Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137

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Journal of Atmospheric and Solar-Terrestrial Physics

1364-68http://d

n CorrE-m

journal homepage: www.elsevier.com/locate/jastp

The midnight temperature maximum from Areciboincoherent scatter radar ion temperature measurements

C. Martinis a,n, D. Hickey a, W. Oliver a, N. Aponte b, C.G.M. Brumb, R. Akmaev c,A. Wright a, C. Miller a

a Center for Space Physics, Boston University, 725 Commonwealth Ave, Boston, USAb National Astronomy and Ionosphere Center, Space and Atmospheric Sciences Department, Arecibo Observatory, Arecibo, Puerto Ricoc NOAA Space Weather Prediction Center, Boulder, Colorado, USA

a r t i c l e i n f o

Article history:Received 4 September 2012Received in revised form10 April 2013Accepted 19 April 2013Available online 23 May 2013

Keywords:Low and midlatitude ionosphereUpper atmosphere neutral dynamics

26/$ - see front matter Published by Elsevierx.doi.org/10.1016/j.jastp.2013.04.014

esponding author. Tel.: +1 6173 535258; fax:ail address: martinis@bu.edu (C. Martinis).

a b s t r a c t

The midnight temperature maximum (MTM) is studied using ion temperature data from the incoherentscatter radar at the Arecibo Observatory (18.31N, 66.21W). The MTM is characterized by fitting the radardata with a function that takes into account diurnal, semidiurnal and terdiurnal components. Under thehypothesis that the MTM is related to the amplification of the terdiurnal wave, a Gaussian amplificationwindow is included in the fitting to automatically determine the time of occurrence, temporal duration,and amplitude of the MTM observed. This study focused initially on altitudes near 300 km, the typicalheight of MTM observations from Fabry Perot Interferometers (FPIs). Out of the 491 days availablebetween 1967 and 2010 only 82 showed reliable temperature determination throughout the night at thistypically bottomside altitude of often low density and sharp density gradient. The analysis was expandedto include 229 usable nights at heights close to 330 km and 367 km, where better conditions fortemperature determination exist. Most of these nights showed an MTMwith amplitudes between 20 and150 K and peak occurrence times during local summer months. The seasonal dependence of MTMparameters is also investigated and compared with previous experimental and modeling studies.

Published by Elsevier Ltd.

1. Introduction

1.1. The midnight temperature maximum

The midnight temperature maximum (MTM) is an enhance-ment of the neutral temperature (Tn) of ∼50–200 K in the night-time equatorial thermosphere. It is thought to be created by thecombination of in-situ thermal excitation, ion-neutral momentumcoupling and lower atmosphere tidal waves penetrating into thethermosphere. This enhancement in Tn generates a localizedpressure enhancement that results in a reversal or abatement ofthe meridional winds that are usually equatorward during thenighttime with significant variability with season, solar andmagnetic activities (Brum et al., 2012). The perturbation in themeridional winds due to the MTM has a direct consequence on thevertical distribution of ionospheric plasma, like the downwarddescent of the F-region plasma, termed ‘midnight collapse’ or‘midnight descent’ (Behnke and Harper, 1973).

The MTM has been traditionally observed in-situ by satellites(Spencer et al., 1979; Herrero and Spencer, 1982), and from

Ltd.

+1 617 3536463.

ground-based optical Fabry-Perot interferometers (Meriwetheret al., 1986; Faivre et al., 2006; Otsuka et al., 2003). It has beenstudied extensively with 6300 Å FPI measurements at Arequipa,Peru (16.51S, 71.51W) (Meriwether et al., 2008), and more recentlyat Cajazeiras, Brazil (6.891S, 38.561W) (Meriwether et al., 2011).

