Time-dependent tomography of hemispheric features using
interplanetary scintillation (IPS) remote-sensing observations
B.V. Jackson, P.P. Hick and A. Buffington
Center for Astrophysics and Space Sciences, University of California at San Diego, LaJolla, CA, U.S.A.
M. Kojima, M. Tokumaru, K. Fujiki, T. Ohmi and M. Yamashita
Solar-Terrestrial Environment Laboratory, Nagoya University, Japan
Abstract. We have developed a Computer Assisted Tomography (CAT) program that modifies a timedependent three-dimensional kinematic heliospheric model to fit interplanetary scintillation (IPS)
observations. The tomography program iteratively changes this global model to least-squares fit IPS data.
The short time intervals of the kinematic modeling (~1 day) force the heliospheric reconstructions to
depend on outward solar wind motion to give perspective views of each point in space accessible to the
observations, allowing reconstruction of interplanetary Coronal Mass Ejections (CMEs) as well as
corotating structures. We show these models as velocity or density Carrington maps and remote views.
We have studied several events, including the July 14, 2000 Bastille-day halo CME. We check our results
by comparison with additional remote-sensing observations, and observations from near-Earth spacecraft.
INTRODUCTION
and solar distance by means of a power law. These
previous IPS tomographic programs all assumed that the
kinematic heliospheric model remains unchanged over
the duration of the observations. Thus the observed
heliospheric structures do not change other than by
outward radial expansion within this time period.
The new tomographic modeling technique described
here relaxes the assumption that heliospheric structure
remains constant over time. In this newest extension a
global kinematic model is formed at regular time
intervals, and the iterative process provides the threedimensional heliospheric parameters that fit observed
data. The next section describes the tomographic
program that has been developed. The third section
compares and calibrates the kinematic models based on
the IPS data to Earth-based in situ measurements. The
fourth section displays and discusses the kinematic
model values as a remote observer would view them. We
conclude in the last section.
In solar physics, there have been numerous attempts
to reconstruct coronal structure and the heliosphere in
three dimensions. These techniques have been developed
for coronal mass ejections (CMEs) to understand better
the physical principles of their initiation. Using slightly
differing techniques others (1, 2, 3) have analyzed views
from the Earth using Thomson-scattering data to obtain
three-dimensional results.
Since the 1960's interplanetary scintillation (IPS)
measurements have been used to probe solar wind
features with ground-based meter-wavelength radio
observations (4, 5). Observations from the UCSD (6)
and Nagoya (7) multi-site scintillation array systems
have been used to determine velocities in the
interplanetary medium since the early 1970's. The IPS
intensity scintillation observations, that arise from smallscale (~200 km) density variations, highlight
heliospheric disturbances of larger scale that vary from
one day to the next and are often associated with
geomagnetic storms on Earth (8).
We have developed a Computer Assisted
Tomography (CAT) program that modifies a timedependent three-dimensional kinematic heliospheric
model to fit IPS observations. The tomography program
iteratively changes this global model to least-squares fit
IPS data. Three-dimensional results for IPS data
covering a wide range of elongations have been obtained
using a heliospheric model that incorporates both
outward solar wind flow and solar rotation (9, 10, 11, 12,
13). Here scintillation strength is caused by small-scale
density variations that is in turn scaled to bulk density
TOMOGRAPHIC ANALYSIS
The IPS technique relies on several assumptions to
relate changes in scintillation level and velocity
integrated along each line of sight to local changes in the
scintillation level and velocity. In weak scattering
(assumed here exclusively) the Born approximation
holds, and the diffraction pattern is a sum of
contributions from each thin scattering layer
perpendicular to the line of sight (14). The analysis
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
75
Generally, valid IPS velocity data are available from
the same radio sources as observed in scintillation level
each day. IPS velocities are based on observations from
up to four scintillation arrays operated STELab, Japan.
To use these data our tomography program assumes that
the line of sight IPS velocity follows a similar line of
sight weighting relationship to that of the intensity
scintillation. We approximate the velocity observed at
Earth as in (11) [and see (12), for a more complete
formulation and validity tests].
The UCSD tomography program (11) applies
corrections to a kinematic model, modifying the model
until there is a least squares best fit match with the
observations. Density (rather than the small-scale density
variation) is used and propagated outward in the UCSD
kinematic model. The density and velocity are projected
outward from a reference surface (source surface) below
the lowest lines of sight. Consistent approximately with
in situ spacecraft observations, the solar wind motion is
assumed to be radial outward from this surface. Thus,
for example, when faster solar wind catches up with
slower wind, the resultant solar wind speed is continued
after merging by assuming both mass and mass flux are
conserved within the latitudinal band resolved by the
model. At the reference surface the velocity structure of
the model is smoothed using a Gaussian filter weighted
according to the angular distance of the adjacent
resolution elements on this surface. Since the resolution
of rectangular Carrington coordinate maps increase in
longitude with increasing latitude, this filter is used to
even the spatial resolution over the whole map.
