A numerical study of the effects of migrating tideson thermosphere midnight density maximumHaibing Ruan1,2, Jian Du3, Matt Cook3, Wenbin Wang2, Jia Yue4, Quan Gan3, Xiankang Dou1,and Jiuhou Lei1

1CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, Hefei, China, 2High AltitudeObservatory, National Center for Atmospheric Research, Boulder, Colorado, USA, 3Department of Physics and Astronomy,University of Louisville, Louisville, Kentucky, USA, 4Department of Atmospheric and Planetary Sciences, HamptonUniversity, Hampton, Virginia, USA

Abstract In this study, we employed the National Center for Atmospheric Research ThermosphereIonosphere Electrodynamics General Circulation Model (TIEGCM) and the extended Canadian MiddleAtmosphere Model (eCMAM) to investigate the role of the migrating terdiurnal tide on the formation andvariation of the thermosphere midnight temperature maximum (MTM) andmidnight mass density maximum(MDM). The migrating terdiurnal tide from the eCMAM was applied at the TIEGCM’s lower boundary, alongwith the migrating diurnal and semidiurnal tides from the Global-Scale Wave Model. Several numericalexperiments with different combinations of tidal forcing at the TIEGCM’s lower boundary were carried outto determine the contribution of each tide to MTM/MDM. We found that the interplay between diurnal,semidiurnal, and terdiurnal tides determines the formation of MTM/MDM and their structure in the upperthermosphere. The decrease of thermospheric mass density after MDM reaches its maximum at ~02:00 localtime is mainly controlled by the terdiurnal tide. Furthermore, we examined the generation mechanismsof the migrating terdiurnal tide in the upper thermosphere and found that they come from three sources:upward propagation from the lower thermosphere, in situ generation via nonlinear interaction, andthermal excitation.

1. Introduction

Daily variation of temperature in the upper atmosphere is mainly driven by solar extreme ultraviolet andultraviolet radiation. Thus, thermospheric temperature is higher during daytime and lower during nighttime.The same diurnal variation is also expected for thermospheric mass density. However, a thermospherictemperature/density maximum during nighttime has been frequently reported by ground-based andsatellite measurements over the equatorial region since 1970s [e.g., Sobral et al., 1978; Spencer et al., 1979;Burnside et al., 1981; Arduini et al., 1997]. These anomalies are called the midnight temperature/densitymaximums (MTM/MDM). In general, the typical magnitude of the equatorial MTM varies from 50 to 150 Karound the midnight. For the MDM, the percentage increase of the nighttime thermospheric density ataround 400 km can be more than 20%. MTM/MDM has also been observed in the upper thermosphere atmidlatitude and high latitude. From observations of 6300Å emission rate by three Southern Hemisphereimaging systems, Colerico et al. [2002] reported that the MTM can extend from the equatorial region tomidlatitudes of ~40°S. Observations from the incoherent scatter radars at Saint Santin (45°N) and MillstoneHill (42.5°N) [Oliver et al., 2012; Ruan et al., 2013] also showed MTM signatures at midlatitudes of theNorthern Hemisphere during the winter nighttime of 02:00–04:00 LT. Recently, Hickey et al. [2015] observedthe MTM at low latitude and midlatitude in spring and summer. The amplitude of radar-observed MTM is30–100 K. Furthermore, the observations from the CHAllenging Minisatellite Payload (CHAMP) satelliteillustrates that MDM occurs at midlatitude and high latitude of the Northern Hemisphere during the winternighttime [Ruan et al., 2014].

Previous studies have associated the nighttime temperature and density enhancements over the equatorialregion with (1) the upward propagation of the migrating semidiurnal tide from the lower atmosphere and (2)terdiurnal tides (including both the migrating and nonmigrating tides) and other higher-order tides from themesosphere and low thermosphere (MLT). Fesen [1996] used the Thermosphere Ionosphere ElectrodynamicsGeneral Circulation Model (TIEGCM) developed by the National Center for Atmosphere Research (NCAR) to

RUAN ET AL. MIDNIGHT DENSITY MAXIMUM 6766

PUBLICATIONSJournal of Geophysical Research: Space Physics

RESEARCH ARTICLE10.1002/2015JA021190

This article is a companion to Haibinget al. [2014] doi:10.1002/2013JA019566.

Key Points:• Terdiurnal tide at the MLT contributesto MTM/MDM

• Interplay between diurnal, semidiurnal,and terdiurnal tides determines MDM

• Terdiurnal tide in the thermospherehas different sources at differentlatitudes

Correspondence to:J. Lei,leijh@ustc.edu.cn

Citation:Ruan, H., J. Du, M. Cook, W. Wang, J. Yue,Q. Gan, X. Dou, and J. Lei (2015), Anumerical study of the effects ofmigrating tides on thermospheremidnight density maximum, J. Geophys.Res. Space Physics, 120, 6766–6778,doi:10.1002/2015JA021190.

