Shidler and Rodrigues Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-021-00417-8(2021) 8:26

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open AccessOn a simple, data-aided analytic
description of the morphology of equatorial
F-region zonal plasma drifts
Samuel A. Shidler*and Fabiano S. Rodrigues

Abstract
We present results of an effort to evaluate the ability of an analytic model to describe the behavior of the equatorial
zonal plasma drifts given inputs provided by readily available climatological models of thermospheric and ionosphericparameters. In a data-model fusion approach, we used vertical drift measurements to drive the model and zonal drift
measurements to evaluate its output. Drift measurements were made by the Jicamarca incoherent scatter radar, andmodel results were evaluated for different seasons and two distinct solar flux conditions. We focused, in particular, onmodel results for different versions of the Horizontal Wind Model (HWM 97, 07, and 14). We found that, despite its
simplicity, the analytic model can reproduce fairly well most of the features in the observed zonal plasma drifts,
including the vertical shear associated with the evening plasma vortex. During daytime hours the model predicts
similar results for the zonal drifts independently of the HWM used to drive the model. More importantly, the modeled
daytime drifts match exceptionally well the behavior and magnitude of the observed drifts for all seasons and solar
flux conditions considered. The nighttime results drive the overall performance of the analytic model, and we foundthat a single HWM cannot provide the best results for all seasons and solar flux conditions. We also examined the main
sources of zonal drift variability. Most of the morphology is controlled by the zonal wind dynamo term of the analytic
model, but with non-negligible contribution from the vertical drift term. Finally, we examined the contribution fromthe E- and F-region to the zonal wind dynamo. The morphology of the zonal drifts in the region of observation(240–560 km altitude) is controlled mostly by the F-region winds, but with significant contributions from the daytime
E-region particularly during December solstice and low solar flux conditions.
Keywords: Equatorial, Ionosphere, Drifts, Model, Climatology, Jicamarca, Pyglow

1 Introduction
Equatorial vertical E × B drifts are well-recognized as
playing an important role in the linear stability of theequatorial F-region and in space weather (e.g., Abdu et al.
1983; Fejer et al. 1999; Kudeki and Bhattacharyya 1999;
Hysell and Kudeki 2004; Kelley and Retterer 2008; Huang
and Hairston 2015; Smith et al. 2015; Huang 2018). For
instance, several studies have pointed out the important*Correspondence: sas141430@utdallas.edu
W. B. Hanson Center for Space Sciences, The University of Texas at Dallas, 800
W Campbell Rd, Richardson, TX 75080, USArole of the vertical drifts in the Generalized RayleighTaylor (GRT) instability (Sultan 1996). The GRT instability is often referred to as being responsible for the wide
spectrum of ionospheric irregularities commonly seen in
the low-latitude F-region and that are referred to as equatorial spread-F (ESF). Additionally, it has been suggested
that the behavior of the zonal plasma drifts as a functionof height, and their relative motion with respect to theneutral winds can also play a role in the stability of theequatorial F-region and in the morphology of ESF density perturbations (Kudeki and Bhattacharyya 1999; Hysell
and Kudeki 2004; Kudeki et al. 2007; Aveiro and Hysell
2010).

© The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit
to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The
images or other third party material in this article are included in the article’s Creative Commons licence, unless indicatedotherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended
use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the
copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Perhaps more importantly, vertical and zonal plasma
drifts provide insight on complex and difficult to directly
measure ion-neutral coupling processes taking place at
low-latitudes. For instance, previous numerical studies
have shown that the behavior of the F-region plasma
drifts is heavily controlled by the E- and F-region neutral wind dynamos (Heelis et al. 1974; Eccles 1998; Eccles
2004; Maute et al. 2012; Rodrigues et al. 2012). Observations of thermospheric winds, however, are difficult to
make, and current observational techniques are limited
to certain times and heights (David et al. 2016). Groundbased Fabry-Pérot Interferometer (FPI) measurements,for example, contribute a significant portion of the observational data used in the development of the empirical
Horizontal Wind Model (HWM) (Drob et al. 2015). This
technique, however, only provides reliable measurements
during clear-sky nighttime conditions and for an altitude
of about 250 km (David et al. 2016).
Despite the importance of plasma drifts for the lowlatitude ionosphere-thermosphere (IT) system, groundbased measurements are limited and studies of the shortterm (day-to-day) variability of the drifts are difficult.
There is, however, a large number of observations madeover a long period (several months to a few tens of years)of time. Long-term observations, such as those made by
the Jicamarca ISR, have allowed various climatologicalstudies of the drifts (Fejer et al. 1991; Scherliess and Fejer
1999; Fejer et al. 2005; Hui and Fejer 2015). The limitationin the observations led these studies to focus on heightaveraged values (Fejer and Scherliess 1997; Scherliess andFejer 1999), despite some case studies having shown significant and important height variations at certain times(Murphy and Heelis 1986; Pingree and Fejer 1987; Kudeki
and Bhattacharyya 1999; Fejer et al. 2014)
More recently, Jicamarca ISR data sets have becomelarge enough that a successful attempt to estimate the climatological behavior of the drifts as a function of local
time and height was possible (Shidler et al. 2019). The
observations quantified the average height variations in
the drifts, including those associated with the equatorial
evening plasma vortex, for different seasons and distinct
solar flux conditions.
The vortex is the manifestation of a complex ionospheric current system around evening hours, which produces a circular pattern of the ionospheric E × B drifts inthe magnetic equatorial plane (Kudeki and Bhattacharyya
1999; Eccles et al. 1999; Rodrigues et al. 2012). A strong
height variation (vertical shear) in the zonal plasma drifts
is associated with the vortex, with strong eastward drifts
being observed at main F-region heights and westward (orweak eastward) drifts in the bottomside F-region.
Haerendel et al. (1992) showed that a two-dimensional
representation of the low-latitude electrodynamics candescribe the height-dependent features of the equatorial

Page 2 of 20

electric fields, including the shear in the zonal plasma
drifts. In fact, a simplified version of their description iscommonly used to explain the observed behavior in thezonal plasma drifts (Ui ) and their relationship with thermospheric neutral winds and the vertical component of
the plasma drifts (Eccles 1998; Chau and Woodman 2004;
Rodrigues et al. 2012; Hui and Fejer 2015; Richmond et al.
2015):Ui (h) ≈ UφP (h) −H (h)Wi (h),
P (h)(1)

where Ui represents the magnetic zonal component of theplasma drifts at apex height h. UφP is the Pedersen conductivity
weighted, field-line integrated magnetic zonal wind for amagnetic field line crossing the magnetic equatorial planeat an apex height h. Finally, H and P are the Hall andPedersen field-line integrated conductivities, respectively,
and Wi is the vertical plasma drift for apex height h.
Here we present results of a study that investigated theability of the simple analytic representation (model) of
Haerendel et al. (1992) to describe the average behavior of
the equatorial zonal plasma drifts given readily available
models of thermospheric and ionospheric parameters. We
evaluated the contributions from different drivers to theresulting morphology of the zonal drifts. We also quantified the performance of the zonal drift model for different
versions of the Horizontal Wind Model (HWM). In adata-model fusion approach, vertical drift measurements
made by the Jicamarca ISR are used to drive the modeland zonal drift measurements are used to evaluate model
performance.
This paper is organized as follows: Section 2 provides
information about the analytic model of the equatorial
zonal plasma drifts derived by Haerendel et al. (1992). It
also provides information about the climatological models and measurements of the thermosphere and ionosphere used as inputs for the analytic model of the drifts.
Section 3 presents and discusses the main results of ourinvestigation. Finally, in Section 4, we summarize ourmain findings.

2 Methods/experimental
2.1 Analytic model of the zonal plasma drifts

The overall electrodynamic behavior of the equatorial
ionosphere is often explained using a two-dimensional(2D) field-line integrated model (Haerendel et al. 1992).
In this model, the three-dimensional (3D) current continuity equation is integrated along magnetic field-lines
from the base of the ionosphere, where parallel currents
are expected to vanish, to produce a 2D current continuity
equation in the equatorial plane (Eccles et al. 2015):


∂Jφ
∂
1
(LJL ) += 0,(2)
RE L ∂L∂φShidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

where RE is the radius of the Earth, L is the radial distance in the equatorial plane measured in Earth radii, andφ is the longitude. The integrated vertical current (JL ), andthe integrated zonal current (Jφ ) are defined as (Haerendel
et al. 1992):JL = P EL + BUφP − H Eφ − BULH˜ P Eφ − BULP + H EL + BUφH ,Jφ = 

(3)(4)

where B is the magnitude of the geomagnetic field, EL is
the vertical electric field, Eφ is the zonal electric field, Pand H are the field-line integrated Pedersen conductivity
and Hall conductivity, respectively, UφP and ULP represent
the field-line averaged zonal and meridional neutral winds
weighted by the Pedersen conductivity, respectively, and
H and U H represents the field-line averaged zonal andU
L
meridional neutral winds weighted by the Hall conduc˜ P represents the field-line integrated
tivity. The tilde in 
Pedersen conductivity with slightly different geometricfactors used in integration. The field-line integrated quantities above are defined in Haerendel et al. (1992) but,for completeness, are reproduced in Appendix B. Additionally, the collision frequencies used in deriving thePedersen and Hall conductivities are given in Appendix A.
We can rearrange Eq. 3 to obtain an expression for thevertical electric field (EL ):EL = −BUφP +


