Thermosphere UFKW Structures and Ionosphere Coupling as Observed by ICON

Two ∼2‐week Ultra‐Fast Kelvin Wave (UFKW) events centered on days 158(203) during 2021 are investigated using winds, temperatures, plasma drifts and electron densities (Ne) measured by the Ionospheric CONnections (ICON) mission. Eastward‐propagating longitudinal wave‐1 (s = −1) structures with periods 2.5–4.0d, thought to mainly reflect Ultra‐Fast Kelvin waves (UFKWs), reveal ±45 ms−1 zonal winds (U) at 100 km for both events. Height‐latitude structures of the 3.0(3.5)d‐period UFKWs are obtained for the first time for both temperature (T, 94–120 km) and U (94–280 km) between 12°S and 39°N latitude. Maximum values of 36(29) ms−1 for U and 12(15)K for T occur at 102(106) km altitude and within ±3° latitude. The U‐T peak height displacement remains unexplained. Vertical wavelengths are in the range 36–43 km for both U and T during both events. Concurrent with the E‐region dynamo winds, topside (580 km) F‐region field‐aligned (±20–40 ms−1), meridional (±5–10 ms−1) and vertical (±5–10 ms−1) drift and Ne (±20–40%) 2.5–4.0d s = −1 variations are also measured. These key elements of atmosphere‐ionosphere (A‐I) coupling, contemporaneously measured for the first time, are relevant to testing the internal consistency of A‐I models. The mean wind propagation environment of the UFKWs is also quantified, showing no appreciable effects on the UFKW structures, consistent with modeling and theory.


Introduction
In Earth's atmosphere, Ultra-Fast Kelvin Waves (UFKWs) are equatorially trapped eastward-propagating oscillations with periods between about 2 and 5 days.UFKWs have latitudinal structures of temperature (T) and zonal wind (U) that are Gaussian-like, with comparatively small meridional wind amplitudes.It is generally recognized that the prevalent UFKWs entering the thermosphere possess zonal wavenumber s = 1 (e.g., Forbes et al., 2023;Gu et al., 2014;Lieberman & Riggin, 1997;Liu et al., 2015), where s < 0 implies eastward propagation for the convention adopted in the present study.Lieberman and Riggin (1997) reported 3-to 4.5-day (hereafter 3-4.5d), s = 1 oscillations in U up to 110 km altitude, with maximum amplitudes of order ±20-40 ms 1 near 105 km.And while UFKWs have been observed separately at 110 and 260 km (Gasperini et al., 2015(Gasperini et al., , 2017)), observations of UFKWs within the intervening altitudes have not been reported in the literature to date; however, modeling of UFKW behavior above 110 km does exist.J. M. Forbes (2000) performed numerical experiments with a linear model to investigate the effects of zonal-mean zonal winds U and dissipation on the height-latitude (htvslat) structures of a 3d, s = 1 UFKW.The same model was recently used (Forbes et al., 2023) to delineate the separate influences of wave period, and solar cycle-varying molecular dissipation and ion drag on s = 1 UFKW structures.
General circulation models have also elucidated UFKW propagation in the thermosphere, including coupling with the ionosphere (Chang et al., 2010;Forbes, He, et al., 2020;Forbes, Maute, & Zhang, 2020;Yamazaki et al., 2020).These models demonstrate that the physical connection between UFKW winds and the ionospheric response is primarily rooted in the electric fields driven by the dynamo mechanism in the E-region, which then map along magnetic field lines to produce E × B drifts in the F-region and accompanying electron density (Ne) variability.Observational evidence for this atmosphere-ionosphere (A-I) coupling process currently rests in correlations between UFKW signatures in MLT winds at heights less than 100 km and those in various F-region ionospheric parameters (Abdu et al., 2015;Gu et al., 2014;Liu et al., 2013Liu et al., , 2015;;Onohara et al., 2013;Takahashi et al., 2007Takahashi et al., , 2009)).This paper responds to the above advances in UFKW modeling and the paucity of UFKW observations in the thermosphere by reporting the first coincident observations of U and T UFKW htvslat structures covering 94-120 km, UFKW winds up to 280 km altitude, and the contemporaneous ionospheric responses to the driving UFKW wind field in the 100-120 km height region.The htvslat wind structures are particularly important, since it is the conductivity-weighted winds that initiate the A-I coupling noted above.In addition, we provide the first depictions of the mean background wind field through which the UFKW is propagating, and assess the corresponding effects against existing modeling and theory.