Meridional winds blowing poleward move plasma to loweraltitudes along magnetic field lines, i.e., the midnight descent, and,as a consequence, an enhancement in plasma recombination andhence 6300 Å airglow emissions can occur. This was seen byColerico et al. (1996), who, using an all-sky imaging system locatedin Arequipa, observed an increase near local midnight in theoverall brightness that propagated poleward through the fieldof view. This optical signature was termed the ‘brightnesswave’ (BW). Although the origin of the MTM can be found nearthe equator, its effects can be detected as far as 401S, as shown byColerico et al. (2006), who examined the latitudinal extent of theMTM influence using data from El Leoncito Observatory (31.81S,69.31W) all-sky imager (ASI). Martinis et al. (2006) showed theoccurrence of a BW at Arecibo and El Leoncito on the same night. ABW appeared at Arecibo at ∼0430 LT, while at El Leoncito (locatedfurther away from the geographic equator) it arrived later, at∼0600 LT. Strong poleward winds would be needed to propagateMTM effects as far as 401S, and thus, pronounced heating of thethermosphere at low latitudes should be required.

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137130

The MTM is not present in the empirical MSIS model (Hedin,1991; Picone et al., 2002) of the neutral atmosphere, nor is theassociated wind reversal present in the horizontal wind model(HWM) of Hedin et al. (1996). Until recently, general circulationmodels were unable to simulate successfully such MTM/BW effects(Colerico et al., 2006; Meriwether et al., 2008).

From satellite (Herrero and Spencer, 1982), ISR (Harper, 1973;Bamgboye and McClure, 1982), and FPI (Meriwether et al., 2008)observations the temperature enhancements were seen to occur ashigh as ∼715–201 geographic latitude. Akmaev et al. (2009) haveshown that significant MTM effects are expected to occur as highas 301S geographic latitude during local summer conditions. Theseresults, added to the observation of BWs propagating as far as401S, indicate that MTM generation mechanisms are not limited tothe equatorial region, and that a latitudinal progression of thesource might be taking place, making the MTM an importantfeature at an extended range of low and midlatitudes.

Recently, Akmaev et al. (2009, 2010) and Ma et al. (2010)presented realistic simulations of the nighttime neutral tempera-ture variations with the Whole Atmosphere Model (WAM) and theThermosphere Ionosphere Mesosphere Energetics Global Circula-tion Model (TIME-GCM), respectively. WAM has been developedunder the Integrated Dynamics in the Earth's Atmosphere (IDEA)project to study and eventually forecast dynamical links betweenthe lower atmosphere and the upper atmosphere and ionosphere.It is based on the US National Weather Service's operational GlobalForecast System (GFS) model, extended upward to cover theatmosphere from the ground to the exosphere at about 600 km(Akmaev, 2011). The modeling studies have shown that the MTMfeature may be traced down to the lower thermosphere, where itis manifested primarily in the form of an upward propagatingterdiurnal tidal wave.

The ground-based MTM climatology has been developedmainly from FPI data (Faivre et al., 2006). In that work, the FPIdata were fitted with a Gaussian curve added to a MSIS curve, plusa constant offset. The residual temperatures obtained wereassumed to be caused by the MTM phenomenon. But these resultsdid not include local summer measurements due to the badobserving conditions encountered on that season. Another limita-tion of the FPI technique is that the data are height-integrated overthe emitting region, situated near 250–300 km (Otsuka et al.,2003) so information on vertical structure is lost. In-situ satellitemeasurements showed MTM effects between 250 and 400 km, butwith no systematic information on how they vary with altitude.Thus, the ISR-determined MTM will allow us to complement thelimited information provided by the FPI and satellitemeasurements.