JL
H 
−BULH + Eφ +
P
P

(5)

Dividing Eq. 5 by −B and substituting the F-region zonal(Ui = −EL /B) and vertical (Wi = Eφ /B) plasma drifts
results in the following expression:
Ui = UφP +H H H
JL
U −
Wi −
P L
P
BP

(6)

In this work, we use Eq. 6 as a simple analytic model
for climatological zonal plasma drifts in the equatorial
F-region ionosphere. Note that this is simply a more
complete version of Eq. 1. The thermospheric and ionospheric parameters used to compute the field-line integrated variables on the right-hand side of Eq. 6 are
obtained from widely used empirical models. Geomagnetic field values are determined from the International
Geomagnetic Field (IGRF-12) model (Thébault et al.
2015). Neutral densities and temperatures are derived
from NRL’s Mass Spectrometer and Incoherent Scatter(NRLMSISE-00) model (Picone et al. 2002). Ionosphericdensities and temperatures are derived from the International Reference Ionosphere (IRI-2016) model (Bilitza
et al. 2017). For this study, neutral winds are determined

Page 3 of 20

from three different versions of the Horizontal Wind
Model (HWM93, HWM07, and HWM14) (Hedin et al.
1996; Drob et al. 2015). Finally, we determine the climatological variation of the vertical plasma drifts (Wi ) from
Jicamarca incoherent scatter radar (ISR) observations.
Currently, there are no empirical models specifying values for the integrated vertical current (JL ). However, paststudies (e.g. Haerendel et al. 1992; Eccles et al. 2015) examined the potential impact of the last term of Eq. 6 on themorphology of the vertical shear in the zonal drifts during
evening hours. They assumed JL to be positive (upward)
and roughly constant with height having a magnitude ofa few mA/m. The fourth term then predicts westward
drifts that are negligible in the topside and stronger inthe bottomside F-region where the Pedersen conductanceis smaller. This results in an enhancement in the vertical shear of the zonal drifts. While the domain of validity
for this assumption still needs to be better investigated,
for this analysis we follow previous studies (e.g. Eccles
1998; Chau and Woodman 2004; Rodrigues et al. 2012;
Richmond et al. 2015) and neglect the JL term.
All the empirical models used in this study are containedin pyglow, an open source Python module that wraps several upper atmosphere models written in Fortran (https://github.com/timduly4/pyglow). A brief description of eachmodel is provided in the next few sections, followed by adescription of the Jicamarca ISR observations used in thisstudy.
2.2 IGRF-12

The IGRF-12 model describes the Earth’s large-scale magnetic field beginning in the year 1900 and extends to thepresent. The magnetic field (B = B(r, θ, φ, t)) is definedin terms of the magnetic scalar potential (B = −∇V ).
In IGRF-12, the magnetic scalar potential (V ) is approximated using a finite series expansion in spherical polar
coordinates. The best-fit coefficients in the series expansion are determined using measurements of the Earth’s
magnetic field made by a global collection of groundbased magnetic observatories. A list of the contributing
observatories, and a table of the series coefficients fordifferent epochs can be found in Thébault et al. (2015).
In this work, we use IGRF-12 to determine the magnitude of the magnetic field used in evaluating the gyrofrequency used in computing Pedersen and Hall conductivities. We also use the model to trace out the magnetic
field lines used in field-line integration. Finally, the spherical vector components of the magnetic field predictedby IGRF-12 are used to determine unit vectors in themagnetic zonal and meridional directions. These unit vectors are used to determine the magnetic zonal (uφ ) andmeridional (up ) neutral winds. A description of the neutral winds used in our modeling is given in the HWM
subsection.

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

2.3 NLRMSISE-00

The NRLMSISE-00 is an empirical model of the neutral
atmosphere extending from the ground to the exobase,and is an upgraded version of the MSISE-90 model(Picone et al. 2002). It is derived using a combination ofground-, rocket-, and satellite- based measurements topredict neutral temperatures and densities. The modeltakes as input: location, local time, F10.7 , and Ap. The
model outputs the temperature of the neutral atmosphere(Tn ), as well as, number densities for H, He, O, N, Ar, N2 ,and O2 .
In this work, the neutral density and temperatures areused in specifying the ion-neutral collision frequency(νin ) and electron-neutral collision frequency (νen ). See
Appendix A for additional information.
2.4 IRI-2016

The IRI-2016 empirical model is the current version of
the International Reference Ionosphere, an international
project sponsored by the Committee on Space Research(COSPAR) and the International Union of Radio Science(URSI). The model is developed using measurements ofionospheric parameters made by a worldwide networkof ionosodes, incoherent scatter radars, and instruments
on-board satellites and rockets.
In addition to location, time, and date, the modeltakes as input several geophysical indices including F10.7 ,sunspot number, the ionospheric IG index, and the magnetic Ap index. The model predicts several ionosphericparameters including electron density (ne ), electron (Te ),and ion (Ti ) temperatures, and ion number densities for
H+ , O+ , He+ , NO+ , and O+
2 . The height range for IRI2016 is between 60-2500 km for electron and ion temperatures, and between 75-2000 km for ion composition.
Different model options are available within IRI-2016.
In this work, we use the default options except for one.
We chose to turn off the storm time prediction for theF2 layer critical frequency (foF2) since we are interested
in modeling geomagnetically quiet conditions. Additional
information, links to source files, and access to an online
version of IRI-2016 can be found in http://www.irimodel.
org.
In this work, the ionospheric parameters predicted by
IRI-2016 are used to evaluate collision frequencies andthe Pedersen and Hall conductivties. See Appendix A for
additional information.
2.5 HWM93, HWM07, and HWM14

For thermospheric neutral winds we used the Horizonal Wind Model (HWM), which is an empirical model
commonly used for global specification of the upper
atmospheric general circulation patterns and migrating tides during geomagnetically quiet conditions (Drobet al. 2015). The HWM model makes predictions forPage 4 of 20

the geographic zonal (u, +eastward) and meridional (v,+northward) winds. The model was developed using alarge historic data set of the neutral wind measurements
inferred from ground-based ISRs, FPIs, and sensors for insitu measurements on rockets and satellites.
Within pyglow, the user has access to three different versions of HWM: HWM93, HWM07, and the most recent
HWM14. The primary difference between these versions
are the underlying data sets. The data set used to develop
the early HWM93 model consists of ∼ 1.2 × 106 observations from 35 different instruments spanning a total of
15 years. The data set used to develop HWM07 includes∼ 60 × 106 observations from 35 different instruments
spanning over 50 years (Drob et al. 2008). In addition to
the data set used to develop HWM07, HWM14 includes∼ 13 × 106 additional observations made between 2004
and 2014 for a total of ∼ 73 × 106 observations from 44
different instruments spanning over 60 years (Drob et al.
2015). One major difference between the models is that
HWM93 includes the solar flux condition (through theF10.7 index) as an input, while HWM07 and HWM14 donot. Additional information, including links to the FORTRAN source code for HWM, can be found in Drob et al.
(2015).
In this work, we use the geographic neutral winds of
HWM to determine the magnetic zonal (uφ ) and meridional (up ) neutral winds used to evaluate the field-line
integrated values UφP , ULP , UφH , and ULH . See Appendix B
for more information.
2.6 Climatological plasma drifts from Jicamarca

As mentioned earlier, we take a data-model fusion
approach in our analyses. We use measurements of thevertical plasma drifts made by the Jicamarca ISR to aid theimplementation of our analytic model of the zonal drifts.
Additionally, we use measurements of the zonal plasma
drifts made by the Jicamarca ISR to evaluate the accuracyof the model.
The zonal and vertical plasma drifts used in this study
were processed as part of a previous investigation (Shidler et al. 2019). In that study, the mean behavior of thezonal and vertical plasma drifts as a function of height
and local time were determined from Jicamarca measurements made between 1986 and 2017. The analyses
covered an altitude range between 200 km and 600 km fordifferent seasons and different solar flux conditions.
The measurements used in deriving the plasma drift
profiles are representative of geomagnetically quiet conditions. That is, only observations made when the Kp index
at the time and 3 previous values were equal to or less than
3 were considered.
The mean drifts were derived for three different seasons: December solstice (Jan, Feb, Nov, Dec), equinox(Mar, Apr, Sep, Oct), and June solstice (May, Jun, Jul, Aug).

