Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7
https://doi.org/10.1186/s40645-021-00462-3

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open AccessAn electrodynamics model for Data
Interpretation and Numerical Analysis
of ionospheric Missions and Observations(DINAMO)
Samuel A. Shidler1,2*

and Fabiano S. Rodrigues1

Abstract
We introduce a new numerical model developed to assist with Data Interpretation and Numerical Analysis of ionospheric Missions and Observations (DINAMO). DINAMO derives the ionospheric electrostatic potential at low- andmid-latitudes from a two-dimensional dynamo equation and user-specified inputs for the state of the ionosphere andthermosphere (I–T) system. The potential is used to specify the electric fields and associated F-region E × B plasma
drifts. Most of the model was written in Python to facilitate the setup of numerical experiments and to engage students in numerical modeling applied to space sciences. Here, we illustrate applications and results of DINAMO in two
different analyses. First, DINAMO is used to assess the ability of widely used I–T climatological models (IRI-2016, NRLMSISE-00, and HWM14), when used as drivers, to produce a realistic representation of the low-latitude electrodynamics.
In order to evaluate the results, model E × B drifts are compared with observed climatology of the drifts derived fromlong-term observations made by the Jicamarca incoherent scatter radar. We found that the climatological I–T models
are able to drive many of the features of the plasma drifts including the diurnal, seasonal, altitudinal and solar cycle
variability. We also identified discrepancies between modeled and observed drifts under certain conditions. This is,in particular, the case of vertical equatorial plasma drifts during low solar flux conditions, which were attributed to apoor specification of the E-region neutral wind dynamo. DINAMO is then used to quantify the impact of meridional
currents on the morphology of F-region zonal plasma drifts. Analytic representations of the equatorial drifts are commonly used to interpret observations. These representations, however, commonly ignore contributions from meridional currents. Using DINAMO we show that that these currents can modify zonal plasma drifts by up to ~ 16 m/s inthe bottom-side post-sunset F-region, and up to ~ 10 m/s between 0700 and 1000 LT for altitudes above 500 km.
Finally, DINAMO results show the relationship between the pre-reversal enhancement (PRE) of the vertical drifts andthe vertical shear in the zonal plasma drifts with implications for equatorial spread F.
Keywords: Ionosphere, Plasma drifts, Modeling, Equatorial, Currents, Electric fields, Potential
1 Introduction
It is well-known that equatorial F-region plasma drifts
play an important role in fundamental ionospheric*Correspondence: sam.shidler24@gmail.com
1
William B. Hanson Center for Space Sciences, The University of Texas
at Dallas, 800 W Campbell Rd, Richardson, TX 75080, USA
Full list of author information is available at the end of the article

processes and space weather phenomena. For instance,
the equatorial upward vertical drifts contribute to the
distribution and structure of ion composition and temperatures of the ionospheric plasma at low latitudes (e.g.,
Balan et al. 1997; Huang et al. 2016; Hysell et al. 2015;
Schunk and Nagy 2009). Additionally, the PRE of the vertical drifts in the evening sector can set up conditions thatare favorable for the development of equatorial spread-F© The Author(s) 2022. 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 theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise 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 thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7(ESF) ionospheric irregularities (Abdu et al. 1983; Fejer
et al. 1999; Huang 2018; Huang and Hairston 2015; Smithet al. 2015; Sultan 1996) which can affect signals used forcommunication, navigation and remote sensing systems(Basu et al. 1988; Carrano et al. 2012; Kintner et al. 2007).
Other studies have pointed out the role of zonal plasma
drifts in the stability of the evening equatorial F-region(Aveiro and Hysell 2010; Hysell and Kudeki 2004; Kudeki
and Bhattacharyya 1999; Kudeki et al. 2007).
Past modeling studies of the plasma drifts (e.g., Eccles
1998; Eccles et al. 2015; Haerendel et al. 1992; Heelis et al.
1974; Huba et al. 2010; Maute et al. 2012) have demonstrated that the main features of the observed F-region
plasma drifts are driven by the E- and F-region neutral
wind dynamo. Further analyses indicated that gradients in the gravity-driven current system near dawn anddusk produce polarization electric fields that modify theplasma drifts by 5–15 m/s (e.g., Eccles 2004). In Heelis et al. (1974), the electric potential is found on a thin
conducting shell at the upper boundary of the E-region
using height-integrated horizontal currents with communication from the F-layer provided by field-aligned currents. The more recent studies (e.g., Eccles 1998; Eccles
et al. 2015; Haerendel et al. 1992; Huba et al. 2010) havesuccessfully used a field line integrated, two-dimensionalmodel to describe the electrodynamics of the low-latitude ionosphere. Within this framework, three-dimensional conductivities and drivers (i.e., neutral winds andgravity) are integrated along magnetic field lines effectively “collapsing” the three-dimensional electrodynamics onto a two-dimensional plane located at the magnetic
equator (Haerendel et al. 1992). Expanding the field line
integrated current continuity equations results in a twodimensional partial differential equation for the electrostatic potential that can be used to specify electric fields
perpendicular to the background magnetic field.
Recent launches of the Ionospheric Connections
Explorer (ICON) (Immel et al. 2018) and FORMOsa
SATellite-7/Constellation Observing System for Meteorology Ionosphere and Climate (FORMOSAT-7/COSMIC-2) (Anthes and Schreiner 2019) will provide thespace physics community with a comprehensive new setof thermosphere–ionosphere measurements in an effort
to advance our understanding of low-latitude ionosphericvariability and space weather. Included in the suite of
instruments onboard these satellites are the Ion Velocity Meters (IVM) which are capable of providing in situ
measurements of plasma drifts (Heelis et al. 2017). The
University of Texas at Dallas (UTD) has been responsible for the design and development of IVM and has also
made advances toward the miniaturization and use ofthis instrument in cubesat missions (e.g., Crowley et al.
2016; Spann et al. 2017). Therefore, the importance ofPage 2 of 17

F-region drifts to fundamental and applied studies of the
low-latitude ionosphere and the increase in the numberof distributed observations motivated us in the directionof new modeling efforts at UTD.
Here, we introduce a new electrodynamics model thatwas created to assist with efforts related to Data Interpretation and Numerical Analysis of ionospheric Missions
and Observations (DINAMO). DINAMO solves the ionospheric dynamo equation using user-specified representations of the ionospheric and thermospheric parametersat middle and low latitudes. More specifically, DINAMO
determines the polarization electric fields that are setup
in response to the neutral wind and gravitational dynamos. Of particular importance is the fact that the model
was written in Python, with the exception of the potential
solver, to facilitate changes, tests, and the engagement ofstudents with numerical modeling in space sciences.
While the model was developed to assist the analysis and interpretation of ionospheric observations, here
we focus on describing its development and illustrating some of its results through two distinct applications.
In the first application, we employ DINAMO to assess
the ability of using current empirical models (IRI-2016,
HWM14, NRLMSISE-00) as inputs to drive realistic
representations of the low-latitude electrodynamics.
More specifically, we evaluate the ability of these widelyused models to produce plasma drifts that are compatible with observations made by the Jicamarca incoherent scatter radar (ISR) (Kudeki and Bhattacharyya 1999).
In the second application, we use DINAMO to evaluate
the contribution of the integrated vertical current ( JL) to
the morphology of the equatorial F-region zonal drifts.
Previous studies invoked a simple analytic expression
describing the zonal drifts to interpret observations or tomodel the drifts (Chau and Woodman 2004; Eccles 1998;
Haerendel et al. 1992; Richmond et al. 2015; Rodrigues
et al. 2012; Shidler et al. 2019). With the exception ofHaerendel et al. (1992), which considered a few different
values of JL, these studies neglected the contribution of
the vertical integrated current to the morphology of thezonal drifts. Analyses of the DINAMO outputs allow us
to quantify the contribution of JL to the equatorial zonal
drifts.
The presentation is organized as follows: In Sect. 2, we
provide information about the development of DINAMO
and the climatological models of the I–T system used as
drivers. In Sect. 3, we present DINAMO model resultsfor different seasons and solar flux conditions. We compare these results with mean plasma drifts measured by
the Jicamarca ISR. The main goal here is to determine towhat extent current climatological models of the thermosphere–ionosphere system can drive low-latitude electrodynamics that are in agreement with the observations.

