solar zenith angle as a driver of seasonal oscillations in the … · 2014-06-24 · between ion...
TRANSCRIPT
The path that solar radiation takes through the Earth's atmosphere varies
over the course of a year due to the changing solar zenith angle, and this is
a significant driver of changes in ionospheric density. Solar zenith angle
(SZA) effects show up in measurements of ion density as a seasonal
oscillation which is approximately sinusoidal. It may be desirable to
remove the SZA effects from ion density data in order to focus on other
variables affecting the ionosphere, and one method that can be used to
remove the SZA oscillation is Empirical Orthogonal Function (EOF)
analysis. We perform EOF analysis on DMSP satellite data and show that
projections onto the first two EOFs correlate strongly with solar EUV
irradiance and SZA, indicating that these two variables explain most of the
variance. We then explain how to create a revised data set, using EOF
analysis to remove SZA effects, and we show that the revised data has a
stronger correlation with solar EUV than the un-revised data.
Abstract
Introduction
Empirical Orthogonal Function Analysis
DMSP and TIMED Satellites
Conclusions and Further Studies
References
The DMSP spacecraft fly in sun-synchronous, dawn-to-dusk, and pre-
midnight and pre-noon orbits at ~800 km altitude with ~99 degree
inclinations and orbital periods near 100 min. The Special Sensor-Ions,
Electrons and Scintillation (SSIES) instrumentation package aboard DMSP
includes a Langmuir probe, ion drift meter, and Retarding Potential
Analyzer (RPA). This altitude places the satellites in the topside ionosphere
above the F peak. The most prevalent ion in this region can be either O+,
H+, or He+ at different times, and the following graphs use the total ion
density measured by the RPA, although future studies may probe the
different ion species densities separately. Daily averages of ion density are
taken separately over the "morning" passes (about 9:00 SLT) and the
"evening" passes (about 21:00 SLT) at each latitude.
Solar EUV flux is measured by the Solar Extreme-ultraviolet Experiment
(SEE) instrument onboard the TIMED satellite, which flies in a circular
orbit at 625 km altitude. SEE contains an XUV Photometer System (XPS)
and EUV Grating Spectrometer (EGS) and provides measurements in the
0.1-195 nm range.
Solar Zenith Angle as a Driver of Seasonal Oscillations in the Ionosphere
J.M. Hawkins and P.C. Anderson, [email protected] and [email protected]
W.B. Hanson Center for Space Sciences at the University of Texas at Dallas
Empirical Orthogonal Functions (EOFs) have been used in atmospheric
research at least since the 1940's and even earlier in the social sciences,
under the name Principal Components Analysis. Zhao et. al. [2005]
identified ion density drivers associated with the first three principal
components and showed that the first principal component correlates with
the F10.7 flux. The idea is to expand a data set extended in space and time on
a new orthogonal basis along the directions of maximum variance. The new
basis vectors are the eigenvectors of the covariance matrix.
EOF analysis is closely related to the process of dimensionality reduction,
i.e. reducing the dimensionality of a data set. In the context of atmospheric
research, it is often used to identify a small number of physical processes
which drive most of the variability in a data set, with the assumption that
these drivers are (to a good approximation) linearly independent of each
other.
