Global Modeling of Equatorial Spread F

with SAMI3/WACCM-X

J.D.Huba1 and H.-L. Liu2

1 Syntek Technologies, Fairfax, VA

2 High Altitude Observatory, National Center for Atmospheric Research, Boulder,

CO

Abstract

We report the first results of a global ionosphere/thermosphere simulation study

that self-consistently generates large-scale equatorial spread F (ESF) plasma bubbles

in the post-sunset ionosphere. The coupled model comprises the ionospheric code

SAMI3 and the atmosphere/thermosphere code WACCM-X. Two cases are modeled

for different seasons and geophysical conditions: the March case (low solar activity:

F10.7 = 70) and the July case (high solar activity: F10.7 = 170). We find that

equatorial plasma bubbles formed and penetrated into the topside F layer for the

March case but not the July case. For the March case a series of bubbles formed

in the Atlantic sector with irregularity spacings in the range 400 - 1200 km, rose

to over 800 km, and persisted until after midnight. These results are consistent

with recent GOLD observations. Calculation of the generalized Rayleigh-Taylor

instability (GRTI) growth rate shows that the e-folding time was shorter for the

March case than the July case.

1

1 INTRODUCTION

Post-sunset ionospheric irregularities in the equatorial F region were first observed

by Booker and Wells (1938) using ionosondes. This phenomenon eventually became

known as equatorial spread F (ESF). It is now known that 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]. Modeling and

forecasting ESF is very important because of its impact on space weather: it causes

radio wave scintillation that degrades communication and navigation systems.

Given the complexity and non-linear development of equatorial plasma bubbles,

computational models are needed to tackle this problem. Scannapieco and Os-

sakow (1976) presented the first numerical results of ESF and demonstrated that

perturbations in the bottomside F layer can develop into bubbles that pene-

trate the topside. Subsequently, numerous and more sophisticated models have

been developed. An excellent review of these models is presented in Yokoyama (2017).

Virtually all of these models are regional: they cover a relatively narrow range of the

ionosphere in latitude and longitude. Typical longitudinal widths are 2 - 4 over

a latitude range ±15 − 30 with spatial resolutions in the range 1 km [Yokoyama

et al., 2015] to 5 km [Huba et al., 2008]. One exception is the work of Huba and

Joyce (2010) who embedded a high-resolution grid (longitude cell size 0.0625) in the

global model SAMI3. They seeded the pre- and post-sunset ionosphere with density

perturbations which developed into full-scale plasma bubbles. However, this model

used the empirical thermosphere models NRLMSISE00 [Picone et al., 2002] and

HWM07 [Drob et al., 2008] to specify the background neutral densities, temperature,

and winds.

In this Letter we report results from simulations using a coupled SAMI3/WACCM-X

2

model at high-resolution (the spatial grid is ≲ 70 km in the low-latitude ionosphere).

The codes are one-way coupled in that the thermospheric variables (i.e., neutral

densities, temperature, winds) from WACCM-X are inputs to SAMI3 but the SAMI3

ionosphere variables (i.e., ion density, temperature, velocity) do not feed back into

WACCM-X. Two seasons (equinox and solstice) are modeled with different levels of

solar activity: the March case (low solar activity: F10.7 = 70) and the July case

((high solar activity: F10.7 = 170). We find that the coupled model self-consistently

generates equatorial spread F plasma bubbles in the post-sunset ionosphere for the

March case. The growth rate of the generalized Rayleigh-Taylor instability (GRTI)

is calculated; we find that the e-folding time is much shorter for the March case than

the July case. Most significantly, for the March case, a series of bubbles formed in

the Atlantic sector with wavelengths in the range 400 - 1200 km, rose to over 800

km, and persisted until after midnight. These results are remarkably consistent with

recent GOLD observations.

2 MODELS

WACCM-X is an atmospheric component of the National Center for Atmospheric

Research (NCAR) Community Earth System Model, which couples atmosphere,

ocean, land surface, sea and land ice, and carbon cycle components through

exchanging fluxes and state information [Hurrell et al., 2013]. It is based on the

Community Atmosphere Model and WACCM. The first version of WACCMX is

described by H.L. Liu et al. (2010) and the most recent version is described in H.L.

Liu et al. (2018). The top boundary of WACCM-X v.2.0 is set at 4.0 × 10−10 hPa

(= 500 to 700 km altitude, depending on solar activity). The vertical resolution in

the mesosphere and thermosphere is a quarter of a scaleheight, and the horizontal

resolution is 0.474 × 0.625 in latitude and longitude, respectively. WACCM-X

has the option to have the tropospheric and stratospheric dynamics constrained to

meteorological reanalysis fields for specifically targeted time periods.