Received 5 MAR 2015Accepted 2 JUL 2015Accepted article online 3 JUL 2015Published online 7 AUG 2015

©2015. American Geophysical Union.All Rights Reserved.

investigate the MTM. Fesen [1996] suggested that the upward propagation of the migrating semidiurnal tidefrom the lower atmosphere can produce the MTM over the equatorial region. The formation of the MTM wasfirst suggested to be associated with the terdiurnal tide by Mayr et al. [1979], who proposed that theterdiurnal tide could be related to the nonlinear interaction between tides and ion drag as well. Thesimulations by the Whole Atmosphere Model [Akmaev et al., 2009, 2010] suggested that MTM/MDM ismainly due to the migrating diurnal, semidiurnal, and terdiurnal tides while other higher-order harmonictides also contribute to the nighttime enhancement in temperature and density. The simulations of thegeneral circulation model (GCM) [Miyoshi et al., 2009; Fujiwara and Miyoshi, 2010] supported the idea that,in addition to the migrating semidiurnal tides, both the migrating and nonmigrating terdiurnal tidespropagating from the lower thermosphere contribute to the MTM. Fesen [1996] and Miyoshi et al. [2009]also suggested that the variability of MTM is closely related to the day-to-day variation of the loweratmosphere. However, these studies did not clearly separate the contributions of the migrating terdiurnaltide propagated from the MLT and the migrating terdiurnal tide generated in situ within the upperthermosphere to the formation of MTM/MDM [Akmaev, 2001].

In this work, we used the TIEGCM and the migrating terdiurnal tide simulated by the extended CanadianMiddle Atmospheric Model (eCMAM) to investigate the relationship between the MTM/MDM in the upperthermosphere and the migrating diurnal, semidiurnal, and terdiurnal tides from the lower thermosphereand the contribution of migrating terdiurnal tide generated in situ to MTM/MDM. Previous numericalstudies had both the migrating and nonmigrating terdiurnal tides, as well as other tides, self-generatedwithin the models, making it very difficult to identify the source of tides and separate the contributions ofeach tidal components from the MLT to the MTM/MDM. On the contrary, in this study, we control the tidalinputs at the lower boundary of the TIEGCM to examine the relative contributions of the lowerthermospheric migrating tides to the nighttime variation of the upper thermosphere. The migratingterdiurnal tide from the eCMAM near 99 km is included in the lower boundary condition of the TIEGCM inthis work. Together with the migrating diurnal and semidiurnal tides from the Global-Scale Wave Model(GSWM), we carried out sensitivity studies by using different combinations of tidal forcing to explore theinteractions between the upward propagating tides and the thermospheric excited tides and theircontribution to MTM/MDM. Note that although nonmigrating tides (either propagated from the loweratmosphere or generated in situ within the thermosphere) may also affect MTM/MDM, which is aninteresting topic for future studies, this paper only deals with the migrating tides and their effect onMTM/MDM. For simplicity, hereafter, the migrating tides will be referred to as tides.

In this paper, we focused our study on March equinox and solar minimum conditions when MDM is mostpronounced [Ruan et al., 2014]. The seasonal and solar cycle variations of the MTM/MDM and the cause of thisvariation will be addressed in a separate paper. In section 2, we will describe the models used in this study. Oursimulated results will be shown in section 3. Discussions and conclusions are given in sections 4 and 5, respectively.

2. Models2.1. TIEGCM

The NCAR TIEGCM [Roble et al., 1988; Richmond et al., 1992] is a time-dependent, three-dimensional modelsolving fully coupled, nonlinear, hydrodynamic, thermodynamic, and continuity equations of neutral gasself-consistently with ion energy, ion momentum, and ion continuity equations from the uppermesosphere to the thermosphere (ranging from near 100 km to around 500 km). The resolution of theTIEGCM is 2.5°× 2.5° in latitude and longitude and a quarter of scale height in the vertical direction. Thelower boundary condition of the model is specified by diurnal and semidiurnal tides from the GSWM[Hagan and Forbes, 2002, 2003]. The terdiurnal tide from eCMAM is also initialized at the lower boundaryfor various sensitivity studies. As mentioned before, no external nonmigrating tides are specified at thelower boundary of the TIEGCM.

2.2. Extended CMAM

The eCMAM is a spectral model extending from Earth’s surface to ~210 km altitude with triangular truncation atwave number 32 (T32) corresponding to a latitudinal-longitudinal resolution of ∼6° ×6° near the equator. Thetidal oscillations are generated self-consistently through internal processes associated with short- and long-wave radiation absorption, large-scale condensation, and convective heating. Physical parameterizations

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appropriate to the MLT region are imple-mented in the model (see Beagley et al.[1997], McLandress [2002], and Fomichevet al. [2002] for details). The amplitudeand phase of terdiurnal tide in the MLTregion from eCMAM are used in thisstudy (see Du and Ward [2010] for moredetails about the terdiurnal tides inCMAM). Note that although eCMAMhas an upper boundary at ~210 kmand a very simple ion drag parameteri-zation, it does not include the neces-sary ionospheric and thermosphericprocesses, such as electrodynamics, toeffectively simulate the upper thermo-sphere, including MTM/MDM.

