With the exception of one rocket observation , the only in situ co-temporal and co-spatial observations of Te, Ti and Tn within the LTI were obtained from satellites AE-C, AE-D and AE-E in the 1970s and early 1980s. Te measurements on board all three AE satellites have been obtained via the cylindrical electrostatic probe (CEP) instruments , which are retarding potential Langmuir probe devices, providing electron temperature measurements by the current–voltage (I-V) characteristic relationship of the Debye sheath . Ti measurements have been obtained from the retarding potential analyzer (RPA) on board the AE satellites and on board the DE-2 satellite , which provide ion temperature by I-V characteristics delivered by the instruments . Similar RPAs have also been used in other space missions, such as the LAICE and DMSP satellites. Finally, Tn measurements have been obtained through the Neutral Atmosphere Temperature Experiment (NATE) instrument on board the AE satellites , and through the neutral mass spectrometer (NMS) on board the DE-2 satellite. NATE and NMS provide neutral temperature through the determination of the velocity distribution of the molecules .

In this study, we focus on the comparison between Ti and Tn measurements; however, Te measurements are also regarded as part of the cross-comparison with ISR Te and Ti data, for completeness of the comparison through the extension of the work of to all available in situ satellite databases.

As a first step of the comparative analysis between in situ and remote-sensing measurements of Te and Ti, all conjunctions between the in situ datasets and ISRs measurements were identified. Remote-sensing measurements were obtained through a collection of different ISR experiments, which are maintained at the Madrigal Database, an upper-atmospheric science database used by scientific groups around the world. Madrigal was created and launched at MIT Haystack in the 1980s, prior to being adopted as the basis for the Coupling, Energetics and Dynamics of Atmospheric Regions (CEDAR) program database. The names, geographic coordinates and L shells of the ISR facilities used in this study are as follows: Arecibo (18.4∘ N, 66.8∘ W; L=1.4), Saint-Santin (44.6∘ N, 2.2∘ E; L=1.8) and Millstone Hill (42.6∘ N, 71.5∘ W; L=3.1). The L shell here represents the McIlwain L, a parameter describing the magnetic field lines which cross the Earth's magnetic equator at a number of Earth radii equal to the L value. The criteria in order to mark a satellite overpass over a radar field of view as a conjunction are as follows: latitude range – ± 0.5∘; longitude range – ± 18∘; altitude range – ± 10 km; time range – ± 60 min. These conjunction criteria are identical to the ones used in , so as to be able to cross-compare the extended datasets that are presented herein with their results. The common dataset for each satellite and ISR is available at .

The total number of conjunctions with valid Te measurements between each of the satellites and all the above ISRs is as follows: AE-C – 79; AE-D – 0; AE-E – 0; DE-2 – 65. This leads to a total of 144 measurements. The total number of conjunctions with valid Ti measurements between each of the satellites and all the above ISRs is as follows: AE-C – 63; AE-D – 3; AE-E – 46; DE-2 – 47. This leads to a total of 159 conjunctions. In comparison, the study of was based on a total of 39 conjunctions for Te and 27 conjunctions for Ti.

Figure  presents the results of the comparison between Te (a) and Ti (b), for the conjunctions between the in situ and ISR measurements as listed above. In this figure, conjunctions of AE-C with all three ISRs (i.e., Arecibo, Millstone Hill and Saint-Santin) are marked in blue, conjunctions of AE-E with ISRs are marked in green and conjunctions of DE-2 with ISRs are marked in red. Linear fits through these data points are shown in blue, green and red lines, corresponding to the above datasets; the equations of the linear fits are shown along the colored lines. In addition, the ratio between the satellite (SAT) and radar (ISR) measurements has been calculated according to RTk=Tk(SAT)/Tk(ISR), where k=e for electrons and i for ions. The numerical values of these ratios are shown in the legend in the upper left corner of each figure. It is noted that AE-D included only three Ti measurement conjunctions, and a similar fit is not presented in the above analysis.