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Additionally, the mean drifts were determined for two distinct solar flux conditions: low and high. The average F10.7of the plasma drift measurements in the low solar flux bin
was around 85 SFU. The average F10.7 in the high solar
flux bin was approximately 150 SFU, except during Junesolstice, where the average F10.7 was closer to 130 SFU. Of
particular importance to this study is that the mean F10.7
is the same for both zonal and vertical plasma drifts.
In their analysis, Shidler et al. (2019) found several cases
where the post-sunset plasma drift measurements were
contaminated by ESF (Fejer and Kelley 1980). Past studies have found a strong correlation with the occurrenceof ESF and the pre-reversal enhancements (PRE) of thedrifts (Huang and Hairston 2015; Smith et al. 2015; Huang2018). The PRE is commonly seen in the evening sector
during equinox and December solstice months for the longitude of Jicamarca. Therefore, measurements contaminated by ESF occurred most frequently in the post-sunset
sector during equinox, and December solstice, and highsolar flux June solstice when the PRE is well developed.
Additionally, the data set had few measurements of thezonal plasma drifts in the early morning topside ionosphere when plasma densities are low. During these times,
the number of good quality Jicamarca ISR measurements
were very limited and mean drifts were not computed.
Figure 1 shows the JRO vertical drifts used as input tothe zonal drift model. The top (bottom) row shows thevertical drifts for each season during LSF (HSF) conditions. Regions in black indicate times and heights where
drift measurements were limited in number and did not
produce reliable statistics. As mentioned above, most of
the limitation in measurements were caused by ESF coherent echoes contaminating the ISR measurements and by

Page 5 of 20

low plasma densities causing ISR echoes with low SNR.
The JRO zonal drifts will be shown along with modeled
zonal drifts in the following sections.

3 Results and discussion
Figures 2 and 3 summarize the behavior of the climatological zonal drifts estimated from Jicamarca observations
and the zonal drifts predicted by the analytic model for
low solar flux (LSF) and high solar flux (HSF) conditions,
respectively.
Results for each season are grouped in the columns foreach figure. The top row shows the climatological zonal
drifts observed by the Jicamarca ISR. The second, third,
and fourth rows show the results for the modeled zonal
drifts using HWM14, HWM07, and HWM93 as neutral
wind input drivers, respectively.
Figures 2 and 3 show the behavior of the zonal drifts
as a function of height and local time. Similarly to Fig. 1,
the regions in black indicate times and heights where
drift measurements were limited in number and did not
produce reliable statistics.
For the LSF conditions, the geophysical indices used by
the driving empirical models were F10.7 = 85 SFU and Kp =2. For HSF conditions, we used Kp = 2 and F10.7 = 150 SFU
during Equinox and December solstice, and F10.7 = 130
SFU during June solstice. Day-of-year (DOY) numbers 80,
172, and 355 were used to represent equinox, June solstice,and December solstice, respectively.
3.1 On the behavior of the observed zonal drifts

The observed zonal drifts (top panels in Figs. 2 and
3) were discussed in detail by Shidler et al. (2019).
Here, we limit ourselves to summarize some of theFig. 1 Vertical drifts estimated from the Jicamarca incoherent scatter radar measurements for different seasons (columns) and solar flux conditions(rows). These vertical drifts are used as inputs to the analytic model of the zonal drifts

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 6 of 20

Fig. 2 Local time versus height color plots for the Jicamarca climatological zonal drifts and the model zonal drifts using HWM14, HWM07, andHWM93, during LSF conditions

main features. As expected, the observations show westward (negative) drifts during the day and eastward (positive) drifts at night. The overall behavior is in very
good agreement with results obtained in previous altitude independent studies (Fejer et al. 1991; Fejer et al.

2005) using different sets of Jicamarca ISR measurements. The drifts show noticeable seasonal differences,
particularly during nighttime hours. The observations
also show that solar flux effects are weak on daytime
drifts. Nighttime drifts, however, vary significantly with

Fig. 3 Local time versus height color plots for the Jicamarca climatological zonal drifts and the model zonal drifts using HWM14, HWM07, andHWM93, during HSF conditions

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

solar activity with larger drifts being observed during HSF
conditions.
The results also show that height variations in the zonal
drifts are negligible during daytime hours. At night, however, height gradients in the zonal drifts are noticeable,
particularly in the evening sector, between about 1800 LT
and 2000 LT at bottomside F-region heights (below ∼350km). This height variation is associated with the vertical shear in the zonal plasma drifts that is part of theevening plasma vortex (Kudeki and Bhattacharyya 1999;
Rodrigues et al. 2012). The drift measurements are not as
severely affected by ESF during June Solstice and the shear
can be better identified in the observations for the period.
Nevertheless, despite data gaps, the evening height gradients in the zonal drifts can also be observed in December
solstice and Equinox. Finally, the observations in Figs. 2
and 3 also show that the evening shear in the zonal drifts
is more pronounced during HSF conditions.
3.2 On the behavior of modeled zonal drifts

We now turn our attention to the modeled zonal plasma
drifts shown in the lower three rows of panels in Figs. 2
and 3. Again, results were obtained for three different
HWM models as inputs to our analytic model.
The most striking result is that the simple analytic
model is capable of producing most of the features seen in
the observed zonal drifts. As expected, the analytic modelshows the predominant diurnal variability of the drifts,
being westward during the day and eastward at night. The
model results also show that the amplitude of the zonal
drifts is larger during nighttime compared to daytime values. Additionally, in agreement with the observations, themodeled drifts show negligible variation with height during daytime hours but significant height gradients at night,
especially in the evening sector during HSF conditions.
Nevertheless, while the overall features of the observed
drifts are reproduced by the analytic model, more detailed
analyses show quantitative differences in the model resultswith respect to the observations. These differences are
more explicit during nighttime hours when the drifts
show more variability with height. The magnitude of thesedifferences vary with the HWM model used.
In order to aid our analysis and comparison of thedrifts, Figs. 4 and 5 show height profiles of the measured and modeled drifts for LSF and HSF conditions,
respectively. The profiles also serve to show the variability of the observed drifts used in the averages, andhelp us to assess how the models compare to the measurements. The black solid lines represent the observed(average) drift profiles. The horizontal bars represent thevariability (standard deviation) of the measurements used
to compute the averages. Solid lines of red, green, andblue represent model results using HWM93, HWM07,
and HWM14, respectively.

Page 7 of 20

The profiles show that the variability of the observed
zonal drifts is larger during nighttime hours. This is, atleast in part, due to larger errors in the measured drifts
associated with ISR observations made under reducednighttime electron densities (lower SNR echoes). Considering all the observations, the median variabilities fordaytime (0600 - 1800 LT) and nighttime (1800–0600 LT)
hours were 29 m/s and 56 m/s. In some extreme cases,
however, particularly in the topside during nighttime LSF
conditions the variability exceeded 90 m/s. More importantly, the results in Figs. 4 and 5 show that the analytic
model tends to predict zonal drifts within the variabilityof the observations during most of the local times. This istrue for all the three HWM models.
Another noteworthy finding that can be better observedin the drift profiles is the convergence of all model results
to very similar drift values during daytime hours, fromabout 0800 LT to 1600 LT, for all seasons and solar flux
conditions. The convergence of our analytic model for all
the HWM drivers during daytime hours is a result of therelatively weak differences in the field-line averaged zonal
neutral winds (UφP ) between each HWM model. During
the daytime, differences between UφP for each of the different HWM wind models are typically around 5 m/s to 20
m/s, while at night the differences can exceed 80 m/s.
Finally, the results in Figs. 4 and 5 show a remarkableagreement between modeled and observed drifts during daytime, especially considering the reduced error andvariability of the drifts during that period. The accuracyof physics-based models of the equatorial plasma drifts,
including our simple model of the zonal drifts (Eq. 6),
rely heavily on predictions of the neutral winds. This isbecause the neutral wind dynamo is the primary driver
for the polarization electric fields and associated E × B
plasma drifts observed in the equatorial F-region ionosphere (Heelis et al. 1974; Eccles 1998; Eccles 2004; Heelis
2004; Maute et al. 2012). Consequently, our results serveas an independent indicator of a good representation of
the daytime neutral winds by the HWM models and of the
daytime conductivities.
An overview of the instrumentation and observations
used to derive daytime predictions of the meridional andzonal winds in HWM93 are given by Hedin et al. (1988),
Hedin et al. (1991), and Hedin et al. (1996), but sparse
spatial and temporal coverage of the data resulted in several technical challenges in constructing this model (Drobet al. 2008). Daytime model predictions of the neutral
winds in the more recent HWM07 and HWM14 versions
benefited from a large increase (∼ 55 × 106 data points)
in neutral wind observations made by two instruments on
the Upper Atmospheric Research Satellite (UARS) (Drobet al. 2008) The first instrument is the Wind Imaging
Interferometer (WINDII) which uses Doppler shifts coming from 557.7 nm O(1 S) optical emission lines to measureShidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 8 of 20

Fig. 4 Altitude profiles for the three seasons during LSF conditions. The blue, green, and red lines represent model zonal plasma drifts using
HWM14, HWM07, and HWM93, respectively. The black curves and error bars represent the average and standard deviations of the Jicamarca zonal
plasma drifts, respectively

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 9 of 20

Fig. 5 Altitude profiles for the three seasons during HSF conditions. The blue, green, and red lines represent model zonal plasma drifts using
HWM14, HWM07, and HWM93, respectively. The black curves and error bars represent the average and standard deviations of the Jicamarca zonal
plasma drifts, respectively