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Then, we use DINAMO model results to evaluate theintegrated vertical current ( JL). The goal is to quantify thecontribution of JL to the morphology of the zonal drifts.
Finally, Sect. 4 summarizes our main findings and provides concluding remarks.

2 Model description: DINAMO
Here, we describe a new ionospheric electrodynamics model that has been developed to assist with Data
Interpretation and Numerical Analyses of ionospheric
Missions and Observations (DINAMO). DINAMO isa numerical model that solves the ionospheric dynamo
equation for the low-latitude ionospheric electrostatic
potential at the magnetic equator given user inputs forthe state of the I–T system. The electric potential allows
for the specification of electric fields perpendicular to thebackground magnetic field (E) and the associated verticaland zonal E × B plasma drifts.
Most of the DINAMO code was written in Python.
This facilitates implementations of numerical experiments and modifications of input parameters. The choiceFig. 1 Block diagram showing the components of the DINAMO model

Page 3 of 17

of Python also facilitates the engagement of students innumerical modeling and space sciences. Of specific relevance to this report is Pyglow (https://​github.​com/​timdu​
ly4/​pyglow). Pyglow is a community-developed Python
module that wraps several widely used empirical modelsof the I–T system into one easy-to-use package. Pyglow
is particularly useful in the present study where one of
the goals is to evaluate the electrodynamics produced by
DINAMO given inputs provided by current climatological models of I–T system.
The numerical method for solving the dynamo equation is provided by MUDPACK, a collection of FORTRAN subroutines that efficiently solves elliptic partial
differential equations (Adams 1989). This software is
the same used by the National Center for AtmosphericResearch (NCAR) in their Thermosphere-IonosphereElectrodynamics General Circulation Model (TIE-GCM)
for the solution scheme of the electric potential (Maute2018).
Figure 1 provides an overview of the DINAMO pipeline. Model runs start by tracing out the magnetic fieldShidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

lines using a user-specified model for the backgroundmagnetic field. DINAMO then gets the physical parameters of the ionosphere, thermosphere, and magnetic field
for each point along the field line again using user-specified models. The conductivities and magnetic meridionaland zonal winds are calculated from the physical parameters and are then used to numerically compute the twodimensional field line integrated quantities. Next, thecoefficients of the ionospheric dynamo equation are computed and fed into MUDPACK which numerically solves
for the electrostatic potential at the magnetic equator.
Finally, the electric potential is used to determine theelectric fields and associated E × B plasma drifts. The following subsections provide more details about the model.
2.1 The dynamo equation

The prevailing starting point for modeling electric fields
within the low-latitude ionosphere is the current continuity equation. These electric fields develop to ensurethat the net current density is divergence-free (∇ · j = 0)
(Eccles 2004; Eccles et al. 2015; Haerendel et al. 1992;
Heelis et al. 1974; Huba et al. 2010). In this work, themodeled electric fields are setup in response to neutral
wind and gravity driven current systems perpendicular to
the magnetic field. Here, we have chosen to neglect currents driven by pressure-gradients force as Eccles (2004)
showed that they do not have a significant effect on theequatorial plasma drifts. We point out, however, thatpressure-gradient currents can be important when interpreting high accuracy satellite magnetic observations(Alken 2016; Alken et al. 2011).
A natural coordinate system for analyzing the behaviorof a magnetized plasma is the dipole coordinates system(q, p, φ ). The coordinate q and associated unit vector eq isparallel to Earth’s magnetic field B. The coordinate p andunit vector ep is perpendicular to B and pointed poleward
and is contained within the magnetic meridian. Finally, φpoints in the magnetic zonal direction (eφ = eq × ep). In
this coordinate system, the currents perpendicular to B
are given by:



 
mi gp
jp = σP Ep + Buφ − σH Eφ − Bup +
σPi
e
i
(1)



 
mi gp
,
jφ = σP Eφ − Bup + σH Ep + Buφ −
σHi
e
i
(2)
where
• σP - Pedersen conductivity [mho/m]• σH - Hall conductivity [mho/m]• Ep - Meridional electric field [V/m]Page 4 of 17

•
•
•
•
•
•
•

Eφ - Zonal electric field [V/m]up - Magnetic meridional neutral wind [m/s]uφ - Magnetic zonal neutral wind [m/s]B - Magnetic field strength [T]mi - Ion mass [kg]e - Electron charge [C]
gp - Meridional gravitational acceleration component[m/s2]

We do not specify the parallel current ( jq), but as we willshow, our model results are independent of this quantity.
In this work, the electrodynamics of the low-latitude ionosphere are described using the two-dimensional field line
integrated model derived by Haerendel et al. (1992), andsuccessfully used in various previous studies (e.g., Chau
and Woodman 2004; Eccles 1998, 2004; Eccles et al. 2015;
Huba et al. 2010; Richmond et al. 2015; Rodrigues et al.
2012; Shidler and Rodrigues 2021) to advance the understanding of the low-latitude ionospheric electrodynamics.
Within this framework, three-dimensional quantities areintegrated along magnetic field lines starting at the baseof the ionosphere where parallel currents are expected tovanish. The resulting two-dimensional quantities are thenassigned to points at the magnetic dip equator defined by
the location of the apex heights of the field lines. The twocoordinates used in this plane are the McIlwain parameter
L = R/RE and ϕ, where R is the distance from the centerof the Earth to the apex height of the field line, RE is theradius of the earth, and ϕ measures the angle in the magnetic zonal direction.
Therefore, a two-dimensional current continuity equation is found by integrating the three-dimensional current
continuity equation along magnetic field lines (Wohlwend
2008):∇ ·J=
+∇ · j hq dq =






1
∂ 
∂ 
jq hp hφ +jφ hq hp
hq hp hφ ∂q
∂φ



∂ 
jp hφ hq hq dq,∂p(3)
where hq , hp, and hφ are geometric scale factors. The limits of integration start and end at the bases (northern andsouthern hemispheres) of the ionosphere where parallel currents are zero. This results in the first term on theright-hand side of Eq. 3 evaluating to zero. Carrying out
integration for the remaining terms gives the two-dimensional current continuity equation:


∂LJL
∂Jϕ
1
+
= 0,
∇ ·J=
(4)
RE L ∂L∂ϕwhere components JL and Jϕ of the integrated current
density (J) are given by:

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

JL = �P EL + B(L)UϕP − �H Eϕ − B(L)ULH + g0 �Pg

(5)





˜ P Eϕ − B(L)ULP + �H EL + B(L)UϕH − g0 �Hg ,Jϕ = �

(6)
where EL, Eϕ , B(L), and g0 are measured in the magnetic
equatorial plane. The three-dimensional quantities in
Eq. 1 and 2 have been replaced with the field line integrated quantities. More specifically, P and H are thefield line integrated Pedersen and Hall conductances,
˜ P represents the Pedersen conrespectively. The tilde in 
ductance with slightly different geometric scale factors
used in integration. The terms UϕP , ULH , ULP , and UϕH are
the average magnetic neutral winds along the field line
weighted by the Pedersen and Hall conductivities. Finally,Pg and Hg are the sum of the field line integrated Pedersen and Hall conductivites for the ion species scaled by
the mass-to-charge ratio. The exact definition of these
integrated quantities is given in Appendix A.
Using the electrostatic potential (), the perpendicularelectric fields in the equatorial plane are given by:
EL = −

1 ∂�
RE ∂L

(7)

Page 5 of 17

collection of ground-based magnetic observatories(Thébault et al. 2015).
The grid extends from 90 up to 20,000 km and has nonuniform spacing in apex heights with 5 km spacing below
2000 km, and 500 km spacing above 2000 km. The gridhas a resolution of 4 ◦ in geographic longitude.
The potential is set to zero at the upper boundary of
the grid (R = 20,000 km). At the lower boundary (R =90 km), the model uses the Neumann boundary condition ∂�/∂L = 0. These boundary conditions are the sameas those used internally for the potential solver in SAMI3(Huba et al. 2010). These boundary conditions do notstrongly impact the results for the potential at interior
points.
2.3 Collision frequency and conductivity

The Pedersen and Hall conductivities for a multi-species+
plasma (H+, He+, O+, O+
2 , NO ) are given by:
 n i e κin e e κe
σP =
+
(10)
2
B 1+κ
B 1 + κ2
e

