A study of the midnight temperature maximum (MTM) climatology has been made for the low-latitude station at Arequipa, Peru (16.2°S, 71.5°W) using Fabry-Perot measurements for the period 1997–2001. Examination of the Arequipa nighttime temperature data after removal of the nocturnal cooling (as represented by the semiempirical NRLMSISE-00 model) shows a Gaussian-like time dependence with amplitudes between 20 and 200 K centered on 0400–0600 UT. A typical value of 50 to 75 K was found for data averaged over the nights from late March to early October, cloudy skies preventing measurements during summer months (November–February). These data show the MTM activity to fluctuate sporadically throughout the austral winter. Also evident are large variations of the offset between the observed temperatures and the MSIS model, with individual nightly offsets between ±200 K. Averaging these offsets over all nights for any 1 year and for all 5 years reduces the offset to a value of ∼20 K. The observed time for the occurrence of the MTM peak amplitude exhibits a seasonal variation; during winter solstice the peak typically occurs between 0500 and 0700 UT, later than during the fall and spring equinoxes, when the peak occurs between 0300 and 0500 UT. The variation of the MTM amplitude with day number shows a weak semiannual oscillation with peak values of 150–200 K near equinoxes and a small secondary maximum of 50 to 70 K near the winter solstice. Examination of the variation of the yearly-averaged MTM amplitude between solar minimum and solar maximum show a slight trend featuring a ∼20 K reduction.
 Aeronomical features associated with the MTM phenomenon include the “midnight collapse” [Nelson and Cogger, 1971], the “midnight pressure bulge” [Spencer et al., 1979; Herrero et al., 1983; Fesen, 1996], the “midnight density maximum” [Arduini et al., 1997], and the “brightness wave” [Colerico and Mendillo, 2002]. The term “midnight collapse” arose from examination of low-latitude ionosonde data by Nelson and Cogger  in which the height of the F layer, hmax, often displayed a sudden rapid descent of 50 to 100 km in the period 0000 to 0200 LT. This descent was coincident with a meridional wind reversal inferred from radar measurements of ion velocities by Harper , who suggested that the reversal was generated by an outflow of air from the “midnight pressure bulge.” Normally, at low latitudes, during the night the direction of the meridional component of the thermospheric flow is equatorward. The passage overhead of a thermospheric pressure bulge induces a reversal of the flow to poleward. This poleward motion, in turn, shifts the F layer to lower heights. Increased production of the 630-nm airglow emission may then occur, generated by the increased dissociative recombination of O2+ forming O(1D) [Burnside et al., 1981; Colerico et al., 1996; Mendillo et al., 1997]. During the “midnight collapse” at Arecibo, the 630-nm airglow intensities and thermospheric temperatures increase threefold to fivefold and by 30 to 100 K, respectively [Harper, 1973; Cogger et al., 1980; Burnside et al., 1981, 1988]. The airglow morphology of this phenomenon as seen at the low-latitude location of Arequipa, Peru (16.2°S, 71.4°W) is thus characterized by the regular appearance between midnight and dawn of a 630-nm airglow enhancement ranging from a few to 150 Rayleighs [Cogger et al., 1974, 1980] that moves southward (poleward). This poleward motion is the identifying feature for the “brightness wave” (BW) introduced by Colerico et al.  to characterize the airglow signatures in all-sky imaging observations of the 630-nm emission at Arequipa, Peru. This work also noted the considerable night-to-night variability in the BW, which is also true of the MTM.
 Theoretical explanations of the MTM were developed by Mayr et al.  and Herrero et al. , who ascribed principal importance for production of the MTM to ion-neutral momentum coupling in which semidiurnal oscillations are generated by the coupling between diurnal wind variations and diurnal ion density variations. The variability of the neutral winds, electron densities, and the tidal waves excited in the lower atmosphere which penetrate into the thermosphere may all contribute to the observed variability of the MTM.
