Neutral winds affect the composition in the thermosphere as well as the motion of the charged particles by dragging the plasma up and down magnetic field lines, changing rates of production and recombination (Kelley, 2009) and by creating electric fields via the neutral wind dynamo (Maute and Richmond, 2017). Thermospheric neutral winds are known to be affected by geomagnetic conditions, seasons, local time and atmospheric tides, among others (Wang et al., 2021) and vary over large temporal scales ranging from minutes to years. Understanding their variability becomes critical, as they transfer energy and momentum in the upper atmosphere and directly or indirectly affect the dynamics, morphology and composition of the ionosphere, which can disrupt radio communication and navigation systems (e.g., Calabia et al., 2023).

A powerful approach to quantify the variability in thermospheric winds is to calculate spatial and temporal correlations, which indicate a statistical relationship between variations in the winds at different times and locations on the globe. Spatial and temporal correlations are also important for model validations, which involve comparisons of correlations obtained from observations with those obtained from the models (e.g., Bruinsma et al., 2014). Correlations can also help to gain insight into physical processes that produce variability seen in observations (e.g., Forbes et al., 2005) and provide critical constraints for model error covariances used in various data assimilation schemes.

Correlations of different physical parameters are widely used to study the global morphology and variability in the atmosphere. Alken and Maus (2007) studied correlation lengths in the equatorial electrojet using CHAMP, Ørsted and SAC-C magnetic observations; Shim et al. (2008) studied the spatial correlations of day-to-day GPS Total Electron Content variations; Garcia et al. (2016) used correlations from GOCE density and cross-wind variations for gravity wave detection and characterization; Bruinsma et al. (2021) used density correlations as part of model assessments during geomagnetic storms. Liu (2014) and Liu (2016) investigated the correlation time of the zonal mean zonal wind, as well as the amplitudes of four main tidal components (DW1, SW2, DE3 and SW1) with winter stratospheric temperature anomalies using detrended time series of these quantities from a 20-year model simulation of the Whole Atmosphere Community Climate Model with thermosphere extension (WACCM-X).

In this paper, latitudinal and longitudinal/temporal correlations are presented for the GOCE zonal wind data at low- and mid-latitudes, and the results are discussed. In a companion paper Molina and Scherliess (2023) have used the same GOCE zonal wind observations to determine the zonal wave structures associated with nonmigrating tides.

This paper is organized as follows. Initially, the data and the methodology are described. Next the GOCE zonal wind latitudinal correlations are presented for December solstice 2009–2012 and June solstice 2010 followed by the longitudinal/temporal correlations for December solstice 2009 and June solstice 2010. Finally, the results are summarized and discussed.

The Gravity Field and Steady-State Ocean Explorer (GOCE) mission provided cross-track thermospheric (zonal) neutral winds from November 2009 to October 2013. The satellite was launched on 17 March 2009 into a dawn-dusk Sun-synchronous orbit with an inclination of 96.7° (near-polar orbit). The mean altitude of the satellite was near 270 km during the initial years of the mission and gradually decreased to about 250 km during 2012 and 2013, with variations in the height of the satellite within one orbit of about 20 km. Although the main objective of GOCE was to investigate the gravitational field of the Earth, thermospheric parameters, including the densities and winds were also provided in 10-s increments by combining the accelerometer and ion thruster data, together with GPS tracking and star camera data (Doornbos et al., 2013). For the current study we used data set version 2.0.

Due to the very small orbital precession, the local solar time corresponding to the equatorial crossing of the satellite only slightly changed throughout the mission by about 20 min/year from initially 06:15/18:15 LT to 07:30/19:30 LT by the end of the mission. As a result, GOCE produced a large data set of zonal winds in the dawn-dusk sectors.

The errors in the GOCE zonal wind are of the order of ∼10%–20%, with the dominant source of errors being biases due to instrument calibration and external models used in the calculation of the winds (Doornbos et al., 2010).

To investigate the correlations in the GOCE zonal winds, we focused on geomagnetically quiet 27-day periods (one solar rotation) that were centered as close as possible to the December solstice for the years 2009, 2010, 2011, and 2012 and the June solstice for the year 2010. These periods were chosen due to data availability and geomagnetic activity. The selected windows are:

• December 2009: 12 December 2009 to 07 January 2010

Figure 1 shows the daily F10.7 cm radio flux (1A) and daily Kp index (1B) for the span of the GOCE thermospheric data set. The December and June solstice periods selected for this study are indicated by yellow and purple vertical bars, respectively. During 2009 and 2010 the solar flux was significantly lower than during 2011 and 2012. The average F10.7 value for the selected window in December 2009 was 76 sfu and 81 sfu for the corresponding 2010 period. The average values for the 2011 and 2012 periods, on the other hand, were 132 sfu and 109 sfu, respectively. The average F10.7 value for the June 2010 period was 75 sfu and 95 sfu for the June 2011 window. Geomagnetic activity was generally very low during all selected periods with average Kp values over the individual 27-day periods not exceeding 1⁰ for each of the December solstice periods and below 2^- for the June solstice periods. Figure 1B shows that the daily Kp reaches a value of 3 only once during December 2011 and a value of 3.3 once during each June period. The total number of 10-s observations at low- and mid-latitudes for each 27-day time period is about 60,000.