3

SAMI3 (Sami3 is Also a Model of the Ionosphere) is a seamless, global, three-

dimensional, physics-based model of the ionosphere. It is based on SAMI2 [Huba et

al., 2000]. SAMI3 models the plasma and chemical evolution of seven ion species

(H+, He+, N+, O+, N+2 , NO

+ and O+2 ). The temperature equation is solved for three

ion species (H+, He+ and O+) and for the electrons. Ion inertia is included in the

ion momentum equation for motion along the geomagnetic field. SAMI3 nominally

uses the EUVAC [Richards et al., 1994] model for solar radiation and the Richmond

apex model for the magnetic field [Richmond, 1995]. The neutral composition,

temperature, and winds can be specified in SAMI3 by analytical models, empirical

models, or physics-based models. The electrostatic potential used in SAMI3 in

the low- to mid-latitude ionosphere is determined by the solution of a potential

equation driven by the neutral wind dynamo [Huba et al., 2008]. The potential in the

high-latitude region is specified by the Weimer05 model [Weimer, 2005]. One new

feature of the SAMI3 model used in this study is the implementation of a 4th order

flux-corrected transport scheme for E × B transport perpendicular to the magnetic

field. The partial donor cell method [Hain, 1987; Huba, 2003] is used which reduces

numerical diffusion and allows steeper density gradients to develop.

Details of the simulation parameters are as follows. The WACCM-X grid is 0.474

× 0.625 in latitude and longitude, and covers the entire earth. The SAMI3 grid

is also 0.625 in longitude but is variable in latitude. The grid in latitude is ∼ 1

for latitudes 40, decreases to ∼ 0.15 near the magnetic equator, and increases to

∼ 1.5 in the high-latitude region. The SAMI3 grid extends to ±80 latitude in

magnetic coordinates.

Two simulation studies were performed for different seasons and solar activity. The

first simulation study is for March 21, 22 and 23 for low solar activity (F10.7 = 70

and F10.7A). The second study is for July 2, 3 and 4 for high solar activity (F10.7

= 170 and F10.7A = 170). We will refer to the first case as the ’March case’ and the

4

second case as the ’July case.’ Only results from the third day are presented. The

rationale for these choices is somewhat arbitrary but was made to highlight potential

differences under very different geophysical conditions with a limited set of runs.

3 RESULTS

In Fig. 1 we show the total electron content (TEC) calculated from SAMI3 at 23:59

UT for the July case (top panel) and the March case (bottom panel). Daytime

is over the Pacific sector with sunset in the American sector. The most striking

feature of the March case is the development of large depletions in TEC over eastern

South America, the Atlantic ocean, and western Africa. These depletions in TEC

are associated with large-scale plasma bubbles that developed after sunset and are

initiated by atmospheric gravity waves in the WACCM-X simulation data. The

spacing (i.e., wavelength) of the irregularities in longitude varies from 400 km to

1200 km at this time, which is consistent with recent observations of irregularity

wavelengths in the range 500 - 800 km [Aa et al., 2020]. The spacing also changes

as a function of longitude during the evolution of the irregularities. It is noted that

gravity waves with horizontal wavelength down to ∼ 500 km are properly resolved by

WACCM-X, according to analysis of the kinetic energy spectrum of model results.

Additionally, there is an enhancement of TEC at midlatitude in the post-midnight

sector; this is associated plasmasphere ‘drainage’ into the ionosphere because of the

low pressure during solar minimum conditions at night [Li et al., 2018]. By contrast,

no large-scale bubbles formed for the July case. There are, however, relatively weak

irregularities in the mid-latitude region over western Russia and the southern Indian

ocean.

To emphasize the role of gravity waves in generating the depletions seen in the

bottom panel of Fig. 1 we show results from a high-resolution SAMI3 simulation for

the March case that used the empirical thermospheric models NRLMSISE00 for the

neutral densities and temperature [Picone et al., 2002] and HWM14 for the winds

5

[Drob et al., 2015]. The TEC for this simulation is shown in Fig. 2 and is to be

compared to the bottom panel of Fig. 1. The gross morphology of the ionosphere

is roughly the same but there are clear differences. There are no plasma bubbles or

nighttime mid-latitude enhancements in Fig. 2 as in Fig. 1, and the daytime equa-

torial ionization crests are not as distinct. This suggests that in addition to gravity

waves being important in seeding the post-sunset structure that the difference in ther-

mospheric winds also plays a significant role in the electrodynamics of the ionosphere.