ICON Data
The data and longitude-Universal Time (UT) fitting employed for the current work closely follow those employed in the study of the quasi-two day wave from Ionospheric CONnections (ICON) measurements as detailed in Forbes et al. (2021).The main differences are the use of newer data versions of the winds in the present study, and the inclusion of temperatures.Therefore abbreviated descriptions are provided here.
The limb-viewing MIGHTI (Michelson Interferometer for Global High-resolution Thermospheric Imaging) instrument provides both eastward (U) and northward (V) winds (Englert et al., 2017(Englert et al., , 2023) ) and temperatures (Stevens et al., 2022) over the latitude range 12°S-42°N.The V05 winds (MIGHTI-A temperatures) used here extend between 90 and 280(90-127) km altitude during daytime and 90-108 km during nighttime.The ionospheric data consist of daytime V06 vertical, meridional and field-aligned plasma drifts (V z , V M , V A ), and total ion (O + + H + ) densities, measured in-situ at an approximate altitude of 580 km by the Ion Velocity Meter (IVM) (Heelis et al., 2017) between about ±27°geographic latitude.The total ion density is considered equivalent to Ne.As in Forbes et al. (2021), we are interested in UFKW-ionosphere coupling during daytime when the dynamo generation of electric fields is active.To avoid possible photoemission contamination effects on drift observations during the morning hours we moreover restrict the use of drift data to LST = 10:00-18:00 hr.For both MIGHTI and IVM data, the same data quality flags and outlier rejection criteria are applied as in Forbes et al. (2021).

UFKW Events
The MIGHTI data for the whole mission were surveyed to find a couple of well-defined UFKW events, reasonably restricted in wave period with relatively large amplitudes, and wherein contemporaneous MIGHTI winds and IVM ionospheric measurements existed during 10:00-18:00 hr LST.As a first step, both ascending and descending node wind observations were averaged over 12°S-12°N and 6°S-6°N at 100 and 106 km.For each combination of latitudes and heights, these data were then sinusoidally fit with respect to longitude to get wave-1 coefficients within 1-day windows moved forward every 6 hr, yielding a complex time series with 6-hr resolution.The amplitude and phase (longitude of maximum) information contained in the coefficients, combined with their UT variation, enables separation of the eastward (s = 1) and westward (s = +1) frequency spectra.This was accomplished by applying a Morlet transform to the complex time series to get a wave period versus day of year (DOY) depiction such as the one shown in Figure 1 for 12°S-12°N at 100 km.Similar results were obtained for the other combinations of latitudes and heights.
Two UFKW events are identified in Figure 1 for further analysis: a quasi-3d UFKW during DOY 149-160, and a quasi-3.5dUFKW during DOY 195-208, both during 2021.The lengths of these time periods are chosen to be 4 times the wave periods, that is, 12 and 14 days, respectively.Since the IVM measurements are made in-situ, and the winds are measured on the limb over a different range of latitudes, there is not a one-to-one correspondence between the spatial and temporal coverages provided by the MIGHTI and IVM instruments.These time intervals were also chosen for analysis due to the contemporaneous availability of MIGHTI and IVM measurements during these periods.Figure S1 in Supporting Information S1 illustrates the MIGHTI and IVM coverages in relation to the wavelet plot in Figure 1.While both ascending and descending node data were employed in the wavelet analysis in Figure 1, it is important to note that only the descending node data fall within the 10:00-18:00 hr LST time frames where contemporaneous ionospheric data are available.We return to this point in the following section.
Wavelet plots were also created for meridional winds and temperatures (not shown).In keeping with identification of these time periods as UFKW events, the temperature spectra appeared very similar in structure and period to those of U, while V amplitudes were much smaller than U and the period versus DOY structures did not correlate with those of U and T.
The two panels in the bottom of Figure 1 consist of longitude versus DOY (lonvsdoy) depictions of the wave-1 components of the raw U winds that went into the wavelet analysis.Eastward phase progressions consistent with the 3d and 3.5d wave periods are evident, but with significant distortion and amplitudes at least twice those depicted in the wavelet plot.This is due in part to the frequency spread of the UFKWs, the fitting constraint of a Gaussian-modulated sinusoid inherent in the Morlet transform, and the influences of other |s| = 1 waves.Although this type of depiction may better represent the dynamical impacts of an UFKW event, the following treatments in terms of monochromatic 3d and 3.5d UFKWs has its advantages; for instance, in depicting height versus latitude structures, and performing data-model comparisons.Lonvsdoy depictions similar to that in Figure 1 are used in Section 6 to quantify the ionospheric variability.