In the following graphs, daily averages of ion density are binned in 5 degree
increments from -60 degrees to +60 degrees geographic latitude and
arranged in an S by I matrix with matrix elements Xsi, where S is the number
of latitude bins and I is the number of days. After removing the time-mean at
each latitude bin, construct the S by S normalized covariance matrix with
matrix elements:
(1)
The EOFs are the S S-dimensional eigenvectors g of the covariance matrix:
(2)
The EOFs form an orthonormal basis and thus can be used to expand the ion
density as a series of orthogonal terms:
(3)
where the coefficients αim, called the principal components, are given by
(4)
The ionosphere is a partially ionized region of the Earth's upper atmosphere extending from about 60 to 1000 km in altitude. Solar radiation in the ultraviolet and extreme ultraviolet range (about 10 to 120 nm) is known to produce most of the ionization, although the injection of energetic particles can play an important role at high latitudes. Solar EUV radiation varies widely with solar activity, the solar rotation, and the solar cycle. Because of the historical lack of adequate solar EUV irradiance data, current space weather models typically use proxies such as the 10.7 cm radio flux observed at local noon (F10.7 index or E10.7, the adjusted F10.7) to estimate solar spectra. Here we use measured solar EUV flux instead of the proxy to investigate its relationship to the ion density. The topside ionosphere mainly contains O+, H+, and He+. Typically, O+ and He+ are produced by photoionization of neutral oxygen and helium, and lost by recombination with O2 and N2. H+ is produced by reversible charge exchange with O+. Solar radiation heats the atmosphere, causing it to expand during the day and contract at night. Because of this daily "breathing" of the atmosphere, as well as diffusion, ionization flows up and down the Earth's magnetic field lines. Neutral winds also help redistribute ionization. The ion density is expected to be enhanced near the equator due to the equatorial fountain effect. The equatorial electrojet generates an electric field at the equator where the magnetic field lines are nearly horizontal, so plasma is transported vertically by E x B drift. This is referred to as electrodynamic lifting. The lifted plasma is able to descend again along the magnetic field lines, which carry the plasma away from the equator in a “fountain.” Typically the ion density shows a small dip over the magnetic equator called the Appleton anomaly (or equatorial anomaly) and two maxima 10 to 20 degrees north and south of it.
Solar EUV Variability Solar Zenith Angle
Figure 1. The F10.7 radio flux and EUV flux measured by the TIMED satellite
at various wavelengths. The long-term variation follows the 11-year solar cycle.
There is also a variation with the 27-day solar rotation. F10.7 shows a good
overall correlation with all wavelengths, but it doesn’t capture the spectral
variations on small time-scales.
Figure 4. Weighted photoionization and photoabsorption cross sections for
O+ for Torr and Torr [1979] bands and lines. A larger cross section
corresponds to more ionization or absorption, for a given EUV intensity and
precursor species density.
Figure 7. DMSP orbital plane at the northern and southern winter solstices.
The Earth’s spin axis is tilted relative to its orbit around the Sun, and the
DMSP’s orbit slowly precesses around the Earth. As a result, the DMSP
orbital plane is tilted away from the Sun in the southern winter and toward
the Sun in northern winter. The tilt away from the Sun during southern
winter solstice, corresponding with a larger solar zenith angle, produces less
ionization than during the northern winter solstice. This is why there is an
asymmetry in the densities between the northern and southern hemispheres
during winter solstices, as shown in Figure 5.
Figure 5. Ion density for DMSP satellite F15, post-dawn at ±60 to ±70
geographic latitude. These latitudes show a dramatic seasonal oscillation in ion
density. The seasonal oscillation becomes much less dramatic near the equator.
North
South
The solar zenith angle (SZA) is the angle between a line connecting the center
of the Sun to the center of the Earth, and a line from the center of the Earth up
to a position where ionization is measured. The changing solar zenith angle
results in a seasonal oscillation in ion density which is especially dramatic at
mid and high latitudes.
At all latitudes, the density is correlated with the solar EUV flux, and the
correlation is stronger at lower latitudes, indicating that removal of the
seasonal oscillations might allow the relationships between solar EUV flux
and ion density to be probed in greater detail. The fact that the seasonal
oscillation often has the same basic shape at all latitudes, but a different
amplitude, motivates us to use an analysis technique which parameterizes
the density into spatial and time components.
Figure 9. The latitude mean (a) EOF 1
(b) and EOF 2 (c) of ion density measured
by DMSP satellite F15, calculated from
daily averages binned in 5 degree
increments from -60 degrees to +60
degrees geographic latitude . The solid
lines are for the morning, and dashed lines
are for the evening. Note that the mean
density (a) is greatest near the equator, as
expected. EOF 2 (c) is associated with the
seasonal variation and is shown here to be
a much stronger effect at mid latitudes
than at the equator.
(a) (b)
(c)
Figure 3. Daily averages of ion density during solar maximum shows a response
to the 27-day solar rotation at various geographic latitudes, during (a) morning
and (b) evening passes.