Figure 1 shows the monthly averagedterdiurnal tide in temperature close to

an altitude of 99 km at 00:00 UT in March. The terdiurnal tide has three peaks at around 30°N, ~15°S, and~45°S with amplitudes of 6 K, 4 K, and 3 K at 99 km, respectively. As the resolutions of the two models aredifferent, the tide shown in Figure 1 is first interpolated onto the TIEGCM grid and then specified at thelower boundary of the TIEGCM to investigate its effect on thermospheric temperature and density. Thediurnal and semidiurnal tides are specified using the GSWM at the lower boundary of the TIEGCM. Yueet al. [2013], using the observations of Sounding of the Atmosphere using Broadband Emission (SABER)instrument, showed that the terdiurnal tide (in temperature) during March has a three-peak latitudinalstructure. The latitudinal peaks occur at midlatitudes of both hemispheres and over the equatorial regionwith amplitudes of ~4 K at 100 km. Thus, the terdiurnal tide calculated by eCMAM is consistent withobservations and can be used to study their effect on the upper thermosphere.

Eight numerical experiments were carried out to investigate the effect of tides on MTM/MDM in this study.Table 1 lists these eight model runs, which consist of different combinations of diurnal, semidiurnal, andterdiurnal tides specified at the TIEGCM’s lower boundary. Geophysical conditions for the runs were thesame for all runs: solar minimum (F107 = 70), quiet geomagnetic activity (Kp=2), and March equinox(day of year 80). All runs were perpetual and achieved diurnally reproducible states.

3. Results

Figure 2 shows the nighttime thermo-spheric density and temperature varia-tions at 370 km from the simulationswithout (Figures 2a and 2b, Run g) andwith (Figures 2c and 2d, Run h) theeCMAM terdiurnal tide at the TIEGCM’slower boundary. Note that nonmigrat-ing tidal signatures might be present inthe thermosphere even if they are notincluded at the lower modal boundary.However, here we show the zonallyaveraged density and temperature.Thus, the nonmigrating tidal effect isminimized in our present results.Figures 2a and 2c give the nighttimedensity variations, and Figures 2b and2d illustrate the temperature variationsfrom 22:00 to 06:00 LT. In both runs,

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Figure 1. Migrating terdiurnal tide in temperature at 00:00 UT and~99 km in March from the eCMAM. This tide is used at the lower boundaryof the TIEGCM.

Table 1. Tides Specified at the Model Lower Boundary for the TIEGCMRuns: Migrating Diurnal Tide (Column 2), Migrating Semidiurnal Tide(Column 3), Migrating Terdiruanl Tide (Column 4), and CorrespondingFigures (Column 5)a

Run

Tides at the Model Lower Boundary

FigureDiurnal Semidiurnal Terdiurnal

Run a Х Х Х Figure 3aRun b Х Х √ Figure 3bRun c √ Х Х Figure 3cRun d √ Х √ Figure 3dRun e Х √ Х Figure 3eRun f Х √ √ Figure 3fRun g √ √ Х Figures 2a, 2b, and 3gRun h √ √ √ Figures 2c, 2d, and 3h

aColumns 2–4, “×” represents that the tidal component is not speci-fied, and “√” represents that the tidal component has been specified atthemodel lower boundary of the TIEGCM runs.

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semidiurnal and diurnal tides are included at the model lower boundary. In Figure 2a, the thermosphericdensity from the TIEGCM simulation is low at 22:00 LT but begins to increase near 23:00 LT and reaches a peakbetween ~02:00 and 03:00 LT. The density enhancement lasts until ~05:00 LT when the thermosphere isheated up by solar radiation and mass density increases again. Therefore, the model simulates an enhance-ment in thermospheric density at nighttime, e.g., MDM.

The nighttime thermospheric density shown in Figure 2c is the result from the simulation with the terdiurnaltide from eCMAM specified at the TIEGCM lower boundary along with diurnal and semidiurnal tides of GSWM(Run h). In Figure 2c, the mass density shows a similar pattern to that in Figure 2a with density increasingbefore 02:00 LT and decreasing afterwards in the equatorial region. Compared to Figure 2a, Figure 2c givesa greater density enhancement during nighttime over the equatorial region. There is a 28% increase in thedensity at 02:00 LT relative to the density by 22:00 LT at the equator. The density increases in Figure 2a butis only at about 18%. In Figure 2c, the nighttime density enhancement extends to higher latitudes of about30° in both hemispheres, whereas in the case of Figure 2a, the enhancement is limited to about ±15°in latitude.

