Cullens et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-020-00330-6(2020) 7:18

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open AccessSensitivity study for ICON tidal analysis
Chihoko Y. Cullens1*, Thomas J. Immel1, Colin C. Triplett1, Yen-Jung Wu1, Scott L. England2, Jeffrey M. Forbes3 andGuiping Liu1

Abstract
Retrieval of the properties of the middle and upper atmosphere can be performed using several different
interferometric and photometric methods. The emission-shape and Doppler shift of both atomic and molecularemissions can be observed from the ground and space to provide temperature and bulk velocity. These
instantaneous measurements can be combined over successive times/locations along an orbit track, or successive
universal/local times from a ground station to quantify the motion and temperature of the atmosphere needed to
identify atmospheric tides. In this report, we explore how different combinations of space-based wind andtemperature measurements affect the retrieval of atmospheric tides, a ubiquitous property of planetaryatmospheres. We explore several scenarios informed by the use of a tidally forced atmospheric circulation model,
an empirically based emissions reference, and a low-earth orbit satellite observation geometry based on the ICON
mission design. This capability provides a necessary tool for design of an optimal mission concept for retrieval of
atmospheric tides from ICON remote-sensing observations. Here it is used to investigate scenarios of limited data
availability and the effects of rapid changes in the total wave spectrum on the retrieval of the correct tidal spectrum.
An approach such as that described here could be used in the design of future missions, such as the NASA DYNAMIC
mission (National Research Council, Solar and space physics: a science for a technological society, 2013).
Keywords: Atmospheric tides, ICON

Introduction
The ionosphere is affected by both solar and lower atmospheric inputs (Forbes et al. 2000). Atmosphericwaves including planetary waves, tides, and gravity waves
are the main agents for transporting energy and momentum from the lower atmosphere to the ionosphere andthermosphere. Among these waves, various observations
and simulation studies have revealed that atmospherictides originating in the troposphere and stratospherehave significant influences on the ionosphere (e.g.,
Immel et al., 2006; England et al., 2006; Forbes 2007;
Forbes et al. 2018; England 2011; National ResearchCouncil 2013; and references therein). Because of theirapparently dominant effects, it is critical to simulate
realistic atmospheric tides in models. The upper atmospheric models (e.g., National Center for Atmospheric* Correspondence: yamashita@berkeley.edu
1Space Sciences Laboratory, University of California Berkeley, Berkeley, USA
Full list of author information is available at the end of the article

Research
Thermosphere-Ionosphere-Electrodynamics
General Circulation Model; NCAR TIE-GCM; Maute2017) use various tidal forcing methods at their lower
boundaries including the Global Scale Wave Model(GSWM; Hagan and Forbes 2002, 2003) and Climatological Tidal Model of the Thermosphere (CTMT; Oberheide et al. 2011). The GSWM is a model that solves fordiurnal and semi-diurnal tides with realistic backgroundconditions that originate in observations and/or empirical models. The CTMT estimates global tides by fitting
Hough Mode Extensions (HMEs) to SABER (the Sounding of the Atmosphere using Broadband Emission Radiometry) and TIDI (the TIMED Doppler Interferometer)
tidal determinations between ± 50° latitude and 80–105
km altitude from 2002 to 2008.
The Ionospheric Connection Explorer (ICON; Immel
et al. 2018) mission (launched October 10, 2019) observes temperatures and winds from the mesosphere to
the thermosphere continuously in day and night from 90
to 105 km in the latitude range of 10°S to 40°N,© The Author(s). 2020 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 ifchanges were made. The images or other third party material in this article are included in the article's Creative Commonslicence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commonslicence 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/.

(2020) 7:18

Page 2 of 13

providing data adequate to evaluate the properties of arange of global tidal fields. The wind and temperature
data will be fit with a set of HMEs that are representative of the tidal components present in the atmosphere(e.g., Forbes and Hagan 1982). Using these data, the
TIE-GCM lower boundary will be specified using the
ICON-HME tidal field in order to provide a realistic
upper atmospheric and ionospheric simulation (Immel
et al. 2018; Forbes et al. 2017; Maute 2017). The ICONHME is a derived Level-4 mission data product that will
be distributed as a product of the ICON mission (Forbes
et al. 2017; Maute 2017).
Tidal analyses from satellite observations have several
difficulties and limitations. The main issue is that a fit totides by the HMEs demands an observational set with
sufficient coverage in latitude, longitude, height, andlocal time to specify the important tidal components. To
provide any data that is complete in this respect, observations are required to accumulate over certain periodsof time. Given the interest in specifying the temporally
variable tides over as short a period as possible, the performance of the HMEs with a partially full matrix is examined. A number of observational factors could reduce
data availability, and so potentially further reduce thedata available to the HME fit. These include the possibility of wind observations that have errors large enough to
be flagged as “do not use,” short-term variations in the
tidal field and short-term global-scale changes in thewind field originating in phenomena other than tides(e.g., planetary waves). It is important to understand thelimitations and sensitivity of the tidal analysis and its influence on the obtained tidal field. In this study, using
the ICON mission as an example, we will examine anddiscuss what can affect the tidal analysis and what needs
to be considered when ICON is flown and when future
missions are designed.