(a)
(b)
-60 < GLAT < -55
-25 < GLAT < -20
-5 < GLAT < 0
15 < GLAT < 20
55 < GLAT < 60
The changing solar zenith angle is a stronger driver of seasonal oscillations in
ion density, particularly at high latitudes. Removal of this seasonal
oscillation may allow the spectral and shorter time-scale variations to become
more apparent.
EOF analysis can be used to remove SZA effects to a first approximation,
although solar effects (such as the 11-year cycle) and SZA effects may not be
completely linearly independent.
Future studies will investigate wavelength-by-wavelength correlations
between ion density and solar EUV flux, as compared with the F10.7 proxy
commonly used in space weather models. New data from the SDO satellite
will be used to supplement TIMED:SEE data in crucial wavelength bands.
In addition to the total ion density analyzed here, the drivers of individual
O+, H+, and He+ densities may be analyzed in future studies.
-60 0 60
Latitude
-60 0 60
Latitude
Figure 2. Ion density shows a good long-term correlation with F10.7 radio flux
over two solar cycles (-5 to 5 degrees latitude, dusk.)
Which wavelength bands do we expect to have the greatest effect on ion density?
This depends on the amount of ionizing radiation available at each wavelength,
as well as the photoionization cross sections for each wavelength, which are
shown in the following figure. 30 nm was used for this study.
The 2nd principal component is multiplied by a constant factor at each latitude,
which is larger at mid and high latitudes, as shown in Figure 9c and explained
in equation (3). Thus, the seasonal oscillation shown in Figure 8b is stronger
at mid and high latitudes. In order to remove this seasonal oscillation, the
second term in the EOF expansion can be zeroed out, and the remaining
density re-normalized. (Note that this is process is analogous, in Fourier
analysis, to applying a Fourier transform to convert to the frequency domain,
zeroing out undesired frequencies, and applying an inverse Fourier transform
to convert back to the time-domain. In Fourier analysis, this general process
is called “filtering.”) The modified ion densities show an increased
correlation with the solar EUV.
2000 2002 2006 2008
2000 2004 2008 2000 2004 2008
(a)
(b) (c)
Figure 6. Ion densities and solar zenith angle (SZA) for F15, dusk, as (a) -55 to
-50, (b) -20 to -15, and (c) 0 to 5 degrees geographic latitude. The solar zenith
angle causes visible changes in ion density at high and mid latitudes, but the
effect disappears near the equator (c).
Torr, M. R., D. G. Torr, and R. A. Ong, “Ionization frequencies for major thermospheric constituents as a function of solar cycle” vol. 6, no. 10, pp. 771–774, 1979. Zhao, B., W. Wan, L. Liu, X. Yue, and S. Venkatraman, “Annales Geophysicae Statistical characteristics of the total ion density in the topside ionosphere during the period 1996 – 2004 using empirical orthogonal function ( EOF ) analysis,” pp. 3615–3631, 2005.
The solar EUV is highly variable across different wavelengths, as shown in
the following figure.
Year Year
Year
Figure 8. The 1st and 2nd principal components of F15 data set (corresponding
with the same data set as Figure 7.) The black line is for the morning, and the
red line is for the evening. The 1st principal component corresponds to solar
EUV. The 2nd principal component shows a seasonal oscillation corresponding
to the changing solar zenith angle (SZA.) The long-term variation in both
principal components corresponds with the 11-year solar cycle. The fact that
the 2nd principal component is not entirely smooth may indicate that the effects
of solar EUV flux and the solar zenith angle are not entirely linearly separable.
2000 2003 2006 2009 2012 Year
Mean Density EOF 1
EOF 2
2nd Principal Component
Morning
Evening
Morning
Evening
cos
(SZ
A)
cos
(SZ
A)
-60 < GLAT < -55
-25 < GLAT < -20
-5 < GLAT < 0
15 < GLAT < 20
55 < GLAT < 60
F15 Morning Ion Density
F15 Evening Ion Density
Morning Evening
Morning Evening
Morning Evening