 Initially, efforts to generate an MTM via the NCAR general circulation models were unsuccessful, even though the model included ion-neutral momentum coupling and realistic solar forcing. Success was achieved when upward propagating tidal waves from the lower atmosphere that were previously neglected in the model were incorporated into the model calculations [Fesen et al., 1986; Fesen, 1996, 1997] Accordingly, Fesen  concluded that the upward propagating tides were a more important source of the MTM events than the ion-neutral momentum coupling mechanism that had been proposed by Mayr et al. . It was argued that, although Mayr et al.  included the effects of upward propagating waves in their calculations, the thermal forcing of these waves was based on outdated parameterizations from Chapman and Lindzen , which only included contributions from the symmetric semidiurnal modes and assumed that the horizontal and vertical structure of the excitation were identical for each mode. It is now known that some of the heating rates are significantly larger and more sharply peaked in altitude than those calculated by Chapman and Lindzen; further, the asymmetric mode contributions are not negligible [Forbes and Garrett, 1978; Groves, 1982a, 1982b; Crary and Forbes, 1986]. In particular, the terdiurnal tidal mode may also be of considerable importance in producing the MTM [Mayr et al., 1979; Herrero et al., 1983; Colerico et al., 2006].
Bamgboye and McClure  used the incoherent scatter radar at Jicamarca Radio Observatory to determine nighttime electron temperatures, obtaining data for 38 nights in 1968 and 1969. At night at the altitudes of the 630-nm airglow layer (225–275 km), the absence of any plasma production by absorption of EUV radiation allows the electron temperature to relax to the neutral temperature. Thus its variation with time reflects the neutral temperature variation. These observations showed evidence of nighttime temperature increases of 100 to 150 K near midnight. They also found a seasonal shift in the appearance of the MTM with the peak amplitude occurring 2 hours before midnight in the local summer and about 1 to 2 hours after local midnight in the winter. This seasonal variation was also inferred by Herrero et al. .
 In this paper we present the results of an analysis of the Arequipa Fabry-Perot interferometer (FPI) determinations of the neutral thermospheric temperature observed over 396 nights from 1997 to 2001, covering the transition from solar minimum to solar maximum. These results provide a picture of the climatology of the MTM phenomenon and its dependence upon the solar cycle variation. Good data were generally obtained between day numbers 100 and 300 for each year. No results were obtained for the remainder of each year owing to cloudy weather.
2. Arequipa FPI Measurements From 1997 to 2001
 The low-latitude thermospheric airglow emission at 630 nm is generated primarily through the dissociative recombination of O2+ to excite a metastable state of atomic oxygen, O(1D). The molecular ions are formed by charge exchange of O+ ions with O2. FPI determinations of equatorial thermospheric winds and temperatures were obtained from measurements of the Doppler shifts and Doppler broadening of the 630-nm nightglow emission in the meridional and zonal directions (N,S,E,W) at a zenith angle of 60°. These observations have been carried out at the NASA Laser Ranging Network Station at Arequipa, Peru (16.5°S, 71.5°W) since 1983 [Biondi and Meriwether, 1985; Meriwether et al., 1986; Biondi et al., 1999; Valladares et al., 2002]. For each night, a series of zenith-direction measurements of the 630-nm line center position was used to provide the reference of zero Doppler shift. Implicit in this approach is the assumption that the vertical winds are small and therefore negligible compared with the horizontal wind speeds.
 The Fabry-Perot interferometer (FPI) used for these measurements has been described elsewhere [Biondi et al., 1985; Meriwether et al., 1986, 1997; Valladares et al., 2002]; therefore only a brief description will be presented here. The spacer gap chosen was 1 cm, corresponding to a free spectral range of 0.0198 nm. The overall finesse (ratio of order separation, 0.0198 nm, to spectral width, ∼0.0020 nm) of the instrument is ∼10 as determined by observations of the 632.8-nm line from a HeNe stabilized frequency laser. The detector was a photomultiplier (PMT) with a GaAs photocathode, and a multiple aperture exit plate was used to capture light from several orders of the Fabry-Perot interference pattern simultaneously. (Since the period of these measurements, the Arequipa FPI instrument has recently been upgraded by the replacement of the PMT with a CCD detector. This provides an estimated 15-fold gain in sensitivity, as a result of the much higher quantum efficiency of the CCD chip and the simultaneous collection of photons across the spectral profile.)