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

winds between 90 km to 300 km for a latitude range of±72◦ N (Shepherd et al. 1993). The second is the highresolution Doppler imager (HRDI) which is a triple-etalon
FPI that measures Doppler shifts of rotational lines of theO2 atmospheric band to measure daytime winds between
50 km to 115 km (Hays et al. 1993). Therefore, the resultsin Figs. 4 and 5 serve to confirm the reliability of theneutral wind observations made by the instruments mentioned above to predict realistic daytime zonal drifts at
Jicamarca. We quantify this assessment in the Section 3.5
by computing the RMSE for the model predictions withrespect to the observations.
Finally, we must comment on the ability of the analytic model to reproduce the vertical shears in the zonal
drifts, which are observed during evening hours. Looking
at the profiles for the evening sector (1800–2400 LT) in
Figs. 4 and 5, one can see that model predictions do not
perfectly match the observed average values but are wellwithin the variability margins in most cases. The results
also show similar drift predictions for models driven by
HWM07 and HWM14 especially during LSF conditions,which indicates similar wind predictions for these models. A noticeable departure from good model-observationagreement, however, occurs for HMW93 profiles between
1900 LT and 2200 LT during LSF conditions (all seasons),
and between 1800 LT and 2100 LT for HSF conditions(June solstice). The HWM93-driven drifts tend to overestimate the observations. This departure is most likely
caused by HWM93 overestimating the eastward zonal
neutral winds, and by extension the first term in Eq. 6,
in the F-region during these times. Monthly comparisons
between the three HWM models at 250 km (at a constantF10.7 value of 107 SFU) with FPI and satellite observationsof the zonal winds found that HWM93 overestimates thedata by more that 50 m/s just after dusk between 1800 and
2100 LT (Drob et al. 2015). A second obvious departurefrom the overall model-observation agreement occurs for
HWM14 and HWM07 profiles between 2100 LT and
2400 LT during HSF conditions (December solstice andequinox). The drifts derived using these models tend tounderestimate the observed drifts. A possible explanation
for these results is that HWM14 and HWM07 do not havea solar flux dependence in the predictions. Additional
details will be provided in the Section 3.5.
3.3 On the sources of the modeled drift morphology

The previous section showed that the analytic model iscapable of reproducing most of the features of the zonal
drifts independent of the HWM model used to drive it.
The magnitude of the modeled drifts are, in most cases,
within the variability of the observations. Disagreements
between models and observations can be found, however, and occur mostly in the evening sector, a period

Page 10 of 20

of significant changes in conductivity and in the relative
contributions from E-region and F-region dynamos.
In order to better understand the drivers of zonal drift
morphology, we now take a closer look at the contribution of the different terms in Eq. 6 and how they control
the behavior of the zonal drifts. For this analysis, we startby looking at June solstice HSF conditions when data isavailable for most local times and heights.
The top row of panels in Fig. 6 show the resulting
modeled zonal drifts for each HWM model input. The
left-hand side panels of Fig. 6 show results for HWM93,
the middle panels show results for HWM07, and the righthand side panels show results for HWM14. The other row
of panels show the contributions from the three first terms
in the right-hand side of Eq. 6. The terms are indicated on
top of each panel. Note the different scales on the colorbar for each term. We remind the reader that the analytic
model neglects the contribution of the JL /(BP ) term.
The second row (from the top) of panels in Fig. 6
show that most of the morphology of the analytic model
zonal drifts (Ui ), particularly the diurnal variation andthe post-sunset vertical shear, is heavily controlled by the
first term in Eq. 6, that is, by the winds in the magnetic zonal direction weighted by Pedersen conductivity(UφP ). This behavior was also observed by Rodrigues et al.
(2012), who performed similar term-comparison analysis
between 1700 LT to 2200 LT using TIE-GCM model run.
Eccles (1998) also provides reasons for neglecting all but
the first term (UφP ) of Eq. 6 in the development of theirsimple model of the zonal plasma drifts.
The third row of panels show that the second termof Eq. 6, associated with magnetic meridional winds,
has negligible contribution to the morphology of thezonal drifts. In the original formulation of the simple model of the zonal drifts, Haerendel et al. (1992)
neglected contributions coming from meridional winds
stating that they are small at near-equator latitudes during
the evening. Other studies also followed this formulation,and neglected meridional wind contributions (Rodrigues
et al. 2012; Richmond et al. 2015). Eccles (1998) usedthe 2D field-line integrated approach to develop a simple model of the zonal drifts to study the behavior of the
low-latitude electric field throughout the day and at different altitudes. They make the claim that ULH and Wi
have the same sign and magnitude throughout the day,and therefore, the second and third term of Eq. 6 cancel
each other.
For completeness and verification, we included the contribution from the Hall-weighted meridional winds (ULH ).
The third row of panels in Fig. 6 show that ULH and Wi ,in general, have the same sign, but ULH has a magnitudeof only a few m/s throughout the day. We find similar
behavior for all seasons and solar flux conditions.

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 11 of 20

Fig. 6 The contribution of each term of Eq. 6 to the modeled zonal drifts. June solstice high solar flux (HSF) conditions

We must point out that while meridional winds predicted by models do not seem to contribute significantly
to the morphology of the zonal drifts, additional efforts
have yet to be devoted to a better understanding of theaccuracy of the wind model predictions. For instance, therecent study of Navarro and Fejer (2019) found a generalagreement between quiet-time averages of the nighttime
northward wind observations from three FPI instrumentin Peru with HWM14 model predictions during moderate
solar flux conditions. They noted, however, that HWM14
underestimated the early night southward winds duringequinox, and significantly overestimated northward winds
in the post-midnight sector during December solstice.
Finally, the bottom row of panels show the contributions from the third term of Eq. 6, which is independentof the wind models. This term is controlled by the product between the vertical drifts and the Hall-to-Pedersen
conductivity ratio. The results show that the contribution from the third term is non-negligible during daytime
hours (up to 15 m/s) at all F-region heights. At night,
the contribution is only noticeable (up to 5 m/s) during
evening hours (1900 - 2300 LT) at bottomside F-region
heights.
H
3.3.1 On the contribution of P Wi : daytime versus
nighttime

The contribution of the third term in Eq. 6 to the morphology of the zonal drifts during daytime hours comesfrom enhanced Hall conductivities and increased Hallto-Pedersen conductivity ratios. In the evening, the ratio
is only non-negligible for a few hours after sunset andfor shorter magnetic field lines, that is, for field lines
with apex heights below the equatorial F-region peak. For
instance, during June solstice HSF conditions, the ratioof the field-line integrated Hall-to-Pedersen conductivity (H /P ) is ∼0.8 during the day and ∼0.2 at night,
except at bottomside F-region heights during evening
hours when H /P ∼ 0.6 at an apex height of 240 km.
Therefore, the contribution to the zonal drifts by thethird term in Eq. 6 during the day is on the order of the
daytime upward drifts. As a result, the third term contributes significantly to the behavior of the daytime zonal
drifts. At night, the contribution is only a fraction of themagnitude of vertical drifts, except at lower apex heights.
As a result, the evening downward drifts contribute toeastward drifts in the bottomside F-region weakening theshear in the zonal drifts.
Figure 7 now shows the results for June Solstice LSF
conditions. The results are similar to those seen for HSF
conditions, that is, the first term on the right side of
Eq. 6 controls most of the morphology of the zonal drifts.
Again, the contribution from the second term is negligible. The contribution of the third term is even more
noticeable during LSF than what it was for HSF. It reaches
up to 20 m/s during the day and 15 m/s at bottomside
F-region heights during nighttime hours.

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 12 of 20

Fig. 7 The contribution of each term of Eq. 6 to the modeled zonal drifts. June solstice low solar flux (LSF) conditions

Unlike June HSF, the enhancement in the bottomside eastward drifts observed during June LSF lasts theentire night, until about 0400 LT. Figure 1 shows that thenighttime downward drifts are weaker during June LSF
compared to June HSF, and so the enhancement in thebottomside eastward drifts predicted by the third termof Eq. 6 is driven by a strong increase in the H /P
ratio for the same region of apex heights. Figure 8 shows
the local time dependence of the Pedersen conductance(left), Hall conductance (middle), and Hall-to-Pedersen
ratio (right) for June solstice and at an apex height of
240 km. The solid and dashed lines correspond to HSF
and LSF conditions, respectively. Figure 8 shows that theHall conductance is approximately constant throughtout
the night, and decreases from ∼4.0 mho during June HSF
to ∼2.6 mho during June LSF. Therefore, the local time
behavior of the Hall-to-Pedersen ratio is controlled by
the Pedersen conductance. At 2000 LT, the Pedersen conductance for both LSF and HSF is ∼7.5 mho and theHall-to-Pedersen ratio reaches its maximum nighttime
value during HSF. However, after 2000 LT the Pedersen conductivity increases (decreases) during HSF (LSF),
and the corresponding Hall-to-Pedersen ratio decreases(increases) until the early morning. The different behavior of the Pedersen conductance during HSF comparedto LSF conditions is driven mainly by a decrease in thenighttime F-region plasma densities occurring during LSF
conditions.

