Empirical Forecasting of CMEs from a Free-Energy Proxy:Performance and Extension to HMI

David Falconer, Ron Moore, Abdulnasser F. Barghouty, & Igor Khazanov

2010 October MURI Meeting

Extract Measure Forecast CMEActive Region Active Region Rates

R=f(x)

•Our method forecasts threat level (high or low/All-Clear).•Verifying forecast performance is being done.•Transitioning to SDO/HMI has started.

Relation between Size, Twist, and Free Energy of an Active Region’s Magnetic Field

Free Magnetic Twist Size Energy

+-

+-

Mor

e

L

ess

~(Twist x Size)

WLSG

WLSS

Magnetic Measures

Active-Region Magnetic Measures

Vector measures (SDO/HMI)

Magnetic Size

Φ=∫|Bz| da (|Bz| >100G)

Free Magnetic Energy Proxy

WLSG= ∫(Bz) dl (potential Bh>150G)

Where Bz is the vertical field and Bh is the horizontal field.

In the line-of-sight approximation (SOHO/MDI)

Bz is replaced by the line-of-sight field and

Bh is replaced by the potential transverse field which is calculated from the line-of-sight field

Only Big Twisted Active Regions Produce CMEs

Proxy of Active-Region Magnetic Free Energy

* Produced CMEs in 24 hours* No CMEs in 24 hours

A Productive Active Region has:

• Large amount of free energy

• Large magnetic size

• Large magnetic twist

• Similar tendencies for production of X and M flares.

Database

• 40,000 Magnetograms

• From 1,300 active regions

• 1996-2004

• Known flare/CME/SPE history

Empirical Conversion Functions

R=A(LWLSG)B

P(t)=100%(1-e-Rt)

LWLSG(G) Proxy of Free Energy

• We have determined event rates as a function of our free-energy proxy, for several types of events.

• The sample is divided into 40 equally populated bins using the magnitude of our free-energy proxy.

• For each bin, the average observed 24-hour event rate is determined, with uncertainties.

• The event rates for bins with event rates of >0.01 events/day are fitted with a power law.

• This fit is used for converting our free-energy proxy to expected event rate.

• Event rates can be converted into a event probability.

Forecasting Tool• A beta tool has been delivered to NASA SRAG, for MDI data.• AFRL is looking at the tool.• Paper submitted to Space Weather

When there are no active regions on the disk that is threatening to produce a powerful, earthward directed CME, then solar wind modeling at L1 is easiest.

LWLSG(G) Proxy of Free Energy

Verification of Forecasting Curve using our Database• We obtain forecast curves from the

first three fourths of the active regions to forecast the performance of the remaining fourth of the active regions, and compare the forecast to actual performance.

• We have binned our test sample into 10 bins of expected event rates. For each bin, we plotted the average forecasted and actual event rates.

• The plot shows the actual rates in the five bins having event rates above 0.01 events/day along with the statistical uncertainties.

• The five data-points fall along the unity line, verifying the forecast technique.

Test 1: X&M flare forecast rates versus actual rate

Expected Rate

Act

ual

Rat

e

Truth TablesTest 2: Predictive Skill Scores and comparison to present McIntosh method

“ Free Energy”

Event No Event

Predict Yes 319 302

Predict No 385 11578

“McIntosh” Event No Event

Predict Yes 180 412

Predict No 524 11468

Same division as previous

Event No Event

Predict Yes A B

Predict No C D

X and M flares are used since they are the most frequent kind of event, and best identified with individual active regions.

Skill Scores from Truth Table

Expression “Free Energy” “McIntosh” Best Possible Score

Probability of Detection

A/(A+C) 0.45 0.26 1

False Alarm Rate B/(A+B) 0.49 0.70 0

Percent correct (A+D)/N 0.95 0.93 1

Heidke Skill (A+D-E)/(N-E) 0.45 0.24 1

Quadratic Score 1/N)∑(fi-σi)2 0.14 0.16 0

SS (QR*-QR)/QR* 0.20 0.06 1

E=((A+B)(A+C)+(B+D)*(C+D))/N

Skill scores are various measures of how reliable a forecast is. The first four scores are based on yes/no forecast, with a forecasted event rate of 0.5/day or greater being counted as a yes forecast, while an event rate of less than 0.5 events/day is counted as a no forecast. The quadratic (Brier) score and SS are a comparison between the forecasted rates (fi) and the observed flare rate (σi), while QR* is the quadratic score if the average flare rate is used (Balch, 2008, Spaced Weather Vol 6).

QR*=(1/N)∑(σ-σi)2=0.17

Our skill scores are always significantly better than McIntosh skill scores.

Steps in Transitioning from MDI to HMI

1. HMI to “MDI” conversion of free-energy proxy.

2. Deproject active region to accurately measure further from disk center, than is possible with MDI.

3. Use HMI’s higher resolution, higher cadence and full-vector measurements to improve forecast.

MDI HMI

Magnetograph Type Line-of-sight Vector

Cadence 96 minutes 45/90 second

Latency Day Minutes

Pixel size 2” 0.5”

Using HMI to Forecast CME Rate from MDI Forecast Curve

Knowing that

RCME=F(WLSG-MDI)

and

WLSG-MDI=G(WLSG -HMI)

we can use HMI to predict CME rate.

To determine G, we first calibrate HMI to MDI Gauss units.

Then determine G. Preliminary result is that we can estimate WLSG MDI to within 10% using HMI.

Summary• Free-energy proxies are strong predictors of future flare and

CME activity.• Initial verification has been done. Misty Crown at AFRL is

conducting an independent verification.• Transitioning to HMI from MDI has begun, the preliminary

results indicate negligible increase in uncertainty in forecast event rates.

• Not shown, adding GONG as a backup instrument has begun, forecast uncertainties will be larger, but GONG’s global-network of 6 ground based sites will guarantee backup capability to forecasters.

Forecasting Tool

Work to do