Ionospheric measurements during the CRISTA/MAHRSI campaign: their implications and comparison with previous campaigns

The CRISTA/MAHRSI experiment on board a space shuttle was accompanied by a broad campaign of rocket, balloon and ground-based measurements. Supporting lower ionospheric ground-based measurements were run in Europe and Eastern Asia between 1 October–30 November, 1994. Results of comparisons with long ionospheric data series together with short-term comparisons inside the interval October-November, 1994, showed that the upper middle atmosphere (h =80–100 km) at middle latitudes of the Northern Hemisphere in the interval of the CRISTA/MAHRSI experiment (4–12 November, 1994) was very close to its expected climatological state. In other words, the average results of the experiment can be used as climatological data, at least for the given area/altitudes. The role of solar/geomagnetic and “meteorological” control of the lower ionosphere is investigated and compared with the results of MAP/WINE, MAC/SINE and DYANA campaigns. The effects of both solar/geomagnetic and global meteorological factors on the lower ionosphere are found to be weak during autumn 1994 compared to those in MAP/WINE and DYANA winters, and they are even slightly weaker than those in MAP/SINE summer. The comparison of the four campaigns suggests the following overall pattern: in winter the lower ionosphere at northern middle latitudes appears to be fairly well “meteorologically” controlled with a very weak solar influence. In summer, solar influence is somewhat stronger and dominates the weak “meteorological” influence, but the overall solar/meteorological control is weaker than in winter. In autumn we find the weakest overall solar/meteorological control, local effects evidently dominate.     

Numerical analysis of global ionospheric current system including the effect of equatorial enhancement

A modeling method is proposed to derive a two-dimensional ionospheric layer conductivity, which is appropriate to obtain a realistic solution of the polar-originating ionospheric current system including equatorial enhancement. The model can be obtained by modifying the conventional, thin shell conductivity model. It is shown that the modification for one of the non-diagonal terms (Σ_θφ) in the conductivity tensor near the equatorial region is very important; the term influences the profile of the ionospheric electric field around the equator drastically. The proposed model can reproduce well the results representing the observed electric and magnetic field signatures of geomagnetic sudden commencement. The new model is applied to two factors concerning polar-originating ionospheric current systems. First, the latitudinal profile of the DP2 amplitude in the daytime is examined, changing the canceling rate for the dawn-to-dusk electric field by the region 2 field-aligned current. It is shown that the equatorial enhancement would not appear when the ratio of the total amount of the region 2 field-aligned current to that of region 1 exceeds 0.5. Second, the north-south asymmetry of the magnetic fields in the summer solstice condition of the ionospheric conductivity is examined by calculating the global ionospheric current system covering both hemispheres simultaneously. It is shown that the positive relationship between the magnitudes of high latitude magnetic fields and the conductivity is clearly seen if a voltage generator is given as the source, while the relationship is vague or even reversed for a current generator. The new model, based on the International Reference Ionosphere (IRI) model, can be applied to further investigations in the quantitative analysis of the magnetosphere-ionosphere coupling problems.     

EDI convection measurements at 5–6 RE in the post-midnight region

We present the first triangulation measurements of electric fields with the electron drift instrument (EDI) on Equator-S. We show results from five high-data-rate passes of the satellite through the near-midnight equatorial region, at geocentric distances of approximately 5–6 R_E, during geomagnetically quiet conditions. In a co-rotating frame of reference, the measured electric fields have magnitudes of a few tenths of mV/m, with the E × B drift generally directed sunward but with large variations. Temporal variations of the electric field on time scales of several seconds to minutes are large compared to the average magnitude. Comparisons of the “DC” baseline of the EDI-measured electric fields with the mapped Weimer ionospheric model and the Rowland and Wygant CRRES measurements yield reasonable agreement.     

