Rayleigh lidar measurements of stratospheric and lower mesospheric temperatures obtained at the Urbana Atmospheric Observatory (40.1°N, 88.1°W) on 17/18 November 1997 revealed large temperature inversions at altitudes between 55 to 65 km. Prior to and during a large increase (by up to about 50K) in the amplitude of the mesosphere inversion layer (MIL), a clear and persistent vertical wave structure between 30 and 65 km was observed. The wave has a vertical wavelength of about 12 km and an apparent period of about 12 hours. However, the intrinsic characteristics of the wave are uncertain due to the lack of information regarding the background wind profile and the relative direction of the wave propagation vector with respect to the background wind vector. Two different cases, corresponding to small and large background wind speeds projected onto the horizontal direction of wave propagation, are studied numerically to represent two scenarios with different intrinsic wave characteristics devised to explain the development of the MIL event observed. When the projected background wind is small, the wave is likely to be an inertial-gravity wave. It is shown that the breaking of such a wave does not produce the large heating rate observed. However, the numerical modeling shows that such an inertial-gravity wave can modulate the stability of a separate internal gravity wave, and the breaking of this internal gravity wave produces a heating rate similar to the observed rate. When the projected background wind is large, however, the observed wave could be an internal gravity wave with a large intrinsic phase speed. The analysis shows that the breaking of this wave can generate a large heating rate and a MIL that is similar to the observed event. We close with a discussion of the observational implications of these two scenarios. Possible wave sources are also discussed, and it appears that the observed MIL event might be related to a developing frontal system in the tropopause region observed just prior to the onset of the observed event.
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 After the initial discovery of its existence by Schmidlin  in the mesosphere over two decades ago, the mesospheric inversion layer (MIL) has recently drawn increasing research interest, due to the more frequent detection of the phenomenon at different locations combined with the improved lidar accuracy made possible by higher values for the power aperture product. Comprehensive reviews of the MIL literature may be consulted for further details [Meriwether and Gardner, 2000; Meriwether et al., 1998b; J. W. Meriwether and A. J. Gerrard, Middle atmosphere thermal layers: A review of mesospheric inversion layers and stratospheric temperature enhancements, submitted to Reviews of Geophysics, 2003]. Briefly, the MIL can be described as a region of the mesosphere roughly ten to fifteen km thick showing a positive temperature lapse rate for the bottom side of this layer. From the numerous observations of the MILs, several features are evident that may provide important clues to the study of its mechanism. First, the temperature lapse rates immediately above MILs are usually close to the dry adiabatic lapse rate, indicative of turbulence mixing [Whiteway et al., 1995]. Second, the MILs have been observed in all seasons and for latitudes from the equator up to 65°N [e.g., Dao et al., 1995; Leblanc et al., 1999a, 1999b; Cutler et al., 2001], though the detailed features with respect to the altitude range and sighting frequency of the MILs may differ. Third, some MILs show downward phase progression with a phase speed similar to that of tides [e.g., Dao et al., 1995; Meriwether et al., 1998a]. On the basis of these observational clues, a process of tidal modulation of gravity wave stability has been proposed as a possible mechanism responsible for the formation of the MILs [Liu and Hagan, 1998]. Recent radar and lidar measurements made simultaneously reported by Sica et al.  suggest modulation of the inversion layers by tidal variation might be significant. The observed relationship between MIL events and changes in the kinetic energy density of the gravity wave vertical wave number spectrum provides further evidence supporting the mechanism of MIL formation due to gravity waves interacting with the tidal structure. Furthermore, the seasonal variation of the mean state and the tidal structure may lead to the different seasonal characteristics of the MILs observed [Liu et al., 2000]. There are, however, two unanswered questions in these two studies: how can the MILs at lower mesosphere altitudes where tidal amplitudes are small be related to the tidal wave modulation of temperature, and is it possible to connect MILs to lower atmospheric sources of the gravity wave(s)?