H
3.3.2 On the contribution of P Wi during equinox

We now turn our attention to Equinox conditions whenthe vertical drifts are known to maximize during evening
hours as a result of the PRE (Fejer et al. 1991). The resultsfor HSF and LSF conditions are shown in Figs. 9 and 10,
respectively. The presentation of equinox results follows
the same format of Figs. 6 and 7 for June solstice conditions. Overall, they show similar relative contributions
from the three terms of Eq. 6 just discussed for June solstice. However, a couple of interesting differences can benoticed in the third term and are discussed here.
The results for equinox HSF conditions (Fig. 9), show,
despite reduced data due to ESF, that the third term in
Eq. 6 (bottom panels associated with Wi ) contributes
even more significantly to the shear in the zonal plasma
drifts, especially between 1600 and 2000 LT, than previously found for June solstice. This is a result of the large
upward drifts and enhanced H /P at bottomside Fregion heights in the evening sector seen during equinox
in the Jicamarca sector.
In addition to a direct effect on the third term of Eq. 6,
the enhanced vertical drifts also have an indirect effect on
the zonal drift model. During periods of large PRE, theF-region is expected to be lifted up to higher altitudes.
This is what is seen in the IRI-2016 predictions, and it
serves to show a good agreement between the empiricalmodels of ionospheric density and drifts. As large vertical drifts move the F-region upward, it lowers the P at

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 13 of 20

Fig. 8 Comparison of the local time dependence of the Pedersen conductance (left), Hall conductance (middle), and Hall-to-Pedersen ratio (right)
during June solstice at an apex height of 240 km. The solid (dashed) lines correspond to HSF (LSF) conditions

low apex heights and increases H /P at those heights.
As a result, westward drifts as large as 15 m/s are seen at
equatorial bottomside F-region heights around 1900 LT.
The results in Fig. 10 show that this effect is not as pronounced during Equinox LSF conditions. This is a resultof the severe reduction in the PRE peak (Fejer et al. 1991)
during conditions of low solar activity.
Another interesting feature observed in the zonal drifts
during equinox is the enhanced contribution of the vertical drift (third) term to the modeled zonal drifts inthe pre-sunrise sector during LSF conditions (Fig. 10).

The bottom panels of Fig. 10 show an enhancement in
the eastward drifts around 0330 LT, particularly at lower
apex heights when eastward drifts can be as large as∼20 m/s. Similar to our previous analysis (see Fig. 8),
an enhancement can be seen in the H /P ratio duringequinox around this time, but that ratio is ∼1.25 compared with ∼1.75 during June solstice. This is mainly due
to the empirical models predicting larger pre-sunrise Fregion Pedersen conductivities during equinox comparedwith June solstice. However, Fig. 1 shows that the presunrise downward vertical drifts are larger during equinox

Fig. 9 The contribution of each term of Eq. 6 to the modeled zonal drifts. Equinox high solar flux (HSF) conditions

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 14 of 20

Fig. 10 The contribution of each term of Eq. 6 to the modeled zonal drifts. Equinox low solar flux (LSF) conditions(∼16 m/s) compared to June solstice (∼8 m/s) during LSF
conditions.
3.4 Contributions from E and F regions to UφP

We already pointed out that a significant portion of
the zonal drift morphology comes from the zonal winddynamo term (UφP ) of Eq. 6. Here, we examine the contributions from the E and F regions to the dynamo as
predicted by the empirical models for the Jicamarca location. Figures 11 and 12 show the results of our estimatesfor LSF and HSF conditions, respectively. The top panels in each figure show the total zonal wind dynamo (UφP
) contribution to the zonal drift model. For this analysis,
we only used results driven by the HWM14 model. Eachcolumn represents a season. The middle panels represent
the contribution from the F-region (UφPF ), that is, frompoints along the magnetic field lines that are above 150
km altitude. The bottom panels, on the other hand, represent the contribution from the E-region (UφPE ), that is,from points along the magnetic field lines that are below
150 km altitude. Note the different scales in the colorbars.
The results show that the F-region controls most of thezonal wind dynamo term during nighttime LSF and HSF
conditions for equatorial altitudes above 240 km. This
is in good agreement with previous observational resultsthat indicated strong neutral-plasma coupling at F-region
heights during nighttime. For instance, several studies
have shown good agreement between zonal plasma drifts
measured by ISRs and zonal neutral winds measured by

FPIs (Biondi et al. 1988; Fejer 1993; Chapagain et al.
2013; Navarro and Fejer 2019; Navarro and Fejer 2020)
or by sensors on satellites (Fejer et al. 1985). Furthermore, our results are in good agreement with studies thatshowed that low-latitude plasma drifts and their coupling
to neutral winds is controlled not only by local parameters
but by the distribution of winds and conductivities along
magnetic field lines (Coley et al. 1994).
The E-region contribution to equatorial F-region zonal
drifts above 240 km altitude is noticeable and must be
considered during daytime hours. This is particularly true
for LSF conditions as shown in Fig. 11. We found that theE-region dynamo contribution to daytime F-region zonal
drifts decreases with solar flux as indicated by the resultspresented in the bottom panels of Figs. 11 (LSF) and 12(HSF). Our results also show that the absolute E-region
contribution to daytime zonal drifts is minimum during
June solstice, increases during equinox and maximizes
during December solstice.
We also found that our model only shows a significant
contribution of the E-region to the nighttime zonal drifts
during December solstice between about 0000 and 0600
LT. This contribution has magnitudes reaching up to 20
m/s near sunrise during LSF. In fact, the E-region contribution is comparable to the F-region contribution at thattime. Our analysis showed that during this time, HWM14
predicts strong westward winds (up to 65 m/s) at points
near the E-region conductivity peaks, especially south ofthe magnetic equator. These points make a significant

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 15 of 20

Fig. 11 The contributions from the E and F regions to the zonal wind dynamo during low solar flux (LSF) conditions. HWM14 was used to drive thezonal drift model

contribution to the westward zonal drifts predicted by theE-region dynamo field-line integral (UφPE ). For those same
field line points, HWM14 predicts weaker westward oreven eastward winds during equinox and June solstice.
Finally, our results show that the empirical models do
not predict any significant contribution from the E-region
to the vertical shear in the evening zonal drifts for the altitude range covered by our observations, that is, between
240 and 560 km at the magnetic equator. Using results ofa self-consistent numerical model (TIE-GCM), however,Rodrigues et al. (2012) found that the E-region can contribute to the shear. Their analyses, however, extended toaltitudes as low as 200 km and their results show significant E-region contributions below about 250 km at 2000
LT during solar flux conditions representing an F10.7 = 220
SFU.
3.5 On model performance

In this section we take a more quantitative look at how
the analytic model, driven by different versions of HWM,
compares to observations.
In order to make a quantitative assessment we usedtwo metrics, the root-mean-square error - RMSE (σ =2=i wi (yi − ŷi ) / i wi ) and the model bias (μ
w
(y
−
ŷ
)/
w
).
Here,
y
represents
anobserved
i
i
i i i
i i
zonal drift value, ŷi , represents a modeled zonal drift
value, and wi is the weight and is given by the inverse of
the standard deviation for measurements used to derive

the average zonal drifts. These metrics were computed foreach season and solar flux condition.
Table 1 shows our results of the RMSE and model
biases for the full day (0000–2400 LT), daytime hours(0600 - 1800 LT), and nighttime hours (1800–0600 LT).
The best performing model, using the RMSE as a metric, is underlined. The most important result in Table 1
is that a single HWM model cannot produce the best
results (lowest RMSE values) for all the seasons andsolar flux conditions. Table 1 also shows that all of
the models perform with reduced errors during daytime compared to nighttime. There are a few cases,
such as HWM07 results for June Solstice and HWM93
results for LSF December Solstice, which show similar performance for nighttime and daytime conditions.
This quantitative assessment of the model performance
confirms our inference about the accuracy of the daytime neutral winds predicted by the HWM models aswell as the empirical model estimates of the ionosphericconductivities.
Additionally, Table 1 shows that the performance of themodel driven by different HWM varies with solar flux
conditions. At LSF conditions, the best performances (fullday RMSE) are shared between model runs driven by
HWM07 and HWM14. At HSF conditions, however, themodel runs driven by HWM93 outperform the other twomodel runs, except for June solstice where HWM14 is thebest performing model.

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

Page 16 of 20

Fig. 12 The contributions from the E and F regions to the zonal wind dynamo during high solar flux (HSF) conditions. HWM14 was used to drive thezonal drift model

Table 1 The weighted root-mean-square error (σ ) and weighted model bias (μ), where the weight is given by the inverse of thestandard deviation of the climatological zonal drifts, for each model during different season and solar flux conditions
LSF

Full Day

DaytimeNighttime

HSF

Dec. Sol.

EquinoxJun. Sol.

Dec. Sol.

EquinoxJun. Sol.

