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, jessica.hawkins@utdallas.edu and phillip.anderson1@utdallas.edu

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