1.2. The MTM and incoherent scatter radar measurements

The absence of plasma production by EUV radiation during thenight allows the electron and ion temperatures to relax to the neutraltemperature in the thermosphere. Thus variations in the nighttimeion and electron temperatures (Ti and Te, respectively), determinedby the ISR technique, should reflect variations in the neutraltemperature Tn. Using Arecibo incoherent scatter radar, Behnke andHarper (1973) showed that during an MTM event nighttime neutralwinds, being typically equatorward, are first seen to abate and thenoften turn poleward by 0200 LT, leading to an observed drop in theheight of the F layer near midnight. During a 5-day case study inMarch 1971, Harper (1973) observed a ∼40 K increase in Ti at 350 kmnear midnight. He attributed this heating to the adiabatic heating ofthe neutral gas. He also inferred the meridional component of theneutral wind. He found a strong decrease in the equatorward windnear midnight and a weak reversal near 02–03 LT. This reversal wasassociated with the observed ionospheric descent, the so-called

midnight collapse. In the southern hemisphere, Bamgboye andMcClure (1982) measured nighttime electron temperatures at300 km with the incoherent scatter radar at Jicamarca Radio Obser-vatory (11.91S, 76.91W, 21N mag). Sixty of 127 nights in 1967–1969showed increases in Te of 100–150 K near local midnight. A seasonaldependence of the local time of occurrence, defined as the time ofpeak amplitude, was also observed. The local time of the maximumTe occurred later during June–July solstice, i.e., local winter.

Even though several studies have shown the midnight collapseat Arecibo (Nelson and Cogger, 1971; Crary and Forbes, 1986; Gonget al., 2012), there are no statistical studies of the MTM using ISRobservations. ISR measurements of nighttime enhancements in Ti(or Te) should fill the gap existing in the seasonal characterizationof the MTM developed from FPI measurements. Besides, ISR-determined Ti can indicate the range of altitudes over which theenhancement occurs. Altitude information may provide evidenceon the source of the MTM.

This work shows initial results obtained using ISR data fromArecibo and addresses some key issues related to MTM character-ization, namely, local time of occurrence, amplitude, and solaractivity dependence.

2. MTM characterization and data

2.1. Fitting method

To characterize the features of the MTM, we have fit each day'sdata with a mathematical function that includes a constant andharmonics representing different tidal modes in the upperatmosphere (the diurnal, semidiurnal, and terdiurnal waves).To account for possible differences in starting and ending tem-perature over a 24-h period, we have also included a slope term:

f 0ðtÞ ¼ p1 þ p2ðt−tÞ þ p3 sin2πt24

� �þ p4 cos

2πt24

� �

þp5 sin2πt12

� �þ p6 cos

2πt12

� �

þp7 sin2πt8

� �þ p8 cos

2πt8

� �ð1Þ

Here p1 and p2 represent the constant and slope terms, respec-tively, and the remaining p's are the amplitudes of the harmonicterms used in the fitting. This fitting function represents very wellthe behavior of the temperature for most of a day, but it does notshow an MTM feature. Our assumption is that the MTM representsan amplification of the terdiurnal component. This is included in ourfitting function by multiplying the 8-h terms by a Gaussian timewindow of adjustable amplitude, location, and width. Thus the finalfunction f(t) used to characterize MTM features is:

f ðtÞ ¼ p1 þ p2ðt−tÞ þ p3 sin2πt24

� �þ p4 cos

2πt24

� �

þp5 sin2πt12

� �þ p6 cos

2πt12

� �

þ p7 sin2πt8

� �þ p8 cos

2πt8

� �� �1þ p9e

−ðt−p10=p11Þ2h i

ð2Þ

The p9 coefficient represents the amplitude of the Gaussianwindow and can be used to quantify the amplitude of the MTM.The p10 coefficient locates the center of the Gaussian, whichcorrelates with the local time peak of the MTM. Finally, the p11coefficient represents the width of the fitted Gaussian, related tothe duration of the MTM. The Gaussian extends over all time, butwas found always to be narrow so as to affect only the 8-h wavecycle near midnight.