σ93

20.75

25.39

29.67

17.79

18.17

23.74

σ07

13.59

16.34

18.44

23.23

32.24

20.66
16.07

σ14

12.95

17.30

13.80

27.74

30.49

μ93

1.60

− 2.10

-4.94

4.29

− 1.23− 7.12

μ07

4.25

11.36

2.69

14.97

23.31

1.73

μ14

8.38

6.70

2.49

22.91

20.83

5.57

σ93

19.24

14.73

17.55

18.18

15.08

13.84

σ07

8.01

12.68

19.32

11.24

17.73

22.54

σ14

11.51

9.93

12.91

17.92

14.71

16.28

μ93

6.09

5.91

7.21

4.88

1.73

3.69

μ07

3.48

9.82

2.00

7.69

12.55

− 3.88

μ14

9.13

6.73

4.74

15.44

9.13

3.94

σ93

24.59

39.88

48.82

16.99

22.88

35.55

σ07

23.07

22.41

15.88

36.71

49.02

16.55

σ14

16.40

27.25

15.89

40.55

47.64

15.66

μ93

− 11.34− 19.78− 36.86

3.15− 6.79− 27.47

μ07

6.47

14.75

4.51

29.18

43.54

12.28

μ14

6.20

6.65

− 3.42

37.50

42.83

8.65

We provide statistics for the full day, daytime (0600–1800 LT), and nighttime (1800–0600 LT). The model with the best RMSE is underlined

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

These results can be explained, to a large extent, by thefact that the majority of the observations used to develop
HWM14 were made during periods of moderate-to-low
solar activity (average F10.7 of 107 SFU) (Drob et al. 2015).
The better performance of HWM93 during December
solstice and equinox HSF conditions can be attributed toa reduced number of HSF observations used to develop
HWM07 and HMW14 and to the solar flux parameterization used by Drob et al. (2008) and Drob et al. (2015). The
best peformance by HMW14 during June solstice HSF
can be explained by the reduced number of Jicamarca ISR
observations for high solar activity during June solstice(see the Section 2.6). The observations for June HSF hada mean F10.7 of 130 SFU instead of 150 SFU for equinox
and December solstice. Therefore, the June HSF observations used to evaluate the model better reflect moderate
solar flux conditions, which are expected to be better
represented by HWM14 than HWM93.
We now take a look at the model biases (μ) provided in Table 1. This metric serves to evaluate whether
the model zonal drifts overestimate/underestimate theobserved average zonal drifts. Focusing on nighttime,
when model predictions and average zonal drifts are eastward (positive), we find that for most seasons and solar
flux conditions, HWM93 tends to overestimate the average zonal drifts, while both HWM14 and HWM07 tend tounderestimate the average zonal drifts. Given the importance of the nighttime F-region wind dynamo to the morphology of the drifts it is worth mentioning that Navarro
and Fejer (2019) also found that HWM14 tends to underestimate the quiet-time zonal winds in the pre-midnight
sector during moderate solar flux conditions. During daytime, when model predictions and average zonal drifts are
westward (negative), all three models tend to overestimate
the average zonal drifts. However, for a given season andsolar flux condition, model biases during daytime hours
have comparable values further indicating that all three
HWM models tend to converge during day.

4 Conclusions
Currently, a climatological model of the equatorial ionospheric zonal E×B drifts as a function of both local timeand height has yet to be developed. While height variations are known to occur especially in the evening sector(Kudeki and Bhattacharyya 1999; Rodrigues et al. 2012;
Richmond et al. 2015; Shidler et al. 2019), the lack of adequate ground-based radar observations forced previous
studies to focus on height-averaged zonal drifts (Fejer et al.
1991; Fejer et al. 2005).
Here, we present results of a new effort that examined
the ability of widely available models of thermosphericand ionospheric parameters to reproduce the observed
morphology of the quiet-time zonal drifts for different
seasons and distinct solar flux conditions. We focused, inPage 17 of 20

particular, on an analytic representation (Haerendel et al.
1992) of the low-latitude electrodynamics that is commonly used to explain the observed behavior of the zonal
plasma drifts (Eccles 1998; Chau and Woodman 2004;
Rodrigues et al. 2012; Richmond et al. 2015).
We also focused on widely used empirical models of
the thermospheric and ionospheric parameters to drive
the analytic model. Noteworthy mentioning is that thesemodels are part of the Pyglow python package that is readily available and commonly used by the geospace community. Pyglow includes the IGRF-12, IRI-2016, NRLMSISE00, and three versions of the HWM (93, 07, and 14).
Finally, advances made in the ISR drift measurements
at the Jicamarca Radio Observatory and long-term semiroutine operations (1986–2017) allowed observations ofboth vertical and zonal plasma drifts as a function of timeand main F-region heights (240-560 km). While observations of the vertical drift were used to drive the analytic
model, zonal drift observations were used to evaluate its
performance for different seasons and distinct solar flux
conditions. We were also able to evaluate the performanceof the analytic representation for different wind model
inputs.
Despite its simplicity, the analytic model can reproduce fairly well most of the features in the observed zonal
plasma drifts, including the vertical shear of the zonal
drifts associated with the evening plasma vortex.
During daytime hours the analytic model predicts similar results for the zonal drifts independently of the HWM
used to drive the model. More importantly, the modeled drifts match well the behavior and magnitude of
the observed daytime drifts for all seasons and solar flux
conditions considered. This result indicates a good representation of the daytime neutral winds by the HWM
models as well as a good representation of the low-latitude
E- and F-region conductivities during the day.
During nighttime hours the analytic model results fordifferent HWM inputs diverge, especially HWM07 andHWM14 from HWM93. Most of the results, however, arewithin the variability of the observations used to evaluate
the models.
The nighttime results drive the overall performance of
the analytic model, and we found that a single HWM cannot provide the best results for all seasons and solar flux
conditions. The performance of the model outputs arequantified using a RMSE metric. HWM07 and HWM14
inputs tend to provide better results for LSF conditions,while HWM93 tend to perform better during HSF. These
results can be explained, in most part, by a predominanceof moderate-to-low solar flux observations used to create
HWM07 and HWM14, and a solar flux parameterization implemented only in HWM93. The results indicate
the necessity of additional work on modeling and validating the behavior of the nighttime winds and ionosphericShidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

conductivities. Additionally, following previous studies weneglected the contribution of the vertical current term(fourth term). This assumption has yet to be properly
tested and requires the use of more complete ionosphericelectric field model.
We also examined the main sources of zonal drift variability according to the analytic model (Eq. 6). Most of themorphology is controlled by the zonal wind dynamo term
(first term). The contribution from meridional winds (second term) is negligible. Finally, the contribution from thevertical drifts (third term) cannot be neglected. This term
makes a contribution to the daytime westward drifts on
the order of the vertical drifts. It also contributes to themorphology of the zonal drifts in the bottomside F-region
in the evening. The enhanced conductivity ratio at thoseheights acts as to weaken the shear in the zonal drifts.
We also examined the contribution from the E- andF-region to the zonal wind dynamo as predicted by the
analytic model. The morphology of the zonal drifts in theregion of observation (240–560 km altitude) is controlled
in most part by the F-region winds. However, our results
show that the E-region contribution is non-negligible during daytime hours, specially during December solstice.
Also during December solstice, the E-region contribution
to the F-region drifts is significant near sunset speciallyduring LSF.
Finally, we would like to mention that the current work
focused on evaluating the ability of current, readily available models of the thermosphere, ionosphere and electrodynamics to reproduce the observed zonal drifts. Givencurrent limitations in the number of observations, we
focused on evaluating the performance of the model for
only two distinct solar flux conditions and specific DOYs
representing each season. The encouraging results led to
us to envision expanding the simple representation of thezonal drifts described here to cover other longitude sectors, and to accept DOY and a more complete range ofsolar flux conditions as inputs. The best approach andsupporting data sets for such an effort are currently being
investigated.

Table 2 The collision frequnecy coefficients Cin × 1010 for
nonresonant ion-neutral interactions
Ion

H

He

N

O

N2

O2

H+

R

10.6

26.1

R

33.6

32.0

O+

R

1.32

4.62

4.01

6.85

6.66

NO+

0.69

0.74

2.79

2.45

4.36

4.28

O+
2

0.65

0.70

2.64

2.32

4.15

4.08

The collision frequency coefficients are given in Table 2.
Coefficients marked R represent resonant collisions.
The temperature dependent resonant collisions are
given by:
νH+ ,H = 2.65 × 10−10 n(H)Tr1/2(1 − 0.083 log10 Tr )2(Tr > 50 K)(8a)1/2
νH+ ,O = 6.61 × 10 n(O)Ti(1 − 0.047 log10 Ti )2 (Tr > 300 K)(8b)−12
νO+ ,H = 4.63 × 10 n(H)(8c)(Tn + Ti /16)1/2 (Tr > 300 K)

−11
1/2
νO+ ,O = max 3.68×10 n(O)Tr (1−0.065 log10 Tr )2 ,

−10
−11

(8d)
4.01 × 10 n(O)

−11
1/2
νO+ ,O2 = max 2.62×10 n(O2 )Tr (1−0.074 log10 Tr )2 ,2
(8e)
4.08 × 10−10 n(O2 ) ,where Tr = (Ti + Tn )/2. Note that the definitions forthe νO+,O and νO2 +,O2 resonant collision frequencies weretaken from Ieda (2020). The final ion collision frequencies
are then given by:
νH+ = νH+ ,H +νH+ ,He + νH+ ,O + νH+ ,N + νH+ ,N2 + νH+ ,O2(9a)νO+ = νO+ ,H +νO+ ,He + νO+ ,O + νO+ ,N + νO+ ,N2 + νO+ ,O2(9b)
νNO+ = νNO+ ,H +νNO+ ,He + νNO+ ,O + νNO+ ,N + νNO+ ,N2+ νNO+ ,O2

5 Appendix A: Collision frequency andconductivity(9c)νO+ = νO+ ,H +νO+ ,He + νO+ ,O + νO+ ,N + νO+ ,N2 + νO+ ,O2
2

Collision frequencies were taken from Schunk and Nagy
(2009). A recent study by Ieda (2020) provided updated
coefficients for O+ , NO+ , and O+
2 collision frequencies.
We have included the temperature-dependent resonant
collisions in our calculations. The temperature independent ion-neutral collision frequencies are given in theformνin = Cin nn ,Page 18 of 20(7)

where Cin is the collision frequency coefficient for nonreasonant interactions, and the nn are the densities in cm−3 .