The results shown in Fig. a and b indicate that AE-C and ISR data yield similar measurements for both Te and Ti during their conjunctions. This is consistent with the findings of the study by . Following the same approach and extending the work of , Fig. a also presents Te measurements from DE-2 and ISRs during times of conjunctions. The comparisons show that DE-2 measurements have a slope that is lower than 1, meaning that DE-2 systematically measures higher electron temperatures than the ISRs. It is noted that no conjugated measurements of Te were found between AE-E and ISRs. Similarly, Fig. b presents Ti measurements from AE-E and DE-2 during times of their conjunctions with ISRs; the comparisons of both AE-E and DE-2 with ISRs during times of their conjunctions yield slopes that are lower than 1, meaning that both AE-E and DE-2 systematically report higher ion temperatures than the ISRs. This could indicate the need for systematic recalibration of AE-E and DE-2 measurements, whereby AE-E and DE-2 measurements might need to be systematically lowered.

In addition to the correlation between in situ and ISR measurements of Te and Ti that is shown in Fig. , the comparative analysis was extended by estimating also the ratio between in situ and ISR measurements as a function of local time and absolute longitude and altitude; these results are included in Appendix Figs. A1 and A2 for Te and Ti comparisons, respectively. Figures A1 and A2 are plotted in the same format as Fig. 2 of , to allow for cross-comparisons with that study. The numbers in the lower right corner in each panel of Figs. A1 and A2 indicate the ratio between satellite and radar measurements. From Figs. A1 and A2 it can be seen that the conjunctions are well distributed over local time, absolute longitude separation between the satellites and radars, and altitude. Furthermore, in Figs. A1 and A2 we also plot the number of measurements as a function of the in situ (SAT) over radar (ISR) measurements in order to visualize the distribution of the measurements under comparison over local time, absolute longitude separation and altitude. The estimated linear fits in these figures are in agreement with the results from , in particular for Te for all satellites and Ti for AE-C and AE-D. However, a larger standard deviation is observed in the linear fit of Ti measurements from DE-2 with respect to the ISR measurements. This is more evident for high Ti, with satellite measurements appearing to underestimate Ti compared to ISRs. Finally, in Fig. A3 we plot histograms of measurements distribution over the calculated ratio. Figure A3 is plotted in the same format as Fig. 3 of , allowing for comparisons between the two studies.

As a first step, from the entire database of Ti and Tn measurements obtained from satellites AE-C, AE-D, AE-E and DE-2, data were only considered when the satellites were located below 500 km. From this subset, all cases with simultaneously valid Ti and Tn measurements were selected. For the selection of valid data points, the WATS instrument data processing of DE-2 was followed . As part of this process, temperatures in the datasets were regarded as valid when the condition 200≤Tk≤4000 was met, where k=e,i,n. After subtracting all data points flagged as erroneous, the dataset of temperature measurements where Ti and Tn are simultaneously valid consists of 52 822, 11 960, 171 775 and 236 785 data points for satellites AE-C, AE-D, AE-E and DE-2, respectively.

Subsequently, the subset of measurements when Ti<Tn was identified for each satellite. From this subset, only data points where Ti<Tn appeared at consecutive points along the orbit were considered, whereas individual (i.e., non-sequential or singleton) points were discarded. Within this dataset from satellites AE-C, AE-D, AE-E and DE-2, the condition that Ti<Tn was met in 18 959, 2934, 4501 and 10 674 data points, respectively, corresponding to 36 %, 25 %, 3 % and 5 % of the total numbers of valid data points, respectively. These numbers indicate that there is a non-negligible occurrence rate of cases when neutrals are (or appear to be) hotter that ions.

In the following we first present two examples of such events where the condition Ti<Tn is observed; we then proceed to investigate the statistical distributions of these events, both in altitude and in longitude vs. latitude.

An example of such an event occurred on 17 January 1975, during orbit 5089 of AE-C. An overview is shown in Fig. , where in the first three panels the spacecraft altitude, latitude and L shell are plotted, whereas in the fourth panel Ti and Tn are plotted in blue and green, respectively. Solar and geomagnetic indices during the time of this event were as follows: Dst ranged from -17 to -15 nT, the auroral electrojet (ae) index ranged from -172 to -62 and Kp ranged from 3+ to 4, indicating moderate geomagnetic activity levels.

