Control of ionospheric plasma velocities by thermospheric winds

Earth’s equatorial ionosphere exhibits signiﬁcant and unpredictable day-to-day variations in density and morphology 1–4 . This presents difﬁculties in preparing for adverse impacts on technological systems even 24 hours in advance 5,6 . This behavior is now theoretically understood as a manifestation of thermospheric weather, where conditions in the upper atmosphere respond strongly to changes in the spectrum of atmospheric waves that propagate into space from the lower and middle atmosphere, modifying the electrodynamic environ-1

new area of research in space weather. This report describes the first evaluation of the electrodynamic impacts of the neutral wind environment on the ionosphere, with an investigation of the relation of the wind field to the motion of the plasma at the equator, where plasma densities are highest.

The Ionosphere
The highest density plasma in near-Earth space is a layer of O + ions surrounding the planet, usually with a peak density between 300 and 400 km altitude. Termed the F-layer, it is constituted of plasma produced by solar EUV radiation above 200 km. This source contributes to plasma densities at higher altitudes where recombination rates are much lower, creating a charged layer that persists into night. This layer of the ionosphere provides a conductive medium that has long been used to reflect radio and radar signals, but vertical and horizontal structuring of the layer can disperse these signals causing phase scintillation. High density also causes significant group delays in navigation systems. Because of its importance to these critical applications, the behavior of this layer has long been studied, and it has become clear that this layer often varies in ways that are impossible to relate to the dominant influences of solar radiation or periodic geomagnetic activity related to solar wind disturbances. The fact that the ionospheric plasma is weakly ionized, with at most 1% of the gas being ionized even at the F-peak, leads one to investigate the ways that interaction of the ionized species with the neutral atmosphere may produce ionospheric variability beyond that normally attributed to solar influences.

The Ionospheric Wind Dynamo
The daytime development of a persistent F-layer is, at high and middle latitudes, due largely to the balance of photochemical production and loss processes, where recently produced ions may easily diffuse to higher or lower altitudes along Earth's magnetic field. At the same time, the plasma in the ion-production region below 200 km (the E-region) strongly interacts with the parent neutral population. At lower latitudes, vertical diffusion is inhibited by the horizontal magnetic field, but a second mechanism can lead to even larger vertical ion transport: the equatorial wind dynamo. Solar heating puts the thermosphere into motion and the resultant thermospheric winds can generate electric currents in the dayside ionosphere that cause the plasma to drift perpendicular to the magnetic field. In general, this introduces vertical drift of the plasma at the equator in response to zonal horizontal winds 12 . For this fact, and the strong insolation near the equator, the equatorial F-layer develops into the greatest reservoir of plasma on Earth. Modification of the thermospheric wind field in the daytime E-region can affect vertical drift of the plasma, and therefore the density of the F-layer produced. What is remarkable is the degree to which understanding of this process is based upon disparate, independent observations of plasma velocity, density, total electron content, and in rare cases, the wind in the E-region. Only recently have coordinated observations become available to allow complete investigations 13 . This report describes the first campaign of coordinated observations of the ionospheric wind dynamo and vertical plasma velocities in the equatorial ionosphere.
It has become clear that thermospheric winds can be affected by atmospheric wave phenom-ena that originate in the neutral atmosphere below, down to the troposphere. This realization has developed over decades, beginning with the original concepts of lower atmospheric waves propagating into space in the 1960s. Hines 14 was the first to derive the atmospheric wave equations that described propagation of energy and momentum in atmospheres via waves whose restoring force is gravity (non-acoustic). In considering these internal gravity waves as a source of ionospheric variability, Hines 15 found that their greatest effects on the ionospheric plasma would be in modifying the electrodynamic environment, but argued that the effect would be minimal overall due to their small scale length. Following this work, the theory of larger scale atmospheric waves such as tides and planetary waves was developed 16,17 , where the impact of tides on ionospheric conditions was evaluated and shown to explain the large scale ionospheric current systems derived from ground-based magnetometer measurements 18,19 . However, the atmospheric tides considered in these studies were types driven directly by solar heating or lunar gravity, and as such exhibited no longitudinal structure and only slow daily variations. Only with new discoveries in the 21st century has the idea of tropospheric or stratospheric processes producing significant modifications of ionospheric density been considered plausible 20,21 .
More recent investigations demonstrate that tides in the thermosphere may well originate from much lower altitudes and are of scales that could drive the larger scale electrodynamics of the system. Although a broad spectrum of waves are generated in the lower atmosphere, the most influential are those with long vertical wavelengths that span the dynamo region. One example is the diurnal, eastward-propagating, wavenumber-3 tide that is driven by cloud formation and solar IR absorption in the tropics, propagating upward to reach its highest amplitude (in horizontal wind and temperature) well above 100 km 2,[22][23][24] . This tide varies throughout the year, and its amplitude and phase in the dynamo region can be evaluated by neutral wind and temperature measurements in the mesosphere and lower thermosphere 25 . A corresponding variation in equatorial ionospheric drifts and densities, with a signature wave-4 structure (consistent with an asynoptic sampling of an eastward propagating wave-3 diurnal tide) has been observed with in-situ instrumentation 26 , ultraviolet imaging 27 and radio occultation experiments 28 revealing a density variation that is much more highly structured than can be explained by solar radiation or solar wind forcing. A number of other tides propagate to and interact in this region, summarized in the review by England 29 .
Efforts to simulate these effects and demonstrate the different interactions between the waves and the net effects on the ionosphere predict that lower atmospheric sources can introduce ionospheric variations on overall time scales of 10 days 10 to as short as 24 hours 7 . Missing from this body of work is any direct investigation of how the dynamo wind modifications are actually transmitted to ionospheric altitudes, and what properties of the system may influence this connection.
Our understanding of the space environment near Earth now relies completely on a new set of models that predict effects 1, 30-33 that have never been observed. Here we will show the degree to which variations in the atmosphere are manifested in the ionosphere via the dynamo mechanism.

