zasshikai 2004.07.12 s.ueno mdi measurement errors: the magnetic perspective y. liu & a.a. norton...

MDI Measurement Errors: The Magnetic PerspectiveLow Light Levels
and data difficulties from the magnetic
perspective.
helioseismology studies.
MDI uses the spectral line Ni I 6767.772
z3P0 at 3.6576 eV → a1S at 1.8262 eV
Zeeman splitting by 30.5 m/kG (g=1.426)
Computing of line profiles from (basically)
Unno-Beckers equations
(HSRA)
An index that is obtained from intensities sampled at four positions is calibrated
to velocity using a look-up-table (see section 3.).
Zasshikai 2004.07.12 S.UeNo
is much better (much accurate) than
using linear polarization to measure velocity (Fig.3),
dynamic range of circular polarization
is a little bit smaller than
dynamic range of linear polarization,
when magnetic strength is large (Fig.4).
When |B| < 2000 G,
< 5 % using circular polari.
using circular polarization and HSRA model.
using linear polarization and HSRA model.
Generally, the error of magnetic field measurement < 10 %
but, the error dramatically increases when velocity exceeds a certain value.
using HSRA model.
When a sunspot model (Maltby et al. 1986) is used,
the measurement accuracy using linear polarization
becomes much better.
using
Maltby
model.
satisfied accuracy if |B| < 2000 G.
(Max of solar rotation velocity ~ 2.0 km/s
Max of satellite speed: ~ 0.60 km/s
so, Max of MDI’s background velocity : 2.6 km/s)
Generally,
In umbra,
20-30% (when the sunspot is near solar center).
The scattered light and focus problem will make the error higher.
If |B| > 3000 G,
only in low velocity zone,
the measurement accuracy from linear polari. is questionable.
(Magnetic flux density of MDI) / (Magnetic flux density of ASP)
= 0.64 - 0.71 (nearly constant)
MDI data had the proven problem in some sunspot umbra;
“Drastical decreasing of the magnetic flux” .
For years, the reason of this effect is considered as “saturation”
of +V and -V profiles from the wavelength sampling range
due to large vdoppler and large |B|.

Fig. 8 “Saturation” effect in a northern hemisphere sunspot (Dec1999)
vs.
vs.
at hi-resolution mode.
1999 Dec 24th
1999 Dec 24th
All datapoints which showed the “saturaton” effect had extremely low intensity values|.
Contamination with scattered light?

MDI on-board processing algorithm
A floating point calculation was contained in the on-board algorithm.
When the intensity gets very small and/or the line gets weak,
the LUT value saturates. So, the “alpha” will be too small.
Then, the velocity and magnetic field will also be too small
by several hundred m/s, ~ one thousand G.
→ After the program was modified to do the calculation in
16-bit shorts as well as in doubles, the “saturation” was
decreased.
2) Shallow line depth.
When the line depth decreases as fraction of continuum, the velocity table is wrong and the velocity will too small
generally by some hundreds of m/s.
(due to the difference between quiet region model and sunspot
model.)
MDI’s indeces for LUT.
When S0>0, generally, the range of S1 was expected 100 to 1000 (continuum is about 3000).
But,
when S2 < S1 < 96, the LUT value shows saturates (at 32767).
Fig. 14
Intensity profiles of a sunspot at 4 wavelengths in the Line Profile campaign.
Fig. 15 Calibrated velocity’s dependency of intensity and line depth
by old algorithm.
4. Scattered Light
From the continuum intensity map, PSF including scattered lights
was estimated.
by using this PSF.