In Fig. 3 we compare 135.6 nm emissions from the simulation for the March case at

23:59 UT (left and middle panels) to GOLD emission observations (right panel) from

geosynchronous orbit [Eastes et al., 2019]. The GOLD results are for October, 2018

which corresponds to equinox conditions at solar minimum, similar to the conditions

of the simulation. For the 135.6 nm emission from OI, the total irradiance (in

Rayleighs) is given by [Melendez-Alvira et al., 1999; England et al., 2008].

IRR =1

4π106

∫α1356(Te)Ne[O

+]ds+β1356k1k24π106

∫Ne[O][O+]

k2[O+] + k3[O]ds. (1)

The coefficients used in Eq. (1) are given in England et al. (2008). The center

panel is on the same color scale as the GOLD data (maximum of 40 Rayleighs); it

shows that the intensity of the 135.6 nm emissions from the model is less than the

data. The left panel reduces the color scale maximum to 12 Rayleighs in order to

highlight the structure in the model results; it shows a remarkable similarity to the

data. The model results capture the extended ionization arcs from the post-sunset

period (eastern South America) to midnight (western Africa) observed in the data.

Moreover, regular plasma striations (bubbles) are also observed in the model as in

the data on similar scale lengths. We note that since the emission rate is roughly

proportional to n2e, the electron density from the simulation is ∼ 1.7 smaller than

needed to agree with the observations.

We show the relationship between F region plasma structure and the generalized

Rayleigh-Taylor instability (GRTI) growth rate (see Appendix). In Figs. 4 (July

6

case) and 5 (March case) we show the electron density as a function of longitude and

altitude (top panel) and the growth rate of the GRTI (bottom panel) at time 17:44

UT. These plots are in the plane of the magnetic equator. In Fig. 4 (July case) the

maximum growth rate is ∼ 7.9 × 10−4 s−1 at ∼ 30 longitude. This corresponds to

an e-folding time τ ∼ 21 min which is consistent with previous estimates [Sultan,

1996]. However, at this time no plasma bubbles have developed that penetrate the

topside F layer; there are undulations in the bottomside F layer which are commonly

observed. On the other hand, in Fig. 5 (March case) the maximum growth rate at

∼ 30 longitude is ∼ 1.0× 10−3 which corresponds to an e-folding time τ ∼ 15 min.

Plasma bubbles are beginning to develop at this time. Moreover, in the longitude

range 35 - 75 several large scale plasma bubbles have developed and penetrate

the topside F layer. The growth rates in these bubbles are ∼ 2.9 × 10−3 s−1 which

corresponds to an e-folding time ∼ 5.8 min.

In Figs. 6 (July case) and 7 (March case) we show the maximum growth rate of

the GRTI in the altitude range 200 - 300 km (left panel) and the electron density

along the magnetic equator at 312 km as a function of local time and longitude. The

GRTI growth rate is positive shortly after sunset (∼ 18:00 UT) for both cases. In

the July case, the growth rate is relatively uniform in longitude at ∼ 19:00 LT with

a maximum of ∼ 1.6× 10−3 s−1 which corresponds to an e-folding time ∼ 10.4 min.

However, no density irregularities are evident at 312 km at this time. On the other

hand, for the March case, the growth rate is non-uniform in longitude at ∼ 19:00 LT

with a maximum of ∼ 2.4 × 10−3 s−1 which corresponds to an e-folding time ∼ 7.0

min. Large scale density irregularities (plasma bubbles) are evident at 312 km that

correspond to regions of fast GRTI growth.

4 SUMMARY

We have presented the first high-resolution (latitude/longitude resolution ≲ 70

km), global simulation study of the ionosphere/thermosphere system that captures

7

the onset and nonlinear development of large-scale equatorial spread F plasma

bubbles. The coupled model comprises the ionospheric code SAMI3 and the

atmosphere/themosphere code WACCM-X. Thermospheric data from WACCM-X

(neutral densities, temperature, and winds) are used as inputs to SAMI3. Two cases

were modeled for different seasons and geophysical conditions: the March case (low

solar activity: F10.7 = 70) and the July case (high solar activity: F10.7 = 170). We

found that equatorial plasma bubbles formed and penetrated the topside F layer for

the March case but not the July case. The spacing between the irregularities is in the

range 400 - 1200 km; this is consistent with the scale of the resolved gravity waves.