HMEs are computed using the GSWM with zero-velocity
background winds and global mean vertical temperatureand density profiles derived from the MSISE90 empiricalmodel (Hedin 1991). Each HME maintains a selfconsistent amplitude and phase relationship for the perturbation fields in temperature, zonal, meridional and vertical wind, and density (T, u, v, w, ρ). HMEs are arbitrarily
calibrated in amplitude to yield a maximum perturbation
horizontal wind speed of 10 m/s (either zonal or meridional, whichever is larger) at 93 km. Absolute values ofphases are also arbitrary. HME fitting involves finding asingle complex normalizing factor for the HMEs that determines absolute amplitudes and phases for all variables
that best fit the input data in a least-squares sense. Figures
1 and 2 show structures of amplitude and phase in zonal
wind tides for the DW1, SW2, and DE3 HMEs. These also
show the first symmetric and first antisymmetric HMEs,
respectively. For antisymmetric HMEs, antisymmetry enters through the phases.
In addition, the HMEs include the effects of dissipation, thus allowing extrapolation of the fitted fields into
the thermosphere where the latitude and height dependences are no longer separable. Given tidal phases andamplitudes at a sufficiently diverse set of latitudes andaltitudes, the HME provides a tool for fitting and reconstruction of the global atmospheric tidal field that is
widely used. For example, Svoboda et al. (2005) tested
and validated HME fitting against output from a generalcirculation model and applied the methodology to UARS
(Upper Atmosphere Research Satellite) wind measurements. More recently, TIMED SABER and TIDI observations of temperatures and winds in the 80–105 km
altitude range are used to create an HME-based tidal climatology of winds in the 80–400 km range and published as the CTMT dataset by Oberheide et al. (2011).
Therefore, HME has been widely used and tested, anddetailed HME methodologies are summarized in Forbes
et al. (1994), and HME for ICON is summarized in Forbes et al. (2017) and references there in.
In this study, HMEs are fit to tidal temperatures andzonal winds from TIME-GCM data (see “TIME-GCM
simulations” section). Unless otherwise specified, a latitude range of 10°S to 40°N and an altitude range of 90–
105 km are used for the input data to the HME fit. The
HME fit produces an output of tidal amplitudes andphases in zonal winds, meridional winds, vertical winds,
temperatures, and densities/geopotential heights from
90°S to 90°N. In this study, our main focus is HME results at ~ 97 km, the height of TIE-GCM lower boundary and most results are shown at this altitude.

Cullens et al. Progress in Earth and Planetary Science

Methods/Experimental
HME (Hough Mode Extension)

Hough’s original work in 1898 presented a critical mathematical representation of oscillations on a rotating
earth as an eigenfunction-eigenvalue problem. The
eigenfunctions are solutions to Laplace’s tidal equationand provide the latitudinal structures, whereas the eigenvalues are related to the depth of the oscillating fluid.
The eigenvalues comprise an orthogonal set of functions
that can be fit through a least-squares method to any appropriate dataset (Hough 1898). However, it is not physically meaningful to fit Hough functions to winds. To
enable fits that include self-consistent relationships between perturbation fields in temperature, zonal, meridional and vertical wind, and density (T, u, v, w, ρ), theHough Mode Extension (HME) was developed by Lindzen et al. (1977) and Forbes and Hagan (1982). The

ICON observations

Temperatures and winds will be measured by the Michelson
Interferometer for Global High-Resolution ThermosphericCullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 3 of 13

Fig. 1 First symmetric HME amplitudes and phases for zonal wind (U) for a, b DW1; c, d SW2; and e, f DE3. HMEs are arbitrarily calibrated inamplitude to yield a maximum perturbation horizontal wind speed of 10 m/s (either zonal or meridional, whichever is larger) at 93 km. Absolutevalues of phases are also arbitrary

Imaging (MIGHTI) instrument (Englert et al. 2017; Harlander et al. 2017; Harding et al. 2017). ICON-MIGHTI
temperature and wind data need to be accumulated overtime to adequately constrain the tides (in height, latitude,
longitude, and local time) that form the basis for the HME
fits (Immel et al. 2018). The ICON-MIGHTI observations
are simulated using an orbital dynamics simulation of theobservatory in science mode and a concurrent run of the
TIME-GCM (see “TIME-GCM simulations” section). The
wind and temperature observations come from locations approximately 1500 km from the observatory and a latitude
range that is nominally from 10 to 15° north of the ICON
orbit track, depending on the angle between observatory velocity vector and the local meridional plane.
ICON provides data with coverage that varies significantly if a window smaller than a full orbital precession
cycle is used. Figure 3 shows the latitudinal coverage of
ICON sampling at a longitude of 30°E and 12 local times(LT) within two 27-day analysis windows. In Fig. 3,
ICON sampling from day of year (DOY) 220 to DOY
246 (27-day sampling) extends from 10°S to 40°N, thefull range of possible latitudes. However, as the center of

the analysis window advances from DOY 230 to DOY
256, the only latitudes measured are in the Northern
Hemisphere. One can address this with a longer window,
but the optimal window for revealing the shorter-period
tidal variations uses the fewest days of data. Figure 4
shows local time coverage of ICON sampling vs. window
size. A window size of n days indicates ICON data collection through day and night during n days to calculate tidal
amplitudes and phases. Based on Fig. 4, a window size of
39 days provides 22 h of local time for the worst-case maximum excursion in latitude (with similar coverage in thesouth, not shown). Given our numerous experiments withdifferent coverage, we can state that this local time coverage at every latitude provides wind and temperature datathat is adequate to constrain the HME fit. As a baseline
for the examination of missing data on the HME fits, full
local time coverage with 41-day window will be used here.
TIME-GCM simulations