σH =

i

 ni e κ 2
ne e κe2i,−
B 1 + κe2
B 1 + κi2i

Eϕ = −1 ∂�
RE L ∂ϕ(8)

Substituting Eqs. 5–8 into Eq. 4 and rearranging theterms, we find the dynamo equation:




∂�
1 ∂
∂�
∂
∂�H ∂� ∂�H ∂�
˜P
+
�
L�P
+
−
∂L
∂L
L ∂ϕ
∂ϕ
∂L ∂ϕ
∂ϕ ∂L


∂
R B(�P UϕP + �H ULH ) + g0 �Pg
=
∂L


∂
˜ P ULP ) − g0 �Hg+
RE B(�H UϕH − �∂ϕ(9)Given user-defined ionosphere and thermosphere inputs,
DINAMO computes all the coefficients for and solves
Eq. 9. Additionally, it computes the electric field components from the potential solution and outputs estimates
for the E × B drifts.
2.2 The solution domain and gridSpecification of the two-dimensional plane that defines
the magnetic equator is done using realistic magnetic
field lines specified by the 2012 version of the International Geomagnetic Reference Field (IGRF-12). The
IGRF-12 model describes Earth’s large-scale magnetic
field (1900-present) using observations from a global

i

(11)

where κe,i = �e,i /νe,i is the gyro-frequency (e,i ) to collision frequency (νe,i ) ratio, and the summation is over allof the ion species. The subscripts e and i refer to electron
and ion species, respectively. 
The ion densities (ni ) andelectron plasma density (ne = i ni ) are in m−3.
The gyro-frequency is given by:(12)

�e,i = eB/me,i ,where the magnetic field strength (B) is provided by
IGRF-12.
The collision frequencies for ions and electrons only
consider collisions with neutral species. The non-resonant and temperature-dependent resonant collision frequencies for the ions are described in Schunk and Nagy
(2009) with the updated coefficients for O+, O+
2 , and
NO+ provided by Ieda (2020). The non-resonant ionneutral collision frequencies have the form:

νin = Cin nn(non-resonant),(13)

where nn is the neutral species density in cm−3 and Cin
is the coefficient. Table 1 shows the non-resonant ionneutral collision frequency coefficients (Cin × 1010) for
each ion species with the six species of neutrals used in
the model (H, He, N, O, N2, O2). Values marked by R
in Table 1 represent temperature-dependent resonant

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

collision frequencies and have a different form. Table 2
shows the resonant collisions frequencies. We have used
the updated resonant collisions for O+ and O+
2 provided
by Ieda (2020). The final collision frequency for a given
ion species is:

νi =
νin ,
(14)
n

where the sum is over all neutral species.
Finally, for the electron-neutral collision frequency, we
use the formula provided by Nicolet (1953):

νe = νen = (5.4 × 10−10 )nN Te 1/2 ,(15)

where nN is the sum of neutral densities in cm−3, and T e
is the electron temperature in Kelvin.
In this work, the temperatures and densities for theions and electrons are specified by the 2016 version of theInternational Reference Ionosphere (IRI-2016). IRI-2016
is the result of a global effort to model the parameters in
the Earth’s ionosphere using a variety of ground and satellite measurement techniques (Bilitza et al. 2017).
Temperatures and densities for neutral species areprovided by the 2000 version of Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar(NRLMSISE-00) model (Picone et al. 2002). NRLMSISE-00 is an empirical model of the neutral atmosphere
extending from the ground to the exobase derived using a
combination of ground, rocket, and satellite-based measurements to predict neutral temperatures and densities.
2.4 Neutral winds

The E- and F-region neutral wind dynamos are the primary drivers for the electric fields in the low-latitude ionosphere (Eccles 1998, 2004; Heelis 2004; Heelis et al. 1974;
Maute et al. 2012). Model results in this work use neutral winds provided by the 2014 version of the Horizontal Wind Model (HWM14). HWM is an empirical model
commonly used for global specification of the upper
atmospheric general circulation patterns and migratingtides. The current HWM14 version is developed using
a total of ∼ 73 × 106 observations from 44 different
instruments spanning over 60 years (Drob et al. 2015).
HWM specifies the geographic zonal (U) and meridional (V) neutral winds. The field line integrated quantities of interest, however, require the magnetic zonal (uφ )and magnetic meridional (up) winds which are found byprojecting the HWM geographic winds onto the unit
vectors in the magnetic zonal (eφ ) and magnetic meridional (ep) directions. These units vectors are determined
locally from IGRF-12, which provides spherical components (eastward, northward, and upward) of the magnetic
field.

Page 6 of 17

2.5 Field line integration

Realistic magnetic field lines are traced out througheach point of the magnetic equatorial grid using IGRF12. Tracing starts at the magnetic equator and extends
down to 80 km in altitude. Non-uniform spacing is used
for points along the field line. Field line points are spaced
every 1 km in altitude below 110 km. Between 110 and2000 km points are spaced every 5 km in altitude, andabove 2000 km points are spaced every 100 km. This isdone to better capture the structure of the ionosphereand thermosphere at lower altitudes.
Integration is done with respect to magnetic latitude.
In this work, quasi-dipole magnetic latitudes are usedand defined by Laundal and Richmond (2017):
RE + h(16)
 = ± cos−1,
RE + hA
where h is the height of the field line point, and hA is the
apex height of the field line.
To simplify integration, the geometric scale factors hq ,hp and hφ in Eq. 3 are derived from dipole field lines.
2.6 MUDPACKMUDPACK is a software library for geophysics developed at NCAR. Equation 9 is solved using a MUDPACK
subroutine that produces a second order finite difference
approximation for two-dimensional non-separable elliptic partial differential equations using multigrid iterationthat combines the classical Gauss–Seidel line relaxation
technique on finer grids with a coarse-grid correction
procedure. Detailed information regarding this technique
can be found in Adams (1989) and the references therein.
MUDPACK takes the coefficients of Eq. 9 as well as specified boundary conditions as input. As mentioned earlier,
MUDPACK is the same software used by NCAR’s TIEGCM (Maute 2018) for the solution of the ionosphericelectric potential.

3 Results and discussion
We now present and discuss results of DINAMO simulations in two distinct applications.
First, we use DINAMO to evaluate the ability of current climatological drivers (HWM14, IRI-2016, and
NRLMSISE-00) to produce realistic ionospheric electrodynamics for different seasons and solar flux conditions(Sect. 3.1). We assess DINAMO results by comparing
modeled zonal and vertical equatorial E × B drifts withobservations. Next, we use DINAMO to quantify thecontribution of the integrated vertical current ( JL) to themorphology of the drifts (Sect. 3.1.1).

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Focus is given to results for the Peruvian longitude sector (∼ 284◦E), which allows a comparison of model drift
results with mean plasma drifts derived from long-term
Jicamarca ISR observations.
3.1 On DINAMO equatorial E × B plasma drifts

Figures 2 and 3 show DINAMO results for the equatorial zonal and vertical E × B plasma drifts, respectively.
The DINAMO model results are represented by the blue
curves. They show the behavior of the zonal and verticalplasma drifts as a function of local time for different seasons (rows) and solar flux conditions (columns) for the
Peruvian sector at an altitude of 360 km. The top, middle, and bottom rows correspond to December solstice,equinox, and June solstice conditions, respectively. Morespecifically, DINAMO model results are for day-of-year
21 (December solstice), 172 (June solstice) and 264 (equinox). The left column in each Figure corresponds to low
solar flux (LSF) conditions, and the right column corresponds to high solar flux (HSF) conditions. The solar andgeomagnetic input conditions of the climatological models that were input for the DINAMO simulations werechosen to match the average conditions of Jicamarca
ISR observations presented by Shidler et al. (2019) andPage 7 of 17

available to this study. DINAMO simulations use climatological drivers set for F10.7 of 80 SFU and 150 SFU representing LSF and HSF conditions, respectively. During
June solstice, however, we use 130 SFU to represent the
HSF conditions. Finally, these simulations results are forgeomagnetically quiet conditions with the climatologicaldrivers set to Kp = 2 (Ap = 7).
For comparison purposes, Figs. 2 and 3 also show
Jicamarca observations which are represented by thegreen curves. These observations were derived and firstpresented by Shidler et al. (2019). Shidler et al. (2019)
estimated the mean behavior of geomagnetically quiet
vertical and zonal plasma drifts as a function of local
time and altitude (range between 200 and 600 km) fromobservations made by the Jicamarca ISR between 1986
and 2017. The mean drifts were derived for three seasonal bins: December solstice (Jan, Feb, Nov, Dec), equinox (Mar, Apr, Sep, Oct), and June solstice (May, Jun, Jul,
Aug). The drifts were further split into a low solar flux
bin with an average F10.7 of 80 SFU, for all seasons, anda high solar flux bin with an average F10.7 of 150 SFU for
December solstice and equinox and an average of 130
SFU for June solstice. The difference in mean solar flux
for June solstice was caused by lack of data. The averageFig. 2 Behavior of the zonal plasma drifts as a function of local time for different seasons (rows) and solar flux conditions (columns). The blue curves
represent results from the DINAMO model at 360 km. The green curves represent the Jicamarca ISR observations presented by Shidler et al. (2019)
for altitudes of 360±40 km