The model-simulated local time and latitudinal structure of the MDM (in Figure 2c) is similar to that from theCHAMP observations [Ruan et al., 2014]. In the CHAMP observations, MDM occurs between 00:00 LT and~03:00 LT, but it occurs later at midlatitudes in the Southern Hemisphere than over the equatorial region.These features are reproduced by the simulation with terdiurnal tide included at the lower modelboundary (Run h). However, the density enhancement in the CHAMP data is less than 10% over theequatorial region, whereas Run h shows an ~28% density increase. The discrepancy between model resultsand observations may be the result of averaging over the CHAMP data. Ruan et al. [2014] averaged 90 daysof CHAMP data around March equinox for 4 years to obtain the local time and latitudinal structure ofnighttime thermospheric density. The magnitude of MDM in Ruan et al. [2014] could be significantlyreduced by this averaging process due to the day-to-day variation in the magnitude and peak time ofMDM. More observations are needed to fully reveal the variability of MDM with different geophysical

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Figure 2. Latitudinal and local time variations of the nighttime (a and c) thermospheric density (in the unit of 10�13 kg/m3)and (b and d) temperature (in the unit of K) in March at 370 km. Figures 2a and 2b are the simulations with both themigrating diurnal and semidiurnal tides specified at the lower boundary of the TIEGCM; Figures 2c and 2d are the resultswith migrating diurnal, semidiurnal, and terdiurnal tides specified at the lower boundary of the TIEGCM.

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conditions. Nevertheless, the differences between Runs g and h indicate that the terdiurnal tide from theMLTregion can significantly increase the magnitude of MDM over the equatorial region and broaden thelatitudinal distribution of MDM.

Figures 2b and 2d show the nighttime temperature variations at 370 km from the same model runs. We cansee that there are MTMs in both runs. However, the MTM in Figure 2d is stronger than that in Figure 2b,indicating that the terdiurnal tide from the lower thermosphere enhances the MTM. The peak temperatureenhancement reaches ~30 K in the simulation with the terdiurnal tide at the lower boundary of theTIEGCM, whereas it is only about 16 K in the simulation without the terdiurnal tide. This magnitude of MTMis smaller than the observation and simulation results in Akmaev et al. [2009]. However, higher-order tides,which are suggested in Akmaev et al. [2009] and might contribute to MTM/MDM as well, are notconsidered in this work. The latitudinal distribution of the MTM in Figure 2d is broader than that in Figure 2b,which suggests that the terdiurnal tide specified at the lower boundary of the TIEGCM also affects thelatitudinal distribution of the nighttime enhancements in thermospheric temperature. It should be pointedout that the phase of the terdiurnal tide used in our simulations is fixed, while the terdiurnal tide at MLTactually has variable phase [Yue et al., 2013]. This may lead to discrepancies between the simulations andobservations. Note here that, compared to local time variation in mass densities in Figures 2a and 2c, thepercentage increase of nighttime temperatures is relatively small. The peak magnitude of the percentageincrease of the nighttime temperature in Figure 2b is about 2.5%, whereas the increase in Figure 2d isabout 4.5%. The reason for the difference between mass density and temperature increases is that thedensity variations are the result of the height integration of the temperature variations [Lei et al., 2010];thus, the increase in mass density is much larger than that of the temperature at the altitude of 370 km.Overall, the comparison shown in Figure 2 between the results of the terdiurnal-tide run and those ofthe nonterdiurnal-tide run strongly suggests that the terdiurnal tide propagating upward from the loweratmosphere can significantly enhance the magnitudes of MTM/MDM and affect their latitudinaldistributions. Because MDM and MTM are two aspects of the same physical phenomenon, hereafter, wewill show and discuss mainly the model results of MDM.

To further study the effects of the tides on theMDM, TIEGCM runswith other combinations of diurnal, semidiurnal,and terdiurnal tides at the TIEGCM lower boundary were also carried out (Table 1). Figure 3 gives the nighttimevariations in thermospheric mass density at 370 km from the eightmodel runs. In Figure 3a (no tides are includedat the model lower boundary), the nighttime mass density keeps decreasing until 04:00 LT when solar heatingbegins to warm the thermosphere therefore, increasing its density. The situation is different for the run withonly terdiurnal tide at the model lower boundary (Figure 3b). The mass density in Figure 3b increasesevidently from 23:00 LT to ~02:00 LT in the equatorial region when solar heating is absent. The densitydecreases from ~02:00 LT and has a minimum near 04:30 LT before solar heating occurs in the morning. Themaxima of nighttime density enhancements extend from high latitudes of ~50°S and 40°N toward theequatorial region. The Southern Hemisphere peak of the enhancement occurs first at 00:00 LT, followed bythe Northern Hemisphere peak at 01:00 LT, and the equatorial one at 02:00 LT. The density maximum andminimum at the midlatitudes are separated by about 4 h implying the signature of terdiurnal tide.

The mass density from the run with only the diurnal tide at the TIEGCM lower boundary (Run c) is shown inFigure 3c. It has a similar nighttime variation to that in Figure 3a, although there is a small difference betweenthese two: there are two symmetric density minima at ~50° latitude in both hemispheres in Run c (Figure 3c)but only one minimum at the equator in Run a (Figure 3a). It is evident that the diurnal tide from the loweratmosphere does not directly produce the MDM. Although it appears to produce a slight density increase inthe equatorial region, the overall density decreases from low latitudes to midlatitude and high latitude. Thus,when comparing Figure 3b with Figure 3d (with both terdiurnal and diurnal tides at the TIEGCM lowerboundary), the nighttime mass density in Figure 3d is generally smaller than that in Figure 3b, althoughthere is a small increase in mass density before midnight near the equator. Note that in Figure 3d, thenighttime mass density shows a similar latitudinal distribution and local time variation in Run b with onlyterdiurnal tide at the TIEGCM lower boundary (Figure 3b). These results indicate that the terdiurnal tide atthe model lower boundary plays an important role in the formation of the MDM.

