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SH53A-2151: Relationships Between
Photospheric Flows and Solar Flares
by Brian T. Welsch & Yan Li
Space Sciences Laboratory, UC-Berkeley
Fourier Local Correlation Tracking (FLCT) has been applied to the entire database
of 96-minute cadence line-of-sight (LOS) magnetograms from the SOHO/MDI
mission, to derive photospheric transverse velocities (ux ,uy).
In a previous study, we applied FLCT to a few dozen active regions (ARs), and
found that the "proxy Poynting flux” (PPF) --- the product |u|B2, where |u| is the
FLCT flow speed and B is the LOS field divided by the cosine of viewing angle,
integrated over each AR --- was statistically related to flare activity.
We will present preliminary results of our investigation of the relationship
between PPF and flare activity from NOAA's GOES catalog for several hundred
ARs identified in NOAA's daily Solar Region Summaries.
Background: Faraday’s & Ohm’s laws imply that v is
related to field evolution tB in magnetogram sequences.
The ideal induction equation relates v to tB,
tB = -c( x E)=  x (v x B)
assuming the ideal Ohm’s law applies,* relating v to E via
E = -(v x B)/c
Hence: Bz/t = [  x (v x B) ]z = - h (vhBz - vzBh)
*One could instead use E = -(v x B)/c + R, if some known
resistivity R is assumed.
Why do we care about photospheric flows? Flows (or
electric fields) can quantify aspects of evolution in Bcorona.
• The fluxes of magnetic energy & helicity across the
photosphere into the corona depend upon Eph:
dU/dt = ∫ dA (Bph x [vph x Bph])z /4π
dH/dt = 2 ∫ dA (Aph x [vph x Bph])z
U and H probably play central roles in coronal heating,
flares, and CMEs.
• Coupling of Bcorona to Bph also implies that vph can provide
boundary conditions for data-driven, time-dependent
simulations of Bcor (e.g., Cheung & DeRosa 2012).
Method: Fourier local correlation tracking (FLCT) estimates u(
x, y) by correlating evolution in regions to find local shifts.
=
*=
=
Windowing implies spatial averaging of the underlying flow field.
4
How is the apparent movement of magnetic flux, u,
in magnetograms related to the plasma velocity, v?
u is not equivalent to v:
• u is the apparent horizontal velocity (2 components)
• v is the actual plasma velocity (3 comps)
(Note: non-ideal effects can also cause flux transport!)
Démoulin & Berger (2003):
u = vhor - (vn/Bn)Bhor
Schuck (2008):
u = a biased estimate of vhor
Approach
1. Apply FLCT to all “not bad” pairs of full-disk, 96-minute
magnetograms in the MDI database from 1996-2010.
- 1 pix. = 1.4 Mm, sigma = 8 pixels, dt between magnetograms = 96 min.
2. From each daily NOAA Solar Region Summary (SRS), find all
active regions (ARs).
3. Quantitatively characterize magnetic and flow fields in each
AR once per day, at t0 nearest the SRS (00:30 UT).
4. Using NOAA’s GOES flare catalog, quantify subsequent flare
activity in each AR during t0 + t --- here we use t = 24 hr.
1. Investigate relationship(s) --- if any! --- of properties of
magnetic and flow fields to flare activity.
Magnetogram Data Handling
• Pixels > 45o from disk center were not tracked.
• To estimate the radial field, cosine corrections
were used, BR = BLOS/cos(Θ)
• Mercator projections were used to conformally
map irregularly gridded BR(θ,φ) on the sphere to a
regularly gridded BR(x,y) prior to tracking.
• Corrections for scale distortion from projection
were applied to estimated flows.
Here is a sample NOAA Solar Region Summary,
for 2001 Mar. 27:
• Errors (though rare) in the SRS-derived
NAR database in SSWIDL motivated
using the SRS reports directly.
• Files were automatically parsed.
• In the process, several minor
inconsistencies and errors were
identified and manually corrected.
SRS files are online at:
ftp://ftp.ngdc.noaa.gov/STP/swpc_products/daily_reports/solar_region_summaries/
Descriptions of fields are online at:
http://www.swpc.noaa.gov/ftpdir/forecasts/SRS/README
For each SRS, neighborhoods of all ARs within 45o of disk
center were found in the corresponding magnetogram.
• Field outside 45o from disk
center is zeroed.
• Red asterisks show (longitude,
latitude) of each NOAA AR
location.
• Colored lines show 10o zones
around each AR within 45o of
disk center.
• Pixels within 10o of multiple
ARs are assigned to the closest
AR.
• Properties of magnetic and
flow fields within each zone
were computed (see below), to
be associated with flaring.
Our sample consists of 7164 “active-region days,”
associated with 2264 unique NOAA ARs.