Atmospheric simulations from TIME-GCM are used to conduct this sensitivity study (Roble and Ridley 1994). In orderto have a realistic simulation for testing, the lower boundaryCullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 4 of 13

Fig. 2 First antisymmetric HME amplitudes and phases for zonal wind (U) for a, b SW2 and c, d DE3. The latitude structure HME2 amplitude for
DW1 does not resemble the first antisymmetric mode of classical tidal theory (maxima near ± 24° latitude) due to the strong influence ofmolecular dissipation, which couples the vertically-propagating DW1 with short vertical wavelength into an evanescent tidal mode

at 10 hPa is specified by 3-hourly Modern-Era Retrospective
analysis for Research and Applications (MERRA) data. The
horizontal resolution is 2.5° × 2.5° (latitude × longitude), andthe vertical resolution is four grid points per scale height.
MERRA data are interpolated to TIME-GCM longitudelatitude grid. TIME-GCM uses gravity wave parametrization
scheme based on Lindzen (1981). Comparison of tidal amplitudes from SABER observations and MERRA-forced TIMEGCM simulations can be found in Forbes et al. (2017). These
TIME-GCM simulations conducted for the solar minimum
year of 2009. The 3-hourly KP index and daily solar fluxes
are used as input to the model. The model domain is from ~30 km (10 hPa) to ~500 km with 97 vertical levels. TIMEGCM data from DOY 220 to 260 (41 days window) are sampled based on the predicted ICON sampling locations formost of the sensitivity study. Detailed model setup is described in Häusler et al. (2014, 2015).

of ~ 97 km altitude. Its performance vs the TIME-GCM
runs in simulating the tidal spectrum is evaluated here.
Zonal-mean wind, temperature, and geopotential heightfrom Mass Spectrometer Incoherent Scatter Rader Extended (MSIS E00) (Picone et al. 2002) and the horizontal
wind model (HWM07) (Drob et al., 2008) are specified at
the lower boundary. In accordance with the above statedgoal of comparing the TIME-GCM to the TIE-GCM forcedby simulations of MIGHTI measurements of that same
TIME-GCM atmosphere, diurnal and semi-diurnal tides
are specified using HMEs developed in this study as described above. Detailed model setup and ionospheric simulations for the ICON mission can be found in Maute(2017). HME fits are performed on TIME-GCM output
with ICON sampling for this study, and results are shownin the “Results and discussion” section.

Results and discussion
TIE-GCM simulations

The NCAR TIE-GCM V2.0 is also used for this work
(Maute 2017). In the course of the ICON mission, this willbe the model that ingests the HME fit at its lower boundary

Sensitivity study
Sampling window size

The effect on the HME fit of reducing the window size
to less than 41 days is shown in Fig. 5. HME-determinedCullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 5 of 13

Fig. 3 Latitudes of ICON sampling at 30° longitude and 12 local time within two 27-day analysis windows

Fig. 4 a Local time coverage in 2 latitude ranges. Solid lines indicate average local time coverage and dashed lines represents maximum andminimum local time coverage at each latitude range. b Contour plots of local time coverage with window size of 41 days, with 24 h indicating
full local time coverage

Cullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 6 of 13

Fig. 5 Comparisons of tidal amplitudes using different window size from 41 to 25 days. Colors represent different latitudes for solid-black (35°N–
40°N), solid-blue (25°N–35°N), solid-green (15°N–25°N), solid-red (5°N–15°N), dashed-blue (5°S–5°N), and dashed-red (10°S–5°S). Amplitudedifferences between with and without ICON sampling are shown in a and b for DE3 and SW2, respectively. Percentages of these differences areshown in c and dtidal amplitudes using ICON sampling windows ranging
from 41 down to 25 days are compared to tides determined from complete sampling. The latter are simply theactual averaged tidal amplitudes over the corresponding
window size. Hence, differences of tides in Fig. 5 are simply representing the influence of varying ICON samplingon tidal extraction. DE3 (eastward-propagating diurnal
tide with zonal wavenumber 3) and SW2 (westwardpropagating semi-diurnal tide with zonal wavenumber 2)
are selected to highlight due to the likely importance ofeach in influencing the ionosphere and also to provide diurnal and semi-diurnal tidal results. In this study, to represent different tidal components, the notation DWs or DEs
will be used to indicate a westward or eastwardpropagating diurnal tide, respectively, with zonal wavenumbers. “D” will be replaced with “S” for semi-diurnal
tides. For example, DE3 will be eastward propagating diurnal tides with zonal wavenumber 3.
As expected, differences get larger as window size getssmaller because of missing local time coverage. However, largest absolute amplitude differences for DE3 andSW2 are ~ 2 m/s and ~ 3 m/s, respectively, within a 27day window size from Fig. 5 a and b. These changes are~ 20% as shown in Fig. 5 c and d. Blue and black lines
in Fig. 5c and dashed-red and dashed-blue lines in Fig.
5d show significantly large changes in percentages, andthese are due to very small tidal amplitudes in these latitude ranges. Absolute differences for these abnormal
percentages are still less than ~ 2 m/s, indicating that
only moderate influences are anticipated on the HME
fits to these data. For temperature and meridional windtides (not shown), the largest absolute amplitude differences are also ~ 2.5–3 m/s and ~ 1 K for DE3,

respectively. Percentage changes of temperature and meridional wind tides for DE3 and SW2 are similar to zonal
wind change shown in Fig. 5.
Terminator and missing local time