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Page 8 of 17

Fig. 3 Behavior of the vertical plasma drifts as a function of local time for different seasons (rows) and solar flux conditions (columns). The blue
curves represent results from the DINAMO model at 360 km. The green curves represent the Jicamarca ISR observations presented by Shidler et al.
(2019) for altitudes of 360±40 km. The red curves correspond to vertical drifts predicted by the SF99 model

Table 1 Collision frequency coefficients Cin × 1010 for non-resonant ion-neutral interactions
Ion

H

He

N

O

N2

O2

H+

R

10.6

26.1

R

33.6

32.0

He+

4.71

R

11.9

10.1

16.0

15.3

O+

R

1.32

4.62

R

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

R

Table 2 Resonant ion-neutral collision frequencies. Densities are in cm−3. Ion temperatures (T i ) and neutral temperatures (T n ) are in
KelvinSpeciesTr (K)

νin ­(s−1)

H+ , H> 50

2.65 × 10−10 n(H)Tr (1 − 0.083 log10 Tr )2

He+ , He> 50

8.73 × 10−11 n(He)Tr (1 − 0.093 log10 Tr )2

H+ , O> 300

6.61 × 10−11 n(O)Ti

O+ , H> 300

1/2
n + Ti /16)
1/2
max[3.68 × 10−11 n(O)Tr (1 − 0.065 log10 Tr )2 , 4.01 × 10−10 n(O)]1/2
max[2.62 × 10−11 n(O2 )Tr (1 − 0.074 log10 Tr )2 , 4.08 × 10−10 n(O2 )]O+ , O–O+
2 , O2

–

1/2

1/2

1/2

4.63 × 10−12 n(H)(T(1 − 0.047 log10 Ti )2

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Kp index for the observations was approximately 2. Missing data points in the post-sunset sector are caused bycoherent echoes from ESF events contaminating measurements of the background plasma drifts. Past studies have shown the occurrence rates for these events are
directly proportional to the magnitude of the PRE (e.g.,
Fejer et al. 1999; Huang and Hairston 2015; Smith et al.
2015) which explains more prominent gaps in December
and equinox during high solar flux periods. Additionally,
missing values in the early morning are the result of low
quality measurements (reduced signal-to-noise ratio)
during that time due to decreased plasma densities.
Finally, for completeness, the red curves (in Fig. 3 only)
represent the vertical drifts predicted by the Scherliess
and Fejer (1999) climatological model (SF99). SF99 is a
global model of the equatorial vertical drifts derived fromin situ measurements made by the Atmospheric Explorer
E (AE-E) satellite with additional measurements in the
Peruvian sector made by the Jicamarca ISR between 1968
and 1992 (Scherliess and Fejer 1999).
A comparison of model results and measurements
in Figs. 2 and 3 serve to show that DINAMO is capableof producing realistic estimates of the zonal and vertical plasma drifts. That is, it shows most of the features
expected for the vertical and zonal drifts based on previous studies and observations. This is an indication of
the fair representation of the ionospheric electrodynamics by the underlying driving conditions provided by
the input climatological models (IRI2016, HWM14 and
NRLMSISE-00).
Here, we must mention the good agreement of ourresults with those of the recent work of Eccles and Valladares (2021). They coincidentally also evaluated theimpact of climatological models on producing realistic
equatorial plasma drifts. However, they used the Electric
Field Model–EFM (Eccles 2004) and focused on proper
tide specification for a single solar flux condition ( F10.7 =110 SFU). More importantly, perhaps, is that their results
reinforce the correctness of DINAMO and provide independent evidence of some of our findings. To avoid repetition, we highlight some aspects that were not addressedby Eccles and Valladares (2021).
3.1.1 On DINAMO F‑region zonal drifts

Figure 2 shows that DINAMO, when driven by current
climatological models (HWM14, IRI-2016 and NRLMSISE-00), is capable of reproducing the expected diurnal variability of the zonal drifts. More specifically, it iscapable of producing the expected weak westward drifts
during the day (e.g., Fejer et al. 2005, 1991), a rapid eastward acceleration in the post-sunset sector, and strong
eastward plasma drifts at night. Therefore, current climatological drivers are capable of reproducing the main

Page 9 of 17

features of the equatorial zonal drifts including an eastward super-rotation of the ionosphere which is in good
agreement with previous experimental studies (Pacheco
et al. 2011).
There are, however, noticeable differences between
model and observations. In all seasons and for all solar
flux conditions, the reversal time for the modeled drifts
occur at an earlier time in the morning, and at a latertime in the evening compared to the observations. Additionally, the nighttime eastward modeled drifts tend tobe weaker than the observations. Eccles and Valladares(2021) also found weaker model zonal drifts comparedto observations. Here, we point out that our results
indicate that the discrepancy between nighttime modeled and observed drifts is more accentuated during
HSF conditions. Given the strong correlation between
the motion of the plasma and neutrals during this time(e.g., Biondi et al. 1988; Chapagain et al. 2013; Fejer 1993;
Fejer et al. 1985; Navarro and Fejer 2020), this behavior
most likely stems from the specification of the F-region
thermospheric neutral winds provided by HWM14. In a
recent study, Navarro and Fejer (2019) compared quiet
time values of the nighttime neutral winds predicted
by HWM14 with observed neutral winds in the Peruvian sector during moderate solar flux conditions. They
found, for example, that HWM14 significantly underestimates the eastward winds in the pre-midnight sector
during equinox. Furthermore, HMW14 better represents
moderate solar flux conditions. It does not include a solar
flux dependency, and the observational database used in
the derivation of HWM14 corresponds to measurements
made during moderate solar activity with an average F10.7
of 107 SFU (Drob et al. 2015).
3.1.2 On DINAMO F‑region vertical drifts

We now turn our attention to the vertical drifts output
by DINAMO which are illustrated by the results shownin Fig. 3.
Similar to our findings for the zonal drifts, the results
indicate that the climatological drivers can produce mostof the features expected for equatorial vertical drifts
based on previous theoretical and experimental studies. We start by pointing out that the drivers are capableof reproducing the PRE during equinox and December
solstice. The model is also capable of reproducing theincrease in the PRE magnitude with solar flux which has
been observed in previous studies (e.g., Fejer et al. 2008,
1991). Additionally, the magnitude of the PRE modeledby DINAMO is in fair agreement with the observations(within around 10 m/s). More noticeable is the excellent
agreement of the PRE peak times and of the times when
the drifts revert from upward to downward.

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Page 10 of 17

The section below presents results related to thesources of the unusual behavior in the model F-region
drifts.
3.1.3 Abnormal nighttime F‑region drifts

Fig. 4 Jicamarca vertical drifts (black line) due to the gravitation
dynamo (green line), the E-region dynamo (blue line), and theF-region dynamo (red line)

Figure 3 also shows obvious differences between modeled and observed vertical drifts. For instance, the climatological drivers tend to produce daytime drifts thatdepart from the observations. More specifically, theresults show weak peak values and downward verticaldrifts in the afternoon. Additionally, the results show thatthese discrepancies are more evident during LSF (all seasons) and December solstice of HSF conditions. Eccles
and Valladares (2021) also found that the tidal representation in HWM does not produce daytime drifts thatmatch the predictions of the SF99 model. For instance,
close inspection of their Fig. 4c shows the afternoon
downward drifts for F10.7 = 110 SFU conditions as well.
Here, we must point out that our modeled daytime drifts resemble those seen by C/NOFS during theextreme solar flux conditions of 2008/2009. For instance,
Stoneback et al. (2011) examined median values of themeridional plasma drifts using observations from the C/
NOFS satellite and found downward afternoon drifts inall seasons for certain longitude sectors. Stoneback et al.
(2011) proposed the increased role of the semi-diurnal
tide in the E-region to explain downward afternoon
drifts.
Additionally, perhaps the most striking difference
between modeled and observed vertical drifts occur atnight during LSF conditions, particularly in June solstice.
Figure 3 shows that the climatological models driving
DINAMO produce nighttime drifts that depart significantly from the observations during LSF conditions. In
particular, large upward drifts are seen in June solsticewhen observations show downward drifts. Again, Fig. 4cin Eccles and Valladares (2021) also shows these abnormal drifts developing in May–July.