 An opportunity to explore these two questions was provided by the observations of an event featuring a large temperature increase that developed quickly leading to the appearance of a strong MIL located between 55 and 65 km. This MIL event was observed by a dual Rayleigh temperature and sodium resonance temperature lidar system operating from the Urbana Atmospheric Observatory (40.1°N, 88.1°W) on the night of 17 November 1997 so observations regarding the temperature structure were obtained over almost the entire range of 30 to 105 km. Details regarding the dual lidar instrument and these observations are provided by Meriwether et al. [1998b]. This event is analyzed in detail in this study in an effort to determine, at least qualitatively, the possible mechanism for the rapid large temperature change observed during the formation of the MIL. Possible wave sources are also discussed through analysis of the National Center for Environmental Protection (NCEP) data [Randel, 1992] for the same time period. In section 2, the wave characteristics and possible wave sources are analyzed. In section 3, two different scenarios are studied through numerical simulations and the simulation results are synthesized for comparison with the observations. A discussion of these results and a summary of our conclusions are presented in section 4.
2. Wave Characteristics and Possible Sources
2.1. Temperature From the Sodium and Rayleigh Lidar Systems
Figure 1 presents a comparison of the MSIS-90 model profile with both the nightly mean average, panel a, and also the hourly sequence, panel b, of Rayleigh and sodium lidar temperature profiles plotted as a function of local time and altitude during the night of 17/18 November 1997 [Meriwether et al., 1998b]. The mean temperature profile was determined from the analysis of relative density profiles averaged over the period from 21.2 LT to 07.1 LT. Each relative density profile was calculated from each 3 minute lidar photocount profile by first removing the background continuum estimated from the lidar returns observed from the altitude range of 115 to 125 km and then correcting for the dependence of the lidar signal upon the square of the range.
 The improved quality of the signal represented by the averaging of lidar returns over ten hours meant that there was a significant overlap between the lower end of the averaged sodium temperature profile and the upper end of the Rayleigh mean relative density profile (Figure 1a). Consequently, the starting temperature, T0, required for the Rayleigh temperature retrieval analysis [Gardner, 1989] can be selected from the sodium results rather than resorting to the use of a value based upon the MSIS-90 temperature profile calculated from the model [Hedin, 1991] for the nightly mean temperatures. The starting altitude chosen for this retrieval analysis was that altitude for which the ratio of noise to signal was 5%, which was ∼82 km. For some of the hourly mean temperatures, on the other hand, there are gaps between the sodium and Rayleigh profiles (Figure 1b). Selection of a temperature profile from a model such as the MSIS-90 will still be necessary to estimate the starting temperature for the Rayleigh retrieval. However, as the mean temperature profile in Figure 1a shows, the temperatures in the altitude range between 70 to 80 km are typically 10 to 15°K above the MSIS profile. Consequently, the starting temperatures used for the hourly averaged Rayleigh temperature profiles were adjusted by setting T0 to the MSIS model value plus 15K. Again, the starting altitude for the hourly temperature retrievals was determined by the same criterion of selecting the altitude for which the ratio of noise to signal is 5%, which was 75 km for the first hour and 72 km for later times. The reduction in the altitude chosen was a consequence of a slightly lower laser power and a slight decrease in atmospheric transmission due to haziness. This procedure of using the sodium temperature results minimizes the systematic error in the Rayleigh temperature profile that might appear in the top end of the altitude range caused by the lack of knowledge as to the correct value of T0 in the analysis. The relative density profile data for each one hour of observations obtained at 45 m vertical resolution were averaged over varying height intervals ranging from 1.0 km for 30 km to 45 km, 1.5 km for 45 to 55 km, 2.0 km for 55 to 65 km, and 3.0 km for altitudes above 65 km. The temperature profile is then derived from the relative density profile following the procedures prescribed by Gardner . The error in temperature is less than 2 K below 65 km and increases up to ±8°K above.
 The temperature perturbations were determined by calculating the differences of each density profile relative to the mean nightly average profile, ρ′ = ρ − . To reduce the effects of variations caused by noise, these relative density profiles (after normalization by the nightly averaged density profile) were filtered with a two dimensional digital filter using a temporal interval of 30 minutes and an altitude width of 2 km. Using the relation, ρ′/ = −T′/, the temperature fluctuation profile was then determined. A color shade plot of the computed Rayleigh temperature perturbation profiles is shown in Figure 2.