Observations of dynamo wind effects
For the first time, ICON makes remote sensing measurements of the wind in the E-region region in conjunction with in-situ measurements of the plasma density and velocity in the F-region. This is achieved through selection of an orbit and science payload that provide the coordinated measurements during each crossing of the magnetic equator [34][35][36] . The geometry of the observation is illustrated in Figure 1 The physical process of generating an electromotive force with wind is understood in terms of Ohm's law applied in a weakly ionized atmosphere. Original work in this area was advanced in the 1960, culminating in work by Stening 18,37 . Here the approach of Richmond 38 is followed, where the current is calculated in an non-orthogonal coordinate system defined by the magnetic field vector and the local horizon. Ohm's law is written: wherej is the current density,Ē is the electric field in a frame rotating with the Earth,ū is the neutral wind in the same frame, andB is Earth's magnetic field. σ is the conductivity tensor.
In the daytime ionosphere, the conditions under which the ionosphere is produced, ICON can in principle provide each of the measurements that are needed to solve Ohm's Law for j. Although the neutral wind dynamo is a global system, the ionospheric drift can be approximated to be driven locally near noon, where horizontal conductivity gradients are lowest, and zonal gradients in the zonal current are small. The full derivation is shown in the Methods section but is briefly described here.
The local relationship is derived by calculating the terms of Ohm's law and integrating the key quantities along the magnetic field line to predict the meridional plasma drift in the coordinate system described in Figure 2. This coordinate system is defined such that the zonal (x 1 ) and meridional (x 2 ) directions are both perpendicular to the local magnetic field (which is defined as the x 3 direction). The meridional direction (x 2 ) is defined to be positive downward at the magnetic apex, and the zonal direction (x 1 ) completes the coordinate system, generally horizontal eastward.
For each MIGHTI wind measurement, the field-line integrated quantities of the Pedersen, Hall and Cowling conductivities (Σ P , Σ H , and Σ C , respectively), and the conductivity-weighted zonal and meridional wind components (U H,P 1 and U H,P 2 , respectively) are calculated. Requiring current continuity, a relationship is defined between the meridional drift at the apex of a magnetic field line and the wind drivers at the footpoint of that field line: where the constant C ext captures any offsets originating from non-local sources (as discussed in Section 4). This local relationship between meridional plasma velocity v 2 and conductivityweighted horizontal neutral winds U U,P 1,2 can be directly tested by ICON observations.
Our analysis focuses on periods where the precession of ICON's orbit causes it to make repeated equatorial crossings near noon, where the height integrated wind-driven terms can be compared with the electric field measured at the magnetic apex. The ICON orbit crosses the equator at noon for several days a month, alternating between the ascending and descending node of the orbit.
Once the orbit precesses to a noon-crossing configuration, ICON provides magnetically-connected wind and plasma drift measurements 11-12 times each day, performed over all geographic longi-tudes except regions near South America where precipitating energetic particles disrupt the measurements and preclude the collection of valid wind data (the plasma drift measurements are unaffected). With these data, we can test our ability to use the wind observations to predict the plasma velocities.
For this test, we select three successive periods of noon-crossing observations from early in the ICON mission for analysis. Samples from the IVM and MIGHTI instrument are used when the  (2)) with the value predicted from the winds (right-hand side of (2)). Each marker represents one equatorial crossing. The Pearson correlation coefficient varies from 0.47 to 0.56 (p < 0.01, two-tailed t-test).
The population of equatorial crossings in the top panels comprises samples from many longitudes and several days. In order to isolate the longitudinal patterns (e.g., those arising from nonmigrating tides), we next collect all noon-time data in these periods when the retrieved MIGHTI The result is shown in Figure 3 (bottom). The green trace is the measured v 2 . The blue trace is the negative predicted v 2 , i.e., the term in parentheses in (2), or the total dynamo wind forcing term. For both traces, a constant zonal mean has been subtracted (the constant C ext as discussed in the Methods section) to vary around a reference baseline of zero. If the dynamo were fully activated in the sense of zonal polarization current balancing wind-driven current perturbations, these two traces would be equal and opposite. In these data, opposing longitudinal patterns are seen.
