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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