One potential problem of ICON observations is the possible gap in local time coverage near Earth’s solar terminator. Because of the rapid variation in the airglow
profiles with altitude, the wind retrievals may have large
uncertainties. Therefore, the effect of the absence of dataat the terminator is examined in this section. DE3 results
are mainly presented in this paper because of its dominant presence in the lower thermosphere during certain
months. SW2 results are also shown here as an example
of semi-diurnal tides.
The amplitudes of the DW1, DE3, and SW2 tides retrieved from the tidal fits where data are excluded in
specific local time ranges are shown vs latitude in Fig. 6.
These tides are calculated from ICON-sampled TIMEGCM with MERRA lower boundary simulated for DOY
220 to 260, 2009. Tests using different gaps in local time
are indicated by different colors, noted in the figure legend. Black represents the base case with full local timecoverage. Blue lines, for example, indicate missing morning local times from 4 LT to 8 LT. For DW1, DE3, andSW2 (Fig. 6a, c, and e), the most notable features arethat a 4–8 LT data gap results in the largest differencesfrom the base case, with departures up to ~ 10–15 m/s
in winds. On the other hand, cases of missing local time
both in the morning and evening sector (green lines)(“5–7 LT + 17–19 LT”) show only changes of ~2–5 m/s
in zonal winds. For DE3, the largest changes are where
amplitudes of DE3 are normally small (less than 5 m/s).

Cullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 7 of 13

Fig. 6 Line plots of a, b DW1; c, d DE3; and e, f SW2 tidal (left) amplitudes and (right) phases for zonal wind tides at 97 km. Different colors
indicate different missing local times. For example, “5–7 LT + 17–19 LT” means that tidal amplitudes are calculated using data with missing local
times of 5, 6, 7, 17, 18, and 19 LT

DE3 amplitudes between 10°S and 20°N where the DE3
peak usually lies show no significant influences frommissing local time around the terminator. For DW1 andSW2, all missing data tests introduce only small changes
in the observed phases of DW1 and SW2. The general
latitudinal structures of DW1 and SW2 amplitudes are
similar with and without missing local times, and missing local times from 5–7 LT (3 h) cause ~ 5 m/s changes,
which translate to ~ 35% differences in SW2 and ~ 25%
differences in DW1.
Effects of data gaps on the DE3 amplitudes and phases
vs altitude and latitude are shown in Fig. 7. Here we use
HME extensions above 97 km for these numerical experiments, although when applied in the ICON mission theextensions will be performed using the TIE-GCM. Figure 7 a and d illustrate amplitudes and phases of zonal
wind based on the HME fit at 97 km wherein data fromall local times are included. Figure 7 b and e illustratedifferences in amplitude and phase from those in Fig. 7
a and d when observations in the 5–7 h LT range are absent. Differences in DE3 are greatest (2–4 m/s) around
110 km and in the 0–20°N range. Peak amplitudes of
DE3 in Fig. 7a in this area are ~ 12–16 m/s, indicatingthat changes up to ~ 15–25% with 3 h of continuous
missing data can occur. Figure 7 c and f show the sameas Fig. 7 b and e but with 5 h of continuous missing datafrom 4 LT to 8 LT. The largest differences grow to ~30% and are again in the latitude range of 0–20°N in the
100–110 km altitude range. Changes in phases are greatest (2–4 h) in the latitude range of 20–40°N and altitude
range of ~ 95–110 km with 3 h of missing local time.
Small differences in amplitudes are approximately associated with the largest shifts of phases of DE3 in the
Northern Hemisphere where, as noted in Fig. 6, the largest amplitude changes are found. From these results,
we find that DE3 will be reasonably estimated even withterminator influences on local time coverage as long as
missing local times are less than ~ 4 h continuously, andmissing both dawn and dusk terminator data does nothave large effects on DE3 tidal amplitudes.
In addition to missing local times, effects of randomly
missing data on the tidal analysis for DW1, DE3, andSW2 are examined here using an ensemble approachthat effectively simulates a reduction in duty cycle of the
instrument. Tides are estimated from observations limited to a total of 21, 19, and 17 h of local time coverageout of 24 h. Missing local times, in 1 h increments are
randomly selected for these cases, with 10 separate,
random-sampling cases fitted for each. The results areshown with 10 colors in Fig. 8. Tidal analysis with missing 3 h, 5 h, and 7 h LTs are shown. DE3 in Fig. 8 a, c,and e show the growing range of tidal amplitudes

Cullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 8 of 13

Fig. 7 Height vs. latitude structures of DE3 HME a, b, c amplitudes and d, e, f phases. Left plots a, d show zonal wind tidal amplitudes (m/s)
based on fits including all local times. Middle and right plots show differences of zonal wind tidal amplitudes between fits to data with complete
all local time coverage and data with missing local time b and e from 5 LT to 7 LT and c and f from 4 LT to 8 LT

resulting from increasingly sparse data. SW2 fits in Fig. 8b, d, and f show variations of similar percentage, but also
possibly a more resilient fit to missing data, with the 7 htotal missing data case no worse than the 3 h case.
Limited altitude coverage

All satellite observations have limited altitude coverage.
For ICON, a mission requirement is to provide continuous observations of winds and temperatures from ~ 90
to ~105 km. This section tests the sensitivity of HME fits
to both wider and more limited observational ranges. Allanalyses here use the latitude range of 10°S–40°N withfull local time coverage for the tidal fit. Figure 9 a shows
ICON-sampled TIME-GCM DE3 zonal wind amplitudes
between 10°S and 40°N and 90–140 km; values between
90 and 105 km are the source data for the various HME
fits shown in Fig. 9b–d. Figure 9b illustrates the heightlatitude HME amplitude structure based on fitting to thebaseline 90–105 km observations, and its vertical extension to 140 km. Additionally, DE3 zonal wind amplitudes
determined via HME fits to 95–105 km, and more limited 100-105 km input altitudes are shown in Fig. 9c andd, respectively.
There are several points to be made concerning thisfigure, which elucidates several important points aboutthe HME methodology and its application within the
ICON mission. The first, which gets at the main purposeof this subsection, is that HME fitting of the input DE3
tide is very similar between the three cases, albeit withslightly different amplitudes. The amplitudes with inputs
from 90 to 105 km are larger and closer to the actual
DE3 amplitudes than those with 95–105 km and 100–105 km. Amplitudes from 100 to 105 km inputs areslightly smaller than the input tides. Although there aresome differences, the conclusion is that HME fitting is
not very dependent on complete altitude coverage of
ICON data between 90 and 105 km.
A second point concerns the differences in structure
between the input DE3 tide between 90 and 105 km in
Fig. 9a, and those depicted in Fig. 9b–d. For HME fittingof DE3, only the first symmetric and first antisymmetricmodes are utilized. There are two reasons. The first isthat the first 3 modes of DE3 have vertical wavelengths(λz) of 56, 30, and 19 km based on classical tidal theory.
Molecular dissipation of these 3 modes increase as 1/(ρλ2z ) where ρ is the background density. The first modecan effectively penetrate into the thermosphere above
100 km, the second mode significantly less so, and thethird mode is not at all effective. A tide with the vertical
wavelength of 19 km would also not be at all effective in
generating electric fields in the dynamo region, since thisprocess involves height-integrated conductivity-weighted
winds. In a fitting process, the purpose of including
higher-order modes is to capture higher-order horizontal

Cullens et al. Progress in Earth and Planetary Science(2020) 7:18

Page 9 of 13

Fig. 8 Line plots show a, c, e DE3 and b, d, f SW2 tidal amplitudes in zonal winds calculated using ICON-sampled TIME-GCM simulations at 97
km. Tidal amplitudes calculated using data with missing a, b 3 h; c, d 5 h; and e, f 7 h of local time randomly. Each panel contains 10 tidal
amplitudes calculated using randomly generated local time gap

Fig. 9 a ICON-sampled TIME-GCM DE3 zonal wind amplitudes (m/s) and remaining plots are HME DE3 zonal wind amplitudes based on fits to
ICON-sampled TIME-GCM DE3 tidal amplitudes in the altitude range of b 90–105 km, c 95–105 km, d 100–105 km. White lines indicate 105 km toindicate ICON sampling altitude(2020) 7:18

Page 10 of 13

structure, but doing so is not beneficial when thosemodes do not contribute to vertical coupling. Our experience furthermore shows that fitting to the low-order
HME components is much more stable and reliable than
to the higher-order components. For all of these reasons,HME fitting with respect to DE3 is restricted to the firstsymmetric and first antisymmetric HMEs, recognizingthat not capturing all of the fine structure between 90
and 105 km is not consequential to the problem at hand.
A third point concerns the differences in heightlatitude structure of DE3 between Fig. 9a and the rest of
the panels in Fig. 9 at altitudes above 105 km. The feature above 110 km near 40°N is not representative of
DE3 in the full-sampled TIME-GCM output but is more
likely attributable to aliasing into the ICON sampling by
one or more other waves (e.g., SE3) in this highly dynamic environment presented by the MERRA-forced
TIME-GCM (see, e.g., Forbes et al. 2017). It is a good
example of why diligent oversight of the HME fitting
process will be required during the ICON mission. In
this case, the feature did not appreciably influence theHME fitting since it does not project onto the DE3
HME structures. The differences in structure equatorward of 20°N, in particular the higher altitude of thepeak near 117 km versus 110 km in Fig. 9b–d, may also
be due in part to sampling but may also reflect a deficiency of the GSWM at these altitudes, i.e., an overestimate of mechanical dissipation. However, this isinconsequential insofar as ICON is concerned, since it is
the TIE-GCM that will specify the dynamics at these altitudes. The reader is referred to the comparison between TIME-GCM and TIE-GCM tidal structures in the“Comparisons between TIME-GCM and HME forced
TIE-GCM” section for more insights.