It is informative to investigate the relative contribution of the specific wind-related terms in Equation 2 to the overall prediction of v 2 . Each of the four specific terms of the wind-driven dynamo calculation are shown for the last 10-day observation period in Figure 4. The black lines indicate terms associated with magnetic zonal winds, the grey lines with magnetic meridional winds. One finds that the zonal winds contribute to the largest variations of predicted meridional drifts, though the meridional winds provide significant inputs in some regions. Though the correlations with zonal wind drivers themselves are usually clear, the meridional wind is an important contributor in some cases. This provides support for a finding that the dynamo operates in a manner that is supported by theory, and that the derivation of its effects is correct in its inclusion of even minor terms that include the meridional wind.
The results we report here represent the first direct measurement of the Earth's equatorial wind dynamo, as winds just beyond the boundary of space drive changes in its plasma environment. It when co-added in the ∼4-minute period of observations with each equator crossing, which are no more than ∼3 m/s . These are notably low, and we find therefore that instrumental effects are likely not germane in the discussion of the spread of data around a linear relationship. There are other key areas to consider.
First, the potential lack of coherence of the wind field across the distance between the two footpoints of the field line, only one of which is observed, is likely a significant source of uncertainty. ICON is designed with an inherent ability to make wind observations at both footpoints about times per month and this capability is being exercised on orbit now to further investigate the potential effects of asymmetric forcing on meridional plasma drifts. Should the wind drivers at the unobserved conjugate footpoint differ from those observed to the north, then given the relationship revealed above, their inclusion would produce a likely-beneficial correction to the prediction of v 2 . Because these observations are localized in regions of high magnetic declination over the Pacific and Atlantic, a full daily-zonal characterization of drifts is not achievable and will require a different analysis.
Second, one must consider that the component of noon-sector plasma drift resulting from externally driven currents, as expressed by C ext in Equation (20), may vary over the collection periods used in 3. This study shows that local forcing is specifically important in driving currents, but does not rule out sources of current outside of the observation window. With roughly 25% of the observed variation attributable to locally measured sources, a good portion of the variability remains to be attributed to other sources. Given the low solar activity, changes in E-region conductivity across the dayside are minimal, and it is rather the thermospheric wind environment, driven by varying atmospheric tides from the troposphere, that may modify the electrodynamics on a global scale and introduce additional variability in the plasma drifts at noon.
Lastly, any small deviations from the approximation of J 2 ≈ 0 would introduce variability in the plasma drift v 2 , not predicted by the wind observations. Future work combining the observations of ICON and orbiting magnetic observatories such as the ESA SWARM mission 42,43 could provide further constraints on the sampling of wind first used here. Furthermore, such observations will allow the approach described here to be extended away from noon and toward the evening terminator, continuing to test our ability to predict the plasma velocity field.
The remarkable fact is that in each case reported here, the noon-time plasma drifts are always correlated with the wind drivers as they are repeatedly observed in magnetic conjunctions around the planet. This provides strong support for the recent, extensive effort in developing weather models to predict conditions in the middle and upper atmosphere, in simulations that assimilate measurements of tropospheric weather 44 . It is clear that space weather cannot be predicted without good knowledge of tropospheric weather, and these models have been extended to altitudes above 100 km, where electrodynamic parameters including the full current equation are solved. The skill of these models in reproducing the MIGHTI-measured wind fields must be assessed, because in the case of success, it is then likely that they will also be able to provide the key to predicting the state of the ionosphere, as it changes remarkably from one day to the next.