Eq. (2) is non-linear and one must iterate to obtain a proper fit. Thefirst step was to fit the data with the function described in Eq. (1)

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137 131

(i.e., just constant, slope and sinusoidal terms). These eight p para-meters were used as starting values in the ensuing nonlinear fit of Eq.(2). A least squares fit of Eq. (2) to the data was made and the entireset of 11 p parameters was determined. Adjustments were made tothe fitting procedure when data availability did not cover an entire24 h period, or significant data gaps existed during the nighttimeperiod; specifically, if the data covered only the nighttime region ofinterest, a simple Gaussian and a straight line were used to fit the data,similar to the procedure applied to nighttime FPI measurements toextract MTM characteristics (Meriwether et al., 2008).

Because the center of the Gaussian is not constrained to occur atthe time of the peak of the nighttime 8-h sinusoid, we have chosento characterize the MTM as illustrated in Fig. 1 for 16–17 November,1990 at 293 km. This figure shows data from more than 24 h,allowing us to compute all the parameters in Eq. (1) and (2). Herewe show Ti data averaged to 15-min resolution fitted by Eq. (2) (bluethick curve with a bump around 0000 LT). The red thin curve is theresult of fitting Eq. (1), i.e., without the Gaussianwindow. The time ofthe peak smooth-curve temperature at night is shown by the greenvertical line. The turquoise straight line connects the locations of theminima to the left and right of this peak. The amplitude of the MTMis defined as the distance along the green line between its intersec-tions with the blue and turquoise lines.

2.2. Data

Temperature data between 1967 and 2010 were taken from theMadrigal, CEDAR and Arecibo databases. The total number of analyzeddays was 491, of which 283 had nighttime data suitable for this work.The study originally focused on data at a height close to 300 km that,in general, is below the ionospheric peak during the post-sunsetperiod. Ion and electron temperatures are typically obtained using thestandard ion-line multiple radar autocorrelation function (MRACF)program (Sulzer, 1986), which provides excellent temporal resolutionbut a relatively coarse altitude resolution (∼38 km). Most of thespectra from this latitude were unreliable at this height due to low

Fig. 1. Typical example of nighttime MTM observed in the data. The blue thick curve isGaussian amplification. The turquoise straight line is used to compute the temperatur(For interpretation of the references to color in this figure legend, the reader is referred

electron density or distorted due to the large electron density heightgradient that exists below the peak. Due to this limitation in thetechnique, only approximately 25% of the nighttime data at 300 kmwere usable and the study was expanded to include heights close to330 km and 367 km. At these heights the electron density is generallylarger and has no strong altitude gradient, so the number of reliabledeterminations of Ti was much greater.

Fig. 2 shows the number of cases observed by month during theentire period. At 300 km only 82 cases were included while at367 km (and 330 km) the total number increased to 229. MTMeffects were observed on 66 of 82 nights at 300 km. Fig. 2 shows thatthere is no preferred month for the occurrence of MTM cases. Severalnights showed the occurrence of double temperature enhancements,one close to midnight and the other much earlier (pre-MTM) ormuch later (post-MTM). Pre-MTM features have been observed usingFPIs by Faivre et al. (2006) at Arequipa (161S, 71.51W) and ASIs byColerico et al. (2006), at Arequipa and El Leoncito (31.81S, 69.31W),and modeled by Akmaev et al. (2009), who showed the presence of asecondary maximum between 2000 and 2100 LT. There was no clearseasonal trend in the occurrence of these double cases. These early-time Ti increases were not included in our MTM statistics. Some ofthe late or post-MTM effects occurred very close to local sunrise atthese heights (∼0430 LT in summer and ∼0630 LT in winter) whileothers occurred closer in time to conjugate hemisphere sunrise,around ∼0330 LT (Carlson et al., 1966; Chao et al., 2003). These late-time Ti enhancements, occurring after ∼0330 LT, are not related toMTM effects, and are not included in our MTM statistics.