Scattered light was not the primary problem in umbral “saturation”.
Estimated PSF including scattered light.
Comparison to MDI instrumental PSF (Rabello-Soares et al. 2001).
X-slice profiles.
5. Filtergram Cadence
MDI time cadence for 1 series: ~ 30 sec
(I1(I+V), I1(I-V), I2(I+V), I2(I-V), I0, I3(I+V), I3(I-V), I4(I+V),
I4(I-V), I0 × 3sec,
or
I0, I1(I+V), I2(I+V), I3(I+V), I4(I+V), I4(I-V), I3(I-V), I2(I-V),
I1(I-V), I0 × 3sec.)
1) making artificial Stokes I & V-profiles with the simulation
( |B|=2000 G ).
2) generating an artificial sinusoidal velocity field (P=300s, A=90m/s,
ignoring the mode-combination of solar oscillations)
3) simulating of MDI measurement with the transmission profile
shifted avery 3 sec.
90° phase lag)
Observation:
Time variation of velocity and magnetic field where averaged B is 1355 G
*A >> 5 G, phase lag is not 90°
&
expected B oscillation due to cadence effect
It does not appear that the MDI’s B oscillation is heavily contaminated by this effect.
Fig. 20
Expected amplitudes of MDI’s B oscillation introduced by measurement cadence vs.
amplitudes of input velocity time variation,
and dependency of magnetic field strength.
Symbols stand for observed amplitudes with MDI on Nov.10 1999.
(A bipolar active region in the hi-resolution mode.)
Conclusions of this section
MDI filtergram cadence imparts an oscillatory component to the magnetic field strength.
Oscillatory component to field strength always has a phase value of (v, dB)=-90°. The maximum introduced RMS amplitude is a function of velocity amplitude and field strength, the realistic errors (amplitudes) are on the order of 5/2000 G or 0.25%
The cadence effect also makes the velocity values have errors (~20%)
The observed magnetic variation is not consistent with expected variation. It does not show the predictable phase and often appears to be independent of the velocity and have large amplitudes when the velocity does not so.
with a FPI spectrometer and MDI”
By A. Settele, T.A. Carroll, I. Nickelt, and A.A. Norton, A&A 386, 1123-1128, 2002
Mean magnetic field strengths were overestimated by the simulation by up to 8 %.
The velocity offset increases → the error increases for large B
→ the error decreases for small B
Shorter periods of oscillation → slightly larger errors
The characteristics of observed magnetic field strengths is rather different from
those predicted by the simulation. The temporal behaviour of MDI magnetic
data is not dominated by this effect.
By using the observed velocities and mean magnetic fields, this error can be
reduced or removed.;
If the original velocity time series is perfectly reproduced by this simulation, one
should subtract the artificial magnetic field time series from the one of the observed
data. / If it is not perfectly reproduced but the power spectra is still correct, one can
subtract the power spectra of the artificial magnetic field oscillation from the
observed one.
10 - 15 μs (RMS)
* Estimate of this offset by using Gaussian fitting method
- Assuming the small value data in magnetogram are purely noise
and have a gaussian distribution.
- The shift of the gaussian center would be the “offset” induced
by shutter noise.
Every center values are similar in 0.1G resolution.
Half-width of this noise function is;
16.1 G for
the maximum B value.
the size of target region.
The offset almost keeps constant.
uncertainty.
Offset of 5min magnetograms are systematically 0.46 G lower
than 1min magnetograms.
Conclusions of this section
The small value magnetic field strength (between -50 to 50 G) in MDI magnetogram are almost noise, and it have a gaussian distribution.
Shutter noise appears as “offset”.
So, it can be corrected.
“Offset” values are
“CORRECTION OF OFFSET IN MDI/SOHO MAGNETOGRAMS”
By Y.Liu, X. Zhao and J.T. Hoeksema Sol.Phys. 219, 39-53, 2004
Moreover,
The yearly median value of the “offset” of 1min magnetograms;
1996, 1997, 1998, 1999, 2000, 2001, 2002
0.251, 0.268, 0.273, 0.285, 0.391, 0.352, 0.364 [G]
They believe the increase is related primarily to increased noise in the shutter noise.
This offset influences various distributions, such as “neutral lines”, “the locus of the computed heliospheric current sheet”, “foot points of calculated coronal holes”. This fact has shown potential to induce significant errors in prediction of the polarity of the interplanetary magnetic field and solar wind properties at the Earth for space weather forecasts.
MDI magnetograms with
Left: 1997.10.04
(Solar minimum)
Right: 2001.01.28
(Solar maximum)
Black lines;
magnetic neutral lines
Fig. 8, 9
Synoptic frames and computed magnetic radial components at 2.5R using MDI magnetograms on Oct. 1997.
With “offset” correction.
Without “offset” correction.
Fig. 10, 11
Synoptic frames and computed magnetic radial components at 2.5R using MDI magnetograms on Jan. 2001.
With “offset” correction.
Without “offset” correction.

zasshikai 2004.07.12 s.ueno mdi measurement errors: the magnetic perspective y. liu & a.a. norton...

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