Now we concentrate on the impact of the lower thermospheric semidiurnal tide on MDM. Figures 3e and 3ggive the nighttime variations of the thermospheric mass density from the run with only semidiurnal tide at

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the TIEGCM lower boundary (Run e) and from the run with both diurnal and semidiurnal tides at the lowerboundary (Run g), respectively. In both runs, the mass density shows a clear MDM structure. Over theequatorial region, the mass density begins to increase at 22:00 LT, reaches a maximum near 02:00 LT, thendecreases to a minimum near 05:00 LT. The LT variation of the thermospheric mass density clearly cannotbe explained by the solar zenith angle change. The latitudinal distributions of the nighttime densityenhancements from these two runs are similar, but the MDM structure is more prominent in Runs f and hwith terdiurnal tide specified at the TIEGCM lower boundary, as described in Figure 2. In Runs f and h, thethermospheric mass density is lower at 22:00 LT and larger at the MDM peak close to 02:00 LT.

From comparing the nighttime thermospheric mass density variations from the runs without the semidiurnaltide at the TIEGCM lower boundary (Figures 3a and 3c)with thosewith the semidiurnal tide (Figures 3e and 3g),it is evident that the migrating semidiurnal tide at the model lower boundary plays an important role in bothformation and evolution of the MDM. In the runs that include the terdiurnal tide at the TIEGCM lower

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Figure 3. Latitudinal and local time variations of the nighttime thermospheric density (in the unit of 10�13 kg/m3) in Marchat 370 km from different runs. (a, c, e, and g) The results from model runs with no tides, migrating diurnal tide only,migrating semidiurnal tide only, and both the migrating diurnal and semidiurnal tides specified at the lower boundary ofthe TIEGCM. (b, d, f, and h) The results of model runs with only the migrating terdiurnal tide; both migrating diurnal andterdiurnal tides; both migrating semidiurnal and terdiurnal tides; and migrating diurnal, semidiurnal, and terdiurnal tidesspecified at the lower boundary of the TIEGCM, respectively.

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boundary (Figures 3f and 3h), in addition to semidiurnal and diurnal tides, the latitudinal distribution and localtime variation of the nighttime density enhancements are similar to those in Figures 3e and 3g, but peakmagnitudes are larger.

4. Discussion

Based on the results above, both the semidiurnal and terdiurnal tides from the MLT region contributed to theformation and evolution of the MDM, which is consistent with previous works by Miyoshi et al. [2009] andAkmaev et al. [2009, 2010]. Now the question is how do the semidiurnal and terdiurnal tides from the MLTproduce the nighttime density enhancements in the upper thermosphere (370 km)? To answer thisquestion, we examine the relationship between semidiurnal and terdiurnal tides in the thermosphericmass density at 370 km and the MDM, at the same altitude.

Figure 4 gives the nighttime mass density variations at 370 km after removing the local semidiurnal andterdiurnal tidal components from the result of Run h. Note that the local semidiurnal and terdiurnal tidalcomponents are removed by two-dimensional Fourier fitting from the mass density field at the altitude of370 km. In Figure 4a, mass density clearly shows a MDM after removing the semidiurnal tide, and the MDMpeaks at ~15°N near 00:30 LT with a lower magnitude compared to the MDM in Figure 3h. However, inFigure 4b, after removing the local terdiurnal tide, the equatorial mass density keeps increasing after theminimum at ~00:00 LT with no density decrease after 02:00 LT. This is different from the MDM structureusually seen (e.g., Figure 3h). Fesen [1996] suggested that the upward propagating semidiurnal tide canresult in MTM. This can be clearly seen in our simulations in Figure 3 when comparing runs withoutsemidiurnal tide at the model lower boundary (Figures 3a–3d) to those with semidiurnal tide at the modellower boundary (Figures 3e–3h). However, no further investigation has been carried out in previousstudies to assess the processes by which lower atmospheric semidiurnal tide affects the nighttimethermospheric density structure. In this study, we demonstrate (Figure 4) clearly that the local semidiurnaltide in the upper thermosphere alone cannot produce the typical observed MDM structure without the

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Figure 4. Latitudinal and local time variations of the nighttime thermospheric density (in the unit of 10�13 kg/m3) at Marchequinox and 370 km after removing (a) the local migrating semidiurnal tide and (b) the local migrating terdiurnal tide,respectively. Both plots are the results from the model run with migrating diurnal, semidiurnal, and terdiurnal tidesspecified at the model lower boundary.

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local terdiurnal tide. The issues needed to be addressed are the sources of the local semidiurnal and terdiurnaltides in the upper thermosphere and their relationship with the tides in the MLT region. Mayr et al. [1979]suggested, which was supported by Akmaev et al. [2009] and Akmaev et al. [2010], that the terdiurnal tidecan be generated by the nonlinear interaction via ion drag. However, they did not explore the role of thisterdiurnal tide playing in the generation of MTM/MDM.