 Measurements of the 630-nm emission spectral profile were obtained by increasing or decreasing, via a volume changer, the density of argon gas in the FPI chamber quasilinearly with time (“pressure scanning”) through one interference order. The spectral data for increasing and decreasing pressure scans were analyzed separately. Successive scans were accumulated until the desired precision (∼±10 m s−1, ∼±40 K) was obtained. Typically, a measurement in one direction requires only a few minutes of signal acquisition during the period of peak airglow emission (0300–0500 UT) and perhaps as much as 20 min when the airglow intensity is weak (e.g., in the hour before morning twilight). Laser calibrations were obtained for 30 min prior to the start of the measurements and again at the end of each night. Additional calibrations were obtained during the night at intervals between the airglow measurements.
3. Data Analysis
 Considerable care was exercised to remove outliers from the individual pressure scans of the 630-nm spectral profile before summing to obtain a spectral profile to be used for subsequent analysis. These points were generated by noise spikes, which occurred at a rate of one or two for each 30-s scan and were characterized by values that exceeded those of the neighboring spectral channels by 3 to 5 standard deviations or more. These points were replaced by an average of the two neighboring spectral points. In the analysis it was important to separate the data for increasing and decreasing pressure scans and to analyze the summed spectral profiles separately. The two estimates of Doppler shift and broadening determined from these profiles were then averaged together.
 As described previously [Meriwether et al., 1986, 1997], the next step was the application of the Levinberg-Marquardt (LM) fitting algorithm described by Bevington and Robinson  to these 630-nm spectral profiles to generate analysis estimates for the Doppler line center position, the Doppler broadening, the spectral intensity, and the spectral background. This procedure represents a nonlinear least squares fitting method in which the observed 630-nm spectral profile is modeled by convoluting the FPI instrument function with an assumed Gaussian spectral profile for the 630-nm emission. Trial values of the model parameters are varied to minimize the differences between the data and the model function.
 The instrument function is determined by the 632.8-nm line profile from the HeNe frequency-stabilized laser. Owing to slightly nonuniform illumination of the full FPI aperture, the width of the instrument function is underestimated. In the present work the calculated temperatures have been reduced by 35 K to compensate for this effect, which had not been taken into account in earlier published work [Meriwether et al., 1986, 1997].
 Typically, the precision of the temperature determination found for each observing direction was ∼±35–40 K. The temperature data for all directions observed within each 30-min period during the night were averaged together, decreasing the uncertainty to ∼±10 K.
Figure 1 presents a selection of the all-sky averaged temperature data plotted against local time. Also plotted (blue curves) are the predicted nighttime temperature variations calculated from the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter 2000 empirical temperature model (MSIS) described by Picone et al. . The MSIS model curve for each night was calculated using the appropriate information required regarding F10.7 and magnetic activity indices leaving out, however, the terdiurnal harmonic prescribed by the MSIS model code. This component adds about 5 to 10 K to the values of the predicted temperatures for the midnight period and would contaminate the retrieval of the MTM peak by subtraction of the predicted variation. Nine nights are plotted, and these were chosen to characterize the results obtained for the transition from the solar minimum activity levels of 1997 to the solar maximum activity levels of 2001.