• Each AR is typically observed multiple times;
observations 24 hr. apart are treated as “independent.”
• It is plausible that some AR properties relevant to flare
activity vary on time scales > 24 hr. If so, treating
observations as independent would be inappropriate.
To start, we computed 10 quantities from each estimated
radial magnetic field, BR(x,y), and flow field, u(x,y).
1.  = Σ |BR| da2 ; this scales as area A (Fisher et al. 1998)
2. Schrijver's (2007) R, for |BR| > 150 Mx / cm2
–
–
extensive param: should scale as length L
σR = 15 Mm FWHM
3. Schrijver's R, for |BR| > 50 Mx / cm2
–
4.
5.
6.
7.
8.
9.
10.
σR = 4 Mm FWHM
Σ |BR|2
Σ |BR|3
Σ |BR|4
Σ |u|
Σ |u|2
Σ |u|2|BR|
Σ |u||BR|2
Meant to also capture
small-scale, weaker fields.
Nonlinearity weights regions of strong field /
strong flow more or less heavily.
These differences should be mostly irrelevant
for correlation analysis, but nonlinearity might
affect parameters’ discrimination capability.
Given BR(x,y) and estimates of the apparent motion
of flux u(x,y), how can flare activity be predicted?
Extensive Params Matter Most: Welsch et al. (2009) found
extensive parameters were better flare predictors than intensive
- extensives grow with region size, e.g., integrated quantities;
- intensives do not increase with system size, e.g., average properties.
Baseline Params: Barnes & Leka (2008) report that total
unsigned flux Φ and flux near polarity inversion lines R are
among the best known predictors of flare activity.
A Promising Parameter: In their study of 46 ARs, Welsch et al.
(2009) found the“proxy” Poynting flux (“PPF”), Σ u BR2, to be as
or more strongly correlated with flaring than Φ.
Distributions of Φ, R, and PPF in flaring and non-flaring AR
populations are similar. (Best would be separate peaks.)
Barnes et al. 2007: Using Bayes’s
theorem, the probability that a
region belongs to the flaring
population when it is observed to
have properties x is:
So: where the red curve lies
above the dashed line, the
parameter accurately predicts a
greater likelihood of flaring.
This reasoning implies Schrijver’s
R, with a thresh. of 50 Mx/cm2, is
a better predictor.
This result differs from Welsch et al. (2009)!
Welsch et al. (2009) found the distribution of PPF in the flaring population (right
panel, red curve) differed significantly from that of R (red curve at left).
Is this a sample effect? The 46 ARs in the Welsch et al. (2009) sample was not
objective: flare/CME active and flare/CME quiet regions were manually selected.
Discriminant analysis (DA) compares the power of one
or more variables to predict population membership.
In both plots, green is flaring population; means
are circles.
The blue line is the discriminant boundary. At
upper left, values of Φ (T.U.S. flux) & PPF above
it imply flares are more likely than not.
In both plots, the line is more nearly horizontal
than vertical implying the vertical coordinate’s
parameter has more discriminatory power.
This implies PPF has more discriminatory power
than Φ , and R-50 has more than R-150.
Reliability plots indicate under- or over-prediction of
flare activity as a function of forecast probability.
At low forecast probability (“all
clear”), the combo of Φ & PPF
underpredicts – i.e., misses flares.
At high forecast probability (“red
light”), the combo of Φ & PPF
overpredicts – i.e., cries wolf.
These failures are reflected in
limited skill scores.
Outputs of DA -- (1) coefficients of linear fits, and
(2) skill scores -- be used to compare predictive powers.
Param
Solo Skill,
Random
Solo Skill,
Climatology
DA Coeff.
ratio to 

R-50
R-150
PPF
0.37
0.35
0.3
0.40
0.15
0.21
0.15
0.18
-1.88/0.33
0.90/1.15
1.22/0.75
Wheatland 2005: the joint probability
distribution for forecasts (denoted f) and
observations (denoted x) may be
constructed… Averages over all days are
denoted by <…>. For example, <f> is the
average of the forecast probability over all
days.
DA Coeff.
DA Coeff. ra- Best 2-var.
ratio to R-50 tio to R-150 Clim. Skill
-1.7/3.8
0.5/1.73
-1.30/0.80
0.25, R-50
0.26, R-150
“ , R-50
0.24, R-50
the climatological skill score [e.g., Murphy
and Epstein, 1989], [is] defined by
Summary
First, results shown here are preliminary!
Everything --- from the flow fields themselves to
the AR masks to the flare tabulation in each
prediction window --- has not been checked!
Second, our results differ from Welsch et al. (2009)!
They found that PPF slightly outperformed Φ and
R, but we find that R-50 works best in our sample.
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