In order to identify the origin of the abnormal upward
drifts described above, we follow the approach of previous studies (e.g., Eccles 2004; Maute et al. 2012) andisolate different source terms to evaluate their relative
contribution to the overall vertical drifts. Figure 4 shows
June solstice LSF vertical drifts decomposed into contributions from the gravitational dynamo (green curve),
from the E-region neutral wind dynamo (blue curve), andfrom the F-region neutral wind dynamo (red curve). The
total vertical drifts (all source terms included) is shown as
the black curve. The contribution from the gravitational
dynamo to the vertical drifts is found by setting the neutral winds to zero everywhere and solving Eq. 9. For thecontribution from the E-region dynamo, gravity driven
currents and neutral winds in the F-region are set tozero. Finally, the contribution from the F-region dynamo
is found by setting gravity driven currents and neutral
winds in the E-region to zero. Note that the E-region
and F-region neutral wind dynamos are determined bydecomposing the integrals in Eqs. 18d–18g (Appendix A) into a sum of integrals. Field line points below
200 km contribute to the E-region dynamo term, andpoints above 200 km contribute to the F-region dynamo.
For instance, when determining the contribution of theF-region dynamo, the winds below 200 km and respective integrals are set to zero.
We start by pointing out that Fig. 4 shows that thegravitational term in DINAMO produces the same effectshown by the Eccles (2004) model. That is, the gravitational dynamo modifies the vertical drifts by 5 and15 m/s near the solar terminators. During these times,
the conductivity is rapidly changing, and zonal electricfields near the terminators are set up to keep currents
divergence-free.
More importantly, Fig. 4 shows that the E-region neutral wind dynamo, as described by the input climatological models, is responsible for both the downward drifts inthe late afternoon and upward drifts at night.
Finally, we point out that HWM14 does not include asolar flux dependency causing the neutral wind descriptions to be the same for both LSF and HSF conditions.
Therefore, the reduction in downward drifts in the afternoon and upward drifts in the post-midnight sector from
LSF to HSF conditions indicates that the E-region winds
do play a role in these features, but their contribution isheavily modulated by the conductivities.

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

3.1.4 Height variation of F‑region drifts

So far we focused on model results for a single heightnear the F-region peak (∼ 360 km). It is known, however,that vertical and zonal drifts can vary with height, particularly during evening and nighttime hours (Fejer et al.
2014; Hui and Fejer 2015; Kudeki and Bhattacharyya
1999; Lee et al. 2015; Nayar and Sreehari 2004; Richmond
et al. 2015; Rodrigues et al. 2012; Shidler and Rodrigues
2019).
Previous results showed that the climatological drivers
can produce the overall behavior of the observed drifts.
We now examine the ability of the climatological drivers
to produce realistic variations of the F-region drifts withheight. Focus is given to equinox HSF model simulations
as the previous results show that the model drifts at main
F-region heights resemble the observations and, therefore, suggest better accuracy of the input drivers. Duringequinox, height variations in the zonal and vertical drifts
are expected to develop at least near the sunset terminator (Shidler et al. 2019).
Figure 5 shows the local time versus height variability
for the vertical (top) and zonal (bottom) plasma drifts
produced by DINAMO for equinox HSF conditions. It
serves to show that the climatological drivers can indeed
produce the altitude variability associated with equatorial
plasma drifts.

Page 11 of 17

For example, DINAMO results for the zonal drifts(bottom panel) show the vertical shear observed aroundthe time of the PRE that is associated with the evening plasma vortex (Eccles et al. 1999; Haerendel et al.
1992; Richmond et al. 2015; Rodrigues et al. 2012). Daytime westward drifts also show some height variability
between 0900 and 1500 LT. This is in agreement withthe analysis of Hui and Fejer (2015). They showed thatdaytime westward drifts observed at Jicamarca, between
March and October, increase with height for altitudes
below 300 km.
DINAMO results for the vertical drifts (top panel ofFig. 5) also show the expected weak height variation during most times. Height gradients, nevertheless, are positive in the morning and negative starting in theafternoon. Significant height gradients in the verticaldrifts are only observed around 0400 LT and around thetime of the PRE. This behavior is consistent with the curlfree condition for ionospheric electric fields and withprevious observational studies that relate noticeable
height variations of the equatorial vertical E × B drifts tothe strong longitudinal variations in the zonal drifts
occurring near dawn and dusk (e.g., Murphy and Heelis
1986; Pingree and Fejer 1987; Shidler and Rodrigues
2019; Shidler et al. 2019). More specifically, at the mag∂Wi
1 ∂Ui
i
netic equator, ∇ × E = 0 leads to 2W
r − ∂r = r ∂ϕ ,Fig. 5 Vertical (top) and zonal (bottom) plasma drifts at Jicamarca for equinox high solar flux conditions

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

where Wi and Ui are the components of the ionosphericplasma drifts in the vertical (r) and zonal (ϕ) directions,
respectively (Murphy and Heelis 1986).
3.2 On the vertical integrated current ( JL)

We now present results related to our analysis of the integrated vertical current ( JL). More specifically, we evaluate
the JL contribution to the morphology of the zonal drifts.
Again, we focus our analysis on DINAMO simulations
for equinox HSF conditions for which the drivers seem toproduce drifts that best match observations.
The expression for the integrated vertical current(Eq. 5) can be rearranged to solve for the zonal plasma
drifts (Ui ) at the magnetic equator:

Ui = UϕP +g0 �PgJL
�H H �H
U −
Wi −
−
,
�P L
�P
B�P
B�P

(17)
where Wi is vertical plasma drift. Equation 17 has beenused in the past (Haerendel et al. 1992) to describe
the morphology of the zonal plasma drifts in terms of
two-dimensional field line integrated quantities of theionosphere.
A simplified version of Eq. 17 that only takes into conH
sideration the UϕP and − P Wi terms has been commonlyused to interpret observations of the zonal drifts (e.g., Chau
and Woodman 2004; Hui and Fejer 2015; Richmond et al.
2015; Rodrigues et al. 2012). More recently, Shidler andRodrigues (2021) analyzed the ability of Eq. 17 to reproduce
observed zonal plasma drifts made at Jicamarca given field
line integrated quantities specified by climatological models aided by mean vertical drifts derived from Jicamarca ISR
observations. However, like in previous studies, the fourthJLterm (− B), however, had to be neglected since JL couldP
not be estimated from the models alone.
Haerendel et al. (1992) and Eccles et al. (2015) examJL
ined the impact of the − B
term, with emphasis on thePperiod around 1900 LT when a shear in the zonal plasma
drifts is commonly observed (e.g., Kudeki and Bhattacharyya 1999; Lee et al. 2015; Shidler et al. 2019). Additionally, it was simply assumed that JL was positive androughly constant with height having a magnitude of only
a few mA/m. Therefore, the altitude variability was controlled by P which is significantly reduced in the bottomside and, therefore, the fourth term predicted strong
westward drifts in the bottomside and weak drifts at
higher altitudes. This behavior acts to enhance the vertical shear in the zonal plasma drifts.
DINAMO simulations now allow us to better estimate
JL
the contribution of the − B
term to the morphology
P
F-region zonal drifts. Figure 6 shows the contributions
from each term on the right-hand side of Eq. 17 to thezonal drifts as a function of local time and height. The