 Also drawn in this figure (in red) are curves illustrating the composite fits generated by the combination of the MSIS model predictions with a Gaussian fit to the MTM residuals and an offset representing the difference between the residual baseline and the MSIS reference curve. The MTM residual values are the differences obtained by subtracting the MSIS model values from the temperature data points. Relative to the monotonic decay of the MSIS reference curve, an enhancement occurs near or after local midnight (0500 UT) with an amplitude of 50 to 150 K and a typical duration of 3 to 4 hours. In contrast, the MSIS model shows almost no indication of an MTM, presumably as a result of averaging the many sources of its temperature data and the limited spectral resolution (up to terdiurnal) of this model [Mayr et al., 1979; Picone et al., 2002]. Moreover, the variability of the MTM appearance would make detection in these averaged results more difficult owing to smearing.
Figure 2 depicts examples of the local time variation of the residual temperatures after the subtraction of the MSIS reference curve from the data. These values were fitted to a Gaussian distribution representing the MTM together with an offset, positive or negative, to represent the baseline difference between the observed temperatures and the MSIS model. These results show that adding a Gaussian form to a continuum offset generally provides a good fit to the observed variation of the residual temperatures, which we assume is caused by the MTM phenomenon, throughout the midnight period. Consequently, for each night in our data, we have applied the same procedure to estimate the MTM local time variation and amplitude; the red lines in Figure 1 illustrate the resulting composite fit found. For a few cases, because the baseline showed a change in the background values at times before and after the MTM peak, an improved fit of the temperature variation of the MTM was obtained by using only the baseline data between 0000 and 0300 UT (1900 to 2200 LT) to estimate the offset. No MTM contribution is expected during this early evening period because the MTM is known to occur at times near local midnight during winter and equinox [Herrero and Spencer, 1982], the period covered by much of our data.
Figure 3 presents the series of mean temperatures (red points) determined by averaging the Arequipa temperature data for the hours 0000–0300 UT (1900–2200 LT) for each of the 396 nights between 1997 and 2001. This early evening period was selected to illustrate the change in “background” temperature during the transition from solar minimum to solar maximum, because the MTM is known to occur only near or after midnight [Herrero et al., 1983] during winter, and this is indeed the case for our data. Also plotted in this figure (blue points) is the predicted MSIS model temperature for each night for the same local time period. The transition from solar minimum to solar maximum is clearly evident in both the Arequipa determinations and the MSIS temperatures, with the average temperatures increasing from ∼700 K to ∼1150–1200 K. Moreover, although the Arequipa observations often show large deviations from the MSIS model, the overall trend of the observations agrees with the MSIS predictions for the transition from solar minimum to solar maximum. These results also demonstrate the large degree of variability that exists in the thermospheric temperature.
Figure 4 illustrates the MTM amplitudes (top row) and the MSIS offsets (middle row) determined from the analysis of the 5 years of data (396 nights). Also plotted (bottom row) are values for the Ap and F10.7 indices for each of the 5 years. The F10.7 solar flux intensity increased from ∼75 in the early months of 1997 to a maximum of ∼300 in mid-2000. In this figure the mean MTM amplitude for the years 1997 to 2001 is indicated by the number at the top of each panel in the top row. These yearly and monthly averages are shown in each panel by the blue line and the red dots, respectively. The annual averages were obtained from ∼75–100 nights of data per year and are, respectively, 76.1, 65.5, 53.7, 63.2, 57.5 K, indicating a slight decrease in amplitude (∼20 K) with increasing phase of the solar cycle.
 The plot of the MSIS offset values against day number (Figure 4, middle) shows no consistent pattern of variability from year to year; the different offset values, ranging from −200 K to 200 K, tend to occur in groups lasting 1 or 2 weeks above or below the baseline. The average offset over all nights in each of the 5 years, shown by a line in each panel, was ∼20, ∼20, ∼65, ∼15, and ∼25 K, respectively. Overall, the average difference between the temperature data (excluding the MTM feature) and the MSIS model is ∼20 K if the anomalous year of 1999 is not included.
 Scatterplots of the MTM amplitudes plotted against the F10.7 flux and the day number for each year and for all years combined are shown in Figures 5 and 6, respectively. Figure 5 suggests a reduction of the amplitude with the increase in the solar flux index. However, this needs to be qualified by the fact that there were only a limited number of nights obtained during the solar maximum period and this may be more of an indication of limited sampling.