The second example, plotted in Fig. , shows a sequence of five DE-2 orbits. During this event, the transition from Ti≥Tn (first orbit) to Ti<Tn (second to fifth orbits) is observed. Solar and geomagnetic indices during this time are as follows: Dst =-44, ae =81, and Kp =2- to 4. This indicates low to moderate geomagnetic activity levels. It is noted that between each orbit there are data gaps in the DE-2 dataset.

The ground tracks of these events are shown in Fig. , where the ground track of the AE-C orbit of Fig.  is shown with a solid line, whereas the ground tracks of the five consecutive DE-2 orbits of Fig.  are shown with five dashed lines.

In Fig.  we plot all the occurrences of ΔTin=Ti-Tn (both positive and negative) as a function of altitude, separately for each spacecraft. To this direction, panels (a) through (d) of Fig.  present the altitude distribution of all ΔTin for AE-C, AE-D, AE-E and DE-2, respectively. The temperature of thermal equilibrium between ions and neutrals, or ΔTin=0, is plotted with an orange line, whereas the local mean of ΔTin is plotted with a light blue line; the local mean was calculated at altitude steps of 5 km. As it can be seen in these panels, whereas the local mean shows a positive average ΔTin for all missions at all altitudes (with the exception of the lowermost altitudes of AE-C), there is a non-negligible number of cases where negative differences are observed. Furthermore, these plots show a positive trend of ΔTin with altitude, meaning that cases of ΔTin<0 are more likely to be observed at lower altitudes.

In Fig.  we plot the distribution of all cases where Ti<Tn (such as those shown in Figs.  and ) as a function of geographic latitude and longitude. The geographic distribution of the Ti<Tn cases is depicted by plotting the corresponding probability distribution function (PDF) of the occurrence of such events. The PDF is calculated based on the kernel density estimation (KDE) method e.g.,, using Gaussian kernels. More specifically, as part of the fundamental principle of a Gaussian KDE, each data point is given a Gaussian distribution (kernel), and these distributions are subsequently added up to produce a smooth approximation of the underlying probability density. The results are then normalized to produce the relative (unit-less) likelihood. The normalization is performed by subtracting the lowest value that is observed on the map from the PDF value at each point and subsequently dividing by the range from maximum to minimum PDF value; thus the resulting values range from 0 (corresponding to the lowest likelihood for the observation of Ti<Tn), which is marked as blue in Fig. , to 1 (corresponding to the highest likelihood), which is marked as red. In Fig. , the solid line marks the orbit of AE-C on 17 January 1975 that corresponds to the sample event shown in Fig. , and the five dashed lines mark the orbits of DE-2 on 12 December 1982 that correspond to the event shown in Fig. . Letters A through J indicate regions of interest that are discussed in further detail in the section below.

There are several potential sources of uncertainty that can lead to systematic and random errors in the in situ measurement of temperatures in space. The removal or correction of such errors has been the topic of multiple studies over the past decades e.g.,. These errors are primarily due to the high spacecraft velocity and the interaction of the spacecraft with the surrounding plasma and neutral environment. For example, factors that affect the accuracy of measuring ion temperatures include the acceleration of plasma by a charged surface, the generation of a complex plasma cloud that surrounds the spacecraft and interacts with the environment, and impact ionization and reflection of particles off the spacecraft and the subsequent inclusion of reflected ions in the measurements e.g.,. In particular, addressed spacecraft motion effects due to the creation of a wake in the Martian ionosphere and demonstrated the recalibration of the instrumentation on the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft with the aid of kinetic solutions and published results from laboratory experiments, through which they achieved a significant improvement in the systematic uncertainty in Te measurements. Similarly, discussed a series of rigorous processes that they employed to identify and correct various sources of uncertainties in measurements of Ti arising from the supersonic velocities of MAVEN; these include altitude-dependent systematic errors as well as random errors from statistical fluctuations and uncertainties in spacecraft potential.