We employ a methodology similar to Shim et al. (2008) to investigate spatio-temporal variability. The data was first separated according to the local time of the observation into dawn and dusk bins. The data along a given orbit was then binned and averaged in 1°-wide geographic latitude bands from −60° to 60° geographic latitude. Next, the median value was calculated for each latitude band from all orbits in each 27-day period. Finally, the corresponding median value, m, was subtracted from the binned and averaged measurements, u, to calculate the correlation as follows: r i , j , Δ O r b i t = ∑ k = 1 n o r b i t u i − m i k ⋅ u j − m j k + Δ O r b i t ∑ k = 1 n o r b i t u i − m i k 2 1 2 ⋅ ∑ k = 1 n o r b i t u j − m j k + Δ O r b i t 2 1 2

Here, i and j correspond to the reference and comparison points, respectively and the summation is executed over all orbits during the given 27-day period (norbit = 16 orbits/day *27 days = 432 orbits). Due to the orbit of the GOCE satellite longitude and time are intimately coupled and longitudinal/temporal correlations cannot be calculated by using pairs of observations along a given orbit. Instead, data pairs obtained from different orbits need to be used. This is accomplished by introducing the index Δ O r b i t , which indicates the difference in orbit number from a given orbit to all other orbits. Hence, a value of Δ O r b i t = 0 indicates that u _i and u _j are taken along the same orbit whereas positive/negative values of Δ O r b i t indicate that u _j was obtained from temporally later/earlier orbits, respectively. Note that consecutive orbits differ by about 90 min and 22° in longitude. Therefore, values of Δ O r b i t = 16 , 32 , 48 , … correspond to observations taken approximately one, two, three, … days later at the same longitude. Similarly, values of Δ O r b i t = 8 , 24 , 42 , … correspond to correlations between observations with time differences of about half a day, one and a half day, two and a half days, etc., that are located 180° apart in longitude.

Latitudinal correlations are calculated by setting Δ O r b i t = 0 . GOCE takes about 30 min to cross from 60°N to 60°S and vice versa and therefore, the latitudinal correlations do not correspond to perfectly synchronous observations but instead are smeared out by up to 30 min. Furthermore, GOCE does not exactly return to its position after 16 orbits, but instead advances by about 1° in longitude over a 1-day period. This again leads to a slight smearing of our longitudinal/temporal correlations.

So far, our approach will eliminate correlations associated with deterministic variations in solar cycle, season and local time and focuses on stochastic and tidal variations. The results of this analysis will be shown in Sections 4.1–4.3. To investigate correlations not associated with tides (Section 4.4) we subsequently eliminated their contribution from the zonal winds before calculating the longitude/time correlation coefficients. For this, we have used the results presented in Molina (2022), Molina and Scherliess (2023), who have used the same GOCE zonal wind observations to determine the zonal wave structures associated with nonmigrating tides by applying a longitudinal Fast Fourier Transform to the binned and averaged GOCE zonal wind data. We have used their results by subtracting their deterministic monthly-mean wave-1 to wave-5 structures from the GOCE zonal wind observations before calculating the longitude/time correlation coefficients.

We have analyzed GOCE zonal wind observations from low- to mid-latitudes to investigate their spatial and temporal correlations. The year-to-year variations as well as the inter-seasonal differences were established for dawn and dusk. We have focused on geomagnetically quiet 27-day periods (one solar rotation) centered as close as possible to the December solstice for the years 2009, 2010, 2011 and 2012 and the June solstice for the years 2010 and 2011. For the calculation of the latitude and longitude/temporal correlations an approach similar to the one described in Shim et al. (2008) was followed. Our results represent zonally averaged values and do not correspond to a particular location/longitude on the globe. Furthermore, our approach eliminated correlations associated with deterministic variation in solar cycle, season and local time and instead focused on stochastic and tidal variations. Additionally, due to the orbit of GOCE longitudinal/temporal correlations could not be separately analyzed.

We found that for all four December solstice periods the latitude correlations during dawn were larger and more extended in latitude in the northern hemisphere compared to the southern hemisphere.

During dusk for December solstice 2009 and 2010 significantly larger and more extended correlations were found for reference latitudes located in the southern hemisphere and in the northern hemisphere up to ∼20° latitude. During December 2011 the extension of the latitudinal correlations in latitude were seen to be much reduced before increasing again in 2012. The cause of this year-to-year progression is not known at this point but might be related to similar variations, albeit anticorrelated, in the solar activity throughout these years.

We have also evaluated the zonal wind latitudinal correlations for June solstice 2010 and the larger correlation lengths during dawn were found in the southern hemisphere and during dusk in the northern hemisphere. This indicates that during both solstice periods, the latitudinal correlation lengths exhibit their largest values consistently in the winter hemisphere during dawn and in the summer hemisphere during dusk.