Figure 7 presents the MTM amplitude histograms for each of the 5 years and for all years combined. The statistical distributions for each year are somewhat similar: a broad flat distribution with about two thirds of the amplitude values occurring between 25 and 75 K combined with a tail extending to 150 K. About 15% of MTM events have amplitudes greater than 100 K. Only ∼7% of the 396 nights have MTM amplitudes less than 20 K.
 These results show that the MTM amplitudes exhibit considerable night-to-night variability. This figure also suggests that there is no strong correlation of the changes in the range of MTM amplitudes with changes in the F10.7 flux or the Ap magnetic activity indices. Also, the monthly mean MTM amplitude (not shown) shows no consistent seasonal variation.
 The MTM amplitudes for all nights are plotted in Figure 8 in a false color format versus universal time and day number. The data for all nights with a given day number were averaged together, independent of the year. The number of nights for each day number is plotted at the top of the figure; generally 2 or 3 nights were averaged for each day number. Merging the data for all 5 years together shows the seasonal variation of the MTM occurrence and amplitude more clearly, reducing the distortion in these results that missing data introduce. With this technique there were only 8 nights missing between day numbers 100 and 300.
 Inspection of Figure 8 shows a shift of ∼2 hours in the time of the peak temperature of the MTM, from ∼5 UT for the two equinoxes to ∼7 UT for winter nights. There is an overall appearance of an arch for MTM occurrences with the arch peak coinciding with the winter solstice near day 185-day 190. Inspection of similar plots (not shown) for each of the 5 years suggests that this seasonal variation does appear in individual years but, with the numerous gaps in data coverage, this variation is less apparent. Also of interest is that this figure and Figure 6 indicate that the nights with the largest MTM amplitudes appear during equinoxes rather than in winter.
 As noted in the introduction, our results show that the MTM is clearly a distinctive feature of the low latitude thermosphere dynamics, indicating nighttime heating occurring over a period of 3 to 5 hours with a maximum amplitude typically ranging from ∼50 to ∼200 K. Our analysis of the MTM phenomenon became much easier by two steps in the processing of the data. First, the use of the MSIS model as a reference to provide a means for estimating and removing the background, i.e., the normal nighttime cooling of the thermosphere, made the MTM stand out more clearly in the temperature data. Second, the appearance of the MTM feature was much easier to identify in the temperature data once the measurement uncertainty was reduced to typical values of ∼±10 K by averaging the temperature data in all directions within each 30 minute observing cycle. We believe the averaging of the data for all five directions is justified because the MTM is a large-scale structure many thousands of kilometers in latitudinal extent [Herrero et al., 1993]. Thus averaging over five directions in the thermosphere (with observing separations of ∼400 to 800 km) is not expected to smear significantly the observed local time variation of the MTM heating.
 Several conclusions have emerged from the present studies. First, the largest MTM amplitudes seen in our data occur near the equinox rather than at the winter solstice; however, we lack any summer measurements. Herrero and Spencer  noted for the satellite data that the largest amplitudes were observed in the summer months. Second, at the height of the peak 630-nm nightglow emission, ∼240 km, there seems to be no strong dependence of the MTM amplitude on the phase of the solar cycle (while the results show that the mean annual MTM amplitude decreased from ∼75 K to ∼60 K, this reduction may not be significant since fewer nights of measurements were available for analysis in the years of 2000 and 2001). Third, there is a suggestion of a secondary maximum of the MTM amplitude near the winter solstice (Figures 6 and 8). The variability of the MTM amplitudes prevents any stronger claim than this. However, a winter solstice enhancement is consistent with the mechanism of tidal forcing creating a convergence of winds in the nighttime midnight hours. This convergence generates the compressional heating that may cause the observed rise in the nighttime thermospheric temperature. TIEGCM modeling of the MTM feature has included only the diurnal and semidiurnal tidal modes in attempts to simulate the MTM structure. However, the terdiurnal tidal mode may be important [Crary and Forbes, 1986; Fesen, 1996].