To address these issues, we investigate the local semidiurnal and terdiurnal tides of the upper thermospherein runs with different lower boundary conditions.

Figure 5 gives the local semidiurnal tidal component of the thermospheric density at 370 km from the eightruns. Hereafter, the local semidiurnal tide refers to results obtained by the two-dimensional Fourier fittingwith a period of 12 h and a wave number of 2. The semidiurnal tide in the runs without the semidiurnaltide at the TIEGCM lower boundary (Figures 5a–5d) is almost the same in both latitudinal and local timevariations. The local nighttime semidiurnal tide in these four runs peaks at around 02:30–03:00 LT over the

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Figure 5. Latitudinal and local time variations of the migrating semidiurnal tide in thermospheric density (in the unit of10�13 kg/m3). (a, c, e, and g) The results frommodel runs with no tides, migrating diurnal tide only, migrating semidiurnaltide only, and both the migrating diurnal and semidiurnal tides specified at the model lower boundary. (b, d, f, and h) Theresults of model runs withmigrating terdiurnal tide only; both themigrating diurnal and terdiurnal tides; both themigratingsemidiurnal and terdiurnal tides; and all three migrating diurnal, semidiurnal, and terdiurnal tides specified at the modellower boundary, respectively.

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equatorial region. Furthermore, the phase of the semidiurnal tide at high latitudes (higher than 40° in bothhemispheres) is about 2–3 h earlier than those at the equator. As there is no semidiurnal tide imposed atthe TIEGCM lower boundary, the semidiurnal tide in the upper thermosphere is mainly a result from in situthermal excitation [Fesen, 1996] and is the harmonic of the daily solar heating. For cases with thesemidiurnal tide initialized at the TIEGCM lower boundary (Figures 5e–5h), the semidiurnal tide is strongover the equatorial region with a peak close to 04:00 LT. The phase delay between the equatorial region andhigh latitudes is about 5 h. Compared to the amplitudes of the equatorial semidiurnal tide in the runswithout the semidiurnal tide at the TIEGCM lower boundary (Figures 5a–5d), the amplitudes of semidiurnaltide in Figures 5e–5h are about 2 times larger. Thus, the equatorial semidiurnal tide in the upperthermosphere is mainly the result of the upward propagation of semidiurnal tide from the MLT.Furthermore, the results in Figure 5 indicate that the upward propagation of the semidiurnal tide dependslittle on the diurnal and terdiurnal tides of the MLT.

The local terdiurnal tide in the thermospheric mass density at 370 km from eight runs is given in Figure 6.Again, the local terdiurnal tidal component refers to the results obtained from the two-dimensionalFourier fitting with a period of 8 h and a wave number of 3. In Figures 6a and 6c, terdiurnal tide peaks at~01:00 LT with similar amplitudes. The phases of the local terdiurnal tide in these two runs do not vary

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Figure 6. (a–h) Same as Figure 5 but for the migrating terdiurnal tide.

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with latitude. Again, similar to the in situexcited semidiurnal tide in Figures 5aand 5c, terdiurnal tide here is thermallyexcited within the thermosphere, andit is not significantly affected by thediurnal tide in the MLT. In Figures 6band 6d, the latitudinal distributionsand the phases of terdiurnal tide arevery similar. There are two peaks of theterdiurnal amplitudes that are awayfrom the equator in these two runs,one at 50°S and the other at ~30°N.The phase of terdiurnal tide at theequator is about 2 h later than that at50°S and 1 h later than that at ~30°N.The amplitudes of terdiurnal tide inFigure 6b are very similar in the twohemispheres but slightly smaller thanthose in Figure 6d.

Figures 6e and 6g give the localterdiurnal tide in thermospheric massdensity at 370 km from runs with onlythe semidiurnal tide and with bothdiurnal and semidiurnal tides, at theTIEGCM lower boundary, respectively.The terdiurnal tide in both runs peaksat ~01:00 LT over the equatorial region.The phases are about 1 h later at the

equator than those at 50°S and 50°N. However, in Figures 6e and 6g, the most striking feature is the largeamplitudes of the local terdiurnal tide from 370 km at the equator. Since there is no terdiurnal tideinitialized at the TIEGCM lower boundary in these runs, the terdiurnal tide shown in Figures 6e and 6g isexcited within the thermosphere. About one third of magnitude comes from thermal excitation as shownin Figures 6a and 6c, and two thirds is the result of the nonlinear interaction between semidiurnal tide anddiurnal variation within the thermosphere and ionosphere. In order to examine the ion drag effect in thegeneration of the terdiurnal tide as suggested by Mayr et al. [1979], we conducted one more simulation,which was similar to Run g but without the ion drag effect in the neutral momentum equation. As shownin Figure 7b, the simulation without the ion drag effect gives a weak terdiurnal tide with a phase that isabout 2 h earlier as compared with the results from Run g (Figure 7a). Thus, ion drag also has a significantcontribution to the terdiurnal tide in the upper thermosphere, as suggested by Mayr et al. [1979].