Altitude integration effects in the skewness of type-2 coherent echoes

Possible effects of signal reception from different electrojet heights in a skewness of auroral coherent spectra are studied assuming that the “inherent” spectral line due to plasma turbulence is of type-2 and symmetrical. For reasonable ionospheric parameters, the altitude integrated spectra are expected to be skewed negatively for positive mean Doppler shift, in agreement with radar observations at small aspect angles. However, the spectra could be skewed positively if the turbulent layer or the electron density profile is shifted to high altitudes of \sim120 km. This change of spectral shape will not be observed experimentally if, at the same time, either the electron collision frequency is enhanced or the “inherent” spectral width is increased. Observational results are discussed in view of the predictions given.     

Observations of the response time of high-latitude ionospheric convection to variations in the interplanetary magnetic field using EISCAT and IMP-8 data

We have combined ∼300 h of tristatic measurements of the field-perpendicular F region ionospheric flow measured overhead at Tromsø by the EISCAT UHF radar, with simultaneous IMP-8 measurements of the solar wind and interplanetary magnetic field (IMF) upstream of the Earth’s magnetosphere, in order to examine the response time of the ionospheric flow to changes in the north-south component of the IMF (B_z). In calculating the flow response delay, the time taken by field changes observed by the spacecraft to first effect the ionosphere has been carefully estimated and subtracted from the response time. Two analysis methods have been employed. In the first, the flow data were divided into 2 h-intervals of magnetic local time (MLT) and cross-correlated with the “half-wave rectifier” function V²B_s, where V is the solar wind speed, and B_s is equal to IMF B_z if the latter is negative, and is zero otherwise. Response delays, determined from the time lag of the peak value of the cross-correlation coefficient, were computed versus MLT for both the east-west and north-south components of flow. The combined data set suggests minimum delays at ∼1400 MLT, with increased response times on the nightside. For the 12-h sector centred on 1400 MLT, the weighted average response delay was found to be 1.3 ± 0.8 min, while for the 12-h sector centred on 0200 MLT the weighted average delay was found to increase to 8.8 ± 1.7 min. In the second method we first inspected the IMF data for sharp and enduring (at least ∼5 min) changes in polarity of the north-south component, and then examined concurrent EISCAT flow data to determine the onset time of the corresponding enhancement or decay of the flow. For the case in which the flow response was timed from whichever of the flow components responded first, minimum response delays were again found at ∼1400 MLT, with average delays of 4.8 ± 0.5 min for the 12-h sector centred on 1400 MLT, increasing to 9.2 ± 0.8 min on the nightside. The response delay is thus found to be reasonably small at all local times, but typically ∼6 min longer on the nightside compared with the dayside. In order to make an estimate of the ionospheric information propagation speed implied by these results, we have fitted a simple theoretical curve to the delay data which assumes that information concerning the excitation and decay of flow propagates with constant speed away from some point on the equatorward edge of the dayside open-closed field line boundary, taken to lie at 77° magnetic latitude. For the combined cross-correlation results the best-fit epicentre of information propagation was found to be at 1400 MLT, with an information propagation phase speed of 9.0 km s⁻¹. For the combined event analysis, the best-fit epicentre was also found to be located at 1400 MLT, with a phase speed of 6.8 km s⁻¹.     

Spatial distribution of conductances and currents associated with a north-south auroral form during a multiple-substorm period

Using the method of characteristics to invert ground-based data of the ground magnetic field disturbance and of the ionospheric electric field, we obtain spatial distributions of ionospheric conductances, currents, and field-aligned currents (FACs) associated with a north-south auroral form that drifts westwards over northern Scandinavia around 2200 UT on December 2, 1977. This auroral form is one in a sequence of such north-south structures observed by all-sky cameras, and appears 14 min after the last of several breakups during that extremely disturbed night. Our analysis shows that the ionospheric Hall conductance reaches values above 200 S in the center of the form, and upward flowing FACs of up to 25 μA/m² are concentrated near its westward and equatorward edge. The strong upward flowing FACs are fed by an area of more distributed, but still very strong downward-flowing FACs northeastward of the auroral form. In contrast to the conductances, the electric field is only slightly affected by the passage of the form. We point out similarities and differences of our observations and results to previously reported observations and models of ‘auroral fingers’, ‘north-south aurora’, and ‘auroral streamers’ which are suggested to be ionospheric manifestations of bursty bulk flows in the plasma sheet.     

