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A Comprehensive, First-principles Model of Equatorial Ionospheric
Irregularities and Turbulence
J.D. Huba, G. Joyce, and J. Krall
Introduction
Post-sunset ionospheric irregularities in the equatorial F region were first observed by Booker
and Wells (1938) using ionosondes. This phenomenon has become known as equatorial spread
F (ESF). During ESF the equatorial ionosphere becomes unstable because of a Rayleigh-
Taylor-like instability: large scale (10s km) electron density ‘bubbles’ can develop and rise
to high altitudes (1000 km or greater at times) [Haerendel, 1974; Ossakow, 1981; Hysell,
2000]. Attendant with these large-scale bubbles is a spectrum of electron density irregulari-
ties that can extend to wavelengths as short as 10 cm [Huba et al., 1978]. Understanding and
modeling ESF is important because of its impact on space weather: the associated electron
density irregularities can cause radio wave scintillation that degrades communication and
navigation systems. In fact, for this reason, it is the focus of of the Air Force Communica-
tions/Navigation Outage Forecast Satellite (C/NOFS) mission [de La Beaujardiere, 2004].
Figure 1: ESF plasma bubbles (dark regions) and GPS
signal loss (bottom right) [courtesy of J. Makela].
The impact ESF can have on
operational systems is shown in
Fig. 1 [Makela, private communi-
cation, 2005; Kelley et al., 2002].
The top panel is a composite of
optical images at 7774 A from
Mount Haleakala; the darker
areas are regions of low electron
density (i.e., ESF plasma bub-
bles). Note that these bubbles
can have complex structures (i.e.,
tilts, bifurcations). Overlaid
on this figure are the orbits of
three GPS satellites; the actual
satellite locations at this time
are denoted by the symbols. Of
note is the ‘blue’ satellite. The
path of the GPS signal from this
satellite to the ground receiver
passes through the plasma bubble. The signal is strongly scintillated as shown in the lower
left panel where S4 ∼ 1 (the S4 index is a normalized measure of the standard deviation
of the GPS satellites’ received signal power as seen on the ground). In this case it is very
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significant because it causes a complete loss of signal as shown by the break in the blue line
at 22:45 LT in the relative TEC measurement in the bottom right panel.
Theoretical [Sultan, 1996] and computational [Zalesak et al., 1982; Huba and Joyce, 2007;
Huba et al., 2008; Retterer, 2010] models have been developed to describe the large-scale
bubble development shown in Fig. 1; an example is shown in Fig. 2. However, these models
are decoupled from the global electrodynamics of the earth’s ionosphere. Only recently has
a model been developed that can capture both large-scale global ionospheric dynamics (∼1000s km) and small-scale bubble dynamics (∼ 10s km) [Huba and Joyce, 2010]. Although
this model provides a new capability to understand the day-to-day variability of ESF, it falls
far short of modeling the spectrum of irregularities associated with ESF and the small-scale
turbulence (∼ 100s m) that is responsible for scintillating radio wave signals. The purpose
of this white paper is to propose a comprehensive theoretical and modeling program to
address this deficiency.
Scientific and Computational Challenges
The major computational challenge is to seamlessly couple different, spatially overlapping,
physics models. These include (1) thermospheric models that describe neutral dynamics
associated with tidal motions, planetary waves, and gravity waves [Fritts et al., 2009; Fritts
and Lund, 2010], (2) global ionospheric models that describe the neutral wind dynamo and
bubble development [Huba and Joyce, 2010], (3) sub-grid electrostatic fluid models that
capture electron density turbulence on scales 10s m to 100s m [Hysell, 2000], and finally (4)
hybrid and particle-in-cell codes that model small-scale turbulence below the ion Larmor
radius (10s cm to 10s m). This is a daunting challenge since it covers a spatial range
spanning 8 orders of magnitude and a temporal range spanning 6 orders of magnitude.
Figure 2: Electron density [Huba et al., 2008] and tem-
perature [Huba et al., 2009] structure of an equatorial
plasma bubble.
As a first step in this challenging
project, existing thermospheric,
ionospheric, and electrostatic fluid
turbulence models can be coupled to
improve current modeling capabil-
ities and to identify computational
difficulties that need to be overcome
in developing a comprehensive,
integrated model. However, there is
also a need to improve and extend
existing models. One example is
the electrodynamics of the iono-
sphere/thermosphere (IT) system.
All global models of the IT system
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assume that the geomagnetic field lines are equipotentials; this assumption reduces the
potential equation to two dimensions. This assumption is nominally considered valid for
global scale sizes L & 1 km because of σ‖ >> σ⊥ where σ is the conductivity of the plasma
[Farley, 1963]. However, recent simulation studies by Aveiro and Hysell (2010) suggest this
simple scaling argument may not be valid and that 3D electrodynamic model are required.
Thus, to accurately describe the self-consistent coupling of large scale to small scale electron
density irregularities it is necessary to have a fully three-dimensional electrodynamic
model. This will require the solution to a 3D electrostatic potential equation. It will be
necessary to have a 3D solver that is robust, efficient, and uses parallel processing on a
nonuniform grid. A second example is the need to include finite Larmor radius effects in
electrostatic fluid turbulence models [Hysell, 2000]. The oxygen ion Larmor radius is ∼ 3 m
and the spectrum of ionospheric turbulence is altered on this scale [Huba and Ossakow, 1979].
Proposed Program
A comprehensive modeling program is proposed to attack this difficult and important
problem. Resources are needed (1) to develop new numerical algorithms to improve both
the physics and efficiency of existing models, (2) to develop potentially new models of
IT system and sub-system, and (3) to couple existing and new models seamlessly into
a comprehensive framework. This effort requires long term, stable funding involving
several research groups. A nominal program would be a 5 year effort at $2M/year for a
total of $10M. This is consistent with the type of programs suggested by the Advanced
Computational Capabilities for Exploration in Heliophysical Science (ACCEHS). In addition
to model developement, the program also needs to include an data/model comparison
component to ensure that simulation results are consistent with experimental observations.
References
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