Page 12 of 17

results are for the Jicamarca longitude sector. While thetotal zonal drifts are shown in panel (a), the contribution
from the five terms are shown in panels (b–f ).
The magnitude and behavior of the first three terms
panels (b–d) are in agreement with the results of Shidler
and Rodrigues (2021). That is the Pedersen-weighted
magnetic zonal winds (UϕP ) in panel (b) are primarily
responsible for most of the observed features of the zonal
plasma drifts including the diurnal variability and thevertical shear commonly seen in the post-sunset sector.
Shidler and Rodrigues (2021) also found that the contribution from the Hall-weighted meridional winds (ULH ) in
panel (c) was negligible throughout the day.
H
The − P Wi term (panel d) during daytime (when theHall-to-Pedersen ratio is close to 1) makes a contribution
to the zonal drifts with absolute values that are similar to
those of the vertical drifts (Wi).
Perhaps more importantly, this term also makes significant contributions (∼20 m/s) to the zonal drifts inthe bottomside during nighttime acting as to enhance
the shear around the time of the PRE (∼1900 LT). Here,we must point out that recent studies linked the development of ESF to the Collisional Shear (CS) instability and to the strength of the vertical shear in the zonal
drifts (Aveiro and Hysell 2010; Hysell and Kudeki 2004;
Kudeki et al. 2007) The results, however, indicate that thestrength of the shear is dictated by the magnitude of thePRE, which is more traditionally recognized as the mostimportant driver of the Generalized Rayleigh–Taylor(GRT) instability leading to ESF.
The gravitational term is shown in panel (f ), and has
negligible contribution to the overall plasma drifts but is
included here for completeness.
JL
Finally, the contribution from the − B
term is shownPin panel (e). Throughout most of the day, the contribution
from this term is negligible. There are, however, a coupleof times where this term predicts drifts with magnitudes
greater than ∼5 m/s and that are a significant portionof the total zonal drifts. For example, between 0700 and1000 LT at altitudes above about 500 km. Additionally,JL
as suggested by Haerendel et al. (1992), the − B
termPcontributes with relatively strong (up to ∼16 m/s) westward plasma drifts between 1900 and 2100 LT at bottomside F-region heights (below ∼300 km) and weaker drifts(∼10 m/s) at higher altitudes.
Figure 7 provides a closer look at the behavior andimpact of JL on zonal drifts. It shows (apex) height profiles of various parameters for 1900 LT (top) and 2000
LT (bottom). Panels (a1) and (a2) show altitude profilesof the modeled zonal drifts and three of the terms (righthand side of equation 17) contributing to them. The
g0 Pg
H H
P UL and − BP terms are not shown since they do notmake noticeable contributions at these times. Panels (b1)

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Page 13 of 17

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 6 a Zonal drifts modeled by DINAMO for equinox HSF conditions and b–f contributions from different terms of Eq. 17 to these drifts. All values
are given in m/s

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

Page 14 of 17

Fig. 7 On the contribution of JL to the morphology of the zonal plasma drifts at 1900 LT (top) and 2000 LT (bottom). Panels a1 and a2 show theapex height profiles of the zonal plasma drifts modeled by DINAMO for equinox HSF conditions. Panels b1 and b2 show apex height profiles JL.
Finally, panels c1 and c2 shows apex height profiles of Pedersen and Hall conductancesand (b2) show the height profile of JL. Finally, panels (c1)and (c2) show height profiles of the field line integrated
conductances.
At 1900 LT the vertical drifts are still positive (upward).
See Fig. 5. At this time, the Pedersen conductance also
increases significantly with height up to ∼400 km, while
the Hall conductance decreases moderately with heightH
as shown in panel (c1). Therefore, the − P Wi term contributes with westward drifts more significantly in thebottomside F-region as indicated in panel (a1). Around
JL
this time, JL increases with height (panel b1) and − BP
contributes westward drifts that are nearly constant with
JL
height. Therefore, the − B
term acts to reduce the eastPward F-region plasma drifts that are driven by the wind
JL
dynamo term (UϕP ). The − B
term also increases theP
altitude of the transition height between westward andeastward plasma drifts from 200 km to about 245 km. The
result is a strong vertical shear in the zonal drifts aroundthe PRE time that can be seen in panel (a) of Fig. 6.
At 2000 LT the behavior of JL more closely resembles
the situation assumed by Haerendel et al. (1992). That
is, JL is positive (upward) and is nearly constant withaltitude with a magnitude of a few mA/m. The overallbehavior of the conductances do not change much from

JL
that of 1900 LT. Therefore, the − B
term continues toPdrive westward drifts with larger magnitudes at bottomside heights. At 2000 LT, however, the vertical drifts areH
downward (see Fig. 5). This causes the − P Wi to drive
eastward drifts and nearly cancel the westward drifts
JL
driven by − B
. Therefore, during this time the zonalPdrifts are more completely controlled by UϕP.

4 Conclusions
We introduced a new numerical model of the ionospheric electrodynamics that will be used as a tool to
aid in Data Interpretation and Numerical Analysis of
ionospheric Missions and Observations (DINAMO). The
model numerically solves the ionospheric dynamo equation using user-specified inputs for the global state of the
I–T system. In this work, the I–T system is specified by
IRI-2016, HWM14, NRLMSISE-00, and IGRF-12 which
are widely used climatological models within the spacescience community.
Most of DINAMO has been written entirely in Python.
Using Python facilitates modifications in the input drivers and the setup of numerical experiments. Additionally,
Python is a popular programming language will help toShidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

engage students in numerical modeling applied to spacesciences.
In the current version of DINAMO, the polarizationelectric fields and associated plasma drifts are driven by
the neutral wind and gravitational dynamos. The mainfeatures of the predicted vertical and zonal plasma drifts
can be attributed to the neutral wind dynamo, while thegravitational dynamo can modify the vertical drifts by
5–15 m/s near dawn and dusk, which is good agreementwith previous studies (Eccles 2004).
DINAMO results were illustrated in two distinct
applications. First, DINAMO was used to evaluate theextent of which current climatological I–T models (IRI2016, HWM14, NRLMSISE-00, and IGRF-12) are capable of driving a realistic description of the low-latitude
electrodynamics. Modeled zonal and vertical F-region
drifts were compared with Jicamarca ISR drifts. Second,
DINAMO was used to evaluate how much the field line
integrated vertical current JL can contribute to the morphology of the zonal plasma drifts.
With respect to the first study, some of the main findings can be summarized as follows:• Current climatological models can drive most of themain features of the zonal and vertical plasma drifts
observed by the Jicamarca ISR. This includes, forinstance, the weak westward drifts during daytime
and stronger eastward drifts at night. The drivers
are also capable of producing the vertical shear in
the F-region zonal plasma drifts that is commonly
observed in the post-sunset sector. The height variability of the vertical drifts was found to be consistent with the expectation of curl-free electric fields(∇ × E = 0). With respect to vertical drifts, we also
found that the drivers can capture fairly well thevariability of the PRE with both season and solar
cycle. The magnitude and occurrence time of themodeled PRE are in good agreement with observations. Finally, a better agreement between model andobservations for equinox HSF conditions indicate amore accurate description of the I–T state by the climatological models for these geophysical conditions.
• Our analyses also identified abnormal features inthe drifts driven by the I–T models. For instance,
DINAMO predicted different reversal times of thezonal drifts during all seasons and solar flux conditions. Additionally, the magnitude of peak nighttime
eastward drifts were weaker than what was observed
at Jicamarca. This discrepancy was attributed to theF-region neutral winds predicted by HWM14. With
respect to vertical drifts, we found that the drivers
tend to produce weak upward or even downward vertical drifts in the afternoon when observations show

Page 15 of 17

upward drifts. This effect was more exaggerated during low solar flux conditions. Additionally, the drivers tend to produce nighttime drifts that depart fromthe observations. We showed that this behavior was
driven by the neutral wind dynamo occurring along
field line points below 200 km in altitude.
Now, with respect to the second study, findings can besummarized as follows:• Using model results during equinox HSF condiJL
tions, we analyzed the contribution of the − B
termP
(Eq. 17) to the morphology of zonal plasma drifts. We
found that this term only makes non-negligible contributions between 0700 and 1000 LT and 1900 and
2100 LT. We confirmed assumptions made by HaerenJLdel et al. (1992) that this the − B
term can make sigP
nificant contributions to the total zonal plasma drifts
in the bottomside F-region ionosphere in the postsunset sector. We found contributions as large as 16
m/s (westward) around 2000 LT. However, during thistime the vertical drifts are downward and this contribution is nearly canceled by eastward drifts driven byH
the − P Wi term. Around 1900 LT during the PRE, on
JL
the other hand, westward drifts driven by − B
add toPHwestward drifts driven by the − P Wi term. As a result,
this enhances the vertical shear in the zonal plasma
drifts which has been associated with ESF (Aveiro andHysell 2010; Hysell and Kudeki 2004; Kudeki and Bhattacharyya 1999; Kudeki et al. 2007).