The convection electrojet and the substorm electrojet

Enhancements in the auroral electrojets associated with magnetospheric substorms result from those in either the electric field or the ionospheric conductivities, or both. Their relative importance varies significantly, even during a single substorm, depending on the location as well as on the substorm phases. It is predicted that different parts of the electrojets tend to respond in different ways to substorm activity. The unprecedented, unique opportunity for CLUSTER spacecraft observations of electric/magnetic fields and precipitating particles, combined with radar measurements of ionospheric quantities and with ground magnetometers, will provide us with crucial information regarding the physical nature of the separation between the “electric field-dominant” and “conductivity-dominant” auroral electrojets. This study also discusses the implications of these two auroral-electrojet components in terms of solar wind-magnetosphere-ionosphere interactions.     

Formation compaction associated with thermal cooling in geothermal reservoirs

Concepts from the Theory of Interacting Continua are employed to develop constitutive relations for thermoelastic fluid-saturated porous media; these constitutive relations are shown to be equivalent to those of Biot in isothermal limit. For uniaxial compaction, the constitutive theory is simplified to give formation compaction as a function of changes in fluid pressure and temperature. The formation compaction due to thermal cooling is equal to 3hη[(1 + v)/3(1 − v)]ΔT.     

A numerical model of the ionosphere,including the E-region above EISCAT

It has been previously demonstrated that a two-ion (O⁺ and H⁺) 8-moment time-dependent fluid model was able to reproduce correctly the ionospheric structure in the altitude range probed by the EISCAT-VHF radar. In the present study, the model is extended down to the E-region where molecular ion chemistry (NO⁺ and O⁺₂, essentially) prevails over transport; EISCAT-UHF observations confirmed previous theoretical predictions that during events of intense E×B induced convection drifts, molecular ions (mainly NO⁺) predominate over O⁺ ions up to altitudes of 300 km. In addition to this extension of the model down to the E-region, the ionization and heating resulting from both solar insolation and particle precipitation is now taken into account in a consistent manner through a complete kinetic transport code. The effects of E×B induced convection drifts on the E- and F-region are presented: the balance between O⁺ and NO⁺ ions is drastically affected; the electric field acts to deplete the O⁺ ion concentration. The [NO⁺]/[O⁺] transition altitude varies from 190 km to 320 km as the perpendicular electric field increases from 0 to 100 mV m⁻¹. An interesting additional by-product of the model is that it also predicts the presence of a noticeable fraction of N⁺ ions in the topside ionosphere in good agreement with Retarding Ion Mass Spectrometer measurements onboard Dynamic Explorer.     

Ionospheric index of solar activity based on the data of measurements of the spacecraft signals characteristics

The method for estimating an ionospheric index of solar-activity (IISA) based on the processing of spacecraft radio signals is suggested. The IISA values have been obtained by comparison between the measured and calculated variations of radio-signal characteristics. To calculate the variations of radio-signal characteristics, the straight rays approximation and the solar-activity index (Wolf numbers W and/or values of F_10.7 solar flux) as a control parameter of the ionospheric model have been used. The suggested method was tested using spacecraft radio signals from the radio-navigation system “CIKADA”. The reduced differences of phases (ΔΦ) for frequencies 150 and 400 MHz were measured and the same characteristics were calculated by integration along the ray of radio-wave propagation between the receiver and the satellite. The IRI-95 has been used as a background ionospheric model. The satellite co-ordinates were determined using the orbit parameters recorded in the navigation messages. Minimization of the difference measured and calculated ΔΦ using arbitrary time steps, or during whole time intervals of observation, gives the IISA corresponding the satellite pass. Daily IISA values were obtained by averaging over all communication contacts during a day (20–30 passes). Testing this approach based on the measurements during March/April 1997, 1998, shows that on magnetically quiet days differences between IISA and the primary solar activity indices are about 5%.     