Of particular interest are the observed latitudinal correlations at dawn between hemispheric conjugate points observed at mid latitudes during the later December solstice periods. The strength of this conjugacy also appeared to follow similar variations in the solar activity throughout these years, i.e., during December 2009 it was not observed, started to appear in 2010, strengthened in 2011, before weakening again in 2012. This conjugacy was also examined in geomagnetic instead of geographic coordinates which resulted in a much cleaner presentation of the conjugacy. The physical cause for the observed conjugacy, however, is not clear at this point. We speculate that it might be related to midlatitude nighttime MSTIDs, also named electro-buoyancy waves, which map into the opposite hemisphere (Valladares et al., 2016). These waves are found to be magnetically conjugate and preferentially occur during the solstices (Makela et al., 2010; Martinis et al., 2010; Duly et al., 2013). However, Martinis et al. (2010) found that MSTIDs follow an inverse occurrence rate with solar activity conditions in contrast to our observation of the variation of the strength of the conjugate correlation coefficients.

In addition to electro-buoyancy waves, the observed conjugacy at mid-latitudes might also be related to conjugate variations in the high latitude electrodynamics. Wu et al. (2014) reported they observed conjugacy in thermospheric zonal winds in the American sector with varying degrees depending on geomagnetic conditions. They found that conjugacy is highest under moderate geomagnetic conditions, but it is observed for all geomagnetic activity levels, including geomagnetically quiet times. In our case, the average Kp values did not exceed 1⁰ for each of the December solstice periods, but the variation seems to follow the solar activity. Clearly further studies are needed to elucidate the underlying causes of the observed conjugacy.

We have also analyzed the dawn and dusk longitudinal/temporal correlations of zonal wind for December 2009 and 2011 and for June 2010 and found that they exhibit periodic structures with the largest positive correlations every 16 orbits (every 1 day) during all geophysical conditions, albeit with different characteristics. The temporal evolution of the temporal/longitudinal correlations were found to gradually decrease over the course of several days. Based on a 20-model year simulation of WACCM-X, Liu (2016) reported correlation times of zonal mean zonal winds in the thermosphere of the order of days, in agreement with our results. We found that the correlation coefficients for the same location decreased more slowly during dawn and much faster during dusk for both December and June solstice conditions. We also observed that during dawn the maxima in the correlation coefficients were always located in the winter hemisphere. This hemispheric “flip” was also seen during dusk in the summer hemisphere, but not as clearly.

The temporal/longitudinal correlation coefficients for December solstice 2009 were found to be generally larger in the northern hemisphere during dawn and larger in the southern hemisphere during dusk. Specifically, during dawn the temporal/longitudinal correlation for December 2009 displayed a diurnal/wave-1 periodicity in the northern mid-latitudes and a semidiurnal/wave-2 periodicity for lower latitudes and the southern hemisphere. The orientation of these structures was found to be in the north-west direction. During dusk, a semidiurnal/wave-2 structure was observed for all latitudes, with a north-east orientation. The general structure observed during dawn in the correlations in December solstice 2009 could also be seen in December solstice 2011 but larger differences between the 2 years were found during dusk.

The temporal/longitudinal correlation coefficients for June 2010 at dawn displayed a diurnal/wave-1 periodicity in the southern hemisphere and a semidiurnal/wave-2 periodicity in the northern hemisphere. Here, the orientation of the structures was found to be in the north-west direction. During June solstice dusk, a semidiurnal/wave-2 structure was observed for all latitudes, with a north-east orientation. This time, however, the larger correlation values were observed in the northern hemisphere, in contrast to our December solstice results.

Although our study does not allow for a detailed analysis of the underlying causes of the observed periodic structures, we speculate that they are the result of the presence of atmospheric tides, and in particular nonmigrating tides. To investigate correlations not associated with tides we have eliminated their contribution up to zonal wave-5 from the zonal winds before calculating the longitude/time correlation coefficients. The results show that the longitudinal/temporal correlations were strongly attenuated during dawn for both December and June solstices, suggesting that indeed the main structures observed before were the result of nonmigrating tides during this time of the day, irrespective of season and solar flux. Some smaller localized correlations are still apparent in the remaining correlations at dawn, which might be related to the presence of gravity waves that have been reported to be present in GOCE observations (Garcia et al., 2016; Vadas et al., 2019) and/or variations in the phase and amplitude of the tides. A modeling study by Liu (2014), for example, suggests that there is an irregular or stochastic aspect of the day-to-day tidal variability.

In contrast, during dusk, a previously masked structure appears after the removal of the tidal effects that follows a multi-day period for both December (in the southern hemisphere) and June (in the northern hemisphere). Although more investigation is needed, these correlations might be the result of the presence of other waves that we have not included in our analysis. Gasperini et al. (2015), for example, reported the presence of ultra-fast Kelvin waves in the GOCE zonal wind observations with a period of 3.5 days.

Finally, note that our analysis only pertains to geomagnetically quiet conditions at dawn and dusk and an investigation of the correlation coefficients of the zonal winds for other local times and geomagnetically active conditions needs to be performed in the future.