Height and Latitude Structures of 3d and 3.5d UFKWs
Height and latitude structures of the 3d and 3.5d UFKW amplitudes and phases are examined in this section.At a given height and latitude, the data are fit two-dimensionally with respect to Universal Time (UT) and longitude (λ) using the following terms: where ω is the wave frequency (=2π/T where T = wave period in days); t = UT (days); λ = longitude (radians); and s = 1.The amplitudes ) and phases (time of maximum at zero longitude, 1 ω arctan b a ) ) are determined accordingly.
Two approaches to the extraction of UFKW properties are followed here.In one case, we analyze the available MIGHTI U and V data for the two time periods identified in Figure 1 where ionospheric data are also available during 10:00-18:00 hr LST.This corresponds to descending-node-only data (see Figure S1 in Supporting Information S1), which extends from 94 km up to 280 km. Figure S2 in Supporting Information S1 provides typical examples of MIGHTI descending-node-only longitude-UT sampling, including the coverage gap between ∼300 ± 30°longitude due to South Atlantic Anomaly effects on the MIGHTI instrument.However, this longitude coverage is adequate for s = 1 fitting.In the second approach, both ascending and descending node data (refer to Figure S1 in Supporting Information S1) are fit in order to simultaneously acquire U, V, and T while maximizing the altitude range, minimizing the fitting window, and maximizing UFKW amplitudes.This is accomplished within 11d windows centered on DOY 158 (3d UFKW) and DOY 203 (3.5d UFKW) between 90 and 120 km altitude, which correspond closely to the amplitude maxima in the top panel of Figure 1.
Based on the 11d window just described, Figures 2a and 2c illustrate the htvslat structures of the 3d and 3.5d UFKW U amplitudes, respectively, and Figures 2b and 2d   altitude.The peak U amplitudes of 36(29) ms 1 which occur at 3°N and 102 km correspond well with the 3-4.5d, s = 1 oscillations in U observed by Lieberman and Riggin (1997), which maximized at ±20-40 ms 1 near 105 km.The amplitudes at other altitudes are comparable to the UFKWs observed by Gu et al. (2014) and Liu et al. (2015): The s = 1 UFKWs detected by Gu et al. (2014) during 2011 had U amplitudes between 90 and 100 km altitude of order 20-30 ms 1 , and T amplitudes between 100 and 104 km altitude of order 5-15 K.The 3d UFKW T amplitudes during 2009 reported by Liu et al. (2015) at 98 km altitude were of order 4-10 K.
The λ z calculated from the phase progressions between 94 and 106 km over the equator are indicated in the bottom panels of Figure 2, and range between 36 and 43 km.For reference, λ z calculated over 65-97 km from Microwave Limb Sounder data observations of 16 large 2.5-4.5d,s = 1 UFKW events during 2005-2010 ranged between 36 and 52 km, with an average value of 44 ± 2 km (Davis et al., 2012).Thus, the λ z indicated in Figure 2 are consistent with these measurements.UFKW λ z depend on the zonal-and diurnal-mean background wind U) (Holton et al., 2001) and temperature (Forbes et al., 2023), which are likely contributing factors to the observed variability in λ z .
It is not possible to derive the U wind field over the 11d periods centered on DOY 158 and DOY 203, since it takes about 41days of data to separate tides from U in lower-thermosphere MIGHTI observations over the range of latitudes depicted in Figure 2 (e.g., Cullens et al., 2020).Nevertheless, the 41d-mean htvslat distributions of U centered on these DOY is provided in Figure S3 in Supporting Information S1.They both indicate U of order ±20 ms 1 within ±9°latitude, and an eastward jet poleward of 9°N and below 105 km with maximum wind speeds of about +40 ms 1 at 25-35°latitudes.There are no striking relationships between the htvslat distributions of UFKW U and T in Figure 2, and the U in Figure S3 in Supporting Information S1.The 3d UFKW simulations of Gasperini et al. (2017) in the presence of a similar yet even more intense U distribution also confirm the absence of any significant distortion or displacement.This is apparently contradicted by the fact that severe U effects are imposed on the DE3 tide in the same simulation, even though both waves share the same zonal phase speed.Forbes et al. (2023) illustrate similar modeling results and pose theoretical arguments explaining why the UFKW is resistant to any U-imposed distortions.
According to Figure 2, UFKW T amplitudes peak at a higher altitudes than U: near 106 km for T compared to 102 km for U. Similar vertical displacements of T with respect to U for UFKW occur in the modeling of Chang et al. (2010), Yamazaki et al. (2020) and Forbes et al. (2023).The present work is the first to experimentally verify these heretofore unnoticed model predictions.Differences in molecular dissipation and in λ z between U and T (i.e., see Figure 2), are not able to account for these differences in peak height (see Supporting Information S1 for details), which thus remain unexplained.
Figure 3 depicts the vertical amplitude and phase structures of U for the 3d (left two panels) and 3.5d (right two panels) UFKWs at the equator during DOY 149-160 and 195-208, respectively, using daytime-only descending node data from MIGHTI as described at the beginning of this Section.Figure S4 in Supporting Information S1 provides similar depictions for latitudes 9°, +9°, +18°, +27°.These DOY are specifically designed to overlap with the availability of IVM Ne and drifts during 10:00-18:00 hr LST.The use of daytime-only data enables the UFKW winds to be derived up to about 280 km, whereas this is not possible for temperature.These depictions also illustrate typical uncertainties in the amplitudes and phases, in terms of standard deviations (σ) derived from the least squares fits, represented here as horizontal bars.Also shown in Figure 3 are the corresponding UFKW structures based on modeling (Forbes et al., 2023) under solar minimum conditions, which are calibrated to agree with the observed amplitudes and phases near the peak.The results in Forbes et al. (2023) are solutions to the linearized dynamical equations of the atmosphere (0-400 km altitude, pole-to-pole) without background mean winds, but with molecular dissipation and ion drag in the thermosphere.UFKWs of various periods are forced in the lower atmosphere with a horizontal structure given by the Hough mode of Laplace's Tidal Equation, and the solutions above 100 km are thus referred to as thermospheric "Hough Mode Extensions" (HMEs).
The peak amplitudes of U are 21( 23) ms 1 at 100(104) km for the 3d(3.5d)UFKW, smaller than those depicted in Figure 2, the DOY of which were optimized to capture the maximum amplitudes of the UFKW.The λ z of 42(40) km are slightly larger than the 36(36) km depicted in Figure 2. The HME peaks occur slightly higher than the MIGHTI observations, but the amplitude profile captures the basic trend of significantly diminished amplitudes above ∼130 km, asymptoting to a small constant value above 200 km.While the HME and MIGHTI phase profiles are in excellent agreement at the lower heights, significant departures are evident above 160 km.The 3d UFKW phases are attached to very small amplitudes, which renders them practically meaningless.For the 3.5d UFKW there is a near-180°phase shift that remains nearly constant with height associated with 3-5 ms 1 amplitudes.The monotonically decreasing HME phase structure reflects the dominance of thermosphere dissipation (Forbes et al., 2023), which is what one would normally expect to see.The observed structure is reminiscent of the effects of a "secondary" UFKW source aloft associated with GW filtering, as demonstrated by Meyer (1999) for the quasi-two-day wave.