In the kinematic model described here, the
heliosphere can change over time intervals as short as
one day.
This assumption essentially limits the
tomographic reconstruction to rely on outward solar
wind flow to form the perspective views. For each
observed line of sight at a given time, the position along
this line in the model is calculated. The model g-levels
along each line of sight defined by the densities are
summed using the weighting mentioned in Eq. 3. These
model values are then compared with the observed glevels, and this comparison is used to change the model.
For one solar rotation typically 500 to 1000 lines of sight
can be used to determine model density from the
scintillation-level measurements and velocity. This
implies 20 to 40 crossed line of sight components
contribute input to latitude and longitude positions each
day subject to the Gaussian spatial filter described
earlier, and a similar Gaussian filter that combines data
from one day to the next. This implies a possibility of
determining the density and velocity for 20 to 40 latitude
and longitude locations each day. In practice, lines of
sight often extend over several consecutive time steps.
The amount and quality of the available observations
and the heliographic coordinate resolution and temporal
data cadence dictate this resolution even more strongly.
proceeds much as in (11), but using evenly placed time
steps in the analysis.
Radio source scintillation-level observations have
been obtained from several tens of sources measured
each day by the STELab Kiso radio telescope from 1997
to the present. This analysis used data from a relatively
short time interval during July 2000. The value of the
disturbance factor g is defined as
g = m/<m>,
(1)
where m is the fractional scintillation level ∆I/I, the ratio
of source intensity variation to intensity and <m> is the
mean level of ∆I/I for the source at that elongation.
Scintillation level measurements from the STELab radio
facility analyses are available at a given sky location as
an intensity variation of the source signal strength. For
each source, data are automatically edited to remove any
obvious interference discerned in the daily observations.
To yield g-levels in real time, the white noise PWN is
subtracted from the scintillation signal spectrum P(f),
and then system gain corrections are determined by
automatically calibrating with the white noise level at
the high frequency end of the power spectrum. To
obtain m, the white noise is subtracted from the
scintillation signal,
f
(2)
m = ∫ (P(f) − P )/P df .
2
f1
WN
WN
At UCSD, g-values for a source are determined in real
time from m by a least square fit to the axially symmetric
solar wind model. We assume that it is sufficient to fit 8
daily measurements in order to obtain a value of <m>
for a given source. With the STELab 327 MHz analyses
weak scattering results are usually obtained from sources
outward from 11.5° elongation. However, since ample
data are available, our following analyses use a 17.5°
limit to be certain to be in the weak scattering regime.
The scintillation level weighting factor along the line
of sight WC (z) can be approximated in weak scattering
as in (11) at the 327 MHz frequency of the STELab IPS
observations. The scintillation level m is related to the
small-scale density variations along the line of sight by
m2 = ∫ dz ∆Ne(z)2 WC (z).
(3)
Here, ∆Ne(z) are the small-scale density variation values
at distance z along the line of sight. The density values
along the line of sight are not a priori known, but we
assume that the small-scale variations scale with a power
law of heliospheric density,
∆Ne = AC RPWR NePWN,
(4)
where AC is a proportionality constant, PWR is a power
of the radial falloff (13) and PWN is the power of the
density. In the present analysis, the program fits the
value of AC and the values of PWR and PWN to best fit
the data over the interval chosen. For the time period
presented here, AC = 1, and the two powers PWR and
PWN are –3.5 and 0.7, respectively, to best fit in situ
density over a ten-day time interval centered on the time
the Bastille-day CME reaches Earth.
76
IN-SITU COMPARISON
Tomographic model densities and velocities are
available in three dimensions and can be extrapolated to
any heliocentric distance, for example to 1 A.U. Here
they compare directly to the measured results from e.g.
the Advanced Composition Explorer (ACE) spacecraft
near Earth. We smooth the ACE data into 18-hour
averages, consistent with the approximate spatial
resolution present from the longitudinal and temporal
binning of the tomography data. The densities mapped
to 1 AU are shown as a time series for rotation 1965 in
Fig. 2. The correlation for rotation 1965 in model to
ACE in situ values is 0.6 and 0.9 respectively for
velocity and density over the 10-day period centered on
the Earth arrival time of the July 14 CME.