Based on the general agreement between in situ and ISR estimations of Ti, it is noted that Ti measurements are less likely than Tn to include large systematic deviations that could lead to the appearance of ΔTin<0 in a statistically significant percentage of the total number of measurements, indicating that these measurements are less likely to be regarded as outliers. Factors affecting the accuracy of neutral temperature measurements include the applicability of the kinetic theory used in extracting neutral temperatures, in particular at lower altitudes where a shorter mean free path of the measured particles might affect the measurements, and gas–surface interactions, which are also dependent on altitude and neutral density e.g.,.

The altitude dependence that is shown by the light blue curves of Fig.  indicates that the appearance of ΔTin<0 could be dependent on such spacecraft–environment interaction effects, which are expected to be dependent on neutral density. This effect could account for the larger appearance of ΔTin<0 at altitudes below 150 km, as is shown, for example, in AE-C measurements; however, as it can be seen in Fig. a, in the altitude ranges from ∼ 150 to 200 km, there is a decrease in the appearance of such events, which are again enhanced at altitudes upwards of 200 km.

The structured appearance of the occurrence rates of the ΔTin<0 events in Fig.  (as opposed to an even or random distribution of such events in latitude and longitude) indicates that there are, potentially, distinct underlying mechanisms leading to either the enhancement of neutral temperatures or the decrease in ion temperatures in these regions. In the following, the regions of enhanced probability for the appearance of ΔTin<0 events are discussed, followed by a discussion on the possible underlying physical mechanisms that could be the cause of these observations. It is noted that the analysis presented herein is only meant to highlight these intriguing results and to point to potential mechanisms but cannot, at this point, yield a dominant mechanism or combination of mechanisms that can conclusively explain these results.

In Fig. , there are seven distinct regions of enhanced occurrences of ΔTin<0 measurements; these are marked from A through G, as follows. There are four primary peaks of high occurrences, marked as A through D, that are located close to the geomagnetic equator. Of these, A and B are located in the South Atlantic and Indian oceans, respectively, whereas secondary peaks marked as C and D are observed in the western and eastern Pacific Ocean, respectively. A distinct enhancement is observed in the north Mexico/Baja California region and is marked as E. An enhancement is also observed in the northern Atlantic Ocean (as compared, e.g., to the continental regions of North America and Europe) and is marked as F. A distinct peak can be observed off the southern coast of Alaska and western Canada (compared to the corresponding continental regions) and is marked as G. Furthermore, there are four regions which have distinctly smaller concentrations of observations of ΔTin<0 events: these are observed in the northern and southern high-latitude regions, which are marked as H; in the European continental region, which is marked as I; and in the northern Russian region, which is marked as J.

A first candidate mechanism that can significantly impact the LTI, altering neutral temperatures, concerns gravity waves (GWs). Gravity waves are dissipated in the thermosphere at altitudes between 100 and 200 km through molecular damping, modifying thermospheric temperatures . Gravity waves generally form in the troposphere and lead to the transfer of momentum from the troposphere to the stratosphere and mesosphere and even further upwards to the thermosphere . These waves propagate upwards from the troposphere, and, in doing so, they grow exponentially in terms of wave amplitude e.g.,. The subsequent wave breaking of these large-amplitude waves leads to significant energy and momentum deposition. The detailed parameterization of GWs is an open issue in upper-atmosphere research, in particular for medium- (meso-β) and small-scale (or meso-γ) GWs, measurements of which are completely lacking see, e.g., and whose effects could be significant for LTI energetics and dynamics.