Note that the terdiurnal tide initialized in the TIEGCM lower boundary leads to the terdiurnal tide of massdensity in the upper thermosphere at middle latitudes (Figures 6b and 6d), whereas the terdiurnal tidefrom nonlinear interaction produces density peaks in equatorial regions (Figures 6e and 6g). Therefore,combinations of these two processes result in a complicated pattern of terdiurnal tide in the upperthermosphere; these are shown in Figures 6f and 6h. In Figure 6f, with the run for both semidiurnal andterdiurnal tides initialized at the TIEGCM lower boundary, the terdiurnal tide has a single peak close to~15°N and 01:30 LT. In Figure 6h with the case of specifying diurnal, semidiurnal, and terdiurnal tides atthe TIEGCM lower boundary, the local terdiurnal tide of upper thermosphere has two peaks, a relativelyweak one at ~50°S and 01:00 LT and a strong one at ~15N° and 01:30 LT.

Therefore, the local terdiurnal tide in thermospheric mass density at 370 km has three sources: (1) theharmonic of diurnal solar heating (in situ thermal excitation [Fesen, 1996]), (2) the upward propagationof the terdiurnal tide from the lower atmosphere [Akmaev et al., 2009, 2010], and (3) the nonlinearinteraction between the diurnal variation within the thermosphere and ionosphere and the semidiurnaltide propagated from the MLT [Mayr et al., 1979; Teitelbaum et al., 1989]. The semidiurnal tide is mostly

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Figure 7. Latitudinal and local time variations of the migrating terdiurnaltide at the altitude of 370 km in thermospheric density (in the unit of10�13 kg/m3) from the simulations with diurnal and semidiurnal tidesincluding at the lower model boundary. (a) The simulation with ion dragand (b) the result of the simulation without ion drag.

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due to the upward propagation fromthe lower atmosphere. Therefore, asneither terdiurnal nor semidiurnal tidesare included at the TIEGCM lower bound-ary in Runs a or c, the local terdiurnal tidein Figures 6a and 6c could be generatedby solar heating. There is also a possibi-lity that the local terdiurnal tide is gener-ated from the nonlinear interactionbetween the diurnal tide generatedwithin the thermosphere and the in situthermal-exited semidiurnal tide withoutthe semidiurnal tide specified at theTIEGCM lower boundary. As shown inFigures 5a and 5b, the phases of the insitu exited semidiurnal tide changewith latitude, whereas the diurnal tideusually peaks close to 14:00 LT. Thisimplies that the phase of terdiurnal tideresulting from nonlinear interactionshould change with latitude as well.However, in Figures 6a and 6c, the localterdiurnal tide peaks at ~01:00 LTwithout obvious phase change withlatitude, indicating that here theterdiurnal tide is unlikely generatedfrom nonlinear interaction. On theother hand, when running the model

with the terdiurnal tide at the TIEGCM lower boundary (Figures 6b and 6d), the upper thermosphericterdiurnal tide is greatly enhanced, and thus, the upward propagating terdiurnal tide from the lower atmo-sphere contributes significantly to the local terdiurnal tide in the upper thermosphere. Furthermore, whenrunning the model with semidiurnal tide but without terdiurnal tide at the TIEGCM lower boundary(Figures 6e and 6g), stronger terdiurnal tide than that in Figures 6a and 6c occurs at 370 km. This suggeststhat nonlinear interaction also plays an important role in the generation of the terdiurnal tide in the upperthermosphere.

Figure 8 further demonstrates the contributions of these three sources to the local terdiurnal tide in theupper thermosphere. For this, we assume them to superpose quasi linearly. Figure 8a is the difference ofterdiurnal tide at 370 km between Runs h and d, which indicate the terdiurnal tide resulting from thenonlinear interaction. The magnitude of the equatorial terdiurnal tide, with the peak time of ~01:30 LT, islarger than that at high latitudes. Figure 8b gives the terdiurnal tide (the difference between Runs h and g)generated by the upward propagation of the terdiurnal tide in the MLT. The terdiurnal tide at 10°S isdelayed by 2 h when compared to that of midlatitude and high latitude, and the magnitude of theterdiurnal tide near the equator is smaller than that of high latitudes. Obviously, this latitudinal structure isrelated to the terdiurnal tide at the TIEGCM lower boundary (Figure 1). Thus, the latitudinal and local timestructure of the terdiurnal tide that propagated upward from the lower atmosphere is different from thatof the terdiurnal tide generated by nonlinear interaction. In the equatorial region, the primary cause of thelocal terdiurnal tide in the upper thermosphere is due to nonlinear interaction, while the contributions dueto solar heating and upward propagation from the low atmosphere are secondary cause and comparable.At high latitudes, the upward propagating terdiurnal tide becomes the main contributor in the upperthermosphere, and contributions from nonlinear interaction and solar heating become minor. Therefore,the semidiurnal tide from the lower atmosphere affects the nighttime density enhancement in two ways:(1) through direct upward propagation and (2) through nonlinear interaction with diurnal tide to producethe terdiurnal tide (especially over the equatorial region) in the upper thermosphere.