3. Results and discussion

3.1. Arecibo data at 300 km

We looked initially at ISR data near 300 km altitude, a verydifficult task due to the low electron density and sharp gradientsduring the time of interest. The criterion to select the usable nights

the full fitted function f, and the red thin curve is the fitted function without thee enhancement. The vertical green line around 0000LT indicates the peak center.to the web version of this article.)

Fig. 2. Number of cases showing MTM effects at 300 km (black) and 367 km (gray).No clear seasonal dependence is observed. The smaller number of cases at 300 kmis due to the limitations in the technique to determine temperatures when smallelectron density is measured and/or large height electron density gradients occur.

Fig. 3. Seasonal behavior of the local time of occurrence of the MTM at 300 km.Asterisks represent the mean of the individual data points at a given month. Errorbars represent variability of the data. Some months do not have enough number ofpoints to reach meaningful conclusions.

Fig. 4. Average monthly MTM amplitudes at 300 km show relatively smaller valuesduring the period November-March. Asterisks represent the average of theindividual data points at a given month. The MTM amplitude was defined as thedifference between the peak Ti and the interpolated value obtained from the twominima surrounding the MTM.

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137132

was to look for those cases when Ti was equal to Te, a conditionnecessary to identify reliable data. Data at 330 km and 367 kmwere also analyzed, and the number of cases available for a properdetermination of ion temperatures increased from 82 to 229.The results, summarized in Fig. 2, indicate that the MTM is arecurrent phenomenon and, as such, it provides evidence of theimportance of coupling with the lower atmosphere. These results canbe compared with the study of the ‘midnight collapse’ at Arecibo byNelson and Cogger (1971) who found changes in hmax, the height ofthe peak electron density, of 50–100 km beginning near midnight in85% of the 130 cases analyzed. Our current understanding of themidnight collapse can be directly related to the occurrence of theMTM; specifically, it is caused by poleward winds driven by the MTMpressure bulge. A recent study by Gong et al. (2012) suggests thatelectric field and ambipolar diffusion also might play an importantrole in the occurrence of the midnight collapse.

The monthly behavior of the local time of MTM occurrence,defined as the time of peak effect as indicated by the green line inFig. 1, at 300 km is shown in Fig. 3. Asterisks represent monthlymeans. The local time of occurrence spanned a wide time range,between 2200 and 0300 LT. This limited sample of data shows thatearlier average local time of occurrence between 0000 and0030 LT is observed during the month of June, with October, Novand January months also showing a relatively early local time ofoccurrence. A study using Jicamarca Radar data at the same height(Bamgboye and McClure, 1982), showed an earlier local time ofoccurrence in the October–December period, but the local timewas around 2200 LT, 2 h earlier than the time observed at Arecibo.Neither study has sufficient data to define the seasonal variabilityproperly. The comparison of these two data sets are particularlyinteresting because the sites have geographically similar (181 vs.−121) but geomagnetically very different (281 mag vs. 11 mag)latitudes. The observed differences might be due to the influenceof geomagnetic field lines that preclude vertical diffusion aboveJicamarca, but not at Arecibo.

Satellite measurements show that the MTM occurs earlier inthe northern hemisphere summer than it does in northern hemi-sphere winter (Herrero and Spencer, 1982). They have shown ahorizontal V-shape structure in time and latitude in the tempera-ture enhancement near 285 km, with earlier occurrence time nearthe equator and later times near the northern and southerntropics. They observe an MTM at the location of Jicamarca earlierthan at the location of Arecibo, in agreement with the timing seenby the radars at those locations.

Fig. 4 shows the MTM amplitude, ranging from ∼20 to ∼150 K,with smaller average values found during the Nov–March period.A peak in monthly-averaged amplitude is found during localsummer months, with an average of ∼75 K. The average for theNov–March period is∼50 K. Ground-based results using FPI mea-surements from Arequipa have shown peak amplitudes duringequinox, although southern hemisphere summer values were notavailable due to cloudiness at the site (Faivre et al., 2006). Recently,using an FPI at Cajazeiras (6.891S, 38.561W), Meriwether et al.(2011) have shown peak MTM amplitudes during Septemberequinox. It is not clear which mechanisms could be responsiblefor this seasonal pattern. The 300 km ISI data do not providestatistically significant results, especially considering that severalmonths have only 2 or 3 data points.