Cullens et al. Progress in Earth and Planetary Science

Limited observation variables

The ICON MIGHTI instruments measure temperature,zonal winds, and meridional winds. HME fits presented
in prior subsections are performed using all three measurements. It is possible that ICON-MIGHTI, or any future mission, might measure only one or two variables
and not all three. Hence, influences of missing variables
on HME fit are examined here. Input tides and HME fits
to data between 90 and 105 km with different input variables are shown in Fig. 10 for DE3 and SW2. For DE3 in
Fig. 10, HME fits with TUV (temperature, zonal winds,
and meridional winds), HME fits with UV (zonal windand meridional wind), HME fits with TU (temperatureand zonal wind), and HME fits with T (temperature) arevery similar, and missing variables have small influenceson DE3 in this case. As discussed in connection with
Fig. 9, although HME fits are similar, there are some differences between input DE3 tidal amplitudes and HME
DE3 amplitudes in particular above 35°N.
For SW2, input SW2 tides vs. HME fits with TUV,
UV, and TU in 10°S–40°N compare well. HME fits with

Fig. 10 a, b ICON-sampled TIME-GCM DE3 and SW2 zonal wind tidal amplitudes that are used to fit HMEs (between 90–105 km), and c–j HMEs
based on fits to c, d both temperature, zonal wind, and meridional wind; e, f zonal and meridional winds; g, h temperature and zonal wind; andi, j temperature only for (left) DE3 and (right) SW2

(2020) 7:18

Page 11 of 13

only T (temperature) generally overestimate tidal amplitudes in this case. Therefore, our results indicate thatHME fits works better if two or more variables are used
to constrain it. This is consistent with conclusions
drawn by Svoboda et al. (2005).

HME fits are performed. Then these HME tidal fields
are used to force the TIE-GCM, and results are shownin Fig. 11b. In TIME-GCM for DW1, there are two large
peaks in the latitude range of 60–80°S and 40–60°N
from 120 to 150 km, and these two peaks can also befound in TIE-GCM. These are signatures of the diurnal
tide excited in situ by absorption of solar EUV radiation.
From 90 to ~ 110 km, there are also two peaks around
20°S and 30°N, which are captured by TIE-GCM as well,and these are due to DW1 excited mainly in the troposphere. These DW1 amplitudes are reduced in TIMEGCM compared to TIE-GCM, and this is possibly attributable to inclusion of a Lindzen-based gravity wave
parameterization in the TIME-GCM (Lindzen 1981; Liuand Roble 2002) below 120 km, which is known to reduce DW1 amplitudes (Miyahara and Forbes 1991,
1994; Forbes et al. 1991).
Figure 11 c and d show comparisons between TIMEGCM and HME-forced TIE-GCM for DE3. General
structures of DE3 are well captured by TIE-GCM,
though there are differences between TIME-GCM and
TIE-GCM above 110 km. One of the causes of differences between TIME-GCM and TIE-GCM results canbe inclusion of a gravity wave parametrization scheme in
the former, which may also introduce mean wind effects
that produce some distortions. Another is the presenceof higher-order modes of DE3 in the TIME-GCM which
are damped out by molecular dissipation above 110 km,
as explained in the “Limited altitude coverage” section.

Cullens et al. Progress in Earth and Planetary Science

Comparisons between TIME-GCM and HME forced TIEGCM

As the last part of this current work, the veracity of a
TIE-GCM simulation with ICON-HME tidal forcing isdemonstrated here. For the ICON mission, tidal fields
obtained from HME-ICON will force the lower boundary of the TIE-GCM. To simulate a realistic case, ICONsampled TIME-GCM data are used to calculate tidal amplitudes and phases between 90 and 105 km in the latitude range of 10°S–40°N. The HME fits to these tidal
data are then used to force the TIE-GCM lower boundary at ~ 97 km. One reason to use ICON-HMEs to force
the TIE-GCM is to generate realistic tidal fields in TIEGCM above 97 km. A goal of this test is to see if tidal
fields from TIME-GCM above 97 km and TIE-GCM
above 97 km are similar. Only tidal amplitudes areshown in this section. Detailed analysis of ICON forced
TIE-GCM are discussed in Maute (2017).
Figure 11 a shows DW1 tidal amplitudes obtained
from the TIME-GCM simulation that covers the altitude
range from 30 to ~ 500 km. A white line in Fig. 11a indicates the lower-boundary of the TIE-GCM. Using
TIME-GCM tidal data in 10°S–40°N and 90–105 km,

Fig. 11 a, c TIME-GCM and b, d TIE-GCM simulations of a, b DW1 and c, d DE3. White lines indicate where the 97 km lower boundary of TIEGCM is located and where the HME input is introducedCullens et al. Progress in Earth and Planetary Science(2020) 7:18

Our overall conclusion is that lower boundary conditions extending pole to pole based on HME fitting to
ICON observations that are restricted to 12°S to 40°N
and 90–105 km altitude can lead to realistic tidal structures in the TIE-GCM. This capability will enable us tosignificantly advance ICON science within an observation- and physics-based modeling framework.