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Figure 8. Latitudinal and local time variations of the migrating terdiurnaltide (in mass density) from the differences between the runs with differentlower boundary specifications (in the unit of 10�13 kg/m3). The migratingterdiurnal tide obtained from the differences (a) between Runs h and d and(b) between Runs h and g, respectively.

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Now we can address the issue of howthese three local tides in the upperthermosphere produce the midnightdensity enhancement. Miyoshi et al.[2009] suggested that a superpositionof the local semidiurnal and terdiurnaltides produce the MTM. However, itshouldbepointedout that the terdiurnaltide in their simulations during Marchequinox showed maximum amplitudeat the equator [Miyoshi et al., 2011],which is not consistent with SABERobservations [Yue et al., 2013] and ourresults in Figures 1 and 6.

As shown in Figures 5h and 6h, in theequatorial region the semidiurnal tidehas a peak at 04:00 LT, while theterdiurnal tide peaks close to 01:30 LT.The diurnal tide has a minimum close to02:30 LT. In Figure 9, the reconstructedresults from Run h are used as an

example to further illustrate the variations of diurnal, semidiurnal, and terdiurnal tides at night. The blackline in Figure 9 represents the sum of these tides, which describes the nighttime variation of the massdensity over the equatorial region (without the daily mean of the mass density) in Run h. It shows a densitycycle that decreases before 23:30 LT, and then increases until 02:30 LT, followed by decreasing until 05:00 LTand then increasing again.

As demonstrated in Figure 9, the formation and evolution of the MDM involve the interplay of local diurnal,semidiurnal, and terdiurnal tides. First, the growth in both semidiurnal and terdiurnal tides from 01:30 LT to02:00 LT overcomes the decrease of mass density caused by the diurnal tide, resulting in the mass density toincrease with local time. During the period of 02:00–02:30 LT, the terdiurnal tide begins to decrease the massdensity, while the semidiurnal tide continues to increase the mass density. This makes the overall densityincrease and reach a maximum. After that, during the time period of 02:30–04:00 LT, the declining phase ofthe terdiurnal tide combined with negative amplitude of the diurnal tide overcomes the increasing densitytrend caused by the semidiurnal tide and leads to a decreasing thermospheric mass density. The decreasingof thermospheric mass density from 02:30 to 04:00 LT is mainly due to the declining phase of the terdiurnaltide. After 04:00, the declining phase of the semidiurnal tide also contributes to the mass density minimumat 05:00 LT. The interplay of these three tides at high latitudes with different amplitudes and phases can alsoexplain the early occurrence and fast disappearance of midnight density enhancements at high latitudes.

5. Conclusions

In this study we performed numerical model experiments to investigate the effects of diurnal, semidiurnal,and terdiurnal tides propagating from the lower atmosphere or generated in situ on the nighttime densityand temperature variations in the upper thermosphere. We include the terdiurnal tide from the eCMAM inthe lower boundary of the TIEGCM. The main results are as follows:

1. The magnitude of the equatorial mass density enhancement becomes larger, and the latitudinal distribu-tion becomes wider in both hemispheres when terdiurnal tide is included in the model lower boundary.

2. Both semidiurnal and terdiurnal tides contribute to the nighttimemass density enhancement in the upperthermosphere. The decrease of thermospheric mass density after MDM reaches its peak at ~02:00 LT isdue to the terdiurnal tide, whereas the increase of the density before the peak of MDM is the result ofthe simultaneous occurrence of the growth phase of both the semidiurnal and terdiurnal tides.

3. The terdiurnal tide in the upper thermosphere has three sources: (1) in situ thermal excitation, (2) upwardpropagation from the lower thermosphere, and (3) nonlinear interaction between the diurnal variation

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Figure 9. Nighttime variations of the three migrating tides and their sum(in the unit of 10�13 kg/m3) at 370 km in the equatorial region for Run h.The blue, red, green, and black lines are themigrating diurnal, semidiurnal,and terdiurnal tides and their sum, respectively.

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within the thermosphere and ionosphere and the semidiurnal tide propagating from below. The terdiur-nal tide in the equatorial region is mainly produced by the nonlinear interaction between the diurnal tidegenerated within the thermosphere and the semidiurnal tide propagating upward from MLT, whereas athigh latitudes it is mostly the result of the upward propagation of the terdiurnal tide from the loweratmosphere.

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AcknowledgmentsSimulation outputs used in this studyare archived on the NCAR Yellowstonecomputer system and can be obtainedupon request from Haibing Ruan(haibingr@gmail.com).This work wassupported by the National NaturalScience Foundation of China(41325017, 41274157, 41229001,41174139, and 41421063), the Projectof Chinese Academy of Sciences(KZZD-EW-01), the National Key BasicResearch Program of China(2012CB825605), and Thousand YoungTalents Program of China. Jian Du andMatt Cook are funded by NSF CEDARgrant AGS-1243019. The NationalCenter for Atmospheric Research issponsored by the National ScienceFoundation. Haibing Ruan would liketo thank Logan Riney and CalebGoodpaster for reading the manuscriptbefore submission.

Alan Rodger thanks Rashid Akmaevand Dustin Hickey for their assistancein evaluating this paper.

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