3.2. Arecibo data at 330 and 367 km

One of the advantages of using ISR measurements to study theMTM is the capability of studying characteristics at differentheights, something not possible with FPI or all-sky imaging

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137 133

diagnostics, which provide height-integrated values centered at∼250 km (300 km) for low (high) solar activity. Ti enhancementswere observed to occur as low as 283 km and as high as 467 km inthe radar data.

Fig. 5 shows Ti at two different heights for 27–28 October 1992.The MTM peak occurs slightly earlier (∼30 min) at the higheraltitude. The amplitude of the MTM at 441 km is still large,providing evidence of the large scale (∼100 km) vertical structureof MTM.

Fig. 6 shows the local time of occurrence of the MTM observedat 330 km (left panel) and at 367 km (right panel), with datashown in the same format as Fig. 3. The results indicate that theMTM occurs earlier on average during local summer.

The results at these higher altitudes still show significantvariability but the monthly data are more evenly distributed.Although our MTM results cover a broad range of amplitudesand times of occurrence, we can calculate meaningful averagesand seasonal variations by fitting each set of data, amplitude andtime of occurrence, as a function of day of year. This allow us tofind THE mean amplitude t1, mean seasonal amplitude t2, and

Fig. 5. Example of altitude variation of MTM characteristics. Data were binned in 15 m

mean day of year t3 at which the seasonal variation maximizes.

MTMamp ¼ t1 þ t2n cos 2nπnday−t3

365:2422

� �ð3Þ

The analysis is similar to the one used in Oliver et al. (2012).The results are shown in Fig. 7, with the data now distributedthrough the entire year. The uncertainties in t1 and t2 are ∼5 K forMTM amplitude and ∼0.2 h for MTM time of occurrence. There is atendency for the MTM to have larger amplitude and to occur earlierin summer. The mean amplitude diminishes from 61 K at 300 km to52 K at 330 km to 41 K at 367 km, indicating dissipation as the MTMwave rises. The mean time of occurrence 0.4 LT does not show asignificant trend with altitude, but it does occur earlier in summer atall altitudes. Table 1 lists the coefficients t1, t2, and t3 found from aleast-square fit to the amplitude and time-of-occurrence data sets at300, 330, and 367 km altitude. It also lists coefficients t4 and t5related to solar-activity variation, which we discuss later.

The uncertainties listed are those for the mean trends and donot represent the accuracy with which the MTM can be forecast ona given day. For example, the seasonal amplitude of 6.272.1 K at

in intervals. The data and fitted curves show an MTM extending up to 441 km.

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137134

367 km means that for a large collection of measurements the MTMsummer amplitude will average 6.2 K higher than the MTMyearly amplitude. The stated uncertainty is a one-standard-deviation

Fig. 7. MTM amplitudes (left) and local time of occurrence (right) at three height levels wthe fitting curves show an overall earlier time of occurrence during local summer. Thconfidence levels for the fitted curves.

Fig. 6. Similar to Fig. 3 but now at 330 km (left) and 367 (right). Asterisks represent meanthe data earlier occurrence time seems to be observed in the period April–August at 33

uncertainty, so we are 68% certain that this average summer enhance-ment is between 4.1 and 8.3 K, and 95% sure that it lies between2.0 and 10.4 K.

ith curves fitted to the data points. Significant scatter is observed in all the cases bute amplitude also seems to peak in the same period. See text and Table 1 for the

values and error bars indicate variability. Although not evident due to the scatter in0 km and May–October at 367 km.

Table 1Coefficients t1, t2, t3 found from a least-squares fit to the amplitude and time-of-occurrence data sets at 300, 330, and 367 km altitude. Coefficients t4 and t5 arerelated to the MTM amplitude dependence on solar-activity variation.