Ionospheric imaging of the northern crest of the Equatorial Anomaly

The dominant structure in free electron concentration in the tropical ionosphere is the Equatorial Anomaly, where the largest values of TEC are found. This structure follows the geomagnetic equator and extends some 40° in latitude. The edges of the structure (crests) are characterised by steep, latitudinal gradients in TEC, which are temporally as well as spatially variable.This phenomenology is traditionally explained in terms of the theory of “fountain effect”, which is shortly reviewed in this work before presenting our results.Here we study the northern crest of the Equatorial Anomaly using a program that can perform multi-instrument two- or three-dimensional time-evolving mathematical inversions. This program is designed to unify a number of different measurement techniques, thus allowing the spatial and temporal study of the ionospheric features at hand. The paper reports on experimental results from winter 2000/2001. This is a highly significant period to study the ionospheric anomalies because it is around the maximum of the 11-year solar cycle and TEC is at a maximum.     

Observations of Pc 3–4 and Pi 2 geomagnetic pulsations in the low-latitude ionosphere

Day-time Pc 3–4 (≃5–60 mHz) and night-time Pi 2 (≃5–20 mHz) ULF waves propagating down through the ionosphere can cause oscillations in the Doppler shift of HF radio transmissions that are correlated with the magnetic pulsations recorded on the ground. In order to examine properties of these correlated signals, we conducted a joint HF Doppler/magnetometer experiment for two six-month intervals at a location near L = 1.8. The magnetic pulsations were best correlated with ionospheric oscillations from near the F region peak. The Doppler oscillations were in phase at two different altitudes, and their amplitude increased in proportion to the radio sounding frequency. The same results were obtained for the O- and X-mode radio signals. A surprising finding was a constant phase difference between the pulsations in the ionosphere and on the ground for all frequencies below the local field line resonance frequency, independent of season or local time. These observations have been compared with theoretical predictions of the amplitude and phase of ionospheric Doppler oscillations driven by downgoing Alfvén mode waves. Our results agree with these predictions at or very near the field line resonance frequency but not at other frequencies. We conclude that the majority of the observations, which are for pulsations below the resonant frequency, are associated with downgoing fast mode waves, and models of the wave-ionosphere interaction need to be modified accordingly.     

Characteristics of a stable are based on FAST and MIRACLE observations

A stable evening sector are is studied using observations from the FAST satellite at 1250 km altitude and the MIRACLE ground-based network, which contains all-sky cameras, coherent radars (STARE), and magnetometers. Both FAST and STARE observe a northward electric field region of about 200 km width and a field magnitude of about 50 mV/m southward of the arc, which is a typical signature for an evening-sector arc. The field-aligned current determined from FAST electron and magnetometer data are in rather good agreement within the arcs. Outside the arcs, the electron data misses the current carriers of the downward FAC probably because it is mainly carried by electrons of smaller energy than the instrument threshold. Studying the westward propagation speed of small undulations associated with the arc using the all-sky cameras gives a velocity of about 2 km//s. This speed is higher than the background ionospheric plasma speed (about 1 km//s), but it agrees rather well with the idea originally proposed by Davis that the undulations reflect an E × B motion in the acceleration region. The ground magnetograms indicate that the main current flows slightly south of the arc. Computing the ionospheric conductivity from FAST electron data and using the ground magnetograms to estimate the current yields an ionospheric electric field pattern, in rather good agreement with FAST results.     