However, a more detailed examination of the relationship between gravity waves

and irregularity scale lengths is needed. We emphasize that the bubbles formed

self-consistently (i.e., no artificial perturbations were introduced in the simulations)

which suggests that gravity waves were the dominant seed mechanism [Kelley et al.,

1981; Aa et al., 2020]. To support this hypothesis we performed a high resolution

SAMI3 simulation using empirical thermospheric models and no plasma bubbles

occurred. Additionally the calculation of the GRTI growth rate shows that the

e-folding time was shorter for the March case (growth time τ ∼ 7 min) than the July

case (growth time τ ∼ 12 min).

Although only two cases are considered, these results are consistent with observations

of strong longitiudinal and seasonal dependences for the observation of equatorial

spread F irregularities [Yizengaw and Groves, 2018]. Also, even though large scale

plasma bubbles did not develop for the July case, there were large-scale undulations

of the bottomside F layer which are observed [Woodman and LaHoz, 1976; Hysell,

2000]. Future work will focus on a wider range of geophyscial conditions and a clearer

identification of the underlying thermospheric and ionospheric conditions responsible

for the generation of equatorial spread F irregularities. For example, one area to

investigate in detail is the relationship between post-sunset rise of the F layer and

upwelling growth in controlling the onset of equatorial plasma bubbles as discussed

in Tsunoda et al. (2018).

8

5 APPENDIX

We have derived the flux-tube integrated growth rate, similar to Haerendel (1973)

and Sultan (1996), in dipole coordinates and have included ion inertia. The complex

frequency is given by (ω = ωr + iγ)

ω =2C

−B ± (B2 − 4AC)1/2(2)

where

A =

∫σHi0

1

Ωi

G(s) ds B = i

∫σP0G(s) ds C =

∫1

Ln

F (s)G(s) ds

and

F (s) = σP

( c

BE0ϕ − Vn0p

)+ σH

( c

BE0p + Vn0ϕ

)− σHi0

gpΩi

and

G(s) =1

bs

r0 sin3 θ

∆

and conductivities

σP =nec

B

[νin/Ωi

1 + ν2in/Ω

2i

+νen/Ωe

1 + ν2en/Ω

2e

]σH =

nec

B

[ν2in/Ω

2i

1 + ν2in/Ω

2i

− ν2en/Ω

2e

1 + ν2en/Ω

2e

]σPi =

nec

B

νin/Ωi

1 + ν2in/Ω

2i

σHi =nec

B

1

1 + ν2in/Ω

2i

and n is the density, e is the electric charge, c is the speed of light, B is the magnetic

field strength, ∆ = (1 + 3 cos2 θ)1/2, ναn is the neutral collision frequency, Ωα is the

ion cyclotron frequency, gp = −g p · r, bs = (r30/r3)∆, and

1

Ln

G(s) =1

r0

∆

sin3 θ

1

n0

∂n0

∂p

1

bs

r0 sin3 θ

∆=

1

bs

1

n0

∂n0

∂p

Acknowledgments: This research was supported by NASA (JDH:

NNH17ZDA001N; HLL: 80NSSC17K0007), NSF (JDH: AGS-1931415; HLL:

9

AGS-1552153) and AFOSR (HLL: FA9550-16-1-0050). National Center for

Atmospheric Research is a major facility sponsored by the National Science

Foundation under Cooperative Agreement No. 1852977. CESM/WACCM-

X source code is available at http://www.cesm.ucar.edu. Data available at

http://doi.org/10.5281/zenodo.3735040. We thank Dr. Astrid Maute for a critical

reading of the manuscript and Dr. Scott England for providing the code to calculate

the 135.6 nm emissions.

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Figure 1: The TEC at 23:59 UT for the July case (F10.7 = 170) (top panel) and the

March case (F10.7 = 70) (bottom panel).

14

Figure 2: The TEC at 00:00 UT from a high-resolution SAMI3 simulation using

the empirical thermosphere models NRLMSISE00 and HWM14 for the March case

conditions.

Figure 3: Comparison of 135.6 nm emissions from the simulation for the March

case (left and middle panels) and GOLD emission data (right panel) observed from

geosynchronous orbit [Eastes et al., 2019].

15

Figure 4: The electron density as a function of longitude and altitude (top panel) and

the growth rate of the GRTI (bottom panel) along the magnetic equator at 17:44 UT

for the July case.

Figure 5: The electron density as a function of longitude and altitude (top panel) and

the growth rate of the GRTI (bottom panel) along the magnetic equator at 17:44 UT

for the March case.

16

Figure 6: The maximum growth rate of the GRTI in the altitude range 200 - 300

km (left panel) and the electron density along the magnetic equator at 312 km as a

function of local time and longitude (July case).

Figure 7: The maximum growth rate of the GRTI in the altitude range 200 - 300

km (left panel) and the electron density along the magnetic equator at 312 km as a

function of local time and longitude (March case).

17