Fit coefficient Altitude (km) MTM amplitude MTM time of occurrence

t1 (K,h) 300 61.373.1 0.6370.09t2 (K,h) 300 15.774.4 0.1770.13t3 (d) 300 193717 328747t1 (K,h) 330 52.071.9 0.1670.07t2 (K,h) 330 4.572.8 0.4470.10t3 (d) 330 205734 358714t1 (K,h) 367 40.771.4 0.2970.07t2 (K,h) 367 6.272.1 0.2070.11t3 (d) 367 230719 10728t4 (K) 300 56.373.6t5 (K/F10.7 unit) 300 −0.08770.065t4 (K) 367 41.271.6t5 (K/F10.7 unit) 367 −0.01070.029t4 (K) 300+367 44.471.5t5 (K/F10.7 unit) 300+367 −0.00370.027

Fig. 8. MTM amplitudes at 300 km (red diamonds) and 367 km (black points)plotted as a function of F10.7. Binned data in 20 F10.7 units are also shown as largeblack circles for 300 km and large red diamonds 367 km. 1 sigma error bars,representing variability in the binned-data points are also indicated.

Fig. 9. WAM outputs showing the local time of occurrence of the modeled MTMfrom 250 km to 400 km. Notice the large scatter bars, similar to variability levelsobserved in the radar data.

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137 135

The mean MTM amplitude is seen to decrease significantly withincreasing altitude and have a small but statistically significantseasonal variation maximizing in late summer. The magnitudes ofthe trends are small compared with the magnitude of the day-to-day variability but may provide clues to theorists and modelers onMTM generation and dissipation.

3.3. Solar activity effects on MTM amplitude

The data shown so far cover a wide range of solar activity, andone could argue that this can create a bias on the results. Previousstudies have not been able to provide evidence on the influence ofsolar activity on MTM amplitude. Current interpretation involvescompeting mechanisms that imply a transition from tidal forcingat solar minimum to increased ion-drag at solar maximum(Meriwether et al., 2008). According to this interpretation thetwo mechanisms combine to produce a small solar cycle variationin MTM amplitude. Fig. 8 shows a scatter plot of F10.7 versus MTMamplitude at 300 km (red diamonds) and at 367 km (black dots).The result at 300 km, showing only a slight decrease for large F10.7values, is remarkably similar to the one obtained by Faivre et al.(2006), using FPI data at Arequipa, who attributed this apparent

decrease to the lack of sufficient measurements at high solaractivity. The FPI-determined MTM amplitude also has a largevariability, with individual data points showing significant scatter.We have also bin-averaged the data into 20-unit F10.7 bins andplotted the bin averages and their uncertainties as large symbolswith error bars in Fig. 8. To determine if MTM amplitude has solaractivity dependence, a linear fit to the data shown in Fig. 8 wasperformed, separately for 300 and 367 km altitude:

MTMamp ¼ t4 þ t5nðF10:7−150Þ ð4Þand the results for t4 and t5 are shown in Table 1. At 367 km, theuncertainty in t5 of 0.029 K/(F10.7 unit) means that the limit ofdetectability with this data set is 2.9 K over an F10.7 range of 100units, and we detect no trend at that level. At 300 km a slight trendindicates a negative slope, but again, this result, is affected by thelack of sufficient data points for large F10.7 values.