Letter to the editor First direct observations of the reduced striations at pump frequencies close to the electron gyroharmonics

It is well known that the ionospheric plasma response to high-power HF radio waves changes drastically as the heater frequency approaches harmonics of the electron gyrofrequency. These include changes in the spectrum of the stimulated electromagnetic emission, reduction in the anomalous absorption of low-power diagnostic waves propagating through the heated volume, and reduction in the large scale F-region heating. Theoretical models as well as previous experimental evidence point towards the absence of small-scale field-aligned plasma density irregularities at pump frequencies close to electron gyroharmonics as the main cause of these changes. Results presented in this paper are the first direct observations of the reduced striations at the 3rd gyroharmonic made by the CUTLASS radar. In addition, simultaneous EISCAT observations have revealed that the “enhanced ion-line” usually present in the EISCAT ion-line spectrum during the first few seconds after heater switch on, persisted at varying strengths while the heater was transmitting at frequencies close to the 3rd electron gyroharmonics.     

Hydromagnetic spectroscopy of the magnetosphere with Pc3 geomagnetic pulsations along the 210° meridian

Analysis of Pc3 observational data along the 210° magnetic meridian showed a complicated frequency-latitude structure at middle latitudes. The observed period-latitude distributions vary between events with a “noisy source”: the D component has a colored-noise spectrum, while the spectrum of H component exhibits regular peaks that vary with latitude, and events with a “band-limited source”: the spectral power density of the D component is enhanced at certain frequencies throughout the network. For most ULF events a local gap of the H component amplitude has been exhibited at both conjugate stations at L ≃ 2.1. A quantitative interpretation has been given assuming that band-limited MHD emission from an extra-magnetospheric source is distorted by local field line resonances. Resonant frequencies had been singled out with the use of the asymmetry between spectra of H and D components. Additionally, a local resonant frequency at L ≃ 1.6 was determined by the quasi-gradient method using the data from nearly conjugate stations. The experimentally determined local resonance frequencies agree satisfactorily with those obtained from a numerical model of the Alfven resonator with the equatorial plasma density taken by extrapolation of Carpenter-Anderson model. We demonstrate how simple methods of hydromagnetic spectroscopy enable us to monitor simultaneously both the magnitude of the IMF and the magnetospheric plasma density from ULF data.     

EISCAT observations of unusual flows in the morning sector associated with weak substorm activity

A discussion is given of plasma flows in the dawn and nightside high-latitude ionospheric regions during substorms occurring on a contracted auroral oval, as observed using the EISCAT CP-4-A experiment. Supporting data from the PACE radar, Greenland magnetometer chain, SAMNET magnetometers and geostationary satellites are compared to the EISCAT observations. On 4 October 1989 a weak substorm with initial expansion phase onset signatures at 0030 UT, resulted in the convection reversal boundary observed by EISCAT (at \sim0415 MLT) contracting rapidly poleward, causing a band of elevated ionospheric ion temperatures and a localised plasma density depletion. This polar cap contraction event is shown to be associated with various substorm signatures; Pi2 pulsations at mid-latitudes, magnetic bays in the midnight sector and particle injections at geosynchronous orbit. A similar event was observed on the following day around 0230 UT (\sim0515 MLT) with the unusual and significant difference that two convection reversals were observed, both contracting poleward. We show that this feature is not an ionospheric signature of two active reconnection neutral lines as predicted by the near-Earth neutral model before the plasmoid is “pinched off”, and present two alternative explanations in terms of (1) viscous and lobe circulation cells and (2) polar cap contraction during northward IMF. The voltage associated with the anti-sunward flow between the reversals reaches a maximum of 13 kV during the substorm expansion phase. This suggests it to be associated with the polar cap contraction and caused by the reconnection of open flux in the geomagnetic tail which has mimicked “viscous-like” momentum transfer across the magnetopause.     