Appendix A: Field line integration
The definitions for field line integrals used in our model
come from Haerendel et al. (1992):
 N
�P = RE L
σP (1 + 3 sin2 ) cos d
(18a)
S

˜ P = RE L� NσP cos d

(18b)

 N

σH (1 + 3 sin2 )1/2 cos d

(18c)

 N

σP uφ

(1 + 3 sin2 )cos d(1 − sin2 )3/2

(18d)

S

�H = RE L

S

RE L
UϕP =
�P

S

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(1 + 3 sin2 )1/2
cos d (18e)(1 − sin2 )3/2

RE L
ULP =
˜P
�

 N

σP up

RE L
UϕH =
�H

 N

σH uφ

RE L
�H

 N

ULH =

S

S

(1 + 3 sin2 )1/2
cos d(1 − sin2 )3/2

(18f )
2

σH up

S

R2
�Pg = ER

 N 

RE2
R N 

S

(2022) 9:7

i(1 + 3 sin )cos d, (18g)(1 − sin2 )3/2

σPi micos de(18h)

σHi mi(1 + 3 sin2 )−1 cos d
e
S
i
(18i)
where  is the magnetic latitude, and S and N are themagnetic latitudes at the base of the ionosphere in themagnetic south and magnetic north.
�Hg =Acknowledgements
The authors would like to thank the reviewers from providing helpful comments and suggestions to improve this manuscript.  
Authors’ contributions
SS developed the DINAMO software, analyzed the data, produced the graphs,
and made contributions to the interpretation of results and writing of thismanuscript. FR provided directions for this study, interpreted results, andcontributed to the writing of this manuscript. All authors read and approved
the final manuscript.
FundingWork at UT Dallas was supported by the NSF (AGS-1554926 andAGS-1916055).
Availability of data and materials
Please contact the corresponding author for data requests.

Declarations
Competing interests
The authors declare that they have no competing interest.
Author details
1
William B. Hanson Center for Space Sciences, The University of Texas at Dallas,
800 W Campbell Rd, Richardson, TX 75080, USA. 2 Applied Research Laboratories, The University of Texas at Austin, 10000 Burnet Rd, Austin, TX 78758, USA.
Received: 15 June 2021 Accepted: 16 December 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 88:399–402. https://​doi.​org/​10.​1029/​JA088​
iA01p​00399

Page 16 of 17

Adams JC (1989) Mudpack: multigrid portable fortran software for the efficientsolution of linear elliptic partial differential equations. Applied Math Comput 34:113–146. https://​doi.​org/​10.​1016/​0096-​3003(89)​90010-6
Alken P (2016) Observations and modeling of the ionospheric gravity anddiamagnetic current systems from CHAMP and Swarm measurements. J
Geophys Res 121:589–601. https://​doi.​org/​10.​1002/​2015J​A0221​63
Alken P, Maus S, Richmond AD, Maute A (2011) The ionospheric gravity anddiamagnetic current systems. J Geophys Res. https://​doi.​org/​10.​1029/​
2011J​A0171​26
Anthes R, Schreiner W (2019) Six new satellites watch the atmosphere overearth’s equator. EOS. https://​doi.​org/​10.​1029/​2019E​O1317​79
Aveiro HC, Hysell DL (2010) Three-dimensional numerical simulation ofequatorial F region plasma irregularities with bottomside shear flow. J
Geophys Res. https://​doi.​org/​10.​1029/​2010J​A0156​02
Balan N, Oyama K-I, Bailey GJ, Fukao S, Watanabe S, Abdu MA (1997) A plasma
temperature anomaly in the equatorial topside ionosphere. J Geophys
Res 102:7485–7492. https://​doi.​org/​10.​1029/​97JA0​0039
Basu S, MacKenzie E, Basu S (1988) Ionospheric constraints on VHF/UHF communications links during solar maximum and minimum periods. RadioSci 23:363–378. https://​doi.​org/​10.​1029/​RS023​i003p​00363
Bilitza D, Altadill D, Truhlik V, Shubin VIG, Reinisch B, Huang X (2017) International reference ionosphere 2016: From ionospheric climate to real-time
weather predictions. Space Weather 15:418–429. https://​doi.​org/​10.​1002/​
2016S​W0015​93
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 Atmos Solar Terr Phys 50:937–942. https://​doi.​org/​
10.​1016/​0021-​9169(88)​90081-5
Carrano CS, Groves KM, Caton RG (2012) Simulating the impacts of ionospheric scintillation on l band sar image formation. Radio Sci 47:20.
https://​doi.​org/​10.​1029/​2011R​S0049​56
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/​2004G​L0208​00
Crowley G, Fish C, Pilinski M et al, ES (2016) Scintillation observations andresponse of the ionosphere to electrodynamics (SORTIE). In: Proceedingsof the 30th annual AIAA/USU smallsat conference, SSC16-VI-3
Drob DP, Emmert JT, Meriwether JW, Makela JJ, Doornbos E, Conde M,
Hernandez G, Noto J, Zawdle KA, McDonald SE, Huba JD, Klenzing JH(2015) An update to the Horizontal Wind Model (HWM): the quiet time
thermosphere. Earth Space Sci 2:301–319. https://​doi.​org/​10.​1002/​2014E​
A0000​89
Eccles JV (1998) A simple model of low-latitude electric fields. J Geophys Res
103:26699–26708. https://​doi.​org/​10.​1029/​98JA0​2657
Eccles JV (2004) The effect of gravity and pressure in the electrodynamics ofthe low-latitude ionosphere. J Geophys Res 109:05304. https://​doi.​org/​10.​1029/​2003J​A0100​23
Eccles JV, Valladares C (2021) Low-latitude plasma drifts from the horizontal
wind model and coupled ionopshere-electric field model. J Geophys Res.
https://​doi.​org/​10.​1029/​2020J​A0290​56
Eccles JV, Maynard N, Wilson G (1999) Study of the evening plasma drift vortex
in the low-latitude ionosphere using San Marco electric field measurements. J Geophys Res 104:8133–28143. https://​doi.​org/​10.​1029/​1999J​
A9003​73
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 120:4950–4970. https://​doi.​org/​10.​1002/​2014/​
JA020​664
Fejer BG (1993) F region plasma drifts over Arecibo: solar cycle, seasonal, andmagnetic activity effects. J Geophys Res 98:13635–13652. https://​doi.​org/​
10.​1029/​93JA0​0953
Fejer BG, Kudeki E, Farley DT (1985) Equatorial F region zonal plasma drifts. J
Geophys Res 90:12249–12255. https://​doi.​org/​10.​1029/​JA090​iA12p​12249
Fejer BG, de Paula ER, Gonzalez SA, Woodman RF (1991) Average vertical andzonal F region plasma drifts over Jicamarca. J Geophys Res 96:13901–
13906. https://​doi.​org/​10.​1029/​91JA0​1171