The heating and cooling effects of GWs in the thermosphere have been extensively investigated by many simulation studies. For example, used a GW parameterization that was specifically designed for thermospheric heights, which was implemented in the Coupled Middle Atmosphere and Thermosphere (CMAT2) global circulation model , covering altitudes from the tropopause to the F2 region. They performed simulations for the June solstice and illustrated the regions of GW heating and cooling rates. The simulation results indicated significant irreversible heating in the high latitudes of both hemispheres, which reached 90 to 100 K d-1 near 200–210 km; secondary peaks in heating also appeared in the tropics, predominately below 130–140 km, which reached up to 10 K d-1. Such preferential heating of the neutrals by GWs is compatible with the observations presented herein. However, even though regionally GWs can lead to significant heating in the thermosphere, note that the net thermal effect of GWs is primarily cooling of the thermosphere and that the simulated model temperatures can be decreased by up to 200 K at the summer pole and by 100 to 170 K at other latitudes near 210 km. Simulations by also show that GWs can lead to cooling of the neutrals in the LTI at altitudes above 210 km.

GWs can be generated through a range of different processes: these can be of meteorological origin (convective, shear, geostrophic) or topographic origin (e.g., mountain waves) or even due to strong tropospheric disturbances. In the following we discuss the generation mechanisms and localizations in relation to the appearance of ΔTin<0 events.

Intense GWs are known to be generated by winds flowing over mountain formations; for example, reported the appearance of GWs over the Andes. However, whereas peak D could possibly be associated with the Andes, there are no corresponding signals over North America (Rocky Mountains), Europe (Alps) or India/China (Himalayas); this indicates that there is possibly no clear association of ΔTin<0 events with GWs of topographic origin.

Together with mountain ranges, GWs are known to be generated by hurricanes, typhoons and tropical cyclones. In order to find potential correlations with such dynamical tropospheric events, all relevant occurrences of hurricanes, typhoons and tropical cyclones combined were collected from the NOAA IBTrACS v4 database and are plotted in Fig. for the time period from 1974 to 1976 corresponding to the period of in situ measurements that are plotted in Fig. . It is noted that the region marked as E and F in Fig. , and in particular the region extending from ∼18∘ N to ∼40∘ N and ∼120∘ W to ∼80∘ W, has a particularly high occurrence rate of hurricanes and typhoons and a markedly similar extent in their localizations. The same is observed in the region of the Indian Ocean and north of Australia, from ∼10∘ N to ∼40∘ S and ∼40∘ E to ∼150∘ E, which has a particularly high occurrence rate of tropical cyclones. However, no such events are observed over the regions marked as A, B and D, meaning that different mechanisms are taking place in these regions.

Together with the above regions of dynamical tropospheric events, such as hurricanes, typhoons and cyclones, and the appearance of GWs in association with large mountain formations, there are many other triggers of highly localized and persistent GWs: for example, such phenomenology has been termed a “GW hot spot”, appearing over specific regions and times e.g.,. Other studies have reported the lack of GWs over specific regions: for example, resulting from the diurnal tide's strong poleward winds over the European area, some GWs were found to be moving westward across the Atlantic and eastward over eastern Europe e.g.,, leaving a gap in terms of GW occurrence over Europe. Investigating in detail the appearances of these localizations and their causes is a topic that is beyond the scope of this paper and that is left for future studies.

Recently, reported on GWs that can cause up to 75∘ K changes at 200 km. Interestingly, they report that the locations of these GWs, even though orographically generated, are not centered on mountains but instead radiate from them. They also reported that these GWs are attenuated by horizontal magnetic fields and that they could be located 1 or 2 d after a large polar vortex event. These results indicate that the correlation between the generation mechanism, the region and the effects of GWs can be a much more complicated process than currently thought.

Another potential mechanism that could lead to an enhancement of Tn and hence to the appearance of instances of ΔTin<0 could be associated with the equatorial region fountain effect: during this process, the plasma is driven upwards due to an E×B drift, owing to the eastward direction of E and the northward (parallel to the Earth's surface) direction of B. The plasma motion drives the neutral gas to move upwards as well, through the momentum transferred via collisions between neutral and charged particles, transferring momentum from the plasma to the neutral gas. These collisions end up heating the neutral gas, whose temperature is gradually enhanced. At higher altitudes, the E×B drift stops driving the plasma upwards, which, in the absence of an electric field, follows the magnetic field lines, mapping to latitudes northwards and southwards of the magnetic equator. This process leaves the heated neutrals with an average temperature Tn that is higher than the ion temperature Ti.