3.4. Model comparisons

As described in the introduction, WAM was the first global modelto realistically reproduce the MTM (Akmaev et al., 2009, 2010). Fig. 9shows the seasonal variation of the local time of occurrence of theMTM from 250 km to 400 km produced byWAM. The model was runfor an entire year, and the hourly outputs were inspected to identify amaximum temperature between 2000 and 0400 LT. The vertical barsrepresent7one standard deviation, reflecting a significant day-to-day variability of the MTM (see Fig. 10), also observed in the radardata (see Fig. 6). The MTM occurs at earlier local time during localsummer, around midnight for 300 km and at ∼2300 LT for 400 km.The model results do not reproduced month by month the Arecibodata, but the overall trend is in agreement with the radar observa-tions: on average, earlier local time of occurrence during summermonths. WAM outputs do not exclude pre-MTM or post-MTM effectsas the ISR data do. The model shows an earlier local time ofoccurrence in summer at 400 km than it does at 300 km, somethingnot evident in the ISR data at 330 km and 367 km.

Fig. 10 shows the result of superposing all available March ISRdata (left panel) for 300 km and the model results for thetemperature deviation from the zonal mean at 285 km (rightpanel) adapted from Akmaev et al. (2009). The red curve in theleft panel represents the average of the data. The MTM is distinctlydetected, with amplitude of ∼45 K and an average local time of

Fig. 10. (Left): superposed ion temperature data for all the March days at 300 km. Notice the variability in the absolute Ti values due to different solar activity conditions.The red curve is the average and a clear MTM is observed between 0000 and 0100 LT. The average amplitude is 45 K. (Right): WAM outputs showing the MTM for March at20o N (adapted from Akmaev et al., 2009). A peak temperature variation of ∼50 K occurs at∼- 75o (∼0100LT), close to Arecibo's longitude. The general shape of the averagecurve from the left plot in the time interval 1800LT-0600LT is almost identical to the modeled output at the right.

C. Martinis et al. / Journal of Atmospheric and Solar-Terrestrial Physics 103 (2013) 129–137136

occurrence between 0030 and 0100 LT. Notice the large amplitudevariability in the daily curves of the Ti values, certainly due tochanges in solar activity. The WAM model output (right panel)shows each day of the month of March (thin lines), a monthlymean (green line), the sum of the first three migrating tides (blueline), and the sum of all waves down to 2 h period (red line).The result gives a peak enhancement of ∼50 K at 0100 LT in goodagreement with the ISR data. The blue line does not reproduce themagnitude of the MTM, giving strength to the hypothesis of theneed of an amplification of a terdiurnal wave. Moreover, the modeloutput from 1800 to 0600 LT shows behavior remarkably similar tothe observations.

4. Summary

Arecibo ISR ion temperature data collected between 1967 and2010 were analyzed. A fitting method involving a Gaussianamplification of the terdiurnal tidal wave was used to determineMTM characteristics for the first time. The seasonal dependence inthe time of occurrence and amplitude of radar-determined MTMwas also studied for the first time. Due to limitations in thetechnique to determine Ti at altitudes below the ionospheric peakand/or when large height gradients in Ne exist, only 82 cases wereavailable for study at 300 km, limiting the significance of thestatistical results. At 330 and 367 km the number of nights availableincreased to 229. MTM signatures were seen as high as 467 km.The MTM tended to occur earlier and to have larger amplitude duringlocal summer months. The similarity of the seasonal behavior ofamplitude and local time of occurrence at the different heightsprovided confidence that the smaller sample of data collected at300 km could still be used to characterize MTM features.

No conclusive statistical evidence for earlier local time ofoccurrence at higher altitudes was found. This effect should beanalyzed on a night-by-night basis.

State-of-the-art model simulations of MTM behavior showedrelatively good statistical agreement with the ISR results.

Acknowledgements

This work was supported by NSF grants AGS-0925893 and AGS-0836452. The Arecibo Observatory is operated by SRI International

under a cooperative agreement with the National Science Foundation(AST-1100968), and in alliance with Ana G. Méndez, UniversidadMetropolitana, and the Universities Space Research Association. Thiswork used data accessed from the CEDAR, Arecibo, and Madrigal DataBases. We thank several prior undergraduate students whose ground-work helped develop the method used in this work: Monica Ortiz,Cameron Hall, Nate Wilkison, and Austin Collins.

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