(a)
FIGURE 1. Consecutive-day (July 13 and July 14, 2000
latitude and longitude line of sight projections onto the
source surface. Lines of sight extend outward from
Earth for 2 AU beginning near the projected sub-Earth
point at the center of the map. Some lines of sight
complete their projection on adjacent days. Perspective
views are realized from the different weights on the
source surface maps at each latitude and longitude point.
(b)
FIGURE 2. Rotation 1965. a) 10-day velocity time
series from the three dimensional time-dependent model
projected to 1 AU compared to the velocity time series
from the ACE spacecraft (dashed line). b) Model and
ACE density correlation.
For the UCSD time dependent tomographic program
using STELab data, 20° by 20° heliographic latitude and
longitude resolution is used and a one day cadence. The
regions near the Earth are those most frequently crossed
by different lines of sight while those far from it, over
the solar poles and especially to the south, are not. This
is shown in Fig. 1 for two consecutive days during the
Bastille-Day event.
For several different perspective lines of sight to
produce changes in the modeled values, we require more
than one line of sight crossing on the source surface be
present within a 20° by 20° heliographic interval for
changes to be made at that position. If the model cannot
be updated at some location, these coordinate positions
are left blank in the final result. The reference surface
maps are smoothed at each iteration using a Gaussian
spatial filter that incorporates equal solar surface areas
and a Gaussian temporal filter. These spatial and
temporal filters can be varied to ensure convergence.
Filter changes by large percentages have a significant
effect on the result. Filter parameters were set to a 1/e
width of 13.5° and 0.85 days, for the 20° by 20° and 1day model digitization, respectively during the July,
2000 interval shown here. The tomography program
iterates to a solution, generally converging to an
unchanging model within a few iterations. Convergence
is monitored using techniques as described in (11).
DISCUSSION
Since few other in situ observations exist with
which to compare these results, the only guarantee in the
current analysis is that the three-dimensional model
constructed remotely by the IPS analysis over a large
portion of the heliosphere agrees with in situ data near
Earth. However, we can also view the model’s shape for
these events and see if they match remotely sensed data
from the LASCO coronagraphs.
Fig. 3a shows a LASCO C2 coronagraph image of
the July 11 halo CME compared with two views of the
density modeled as the CME is about to reach 1 AU. The
reconstruction shows that this CME moves mostly to the
east and north of the Earth as also indicated in the
coronagraph image. Similarly, Fig. 3b shows the
Bastille-day CME compared with two views of the
reconstructed density as the CME is about to hit Earth.
Given the expanse of heliosphere that the CMEs have
traversed to reach 1 AU, the comparisons with LASCO
near-Sun observations are excellent. The results of the
present 3-dimensional reconstruction are in good
agreement for the Bastille-day CME with an alternate
reconstruction analysis by (15).
77
(a)
FIGURE 3. LASCO C2 images and
two views of the reconstruction of the
halo CMEs in July, 2000 with Ne >30ecm-3 normalized to 1 AU shown.
Views (left to right) are 3° across from
1 AU; 55° across from 3 AU, 30°
above the ecliptic plane 45° west of the
Sun-Earth line; and 100° across at 1.1
AU on the Sun-Earth line. a) July 11,
2000 CME in LASCO reconstructed
July 13 at 6 UT. b) July 14 CME in
LASCO reconstructed July 15 at 6 UT.
(b)
REFERENCES
CONCLUSION
In comparison with in situ data at Earth, the
tomographic analysis gives superior results to previous
corotating analyses (11, 12). This is true even though the
spatial resolution of the present model is dramatically
decreased from the corotating model to insure
convergence. We reconstruct as complete as possible a
global three-dimensional model to obtain a good fit to
observations at Earth, even though these global models
amount to only a few tens of data points per day. In
real-time analysis, data drop-outs and noise make the
task of forecasting CME arrival using this technique
with the present STELab arrays even more problematic.
We expect that only when new and bigger IPS
systems are available will the technique provide a more
refined tomographic analysis to accurately forecast CME
arrival to within a few hours. Other large array systems
at different Earth longitudes will also be helpful. The
Solar Mass Ejection Imager (SMEI) will allow even
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The kinematic model currently fit by the
tomography can be improved significantly by using a
technique where the boundary conditions (source
surface) for a 3D-MHD model are adjusted to give a best
fit to the three-dimensional tomographic analysis. One
attempt is shown for corotating tomography in (16).
ACKNOWLEDGEMENTS
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7)
8)
9)
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15)
The work of B.V. Jackson, P.P Hick and A. Buffington
was supported at the UCSD by AFOSR grant AF4962001-1-0054, NSF grant ATM 98-199947 and NASA grant
NAG5-8504.
16)
78
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