Shidler and Rodrigues ﻿Progress in Earth and Planetary Science(2022) 9:7

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 104:19859–19869. https://​doi.​org/​10.​1029/​1999J​A9002​71
Fejer BG, Santos AS, Costa Pereira AE (2005) Climatology of F region zonal
plasma drifts over Jicamarca. J Geophys Res. https://​doi.​org/​10.​1029/​
2005J​A0113​24
Fejer BG, Jensen JW, Su S-Y (2008) Quiet time equatorial F region verticalplasma drift model derived from ROCSAT-1 observations. J Geophys Res.
https://​doi.​org/​10.​1029/​2007J​A0128​01
Fejer BG, Hui D, Chau JL, Kudeki E (2014) Altitudinal dependence of evening
equatorial F region vertical plasma drifts. J Geophys Res 119:5877–5890.
https://​doi.​org/​10.​1002/​2014J​A0199​49
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 97:1209–1223. https://​doi.​org/​10.​1029/​91JA0​2226
Heelis RA (2004) Electrodynamics in the low and middle latitude ionosphere:
a tutorial. J Atmos 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 the
E 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
Heelis RA, Stoneback RA, Perdue MD, Depew MD, Morgan WA, Mankey MW,
Lippincott CR, Harmon LL, Holt BJ (2017) Ion velocity measurements
for the ionospheric connections explorer. Space Sci Rev 212:615–629.
https://​doi.​org/​10.​1007/​s11214-​017-​0383-3
Huang C (2018) Effects of the postsunset vertical plasma drift on the generation of equatorial spread F. Prog Earth Planet Sci. 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 120:2263–2275. https://​doi.​org/​10.​1002/​
2014J​A0207​35
Huang C, Wilson GR, Hairston MR, Zhang Y, Wang W, Liu J (2016) Equatorial
ionospheric plasma drifts and O+ concentration enhancements associated with disturbance dynamo during the 2015 St. Patrick’s Day magnetic
storm. J Geophys Res Space Phys. https://​doi.​org/​10.​1002/​2016J​A0230​72
Huba JD, Joyce G, Krall J, Siefring CL, Bernhardt PA (2010) Self-consistentmodeling of equatorial dawn density depletions with SAMI3. Geophys
Res Lett. https://​doi.​org/​10.​1029/​2009G​L0414​92
Hui D, Fejer BG (2015) Daytime plasma drifts in the equatorial lower ionosphere. J Geophys Res 120:9738–9747. https://​doi.​org/​10.​1002/​2015J​
A0218​38
Hysell DL, Kudeki E (2004) Collisional shear instability in the equatorial F region
ionosphere. J Geophys Res. https://​doi.​org/​10.​1029/​2004J​A0106​36
Hysell DL, Milla MA, Rodrigues FS, Varney RH, Huba JD (2015) Topside equatorial ionospheric density, temperature, and composition under equinox,
low solar flux conditions. J Geophys Res 120:3899–3912. https://​doi.​org/​
10.​1002/​2015J​A0211​68
Ieda A (2020) Ion-neutral collision frequencies for calculating ionosphericconductivity. J Geophys Res. https://​doi.​org/​10.​1029/​2019J​A0271​28
Immel TJ, England SL, Mende SB et al (2018) The ionospheric connection
explorer mission: mission goals and design. Space Sci Rev. https://​doi.​
org/​10.​1007/​s11214-​017-​0449-2
Kintner PM, Ledvina BM, de Paula ER (2007) GPS and ionospheric scintillations.
Space Weather 5:28163–28170. https://​doi.​org/​10.​1029/​2006S​W0002​60
Kudeki E, Bhattacharyya S (1999) Postsunset vortext in equatorial F-region
plasma drifts and implications for bottomside spread-F. J Geophys Res
104:28163–28170. https://​doi.​org/​10.​1029/​1998J​A9001​11
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. https://​doi.​org/​10.​1016/j.​jastp.​2007.​04.​012
Laundal KM, Richmond AD (2017) Magnetic coordinate systems. Space Sci Rev
206:27–59. https://​doi.​org/​10.​1007/​s11214-​016-​0275-y
Lee WK, Kil H, Kwak Y-S, Paxton LJ (2015) Morphology of the postsunset vortex
in the equatorial ionospheric plasma drift. Geophys Res Lett 42:9–14
Maute, A TIEGCM V1.94 Model Description. https://​www.​hao.​ucar.​edu/​model​
ing/​tgcm/​doc/​descr​iption/​model_​descr​iption.​pdf
Maute A, Richmond AD, Roble RG (2012) Sources of low-latitude ionospheric
ExB drifts and their variability. J Geophys Res. https://​doi.​org/​10.​1029/​
2011J​A0175​02

Page 17 of 17

Murphy JA, Heelis RA (1986) Implications of the relationship between electromagnetic drift components at mid and low latitudes. Planet Space Sci
34:645–652. https://​doi.​org/​10.​1016/​0032-​0633(86)​90042-5
Navarro LA, Fejer BG (2019) Storm-time thermospheric winds over peru. J
Geophys Res 124:10415–10427. https://​doi.​org/​10.​1029/​2019J​A0272​56
Navarro LA, Fejer BG (2020) Storm-time coupling of equatorial nighttime F
region neutral winds and plasma drifts. J Geophys Res 125:2020–028253.
https://​doi.​org/​10.​1029/​2020J​A0282​53
Nayar SR, Sreehari CV (2004) Investigation of height gradient in verticalplasma
drift at equatorial ionosphere using multifrequency HF doppler radar. J
Geophys Res. https://​doi.​org/​10.​1029/​2004J​A0106​41
Nicolet M (1953) The collision frequency of electrons in the ionosphere. J
Atmos Terr Phys 3:200–211. https://​doi.​org/​10.​1016/​0021-​9169(53)​90110-X
Pacheco EE, Heelis RA, Su S-Y (2011) Superrotation of the ionosphere andquiet time zonal ion drifts at low and middle latitudes observed by
Republic of China Satellite-1 (ROCSAT-1). J Geophys Res. https://​doi.​org/​
10.​1029/​2011J​A0167​86
Picone JM, Hedin AE, Drob DP, Aikin AC (2002) NRLMSISE-00 empirical modelof the atmosphere: statistical comparisons and scientific issues. J Geophys Res. https://​doi.​org/​10.​1029/​2002J​A0094​30
Pingree JE, Fejer BG (1987) On the height variation of equatorial F region vertical plasma drifts. J Geophys Res 92:4763–4766. https://​doi.​org/​10.​1029/​
JA092​iA05p​04763
Richmond AD, Fang TW, Maute A (2015) Electrodynamics of the equatorial
evening ionosphere: 1. Importance of winds in different regions. J Geophys Res 120:2118–2132. https://​doi.​org/​10.​1002/​2014J​A0209​34
Rodrigues FS, Crowley G, Heelis RA, Maute A, Reynolds A (2012) On TIE-GCM
simulation of the evening equatorial plasma vortex. J Geophys Res.
https://​doi.​org/​10.​1029/​2011J​A0173​69
Scherliess L, Fejer BG (1999) Radar and satellite global equatorial F region vertical drift model. J Geophys Res 104:6829–6842. https://​doi.​org/​10.​1029/​
1999J​A9000​25
Schunk RW, Nagy AF (2009) Ionospheres: physics, plasma physics, and chemistry. Cambridge University Press, Cambridge
Shidler SA, Rodrigues FS (2019) On the magnitude and variability of heightgradients in the equatorial F region vertical plasma drifts. J Geophys Res
124:4916–4925. https://​doi.​org/​10.​1029/​2019J​A0266​61
Shidler SA, Rodrigues FS (2021) On a simple, data-aided analytic descriptionof the morphology of equatorial F-region zonal plasma drifts. Prog Earth
Planet Sci. https://​doi.​org/​10.​1186/​s40623-​020-​01227-w
Shidler SA, Rodrigues FS, Fejer BG, Milla MA (2019) Radar studies of heightdependent equatorial F-region vertical and zonal plasma drifts. J Geophys Res 124:2058–2071. https://​doi.​org/​10.​1029/​2019J​A0264​76
Smith JM, Rodrigues FS, de Paula ER (2015) Radar and satellite investigations ofequatorial evening vertical drifts and spread F. Ann Geophys 33:1403–
1412. https://​doi.​org/​10.​5194/​angeo-​33-​1403-​2015
Spann J, Swenson C, Durao O, Loures L, Heelis R, Bishop R, Le G, Abdu M,
Krause L, Fry C, et al. (2017) The scintillation prediction observations
research task (SPORT): an international science mission using a cubesat.
In: Proceedings of the AIAA/Utah State University conference on small
satellites
Stoneback RA, Heelis RA, Burrell AG, Coley WR, Fejer BG, Pacheco E (2011)
Observations of quiet time vertical ion drift in the equatorial ionosphere
during the solar minimum period of 2009. J Geophys Res. https://​doi.​org/​
10.​1029/​2011J​A0167​12
Sultan PJ (1996) Linear theory and modeling of the Rayleigh-Taylor instability leading to the occurrence of equatorial spread F. J Geophys Res
101:26875–26891. https://​doi.​org/​10.​1029/​96JA0​0682
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 Sp. https://​doi.​org/​10.​1186/​s40623-​015-​0228-9
Wohlwend CS (2008) Modeling the electrodynamics of the low-latitude ionosphere. Ph.D. thesis, Utah State University

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