An additional candidate mechanism that could lead to the appearance of ΔTin<0 is related to the South Atlantic Anomaly (SAA), the region over the South Atlantic Ocean where the magnetic field strength is significantly weaker than in other parts of the planet : the low altitude of the mirroring point of energetic particles in this region leads to enhanced fluxes of precipitating high-energy ions and electrons that are higher than at other longitudes. This leads to enhanced collisions with the neutrals, and since the early days of space exploration it has been speculated that this can lead to the deposition of a significant amount of energy to the neutral atmosphere. Indications that the neutral temperatures could be higher in the SAA region than elsewhere were provided early on, e.g., by and and references therein.

Instrumental/measurement effects are also known to be correlated to the SAA: for example, it is known that penetrating high-energy particles can introduce enhanced noise in most instruments. This could be seen as enhanced background noise on the Ti signal as obtained from the RPA instrument or the Tn signal from the NATE instrument or in both signals.

From the results shown in Fig.  it is noted that, whereas the region of primary enhancement of the occurrence rates of ΔTin<0, marked as A, reaches the vicinity of the SAA, its peak is offset in terms of latitude and longitude to the northeast of the SAA; furthermore, it is noted that the SAA region is more restricted in latitude than the region of observations. Finally, plotting the same data shown Fig.  binned by altitude does not indicate a trend in altitude (results not shown herein). For example, SAA signatures would be expected to become more intense and restricted in longitude at low altitudes; hence an increase in the occurrence rates of ΔTin<0 with decreasing altitude would signify a correlation with the SAA, which has not been identified herein. Further complicating the interpretation of these results, the appearance of the second largest peak in the occurrence rates of ΔTin<0 in the vicinity of the Indian Ocean, marked as B in Fig. , cannot be attributed to or be associated with the SAA.

Another mechanism that could significantly affect the dynamics and energetics of the thermosphere is related to the as yet unresolved phenomenon of the ionospheric plasma caves, the unusual decreases in electron density that are theoretically expected to occur in the equatorial regions. For example, , and presented theoretical studies of the equatorial ionization anomaly region's ionospheric plasma cave based on FORMOSAT-3/COSMIC and Dynamic Explorer 2 (DE-2) and simulations, respectively. The plasma cave structures are attributed to neutral winds that are distinguished by two divergent wind zones at off-Equator latitudes and a convergent wind region at the magnetic equator. Since electrons mainly transfer energy to the ions, the absence of electrons within plasma caves is speculated to create the conditions for the occurrences of neutrals that are hotter than ion. Plasma caves are expected through simulations to be observed between ∼0–∼120∘ E, which is in rough agreement with the peaks marked as A and B in Fig. , over the South Atlantic region. They are also expected to show a significant latitudinal asymmetry, which is also observed in Fig. . However, as noted in , there are considerable remaining discrepancies between simulations and observations of plasma caves, primarily due to unknowns in the distribution and structuring of neutral winds in the lower-thermospheric altitudes.

Together with the above analysis that compares the temperatures of ions and neutrals in the ionosphere–thermosphere, the relative temperature of electrons and ions is of extreme importance to the state of the ionosphere. Whereas globally it is expected that it is much more common for Te to be greater than Ti due to the effects of UV radiation, at times Ti>Te has also been observed, associated with storm-time-enhanced joule heating. For example, through analyzing EISCAT ISR data, have shown profiles of very high ion temperatures (greater than 8000 K), observed along geomagnetic field lines, which they attributed to frictional heating between fast-moving species. Similarly, also reported observations of very high ion temperatures (on the order of 12 000 K), which were not accompanied by commensurate changes in the electron temperature; they also attributed such cases of Ti<Te to joule heating. Although believed to be less common, such events are expected to be energetically very significant. Such events are not analyzed statistically herein and are the topic of a future study.