Conclusions
A sensitivity study of tidal analyses pertaining to potential satellite observational sampling constraints are discussed in this paper, including missing local times,
limited altitude coverage, and missing observed variables. The most critical of these is that any systematic
gap in data in some local time range (possibly the terminators) has the potential to cause a 20–30% of change in
the amplitudes of HMEs fitted to tides retrieved fromobservations with these gaps, though this effect depends
on the tide and whether the gaps are symmetric aboutnoon (as is the case with the terminators). Comparatively, an under-sampled parameter space in local time,
if randomly distributed, has a more predictable effect of
introducing a slowly increasing overall error in the HME
that is roughly evenly distributed in latitude. In any case,the effect of missing local times needs careful consideration when analyzing tides from satellite observations.
Further, we show that a reduction in the altitude rangeof observations in the MLT region does not adversely
affect the retrieval of tidal components by the HME fitting procedures.
Tidal amplitudes and phases between TIME-GCM and
TIE-GCM simulations above 97 km are compared. TIEGCM simulations are conducted using HME tidal lower
boundary from TIME-GCM 90-105 km tidal amplitudes
and phases. Results confirm that TIE-GCM with HME
tidal field as a lower boundary input can approximate
well the DE3 and DW1 TIME-GCM tidal fields in themesosphere and the thermosphere. Thus, the HMEforced TIE-GCM provides a representation of the MLT
that is similar to a fully simulated model with inputs originating in the middle atmosphere. As tides are important for reproducing ionospheric variability, further studyof potential influences of missing-local time on the ionospheric simulations will be conducted.
Acknowledgements
We acknowledge Astrid Maute for providing us TIME-GCM simulations andJens Oberheide for valuable discussions on this subject.
Declarations
Results of simulation results are available at University of California Berkeley.
Please contact author for data requests.
Authors’ contributions
CYC analyzed tides and conduct HME fits. TJI, SLE, and JMF provided originalideas, and contributed to writing this manuscript and interpreting results.
JMF provided HME packages. CCT conducted TIE-GCM simulations andPage 12 of 13

interpreting results. YJW provided locations of ICON samplings and generated synthetic ICON data. GL modified HME codes and created HME/tidal
analysis codes for this ICON mission. The author(s) read and approved thefinal manuscript.
Funding
ICON is supported by NASA’s Explorers Program through contracts
NNG12FA45C and NNG12FA42I. JMF was supported under the NASA ICON
Project through the University of California at Berkeley under Award
00008209 to the University of Colorado.
Competing interests
The authors declare that they have no competing interest.
Author details
1
Space Sciences Laboratory, University of California Berkeley, Berkeley, USA.
2
Virginia Polytechnic Institute and State University, Blacksburg, USA.
3
University of Colorado at Boulder, Boulder, USA.
Received: 4 September 2019 Accepted: 22 April 2020

References
Drob DP et al (2008) An empirical model of the Earth's horizontal wind fields:
HWM07. J Geophys Res 113:A12304. https://doi.org/10.1029/2008JA013668
England SL (2011) A Review of the Effects of Non-migrating Atmospheric Tides
on the Earth’s Low-Latitude Ionosphere. Space Sci Rev 168(1-4):211–36.
https://doi.org/10.1007/s11214-011-9842-4
England SL, Maus S, Immel TJ, Mende SB (2006) Longitudinal variation of the Eregion electric fields caused by atmospheric tides. Geophys Res Lett 33:21
Englert CR, Harlander JM, Brown CM, Marr KD, Miller IJ, Stump JE, Hancock J,
Peterson JQ, Kumler J, Morrow WH, Mooney TA, Ellis S, Mende SB, Harris SE,
Stevens MH, Makela JJ, Harding BJ, Immel TJ (2017) Michelson interferometerfor global high-resolution thermospheric imaging (MIGHTI): instrument
design and calibration. Space Sci Rev https://doi.org/10.1007/s11214-0170358-4
Forbes JM (2007) Dynamics of the thermosphere. J Met Soc Japan 85B:193–213
Forbes JM, Gu J, Miyhara S (1991) On the interaction between gravity waves andthe diurnal propagating tide. Planet Space Sci 39:1249–57
Forbes JM, Hagan ME (1982) Thermospheric extensions of the classical expansion
functions for semidiurnal tides. J Geophys Res 87:5253–59
Forbes JM, Manson AH, Vincent RA, Fraser GJ, Vial F, Wand R, Avery SK, Clark RR,
Johnson R, Roper R, Schminder R, Tsuda T, Kazimirovsky ES (1994)
Semidiurnal tide in the 80–150 km region: an assimilative data analysis. J
Atmos Terr Phys 56:1237–50
Forbes JM, Maute A, Zhang X, Hagan ME (2018) Oscillation of the ionosphere atplanetary-wave periods. J Geophys Res Space Physics 123:7634–49 https://doi.org/10.1029/2018JA025720
Forbes JM, Palo SE, Zhang X (2000) Ionospheric variability. J Atmos Solar-Terr
Phys 62:685–94
Forbes JM, Zhang X, Hagan ME, England SL, Liu G, Gasperini F (2017) On thespecification of upward-propagating tides for ICON science investigations.
Space Sci Rev 212(1-2) https://doi.org/10.1007/s11214-017-0401-5
Hagan ME, Forbes JM (2002) Migrating and nonmigrating diurnal tides in the
middle and upper atmosphere excited by tropospheric latent heat release. J
Geophys Res 107(D24):4754 https://doi.org/10.1029/2001JD001236
Hagan ME, Forbes JM (2003) Migrating and nonmigrating semidiurnal tides in
the middle and upper atmosphere excited by tropospheric latent heatrelease. J Geophys Res 108(A2):1062 https://doi.org/10.1029/2002JA009466
Harding BJ, Makela JJ, Englert CR, Marr KD, Harlander JM, England SL, Immel TJ(2017) The MIGHTI wind retrieval algorithm: description and verification.
Space Sci Rev 212(1-2):585–600 https://doi.org/10.1007/s11214-017-0359-3
Harlander JM, Englert CR, Brown CM, Marr KD, Miller IJ, Zastera V, Bach BW,
Mende SB (2017) Michelson interferometer for global high-resolution
thermospheric imaging (MIGHTI): monolithic interferometer design and test.
Space Sci Rev 212(1-2) https://doi.org/10.1007/s11214-017-0374-4
Häusler K, Hagan ME, Baumgaertner AJG, Maute A, Lu G, Doornbos E, Bruinsma
SL, Forbes JM, Gasperini F (2014) Improved short-term variability in thethermosphere-ionosphere-mesosphere-electrodynamics general circulation
model. J Geophys Res Space Physics 119:6623–30 https://doi.org/10.1002/
2014JA020006