 The present results for the MTM amplitude and its seasonal variation are in agreement with the previous study at the Jicamarca Radio Observatory reported by Bamgboye and McClure , who made measurements of nighttime F-region electron temperatures in 18 months of observations from 1968 to 1969. For these conditions, the assumption is that Te = Tn. Their values for the MTM amplitudes are comparable to our results. They also noted a seasonal variation in which the peak MTM amplitude occurred later in the night for the winter solstice, consistent with our data, and earlier for the summer solstice. This last feature could not be confirmed in our data owing to the cloudy summer skies.
 The observed amplitudes of the MTM (∼50–200 K) exceed by a wide margin the result found in a TIEGCM simulation, ∼30 K, [Colerico et al., 2006] which included only the diurnal and semidiurnal tidal forcing functions at the lower boundary. This discrepancy between the simulation and our results suggests that it may be important to include the terdiurnal mode in the TIEGCM calculations. This inclusion might also contribute to the night-to-night variability observed for the MTM due to the expected variability of the tidal forcing.
 Our work has also demonstrated that the MSIS model does represent a model capable of producing accurate predictions for the equatorial thermospheric temperature provided that allowance is made for the considerable day-to-day variability of the thermosphere, which our results show may be typically 10%. The MTM is not evident in the MSIS model predictions unless the MSIS terdiurnal spectral mode (not used in our baseline calculation) is turned on. In this case, MSIS shows a very weak MTM feature of amplitude 5 to 10 K.
 It is interesting to consider why there is an absence of a strong solar cycle variation in the MTM amplitudes. Such a trend was expected as a result of a weakening of the tidal forcing function described by Fesen  that is expected to be strong at solar minimum but weaker at solar maximum. One explanation is a transition of the forcing from the tidal forcing at solar minimum to the ion-neutral coupling mechanism suggested by Mayr et al.  to be dominant at solar maximum. The increased plasma density at solar maximum should increase the importance of the coupling interaction between the EUV heating function during the day and the day-to-night variation of the F-region plasma density. At the same time, it would be expected that the penetration of the thermosphere from below by tidal waves would become more difficult at solar maximum due to increased dissipation caused by the higher plasma density.
 It is also important to consider the height dependence of both of these forcing functions. Since the FPI temperature measurements apply to the low F-region altitudes between 200 and 300 km, the lack of a strong trend in the MTM amplitudes in our observations between 1997 and 2001 may indicate that the solar cycle phase dependence of the tidal forcing is weak at these altitudes, with the expected reduction of tidal forcing at solar maximum occurring at higher altitudes. On the other hand, the ion-neutral coupling may cause increased heating at altitudes above 300 km (where the F-region density is greater) during solar maximum, but such heating would not be detected by the FPI measurements. Simultaneous measurements with the Fabry-Perot interferometer and the Jicamarca incoherent scatter radar would provide one means for investigating the height dependence of the MTM heating.
 Further work will examine the dynamical behavior of the zonal and meridional winds during the period of MTM heating when an outflow from the MTM pressure bulge is expected with an amplitude of a few m s−1 [Burnside et al., 1981]. The improved sensitivity of the Arequipa FPI recently modified with a bare CCD camera, ∼5 m s−1 and 20 K, has indeed detected the MTM modulation of the background thermospheric wind flow and also the resulting heating with the expected precision, and these will be described in a future paper.
 This work was supported by grants from the Aeronomy Program of the National Science Foundation. We are also grateful to the National Aeronautics Space Administration (NASA) Satellite Laser Ranging (SLR) Program and to the Universidad Nacional de San Agustin (UNSA) located in Arequipa, Peru for their hospitality in providing the use of the San Francisco Observatory station in Characato, Peru, for the acquisition of these measurements.
 Arthur Richmond thanks the reviewers for their assistance in evaluating the manuscript.