2

2

2

2

2

2

(9d)
The electron-neutral collision frequency is given by:νe = 2.33 × 10−11 n(N2 ) 1 − 1.21 × 10−4 Te Te


1/2
1/2
Te
+ 1.82 × 10−10 n(O2 ) 1 + 3.6 × 10−2 Te
1/2+ 8.90 × 10−11 n(O) 1 + 5.7 × 10−4 Te Te+ 4.60 × 10−10 n(He)Te



1/2
,
+ 4.50 × 10−9 n(H) 1 − 1.35 × 10−4 Te Te
1/2

(10)

(2021) 8:26

Shidler and Rodrigues Progress in Earth and Planetary Science

where neutral densities are in cm−3 , and Te is the electron
temperature in Kelvin.
The Pedersen (σP ) and Hall (σH ) conductivities for ionsand electrons are defined asσP =ne e κe+
B 1 + κe2

ne e κe2σH =−B 1 + κe2ini e κi
B 1 + κi2ini e κi2,
B 1 + κi2

(11a)
(11b)

where the summation is over all present ion species, e isthe electric charge, B is the magnitude of the magnetic
field, and ne and ni are the electron and ion densities in
m−3 . The kappa term for species α is the ration of the).
gyro-to-collision frequency (κα = ωναα = meBα να

6 Appendix B: Field-line integration
The definitions for field line integrals used in our model
come from Haerendel et al. (1992)
P = RE L
˜ P = RE L
H = RE L
UφP =

RE L
P

ULP =

RE L
˜P


RE L
UφH =
H
ULH =

RE L
H

λN
λS
λN
λS
λN
λS
λN
λS
λN
λS
λN
λS
λN
λS

Page 19 of 20

Authors’ information
Affiliations
The William B. Hanson Center for Space Sciences, University of Texas
at Dallas, Richardson, Texas, USA
Sam Shidler
The William B. Hanson Center for Space Sciences, University of Texas
at Dallas, Richardson, Texas, USA
Fabiano Rodrigues
Authors’ contributions
SS analyzed the data, produced the graphs, and made contributions to theinterpretation of results and writing of this manuscript. FR provided directions
for this study, interpreted results, and contributed to the writing of thismanuscript.
FundingWork at UT Dallas was supported by the NSF (AGS-1554926) and NASA
(80NSSC18K1203). The Jicamarca Radio Observatory is a facility of the Instituto
Geofisico del Peru operated with support from the NSF (AGS-1433968)
through Cornell University.
Availability of data and materials
The JRO plasma drift observations are publicly available on the Madrigal
Database, [http://jro.igp.gob.pe/madrigal/]. Additionally, a copy of all the data
used in this study is available for download at 10.5281/zenodo.4584097.

Declarations
σP (1 + 3 sin2 λ) cos λdλ(12a)

σP cos λdλ(12b)

σH (1 + 3 sin2 λ)1/2 cos λdλ

(12c)

σP uφ

(1 + 3 sin2 λ)cos λdλ(1 − sin2 λ)3/2

σP up(1 + 3 sin2 λ)1/2
cos λdλ (12e)(1 − sin2 λ)3/2

(12d)

σH uφ

(1 + 3 sin2 λ)1/2
cos λdλ (12f)(1 − sin2 λ)3/2

σH up(1 + 3 sin2 λ)cos λdλ,(1 − sin2 λ)3/2(12g)

where λ is the magnetic latitude, λS and λN are themagnetic latitudes at the base of the ionosphere in themagnetic south and magnetic north, σP and σH are thePedersen and Hall conductivity, respectively, and uφ andup are the magnetic zonal and meridional neutral winds,
respectively.
Abbreviations
LSF: Low solar flux conditions; HSF: High solar flux conditions; ESF: Equatorial
spread-F; ISR: Incoherent scatter radar; JRO: Jicamarca Radio Observatory;
RMSE: Root mean square error; IRI: International reference ionosphere;
NRLMSIS: Naval research lab mass spectrometer and incoherent scatter radar;
IGRF: International Geomagnetic Reference Field; HWM: Horizontal windmodel; LT: Local time; FPI: Fabry-Pérot interferometer; DOY: Doy-of-year
Acknowledgements
The authors would like to thank Dr. Douglas Drob (Naval Research Lab) for
helpful comments on this study.

Competing interests
The authors declare that they have no competing interest.
Received: 6 October 2020 Accepted: 9 March 2021

References
Abdu MA, de Medeiros RT, Bittencourt JA, Batista IS (1983) Vertical ionization
drift velocities and range type spread F in the evening equatorial
ionosphere. J Geophys Res 88(A1):399–402. https://doi.org/10.1029/
JA088iA01p00399
Aveiro HC, Hysell DL (2010) Three-dimensional numerical simulation ofequatorial F region plasma irregularities with bottomside shear flow. J
Geophys Res 115(A11321). https://doi.org/10.1029/2010JA015602
Bilitza D, Altadill D, Truhlik V, Shubin V, Galkin I, Reinisch B, Huang X (2017)
International Reference Ionosphere 2016: From ionospheric climate toreal-time weather predictions. Space Weather 15:418–429. https://doi.org/
10.1002/2016SW001593
Biondi MA, Meriwether JW, Fejer BG, Woodman R (1988) Measurements of the
dynamics and coupling of the equatorial thermosphere and the F-region
ionosphere in Peru. J Atmo and Solar-Terr Phys 50:937–942. https://doi.
org/10.1016/0021-9169(88)90081-5
Chapagain NP, Daniel FJ, Meriwether JW, Chau JL, Makela JJ (2013) Comparisonof zonal neutral winds with equatorial plasma and plasma drift velocities. J
Geophys Res 118:1802–1812. https://doi.org/10.1002/jgra.50238
Chau JL, Woodman RF (2004) Daytime vertical and zonal velocities from150-km echoes: Their relevance to F-region dynamics. Geophys Res Lett
31:17801. https://doi.org/10.1029/2004GL020800
Coley WR, Heelis RA, Spencer NW (1994) Comparison of low-latitude ion andneutral zonal drifts using DE 2 data. J Geophys Res 99(A1):341–348. https://doi.org/10.1029/93JA02205
David M, Sojka JJ, Schunk RW (2016) How uncertainty in the neutral wind limits
the accuracy of ionospheric modeling and forecasting. J Geophys Res
121:519–528. https://doi.org/10.1002/2015JA021544
Drob DP, Emmert JT, Crowley G, Pincone JM, Shepherd GG, Skinner W, Hays P,
J NR, Larsen M, She CY, Meriwether JW, Hernandez G, Jarvis MJ, Sipler DP,
Tepley CA, O’Briend MS, Bowman JR, Wu Q, Murayama Y, Kawamura S, Reid
IM, Vincent RA (2008) An empirical model of the Earth’s horizontal windfields: HWM07. J Geophys Res 133(A12304). https://doi.org/10.1029/
2008JA013668
Drob DP, Emmert JT, Meriwether JW, Makela JJ, Doornbos E, Conde M,
Hernandez G, Noto J, Zawdle KA, McDonald SE, Huba JD, Klenzing JH

