degree 2.5 Degree Arge et al Arge et al. 2004

27 Observed & Predicted IMF Polarity Observed & Predicted Solar Wind Speed NSO/SOLIS WSA Model Predictions & Observations: CR / — = Outward/(Inward) Footpoint Field Polarity Coronal Holes Coronal Field (5.0R  ) Photospheric Field & Coronal Hole Boundaries