Cullens et al. Progress in Earth and Planetary Science(2020) 7:18

Häusler K, Hagan ME, Forbes JM, Zhang X, Doornbos E, Bruinsma S, Lu G (2015)
Intraannual variability of tides in the thermosphere from model simulations
and in situ satellite observations. J Geophys Res Space Physics 120(1):751–65
https://doi.org/10.1002/2014JA020579
Hedin AE (1991) Extension of the MSIS Thermospheric model into the middle
and lower atmosphere. J Geophys Res 96:1159
Hough SS (1898) On the application of harmonic analysis to the dynamical
theory of the tides. Part II: on the general integration of Laplace’s dynamical
equations. Philos T R Soc A 191:139–85
Immel TJ, England SL, Mende SB, Heelis RA, Englert CR, Edelstein J, Frey HU,
Taylor ER, Craig WW, Harris SE, Bester M, Bust GS, Crowley G, Forbes JM,
Gérard J-C, Harlander JM, Huba JD, Hubert B, Kamalabadi F, Makela JJ, Maute
AI, Meier RR, Raftery C, Rochus P, Siegmund OHW, Stephan AW, Swenson GR,
Frey S, Hysell DL, Saito A, Rider KA, Sirk MM (2018) The ionosphericconnection explorer mission: mission goals and design. Space Sci Rev 214:13(36 pp.). https://doi.org/10.1007/s11214-017-0449-2
Immel TJ, Sagawa E, England SL, Henderson SB, Hagan ME, Mende SB, Frey HU,
Swenson CM, Paxton LJ (2006) Control of equatorial ionospheric morphology
by atmospheric tides. Geophys Res Lett 33:15
Lindzen RS (1981) Turbulence and stress owing to gravity wave and tidal
breakdown. J Geophys Res 86:9707–14
Lindzen RS, Hong S-S, Forbes JM (1977) Semidiurnal Hough mode extensions in
the thermosphere and their application. Memo Rept Nav Res Lab 3442:69
Liu H-L, Roble RG (2002) A study of a self-generated stratospheric sudden
warming and its mesospheric–lower thermospheric impacts using thecoupled TIME-GCM/CCM3. J Geophys Res 107(D23):4695 https://doi.org/10.
1029/2001JD001533
Maute A (2017) Thermosphere-ionosphere-electrodynamics general circulation
model for the ionospheric connection explorer: TIEGCM-ICON. Space Sci Rev
212(1-2):523–51 Public access. https://doi.org/10.1007/s11214-017-0330-3
Miyahara S, Forbes JM (1991) Interactions between gravity waves and the diurnal
tide in the mesosphere and lower thermosphere. J Meteorol Soc Japan 69:
523–31
Miyahara S, Forbes JM (1994) Interactions between diurnal tides and gravity
waves in the lower thermosphere. J Atmos Terr Phys 56:1365–74
National Research Council (2013) Solar and space physics: a science for atechnological society. The National Academies Press, Washington, DC https://doi.org/10.17226/13060
Oberheide J, Forbes JM, Zhang X, Bruinsma SL (2011) Climatology of upward
propagating diurnal and semidiurnal tides in the thermosphere. J Geophys
Res 116:A11306 https://doi.org/10.1029/2011JA016784
Picone JM, Hedin AE, Drob DP, Aikin AC (2002) Nrlmsise-00 empirical model ofthe atmosphere: statistical comparisons and scientific issues. J Geophys Res
Space Physics https://doi.org/10.1029/2002JA009430
Roble RG, Ridley EC (1994) A thermosphere-ionosphere-mesosphereelectrodynamics general circulation model (time-GCM): equinox solar cycle
minimum simulations (30–500 km). Geophys Res Lett 21:417–20 https://doi.
org/10.1029/93GL03391
Svoboda AA, Forbes JM, Miyahara S (2005) A space-based climatology oftemperatures and densities from diurnal MLT tidal winds, UARS windmeasurements. J Atmos Sol-Terr Phys 67(16):1533–43

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

Page 13 of 13