2.2. Estimates of Wave Characteristics
 The most striking features of the temperature perturbation field in Figure 2 are, first, the wave structure between 30 and 70 km that persists throughout much of the observation period from ∼2100 LT to 0700 LT; and Second, the extremely large temperature increase (about 10–20 K h−1) starting from 02 hour at about 65 km. We will try to understand these two features and their possible relationship.
 Examination of the plot of the Rayleigh temperature perturbations shows that the dominant vertical wavelength of the wave is ∼12 km. Furthermore, its apparent vertical phase speed is about 1 km h−1 (as indicated by the lines with slope of −1 km h−1 in Figure 2). However, to determine the wave intrinsic characteristics it is necessary to know the horizontal direction of the wave propagation and the background wind, which were not measured. We are able, however, to use the wind obtained from a November case computed by the Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (TIME-GCM) [Roble and Ridley, 1994] to estimate the intrinsic characteristics and study their implications by considering two different scenarios: when the Doppler shift due to the background wind is small and when it is large.
 If we assume the background wind shear is not very large, the gravity wave dispersion relation with the Earth rotation considered can be written as [e.g., Andrews et al., 1987]
where k and m are horizontal and vertical wave numbers, respectively; ωa is the apparent wave frequency; U is the wind velocity projected onto the direction of the horizontal wave vector; f and N are inertial and Brunt-Väisälä frequencies, respectively; and H is the pressure scale height of the background atmosphere. With the observed vertical wavelength being ∼12 km and a mean scale height of about 7 km, m ≫ 1/(2H) and hence, the last term in the this equation can be ignored. With equation 1 and this assumption, the horizontal wave number can be written as a function of U with m and ωa derived from the observation, i.e.,
and the intrinsic frequency ωi = ωa − kU can be deduced from k and U. Figures 3a and 3b show the dependence of the intrinsic period and the wavelength on the assumed projected background wind U corresponding to the branch of the solution with larger wave numbers and higher frequencies. For U < N/m ≃ 42 ms−1, the horizontal wave propagation is in the “negative” direction relative to the wind and the ground. Therefore both the intrinsic and apparent vertical phase progression of the wave are downward. For U > N/m ≃ 42 ms−1, on the other hand, the horizontal wave propagation is in the negative direction relative to the wind but in the same direction as the wind to a ground observer and the apparent vertical phase progression is upward, contrary to the observations. Therefore the projected background wind should be less than 42 ms−1. With 0 ≤ U < N/m, the possible values for the derived horizontal wavelengths and for the periods range from 2300 km (close to the Rossby radius of deformation /f ≈ 2800 km) to nearly 0, and from the inertial period to nearly 0, respectively. This suggests that the observed wave could be an inertial-gravity wave if the projected background wind is small or an internal gravity wave (ωi ≫ f) if the projected background wind is large. The other branch of the solution yielding possible wavelengths ranging from 2500 to 8000 km corresponds to the case where the wave vector and the projected wind are in the same direction and thus the vertical phase progression is upward. It is not consistent with the downward trend seen in the observation and thus, this branch is not considered further here.
Figures 4a and 4b show the November mean zonal wind and temperature, respectively, at 40°N calculated from TIME-GCM. It should be noted that this TIME-GCM run was driven by the 1993 NCEP analysis data at its lower boundary, and the profiles are used here to represent the November wind and temperature structures. The meridional wind is less than 5 ms−1 between 30 and 50 km, so the wind projected toward any particular horizontal direction ranges from several meters per second to about 70 ms−1. It is necessary, however, that the projected background wind U used for estimating the intrinsic wave characteristics should be less than about 42 ms−1 as previously indicated. The two scenarios we would consider, therefore, correspond to (1) when the wave propagates more in the meridional direction and the Doppler shift of the wave is small (more to the left side in Figures 3a and 3b) and (2) when the wave propagates more to the westward direction and the Doppler shift is large (more to the right side in Figures 3a and 3b) with U less than 42 ms−1).
 The amplitudes of the observed temperature perturbations vary quite significantly with altitude and with time, especially at higher altitudes. By applying a low-pass filter in the vertical direction, it is found that the peak-to-peak amplitude of the wave at 35–40 km is about 8°K. Between 50–55 km and before the large temperature increase at about 02 LT, the peak-to-peak amplitude varies between 12 and 20°K. Theoretically, the amplitude of a fully developed gravity wave will grow by a factor of about 2.9 over an altitude range of 15 km assuming an isothermal background with a scale height of 7 km. The actual growth rate factor observed is about 1.5 to 2.5 and therefore smaller than but quite close to the theoretical value.