First results from the hot plasma instrument PROMICS-3 on Interball-2

The PROMICS-3 instrument on Interball-2 is nominally identical to the PROMICS-3 instrument on Interball-1. It performs three-dimensional measurements of ions in the energy range 4 eV–70 keV with mass separation and of electrons in the energy range 300 eV–35 keV. Interball-2 was launched on August 29, 1996, into an orbit with the same inclination as that of Interball-1, 63°, but with apogee at 20 000 km. In this study the PROMICS-3 instrument on Interball-2 is briefly described and examples of the first results are presented. Firstly, we report observations of upward moving molecular ions with energies of up to 700 eV at the poleward edge of the auroral oval. Previous observations of outflowing molecular ions have been at lower altitudes and lower energies. Secondly, we show observations of dawnside magnetosheath plasma injections. Using conjugate data from both PROMICS-3 instruments we have found dispersion structures above the morningside auroral oval, which occurred simultaneously with isolated “pockets” of magnetosheath plasma at a distance of X_GSM = −14 to −12 R_E, which had been injected into the inner part of the low-latitude boundary layer. These isolated plasma structures were sites of strong field-aligned currents and are proposed to be the magnetospheric counterparts of the dispersion structures.     

Incoherent scatter radar observations of AGW/TID events generated by the moving solar terminator

Observations of traveling ionospheric disturbances (TIDs) associated with atmospheric gravity waves (AGWs) generated by the moving solar terminator have been made with the Millstone Hill incoherent scatter radar. Three experiments near 1995 fall equinox measured the AGW/TID velocity and direction of motion. Spectral and cross-correlation analysis of the ionospheric density observations indicates that ST-generated AGWs/TIDs were observed during each experiment, with the more-pronounced effect occurring at sunrise. The strongest oscillations in the ionospheric parameters have periods of 1.5 to 2 hours. The group and phase velocities have been determined and show that the disturbances propagate in the horizontal plane perpendicular to the terminator with the group velocity of 300–400 m s^–1 that corresponds to the ST speed at ionospheric heights. The high horizontal group velocity seems to contradict the accepted theory of AGW/TID propagation and indicates a need for additional investigation.     

Stationary magnetospheric convection on November 24, 1981. 1. A case study of “pressure gradient/minimum-B” auroral arc generation

We present two case studies in the night and evening sides of the auroral oval, based on plasma and field measurements made at low altitudes by the AUREOL-3 satellite, during a long period of stationary magnetospheric convection (SMC) on November 24, 1981. The basic feature of both oval crossings was an evident double oval pattern, including (1) a weak arc-type structure at the equatorial edge of the oval/polar edge of the diffuse auroral band, collocated with an upward field-aligned current (FAC) sheet of ≈1.0 μA m⁻², (2) an intermediate region of weaker precipitation within the oval, (3) a more intense auroral band at the polar oval boundary, and (4) polar diffuse auroral zone near the polar cap boundary. These measurements are compared with the published magnetospheric data during this SMC period, accumulated by Yahnin et al. and Sergeev et al., including a semi-empirical radial magnetic field profile B_Z in the near-Earth neutral sheet, with a minimum at about 10–14 R_E. Such a radial B_Z profile appears to be very similar to that assumed in the “minimum B/cross-tail line current” model by Galperin et al. (GVZ92) as the “root of the arc”, or the arc generic region. This model considers a FAC generator mechanism by Grad-Vasyliunas-Boström-Tverskoy operating in the region of a narrow magnetic field minimum in the near-Earth neutral sheet, together with the concept of ion non-adiabatic scattering in the “wall region”. The generated upward FAC branch of the double sheet current structure feeds the steady auroral arc/inverted-V at the equatorial border of the oval. When the semi-empirical B_Z profile is introduced in the GVZ92 model, a good agreement is found between the modelled current and the measured characteristics of the FACs associated with the equatorial arc. Thus the main predictions of the GVZ92 model concerning the “minimum-B” region are consistent with these data, while some small-scale features are not reproduced. Implications of the GVZ92 model are discussed, particularly concerning the necessary conditions for a substorm onset that were not fulfilled during the SMC period.     

Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20/30 January, 1993

We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earths ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20/30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N₂(v) and O₂(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N₂ and O₂ and the second level of O₂, and the calculated distributions of N₂(v) and O₂(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N₂(v > 0) and O₂(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N₂(v > 0) and O₂(v > 0), and inclusion of vibrationally excited N₂ and O₂ brings the model and data into better agreement.