Shidler and Rodrigues Progress in Earth and Planetary Science(2021) 8:26

(2015) An update to the Horizontal Wind Model (HWM): The quiet time
thermosphere: Empirical model of thermospheric winds. Earth Space Sci
2(7):301–319. https://doi.org/10.1002/2014EA000089
Eccles JV (1998) A simple model of low-latitude electric fields. J Geophys Res
103(A11):26699–26708. https://doi.org/10.1029/98JA02657
Eccles JV (2004) The effect of gravity and pressure in the electrodynamics ofthe low-latitude ionosphere. J Geophys Res 109(A05304). https://doi.org/
10.1029/2003JA010023
Eccles JV, Maynard N, Wilson G (1999) Study of the evening plasma drift vortex
in the low-latitude ionosphere using San Marco electric fieldmeasurements. J Geophys Res 104(A12):28133–28143. https://doi.org/10.
1029/1999JA900373
Eccles JV, St. Maurice JP, Schunk RW (2015) Mechanisms underlying theprereversal enhancement of the vertical plasma drift in the low-latitude
ionosphere. J Geophys Res 120(6):4950–4970. https://doi.org/10.1002/
2014/JA020664
Fejer BG (1993) F region plasma drifts over Arecibo: Solar cycle, seasonal, andmagnetic activity effects. J Geophys Res 98(A8):13635–13652. https://doi.
org/10.1029/93JA00953
Fejer BG, de Paula ER, Gonzalez SA, Woodman RF (1991) Average vertical andzonal F region plasma drifts over Jicamarca. J Geophys Res
96(A8):13901–13906. https://doi.org/10.1029/91JA01171
Fejer BG, Hui D, Chau JL, Kudeki E (2014) Altitudinal dependence of evening
equatorial F region vertical plasma drifts. J Geophys Res 119(7):5877–5890.
https://doi.org/10.1002/2014JA019949
Fejer BG, Kelley MC (1980) Ionospheric irregularities. Rev Geophys
18(2):401–454. https://doi.org/10.1029/RG018i002p00401
Fejer BG, Kudeki E, Farley DT (1985) Equatorial F region zonal plasma drifts. J
Geophys Res 90(A12):12249–12255. https://doi.org/10.1029/
JA090iA12p12249
Fejer BG, Santos AS, Costa Pereira AE (2005) Climatology of F region zonal
plasma drifts over Jicamarca. J Geophys Res 110(A12310). https://doi.org/
10.1029/2005JA011324
Fejer BG, Scherliess L (1997) Empirical models of storm time equatorial zonal
electric fields. J Geophys Res 102(A11):24047–24056. https://doi.org/10.
1029/97JA02164
Fejer BG, Scherliess L, de Paula ER (1999) Effects of the vertical plasma drift
velocity on the generation and evolution of equatorial spread F. J Geophys
Res 104(A9):19859–19869. https://doi.org/10.1029/1999JA900271
Haerendel G, Eccles JV, Çakir S (1992) Theory for modeling the equatorial
evening ionosphere and the origin of the shear in the horizontal plasma
flow. J Geophys Res 97(A2):1209–1223. https://doi.org/10.1029/91JA02226
Hays PG, Abreu VJ, Dobbs ME, Gell DA, Grassl HJ, Skinner WR (1993) The highresolution doppler imager on the Upper Atmosphere Research Satellite. J
Geophys Res 98(D6):10713–10723. https://doi.org/10.1029/93JD00409
Hedin AE, Biondi MA, Burnside RG, Hernandez G, Johnson RM, Killeen TL,
Mazaudier C, Meriwether JW, Salah JE, Sica RJ, Smith RW, Spencer NW,
Wickwar VB, Virdi TS (1991) Revised global model of thermosphere winds
using satellite and ground-based observations. J Geophys Res
96(A5):7657–7688. https://doi.org/10.1029/91JA00251
Hedin AE, Fleming EL, Manson AH, Schmidlin FJ, Avery SK, Clark RR, Franke SJ,
Fraser GJ, Tsuda T, Vial F, Vincent RA (1996) Empirical wind model for theupper, middle and lower atmosphere. J Atmo and Solar-Terr Phys
58(13):1421–1447. https://doi.org/10.1016/0021-9169(95)00122-0
Hedin AE, Spencer NW, Killeen TL (1988) Empirical global model of upper
thermosphere winds based on atmosphere and dynamics explorer
satellite data. J Geophys Res 93(A9):9959–9978. https://doi.org/10.1029/
JA093iA09p09959
Heelis RA (2004) Electrodynamics in the low and middle latitude ionosphere: atutorial. J Atmo and Solar-Terr Phys 66:825–838. https://doi.org/10.1016/j.
jastp.2004.01.034
Heelis RA, Kendall PC, Moffett RJ, Windle DW (1974) Electrical coupling of theE- and F-regions and it’s effect on the F-region drifts and winds. Planet
Space Sci 22:743–756. https://doi.org/10.1016/0032-0633(74)90144-5
Huang C (2018) Effects of the postsunset vertical plasma drift on thegeneration of equatorial spread F. Prog Earth Planet Sci 5(3). https://doi.
org/10.1186/s40645-017-0155-4
Huang C, Hairston MR (2015) The postsunset vertical plasma drift and its
effects on the generation of equatorial plasma bubbles observed by the
C/NOFS satellite. J Geophys Res 120(3):2263–2275. https://doi.org/10.
1002/2014JA020735

Page 20 of 20

Hui D, Fejer BG (2015) Daytime plasma drifts in the equatorial lower ionosphere.
J Geophys Res 120(11):9738–9747. https://doi.org/10.1002/2015JA021838
Hysell DL, Kudeki E (2004) Collisional shear instability in the equatorial F region
ionosphere. J Geophys Res 109(A11301). https://doi.org/10.1029/
2004JA010636
Ieda A (2020) Ion-neutral collision frequencies for calculating ionosphericconductivity. J Geophys Res 125(e2019JA027128). https://doi.org/10.1029/
2019JA027128
Kelley MC, Retterer J (2008) First successful prediction of a convective
equatorial ionospheric storm using solar wind parameters. Space Weather
6(S08003):28163–28170. https://doi.org/10.1029/2007SW000381
Kudeki E, Akgiray A, Milla M, Chau JL, Hysell DL (2007) Equatorial spread-F
initiation: Post-sunset vortex, thermospheric winds, gravity waves. J Atmos
Solar-Terr Phys 69:2416–2427
Kudeki E, Bhattacharyya S (1999) Postsunset vortex in equatorial F-region
plasma drifts and implications for bottomside spread-F. J Geophys Res
104(A12):28163–28170. https://doi.org/10.1029/1998JA900111
Maute A, Richmond AD, Roble RG (2012) Sources of low-latitude ionospheric
ExB drifts and their variability. J Geophys Res 117(A06312). https://doi.org/
10.1029/2011JA017502
Murphy JA, Heelis RA (1986) Implications of the relationship between
electromagnetic drift components at mid and low latitudes. Planet SpaceSci 34(7):645–652. https://doi.org/10.1016/0032-0633(86)90042-5
Navarro LA, Fejer BG (2019) Storm-time thermospheric winds over Peru. J
Geophys Res 124(12):10415–10427. https://doi.org/10.1029/2019JA027256
Navarro LA, Fejer BG (2020) Storm-time coupling of equatorial nighttime F
region neutral winds and plasma drifts. J Geophys Res
125(e2020JA028253). https://doi.org/10.1029/2020JA028253
Picone JM, Hedin AE, Drob DP, Aikin AC (2002) NRLMSISE-00 empirical modelof the atmosphere: Statistical comparisons and scientific issues. J Geophys
Res 107(A12):SIA151–SIA1516. https://doi.org/10.1029/2002JA009430
Pingree JE, Fejer BG (1987) On the height variation of equatorial F region
vertical plasma drifts. J Geophys Res 92(A5):4763–4766. https://doi.org/10.
1029/JA092iA05p04763
Richmond AD, Fang TW, Maute A (2015) Electrodynamics of the equatorial
evening ionosphere: 1. importance of winds in different regions. J
Geophys Res 120(3):2118–2132. https://doi.org/10.1002/2014JA020934
Rodrigues FS, Crowley G, Heelis RA, Maute A, Reynolds A (2012) On tie-gcm
simulation of the evening equatorial plasma vortex. J Geophys Res
117(A05307). https://doi.org/10.1029/2011JA017369
Scherliess L, Fejer BG (1999) Radar and satellite global equatorial F region
vertical drift model. J Geophys Res 104(A4):6829–6842. https://doi.org/10.
1029/1999JA900025
Schunk RW, Nagy AF (2009) Ionospheres: Physics, Plasma Physics, andChemistry. Cambridge University Press, Cambridge
Shepherd GG, Thuillier G, Gault WA, Solheim BH, Hersom C, Alunni JM, Brun
J-F, Brune S, Charlot P, Cogger LL, Desaulniers D-L, Evans WFJ, Gattinger RL,
Girod F, Harvie D, Hum RH, Wendall DJW, LLewellyn EJ, Lowe RP, Ohrt J,
Pasternak F, Peillet O, Powell I, Rochon Y, Ward WE, Wiens RH, Wimperis J(1993) Windii, the wind imaging interferometer for the upper atmosphereresearch satellite. J Geophys Res 98(D6):10725–10750. https://doi.org/10.
1029/93JD00227
Shidler SA, Rodrigues FS, Fejer BG, Milla MA (2019) Radar studies ofheight-dependent equatorial F-region vertical and zonal plasma drifts. J
Geophys Res 124(3):2058–2071. https://doi.org/10.1029/2019JA026476
Smith JM, Rodrigues FS, de Paula ER (2015) Radar and satellite investigations ofequatorial evening vertical drifts and spread F. Ann Geophys
33(11):1403–1412. https://doi.org/10.5194/angeo-33-1403-2015
Sultan PJ (1996) Linear theory and modeling of the Rayleigh-Taylor instability
leading to the occurrence of equatorial spread F. J Geophys Res
101(A12):26875–26891. https://doi.org/10.1029/96JA00682
Thébault E, Finlay CC, Beggan CD, Alken P, Aubert J, Barrois O, Bertrand F,
Bondar T, Boness A, Brocco L, Canet E, Chambodut A, Chulliat A, Coisson P,
Civet F, Du A, Fournier A, Fratter I, Gillet N, et al (2015) International
geomagnetic reference field: the 12th generation. Earth Planet Space
67(79). https://doi.org/10.1186/s40623-015-0228-9

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.