Ionospheric Response to UFKWs
To quantify the full ionospheric impact of the UFKWs, lonvsdoy depictions similar to those in Figure 1 were sought.Since the observed ionosphere contains variability due to other waves propagating from below, nonlinear neutral-ion interactions (e.g., Forbes, He, et al., 2020), and solar flux variations and magnetic disturbances (see Figure S5 in Supporting Information S1), the following procedure was used to extract the s = 1 variability at UFKW periods: When data coverage was optimal (Mlat = 18°to +3°, see Figure S6 in Supporting Information S1), wavenumber (s = 4 to +4) versus period (2.0-4.0 days) amplitude spectra were created as in Figures 4a-4c and 4g.Consistent with Figure 1, the s = 1 ionosphere responses are spread over periods 2.5-4.0 days.Superposition of subsets of these waves in the time domain leads to the lonvsdoy interference patterns in Figures 4d-4f, 4h, and 4i, which provide a measure of the total variability associated with the UFKW "packet."See Figure S7 in Supporting Information S1 for other examples of spectrum-lonvsdoy pairs, noting that peaks at s = 1 that stand out from the background are not as numerous for DOY 149-162; a contributing factor may be the more elevated magnetic activity during this period (Figure S5 in Supporting Information S1).The lonvsdoy depictions are analogous to results from band-pass filtering, a technique used by Gu et al. (2014) to reveal UFKW variability in ionospheric data.
Figures 4a-4c show the Ne spectra for DOY 149-160 and 195-208, and the V M spectrum for DOY 195-208 at Mlat = 12°, 0°, and 12°, respectively; Figure 4g shows the V Z spectrum for DOY 195-208 at Mlat = 0°.Given the Nyquist period of 2.0 days, we are only confident in periods ≥2.5 days.Note that while the amplitude peaks in Figure 1 occur at 3 days and 3.5 days, the ionospheric responses near 2.5 days can be equal to or greater than those at longer periods.This suggests that the 2.5d UFKW is more electrodynamically efficient than the longer-period waves, likely due to its longer vertical wavelength, better matching with the conductivity profiles, and ability to penetrate to higher altitudes (see Forbes, He, et al., 2020, 2023 for further insights on this point).S7 in Supporting Information S1 between Mlat = 18°and +3°.Typical standard deviations are of order 2%-3% for Ne, 3-6 ms 1 for V A , and 1-3 ms 1 for V M and V Z , reflecting the other natural variability in the data.

Summary and Conclusions
ICON measurements are analyzed to reveal the first coincident htvslat structures of UFKW U and T fields between 94 and 120 km and 12°S-39°N latitude, and the first measurements of the F-region ionosphere response to contemporaneous driving dynamo-region UFKW winds.Key elements of the A-I coupling chain for UFKW are thus defined, which can serve to verify the internal consistency of A-I coupling models.The specific results to emerge for this study are as follows: 1. Htvslat UFKW structures between 94 and 120 km during 11d periods centered on DOY 158(203) during 2021 reveal the following: The peak 3d(3.5d)U amplitudes of 36(29) ms 1 occur at 102 km and 3°N with λ z of 36 km.The corresponding T amplitudes of 12(15)K occur at 3°S(0°) and 106 km, with λ z of 43(41) km.These values, and those depicted here at other altitudes/latitudes, fall within the bounds of prior observations and expectations based on theory and modeling.The 4 km displacement between U and T peak amplitudes remains unexplained.2. The htvslat structures of the UFKW U winds in the vicinity of the Hall conductivity peak near ∼107 km (Forbes, He, et al., 2020) are particularly relevant, since the Hall conductivity-weighted U winds play a prominent role in initiating and determining the efficiency of the A-I coupling chain that results in the F-region ionospheric response (Immel et al., 2021).3.There are no distortions of the UFKW htvslat structures between 94 and 120 km that are appear attributable to the background zonal-mean zonal wind field, counterintuitive to the fact that tides with similar zonal phase speeds are significantly distorted by mean winds (e.g., Gasperini et al., 2017).The present results provide the first experimental evidence supporting the theoretical explanation for this difference posed by Forbes et al. (2023).4. Daytime-only descending orbital node data were analyzed to obtain 3d(3.5d)UFKW U amplitudes and phases from 94 to 280 km during DOY 149-160 and 195-208, contemporaneous with the ionospheric measurements.These are the first observed UFKW wind structures to be reported in the 100-280 km dissipative regime.The peak amplitudes at 100(104) km were 21(23) ms 1 and λ z below 110 km were 42(40) km.Amplitudes decreased to ≲5 ms 1 above 130 km and downward phase progression ceased above about 130 km.These same basic features exist in the UFKW HME structures, except that the peak amplitudes occur at 108(104) km. 5.The daytime (10:00-18:00 hr LST) ionospheric responses between Mlat = 18°and +3°in V A , V M , and V z drifts and Ne generally fall within the ranges ±20-40 ms 1 , ±5-10 ms 1 , ±5-10 ms 1 , and ±20-40% respectively.

Figure 1 .
Figure 1.Top: Wavelet s = 1 analysis of ascending and descending node U winds at 100 km altitude, averaged between 12°S and 12°N latitude.The periods of joint analysis with ionospheric data, day of year (DOY) 149-160 and DOY 195-208, are indicated with dashed lines for the 3d and 3.5d Ultra-Fast Kelvin Wave events, respectively.Bottom panels: Raw s = |1| data input into the wavelet analysis.A wavenumber value of k 0 = 9 was used to define the Gaussian width of the Morlet wavelet, which provides UFKWs slightly more confined in period than with the usual default value of k 0 = 6, but with similar amplitudes.
depict the T amplitude structures.The phases are provided in Figures2e-2h.The 3d(3.5d) peak T amplitudes are 12(15) K and occur at 3°S(0°) latitude and 106 km

Figure 2 .
Figure 2. (a, b): Htvslat structures of the 3d Ultra-Fast Kelvin Wave (UFKW) U and T amplitudes, respectively.(c, d): same as (a, b) except for the 3.5d UFKW.(e, f): phases corresponding to the amplitudes in panels (a, b).(g, h): phases corresponding to the amplitudes in panels (c, d).

Figure 3 .
Figure 3. Altitude profiles of amplitude and phase for the 3d Ultra-Fast Kelvin Wave (UFKW) (left two panels) and 3.5d UFKW (right two panels) at the equator.Black lines/symbols represent data, and the blue lines are smoothed profiles.Horizontal lines are one standard deviations based on deviations from the longitude-UT fit.Red dashed lines are HME values, scaled to agree with the data near the peak.

Figures
Figures 4d and 4e indicate that Ne variability achieves amplitudes of order ±20% at Mlat = 12°for DOY 149-162 and up to ±40% at Mlat = 0°for DOY 195-208, respectively.Figures 4f and 4h indicate values of V M at Mlat = 12°and V Z at Mlat = 0°typically within ±5 ms 1 , respectively, during DOY 195-208.Figure 4i indicates V A values within ±20 ms 1 .These values are all representative of the additional reconstructions provided in FigureS7in Supporting Information S1 between Mlat = 18°and +3°.Typical standard deviations are of order 2%-3% for Ne, 3-6 ms 1 for V A , and 1-3 ms 1 for V M and V Z , reflecting the other natural variability in the data.

Figure 4 .
Figure 4. Amplitude spectra obtained by least squares fitting sinusoids with zonal wavenumber s over the range ±4 with periods 2.125-4.0d in increments of 0.125 days for (a) Ne during day of year (DOY) 149-160 at Mlat = 12°, and during DOY 195-208 at the indicated Mlats for (b) Ne, (c) V M , and (g) V Z .(d)-(f) and (h): Lonvsdoy reconstructions every 0.25 days based on superimposing waves with amplitudes and phases (longitudes of maxima) from the above spectra with s = 1 and periods 2.5-4.0 d. (i): reconstruction of waves for V A during DOY 149-162 for Mlat = 12°.Given that the Nyquist period is 2.0 days, only waves with periods ≥2.5 days are used in the reconstructions.