Methods
Data for the Ionospheric Connection Explorer are available at https://icon.ssl.berkeley.edu/Data, and are to be permanently archived at NASA Space Physics Data Facility at https://spdf.gsfc.nasa.gov.

Derivation of wind vs. plasma drift
Neglecting currents from gravitational and pressure gradient forces, Ohm's law is written: wherej is the current density, σ is the conductivity tensor,Ē is the electric field in a frame rotating with the Earth,ū is the neutral wind in the same frame, andB is the magnetic flux density. The conductivity tensor is defined in the ionosphere as where σ 0 is the direct conductivity, σ P is the Pedersen conductivity, and σ H is the Hall conductivity.
On the time scales of several minutes, the observation period of each equatorial crossing, the electrostatic approximation holds. The divergence of Ampere's Law thus demands that currents are continuous: The coordinate system used here is shown in Figure 2, where "1" is perpendicular to B, horizontal, and generally eastward, "2" is perpendicular to B and generally downward, and "3" is in the direction of B. Considering a magnetic field line with two "footpoints" in the lower atmosphere, and integrating this equation from the southern footpoint to the northern footpoint yields: Integrating yields: where the last two terms refer to currents in the insulating lower atmosphere, which are negligible, and J 1 and J 2 are field-line integrated currents: Substituting into Ohm's law, J 1 and J 2 can be written: where the U terms represent field-line integrated conductivity-weighted neutral winds, and Σ terms are field-line integrated conductances, shown below.
The 2. Zonal conductance gradients are small ∂Σ P ∂x 1 ≈ ∂Σ H ∂x 1 ≈ 0 . Near local noon the variation in solar illumination is small, and thus the variation in E-region plasma density is also small.
The first approximation yields J 2 = 0 in Equation 12; the relationship between the zonal and meridional electric field may then be written as We consider the second approximation as it applies to Equation 7 which in the local noon sector reduces simply to: Using Equations 11 and 16, we obtain the equation describing the action of the local dynamo near noon: where Σ C is defined as a Cowling-like conductance: Because we are interested in ionospheric motion, we rewrite Equation 18 in terms ofv = −Ē×B B 2 and rearrange terms: In derivative form, this equation represents the relationship between local variations observed in the winds and similar variations in the drift. Written in integrated form: