Regulation of ionospheric plasma velocities by thermospheric winds

Abstract

Earth’s equatorial ionosphere exhibits substantial and unpredictable day-to-day variations in density and morphology. This presents challenges in preparing for adverse impacts on geopositioning systems and radio communications even 24 hours in advance. The variability is now theoretically understood as a manifestation of thermospheric weather, where winds in the upper atmosphere respond strongly to a spectrum of atmospheric waves that propagate into space from the lower and middle atmosphere. First-principles simulations predict related, large changes in the ionosphere, primarily through modification of wind-driven electromotive forces: the wind-driven dynamo. Here we show the first direct evidence of the action of a wind dynamo in space, using the coordinated, space-based observations of winds and plasma motion made by the National Aeronautics and Space Administration Ionospheric Connection Explorer. A clear relationship is found between vertical plasma velocities measured at the magnetic equator near 600 km and the thermospheric winds much farther below. Significant correlations are found between the plasma and wind velocities during several successive precession cycles of the Ionospheric Connection Explorer’s orbit. Prediction of thermospheric winds in the 100–150 km altitude range emerges as the key to improved prediction of Earth’s plasma environment.

Accurate prediction of conditions in near-Earth space (from 100 to 1,000 km altitude) is a goal that requires an understanding of, and a capability to simulate, the interaction between the neutral gas and plasma surrounding our planet. It is therefore important to directly measure the response of the ionosphere to dynamical atmospheric forcing to test and verify simulation developments and improve space weather predictions. The Ionospheric Connection Explorer (ICON) is a National Aeronautics and Space Administration (NASA) mission launched in October 2019 to directly measure the process of ionospheric modification by the dynamics of the neutral atmosphere¹. This report describes the first investigation of the electrodynamic effects of the neutral wind on the motion of the ionospheric plasma during daytime as measured by ICON. We focus on the low-latitude region because processes here generate the largest plasma densities in Earth’s space environment.

Earth’s dense ionospheric F-layer

This high-density plasma is a layer of O⁺ ions surrounding the planet, usually with a peak occurring at altitudes between 250 and 350 km during solar minimum. Termed the F-layer, it is constituted of plasma produced above 200 km altitude by solar extreme ultra-violet radiation². This layer of the ionosphere provides a conductive medium that has long been used to reflect radio and radar signals. Accurate prediction of the ionospheric density distribution is a compelling goal, as it affects the ability to transmit through the layer, or reflect signals to distant locations^3,4. 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. Because the ionospheric plasma is weakly ionized, with at most 1% of the gas being ionized even at the F-peak, the interaction of the ionized species with the neutral atmosphere is now viewed as a likely source of this unexplained ionospheric variability.

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 in the E-region below (~100–170 km) 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 fields that cause bulk motion of the daytime ionosphere perpendicular to the magnetic field. The motion of the plasma in the magnetic meridional plane is of particular importance due to its influence on the production–loss equilibrium described above⁵.

Due to the strong insolation and ionization near the equator, and the potential for meridional drift to lift plasma so produced directly upward, quickly reducing recombination rates, the equatorial F-layer develops into the greatest reservoir of plasma on Earth. What is remarkable is the degree to which understanding of this process is based upon disparate, independent observations of plasma velocity, plasma density, total electron content and, in rare cases, the wind in the E-region. Only recently have coordinated observations become available to allow complete investigations⁶.

Atmospheric tides at ionospheric heights

It has become clear that thermospheric winds can be affected by atmospheric wave phenomena 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. Hines⁷ was the first to derive the atmospheric wave equations that describe propagation of energy and momentum in atmospheres via waves whose restoring force is gravity (non-acoustic). In the years following that work, the theory of larger-scale atmospheric waves such as tides and planetary waves was further developed^8,9, where now it is clear that tropospheric or stratospheric processes can energize atmospheric tides that will propagate well above 100 km (refs. ^10–12).

Recent investigations^13–15 have determined that atmospheric tides may be the cause of large variations in the ionosphere through a number of mechanisms, including modification of the wind dynamo^16–19. Missing from this body of work is any direct observations of how the effects of wind modifications are actually transmitted to ionospheric altitudes and how the properties of the system may influence this connection. Our understanding of the space environment near Earth now relies largely on a new set of models that predict effects^20–23 that have never been observed. Here, we show the degree to which variations in the atmosphere are manifested in the ionosphere via the dynamo mechanism.

Observations of wind-dynamo effects

ICON makes remote-sensing measurements of the wind in the E-region in conjunction with in situ measurements of the plasma density and velocity in the F-region. This is achieved through the selection of an orbit and science payload that provide coordinated measurements during each crossing of the magnetic equator^24–26. The geometry of the observation is illustrated in Fig. 1. For reference, the vertical plasma velocity data from the in situ Ion Velocity Meter (IVM) are shown at the locations of the observatory as sampled every 1 s, and the zonal wind profiles from the Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI) are shown at their locations at the tangent point on the horizon. The wind measurements, retrieved in successive 30-s instrument integrations, are available continuously from 95 to 300 km altitude during daytime. In this illustration, only the zonal winds are shown; the meridional winds are also provided by MIGHTI. This analysis uses MIGHTI data from ICON Data Product 2.2 v03, and IVM data from ICON Data Product 2.7 v02. Meridional drift data from the IVM are pre-processed to ensure that the 24-h running median is zero, consistent with the expected nature of the quiet-time ionosphere.

Fig. 1 |. ICoN’s unique orbit and observational geometry support simultaneous observation of lower thermospheric winds and ionospheric plasma velocities.

Diagram showing the location of the observatory at ~590 km altitude and a succession of magnetic field lines that uniquely connect the observatory to two remote locations at lower altitudes, north and south of the orbit track. Near the equator, in situ ion drift observations are made on field lines whose footpoints fall in the vicinity of the horizontal neutral wind vectors measured at the remote tangent point.

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 1960s, culminating in work by Stening^27,28. Here the approach of Richmond²⁹ is followed, where the current is calculated in a non-orthogonal coordinate system defined by the magnetic field vector and the local horizon. Ohm’s law is written as

$$\mathbf{j}=\sigma \cdot (\mathbf{E}+\mathbf{u}\times \mathbf{B}),$$ (1)

where j is the current density, E is the electric field in a frame rotating with the Earth, u is the neutral wind in the same frame and B is Earth’s magnetic field. σ is the conductivity tensor.

In the daytime, ICON can in principle provide each of the measurements that are needed to solve Ohm’s Law for j. ICON measures u in continuous altitude profiles from 95 to 300 km. The velocity of the plasma measured at the observatory provides a direct measure of E because the guiding centre drift velocity of the plasma is characterized by v = (E × B)/B², and B is well represented by the International Geomagnetic Reference Field³⁰. The conductivity terms are defined by the densities of both the neutral gas and ionosphere, where the International Reference Ionosphere³¹ and the MSISE-00 reference atmosphere³² are used. In contrast to the neutral winds, the density profiles of both ions and neutrals in the 100–150 km altitude range do not vary significantly and are characterized well by climatological reference models. Using this model of the background conductivity along with ICON’s measurements, one can directly calculate j. Errors introduced by inaccuracy in model predictions are considered in Methods section.

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 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 Methods section (Fig. 4). 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 ($U_1^{\text{H},\text{P}}$ and $U_2^{\text{H},\text{P}}$, respectively) are calculated. The requirement for current continuity defines the following relationship between the meridional drift at the apex of a magnetic field line and the wind drivers along that field line:

$$v_2=\left(\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_1^{\text{H}}+\frac{{\mathrm{\Sigma }}_{\text{P}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_2^{\text{P}}+\frac{{\mathrm{\Sigma }}_{\text{H}}^2}{{\mathrm{\Sigma }}_{\text{C}}{\mathrm{\Sigma }}_{\text{P}}}{U}_2^{\text{H}}-\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_1^{\text{p}}\right)+C_{\text{ext}}$$ (2)

where the constant C_ext captures any offsets originating from non-local sources. This local relationship between meridional plasma velocity v₂ and conductivity-weighted horizontal neutral winds $U_{1,2}^{\text{H},\text{P}}$ can be directly tested by ICON observations.

Fig. 4 |. Key properties of the equatorial ionosphere and apex coordinate system.

This coordinate system is defined such that the zonal (x₁) and meridional (x₂) directions are both perpendicular to the local magnetic field (defined as the x₃ direction). The meridional direction (x₂) is defined to be positive downward at the magnetic apex, and the zonal direction (x₁) completes the coordinate system, generally being horizontal and eastward. For illustration, a zonal wind vector u is shown as sampled continuously along the blue dashed track from the moving orbital position of ICON (blue dotted track).

Comparing plasma drifts and conductivity-weighted winds

ICON provides magnetically connected wind and plasma drift measurements 11 to 12 times each day, performed over all geographic longitudes except regions near South America where precipitating energetic particles disrupt the measurements and preclude the collection of valid wind data. For this study, we select three successive periods of noon-crossing observations from early in the ICON mission for analysis. Samples from the IVM and MIGHTI instruments are used when the solar local time is between 12:00 and 14:00, and when the magnetic footpoint of ICON falls within 500 km of the MIGHTI wind data retrieved from the limb observations. This latter condition is met during about 4 min of each magnetic equatorial crossing. The mean meridional drift of the plasma and the mean horizontal wind are determined in each crossing, and such observations are collected over 10 days to form a set of data that extends around the planet. Figure 2a–c compares the measured ion drift (v₂ in equation (2)) with the value predicted from the winds (right-hand side of equation (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).

Fig. 2 |. Predicted and observed meridional drifts in three successive measurement periods in early 2020.

a–f, Measured meridional drift v₂ versus that predicted from wind driving parameters using equation (2) around the planet for 10-day periods starting on 3 February (a,d), 29 February (b,e) and 22 March 2020 (c,f), shown as averages of observations between 12:00 and 14:00 solar local time for individual equator crossings (a–c) with Pearson correlation coefficient and linear fit, and longitudinally binned data (d–f). Error bars represent 1 s.d. confidence in the mean value in each bin.

The populations of equatorial crossings shown in Fig. 2a–c comprise samples from many longitudes and several days. To isolate the longitudinal patterns, including those arising from the influence of non-migrating tides, we next collect all noon-time data in these periods when the retrieved MIGHTI wind lies within 5° of 17° magnetic latitude and the IVM drift when ICON is within 5° of the magnetic equator. Data are subject to the same analysis used above, and collected into 24° bins of longitude (Fig. 2d–f). The green traces show the measured v₂. The blue trace shows the predicted v₂, that is, the term in parentheses in equation (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 Methods section). In these data, the corresponding longitudinal patterns are now evident. The natural variability in thermospheric neutral winds originating from lower-atmospheric tides introduces a strong, zonally varying driver for direct comparison with plasma drifts.

To investigate the sources of this variability, it is informative to compare the relative contribution of the specific wind-related terms in equation (2) with the overall prediction of v₂. Each of the four specific terms of the wind-driven dynamo calculation are shown for the last 10-day observation period in Fig. 3. The blue and purple lines indicate terms associated with magnetic zonal winds, and the green and orange lines those associated with magnetic meridional winds. One finds that, in this case, the zonal winds contribute to the largest variations of predicted meridional drifts, though the meridional winds provide significant inputs in some regions. Though the correspondence between the zonal wind drivers and v_pred is usually evident, the meridional wind is an important contributor in each of these cases, that is, the correlations are lower if meridional wind terms are not included in the calculation. This supports our finding that the dynamo operates in a manner described by theory, and that the derivation of its physical mechanism is correct in its inclusion of even minor terms. Considering each of these four terms, none of them are the clear source of deviations from the predicted linear relation between v_pred and v_obs, which we consider in the next section.

Fig. 3 |. Each of the four terms in the v_pred drift calculation.

The individual terms informed by MIGHTI wind measurements are shown (coloured lines) for the 23–31 March 2020, comparing the resultant v_pred drift values (black) with the observed drifts (grey) and the standard error of the mean value calculated for each term over the observing period (error bars).

Interpretation of correlated motion of winds and plasma

The sizable zonal gradients in Earth’s E-region winds observed at noon by the ICON observatory naturally lead to a prediction of strong variation in the magnetically connected plasma drift. We find that the measured plasma drifts at the magnetic equator respond accordingly, exhibiting a corresponding pattern of maxima and minima in locally averaged v₂ ≈ ±20 m s⁻¹. Plasma velocity variations like these directly influence the abundance of plasma in the F-region³³. Though the zonal gradients in winds are likely attributable to lower atmospheric forcing of the winds in the lower thermosphere, the correlation coefficients reported in Fig. 2 are derived with no specific knowledge of the tides or other forcing mechanisms responsible for the zonally varying pattern. The correlations found in successive noon-crossing periods are all positive, but indicate the presence of additional signals, either in the winds or plasma drifts. Here, we discuss potential sources of uncertainty.

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. 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 probably-beneficial correction to the prediction of v₂. ICON is designed with the ability to make wind observations down to both footpoints 20–30 times per month, a capability currently exercised on orbit to investigate the effects of asymmetric forcing on meridional plasma drifts. Because these observations are localized in regions of high magnetic declination over the Pacific and Atlantic oceans, a full zonal characterization of drifts is not achievable and so requires a different analysis than that used in this report.

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 Fig. 2. This study shows that local forcing is specifically important in driving currents, but cannot rule out sources of current outside the region of measurements, apart from the fact that a good deal of tidal variability can be characterized on monthly time scales³⁴. With roughly 25% of the observed variance attributable to locally measured sources, a large 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. Given the significant actual enhancement of lower-atmospheric effects in the lower thermosphere during solar minimum³⁵, it will be particularly interesting to observe whether local correlation changes with increasing solar activity.

Lastly, any small deviations from the approximation J₂ ≈ 0 would introduce variability into the plasma drift v₂ not predicted by the wind observations. Future work combining the observations of ICON and orbiting magnetic observatories such as the European Space Agency Swarm mission^36,37 could provide further constraints on the sampling of wind first used here. Furthermore, such observations will allow the approach described here to be extended to locations away from noon and toward the evening terminator, continuing to test our ability to predict the plasma velocity field.

The remarkable finding is that, in each case reported here, the noon-time plasma drifts always exhibit a positive correlation with the wind drivers. This provides strong support for the recent, extensive effort to develop weather models to predict conditions in the middle and upper atmosphere, in simulations that assimilate measurements of tropospheric weather³⁸ and simulate the wave spectrum that may have an effect on thermospheric winds. 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 provide the key to predicting the remarkable day-to-day variation in the state of the ionosphere. The idea that predictions of ionospheric conditions could be informed by tropospheric and stratospheric weather models, which have forecast capabilities extending more than a week from a nowcast, offers new hope that ionospheric conditions can be predicted beyond tomorrow.

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 provides a necessary, and hitherto lacking, proof of the theoretical relationship between the circulation of gas in a magnetic planetary ionosphere and the electric fields generated by the transfer of its momentum to charged species.

Methods

Data coordinates.

The derivation that follows involves 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 Fig. 4.

Derivation of wind versus plasma drift.

Neglecting currents from gravitational and pressure gradient forces, Ohm’s law is written as

$$\mathbf{j}=\sigma \cdot (\mathbf{E}+\mathbf{u}\times \mathbf{B}),$$ (3)

where j is the current density, σ is the conductivity tensor, E is the electric field in a frame rotating with the Earth, u is the neutral wind in the same frame and B is the magnetic flux density. The conductivity tensor is defined in the ionosphere as

$$\sigma =\left(\begin{array}{ccc}{\sigma }_{\text{P}}& -{\sigma }_{\text{H}}& 0\\ {\sigma }_{\text{H}}& {\sigma }_{\text{P}}& 0\\ 0& 0& {\sigma }_0\end{array}\right),$$ (4)

where σ₀ is the direct conductivity, σ_P is the Pedersen conductivity and σ_H is the Hall conductivity.

On time scales of several minutes, the observation period of each equatorial crossing, the electrostatic approximation holds. The divergence of Ampère’s law thus demands that currents be continuous

$$\nabla \cdot \mathbf{j}=0.$$ (5)

The coordinate system used here is shown in Fig. 4, where direction 1 is perpendicular to B, horizontal, and generally eastward, direction 2 is perpendicular to B and generally downward, and direction 3 is aligned with 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

$${\int }_{\text{S}}^{\text{N}}\nabla \cdot \mathbf{j}\text{d}{x}_3=0.$$ (6)

Integrating yields

$$\frac{\partial J_1}{\partial x_1}+\frac{\partial J_2}{\partial x_2}+j_3^{\text{s}}-j_3^{\text{N}}=0,$$ (7)

where the last two terms refer to currents in the insulating lower atmosphere, which are negligible, and J₁ and J₂ are field-line integrated currents:

$$J_1={\int }_S^N{j}_{1}d{x}_3,$$ (8)

$$J_2={\int }_{\text{S}}^{\text{N}}{j}_2\text{d}{x}_3.$$ (9)

Substituting into Ohm’s law, J₁ and J₂ can be written as

$$J_1={\mathrm{\Sigma }}_{\text{P}}\left(E_1+U_2^{\text{p}}B\right)-{\mathrm{\Sigma }}_{\text{H}}\left(E_2-U_1^{\text{H}}B\right),$$ (10)

$$J_2={\mathrm{\Sigma }}_{\text{P}}\left(E_2-U_1^{\text{P}}B\right)+{\mathrm{\Sigma }}_{\text{H}}\left(E_1+U_2^{\text{H}}B\right),$$ (11)

where the U terms represent field-line integrated conductivity-weighted neutral winds and the Σ terms are field-line integrated conductivities, shown below:

$$U_{(1,2)}^{\text{H}}=\frac{{\int }_{\text{S}}^{\text{N}}{\sigma }_{\text{H}}{u}_{(1,2)}\text{d}{x}_3}{{\int }_{\text{S}}^{\text{N}}{\sigma }_{\text{H}}\text{d}{x}_3},$$ (12)

$$U_{(1,2)}^{\text{P}}=\frac{{\int }_{\text{S}}^{\text{N}}{\sigma }_{\text{P}}{u}_{(1,2)}\text{d}{x}_3}{{\int }_{\text{S}}^{\text{N}}{\sigma }_{\text{P}}\text{d}{x}_3},$$

$${\mathrm{\Sigma }}_{\text{H},\text{P}}={\int }_{\text{S}}^{\text{N}}{\sigma }_{\text{H},\text{P}}\text{d}{x}_3.$$ (14)

The integrals (equations (8) and (9)) are performed assuming B and E are constant along the field line where the conductivity is substantial. This assumption is supported in three ways: (1) Given the high conductivity parallel to B, it is clear that E can be presumed constant along the integration path. (2) Given that the major contributions to the integrated quantities come from the dynamo regions, the relative variations in B are minor, specifically in light of the fact that (3) the large variation in winds and conductivities along the field line are the major variables in the integrand. When comparing drifts measured at the spacecraft with winds measured in the dynamo region, a correction of order $\sqrt{\frac{B_{\text{s}}}{B}}$ is needed, where B_s and B are the magnitude of the magnetic field at the spacecraft and in the dynamo region, respectively. For ICON, which is at an altitude of 600 km, this correction is on the order of 10–20%. Neglecting this correction does not significantly affect the correlations reported in Fig. 2a–c.

We now focus attention in the low-latitude noon sector, where two simplifying approximations can be made:

1. Meridional currents are small and integrate to zero (J₂ ≈ 0). The selection of noon near the equator places ICON’s observations in a locale where the zonal current is the dominant component³⁹.

2. Zonal conductance gradients are small $\left(\frac{\partial {\mathrm{\Sigma }}_{\text{P}}}{\partial x_1}\approx \frac{\partial {\mathrm{\Sigma }}_{\text{H}}}{\partial x_1}\approx 0\right)$. Near local noon, the variation in solar illumination is small, thus the variation in E-region plasma density is also small.

The first approximation yields J₂ = 0 in equation (11); the relationship between the zonal and meridional electric field may then be written as

$$E_2=-\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{P}}}\left(E_1+U_2^{\text{H}}B\right)+U_1^{\text{P}}B.$$ (15)

We consider the second approximation as it applies to equation (7), which in the local noon sector reduces to simply

$$\frac{\partial J_1}{\partial x_1}=0.$$ (16)

Using equations (10) and (15), we obtain the following equation describing the action of the local dynamo near noon:

$${\mathrm{\Sigma }}_{\text{C}}\frac{\partial }{\partial x_1}{E}_1+\frac{\partial }{\partial x_1}\left({\mathrm{\Sigma }}_{\text{H}}{U}_1^{\text{H}}+{\mathrm{\Sigma }}_{\text{P}}{U}_2^{\text{P}}+\frac{{\mathrm{\Sigma }}_{\text{H}}^2}{{\mathrm{\Sigma }}_{\text{P}}}{U}_2^{\text{H}}-{\mathrm{\Sigma }}_{\text{H}}{U}_1^{\text{P}}\right)B=0,$$ (17)

where Σ_C is defined as a Cowling-like conductance:

$${\mathrm{\Sigma }}_{\text{C}}=\frac{{\mathrm{\Sigma }}_{\text{H}}^2}{{\mathrm{\Sigma }}_{\text{P}}}+{\mathrm{\Sigma }}_{\text{P}}.$$ (18)

Because we are interested in ionospheric motion, we rewrite equation (17) in terms of $\mathbf{V}=\frac{\mathbf{E}\times \mathbf{B}}{B^2}$ and rearrange terms to obtain

$$\frac{\partial }{\partial x_1}{v}_2=\frac{\partial }{\partial x_1}\left(\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_1^{\text{H}}+\frac{{\mathrm{\Sigma }}_{\text{P}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_2^{\text{P}}+\frac{{\mathrm{\Sigma }}_{\text{H}}^2}{{\mathrm{\Sigma }}_{\text{C}}{\mathrm{\Sigma }}_{\text{P}}}{U}_2^{\text{H}}-\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_1^{\text{P}}\right).$$ (19)

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:

$$v_2=\left(\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_1^{\text{H}}+\frac{{\mathrm{\Sigma }}_{\text{P}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_2^{\text{P}}+\frac{{\mathrm{\Sigma }}_{\text{H}}^2}{{\mathrm{\Sigma }}_{\text{C}}{\mathrm{\Sigma }}_{\text{P}}}{U}_2^{\text{H}}-\frac{{\mathrm{\Sigma }}_{\text{H}}}{{\mathrm{\Sigma }}_{\text{C}}}{U}_1^{\text{P}}\right)+C_{\text{ext}},$$ (20)

v₂ is now representative of the observed plasma drift, $U_1^{\text{H},\text{P}}$ and $U_2^{\text{H},\text{P}}$ are representative of the observed conductivity-weighted winds and a constant term is representative of an offset in the relationship between the winds and drifts that can be attributed to an external source of current. This is appropriate for ICON, for the fact that the derivative in the x₁ sense of either quantity is not exactly observed, except if considered between each of the noon crossings that are separated by ~97 min. The value of the drift at the magnetic apex and the corresponding wind observation are observed directly by ICON. For comparisons of two crossings, it is necessary that the constant offset not vary between the cases. Given the remarkably low solar activity and geomagnetic activity during the period of study, this is probably true over each individual period of noon crossings, which are studied separately in this report.

Statistical significance of measurement uncertainties and model inaccuracy.

The significant correlations found in comparisons of the conductivity-weighted wind and plasma drift on the same field line, with values consistently around 0.5 for each noon crossing, show the likely relation between these quantities. A portion of the statistical variance originates in the instantaneous uncertainties of the measured v₂ and u_1,2 when co-added in the ~4-min period of observations with each equator crossing, which are no more than ~3 m s⁻¹. These are notably low, and we find therefore that instrumental effects are likely not germane to the discussion of the spread of data around a linear relationship.

Errors stemming from inaccuracies of the empirical models used to determine j in the International Reference Ionosphere and Mass Spectrometer Incoherent Scatter model (MSIS) products are expected mainly to introduce bias terms that could be accounted for in the determination of C_ext. To understand the importance of model inaccuracies, we have tested the effect of error in the neutral atmospheric density, by reducing the neutral densities provided by MSIS. A reduction of the density profile by 20%, for example, produces changes in the resultant v_pred of 1–2 m s⁻¹ and a slight change in mean values reported in Figs. 2a–c. Also, in fact, because of the variability in the wind drivers, the resultant changes in v_pred cannot be described as a constant bias but essentially as an additional source of noise with a small effect on the resultant correlations. Compared with other sources of uncertainty, we find the models to be a minimal source of error, introducing uncertainty no larger than do the wind measurements themselves.

Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41561–021-00848–4.

Data availability

Data collected by the Ionospheric Connection Explorer are available at https://icon.ssl.berkeley.edu/Data and are archived at the NASA Space Physics Data Facility at https://spdf.gsfc.nasa.gov. Source data are provided with this paper.