 With the given temperature profile (Figure 4), the atmosphere is approximately isothermal (lapse rate 0°Kkm−1) around 55 km and has a lapse rate of about −2.3°Kkm−1 between 60 and 70 km. When a wave is present, the minimum total lapse rate will be less than the dry adiabatic value if the wave perturbation is larger than 19°K at ∼55 km or 14°K between 60–70 km assuming a vertical wavelength of 12 km. The amplitudes required between 60–70 km would be smaller if the atmosphere temperature is already in a state (preconditioned) with nearly neutral stability as seen in some of the observations. Analysis of the temperature perturbation above shows that the wave amplitude between 50–55 km is about 6–10°K (half of the peak-to-peak values). This perturbation is not large enough to cause wave breaking at 55 km. However, with its projected exponential growth with altitude and the preconditioning, the wave may become unstable between 60–70 km as suggested by Figure 2 (see also next section).
2.3. Possible Wave Source
 The NCEP data were used to search for a possible wave source during the observational period. According to Koch and Dorian , the Lagrangian Rossby number is given by Ro = ∣Va/V∣, where V is the total horizontal wind speed and Va the ageostrophic horizontal wind speed. This parameter can be used along with the total wind itself as a measure of ageostrophy and thus be used to assess the strength of the geostrophic adjustment process and the consequent generation of gravity waves. Figure 5 shows the Lagrangian Rossby number (>0.5, solid line contours), geopotential height (in km), and wind vector (with latitude and viewing scaling factors) on 250 hPa pressure level (∼10 km) for 16, 17, 18, and 19 November 1997. We note the time for these plots were 00 UT so the local time at the observation site (40.1°N, 88.1°W) is about 1800 LT on 15, 16, 17, and 18 November.
 It is seen that pockets of high Lagrangian Rossby number progress eastward at the midlatitudes during this period, consistent with the development of frontal systems as can be seen from the plot geopotential height. Specifically, a pocket with large Ro is seen between 110–100°W and 40–50°N near a pressure ridge at 1800 LT of the 15th. It drops below 0.5 at the same time on the 16th due to the weakening of the ridge, but is seen again with larger Ro values and strong wind between 105–95°W and 35–45°N on the 17th and further down stream between 90–80°W on the 18th. On the latter two days, this high Ro pocket is located near a pressure trough. Strong adjustment processes might occur and gravity waves could be generated within this region. The inertial-gravity waves generated from the adjustment will propagate downwind of the jet stream, as demonstrated by O'Sullivan and Dunkerton . It is thus possible that the observed wave originates from the high Ro pocket located up stream of the jet.
3. Analysis of the Two Scenarios
Figure 6 shows the hourly mean temperature profiles at local times of 2230 to 0230. To demonstrate the temperature changes clearly, temperature profiles of two consecutive hours are plotted together. At 2230 LT and 2330 LT, the temperature profiles are similar with the atmosphere being nearly isothermal between 50 and 65 km. Above 67 km, the temperature lapse rate is close to or even smaller then the dry adiabatic lapse rate, though the temperature values show there is significant degree of variability. Part of this is probably due to the increasing noise of the measurement above 65 km. From 2330 to 0030 LT, the temperature around 63 km increases by about 10°K and the lapse rate above is about equal to the dry adiabatic lapse rate. The temperature at 0130 LT is similar to that at 0030 LT below 63 km with the range of temperature variability of about 5°K or less. However, the lapse rate between 63 and 66 km at 0130 LT becomes smaller than the dry adiabatic lapse rate. This is followed by a large temperature change at 0230 with heating of about 20°K at 62 km and cooling of near 20°K at 68 km and 15°K at 56 km. The lapse rate between 62 and 68 km is again approximately equal to the dry adiabatic lapse rate. In fact, the lapse rate is close to the dry adiabatic lapse rate throughout the observation period of 2200 and 0600 LT at varying altitudes between 60 and 70 km, with intermittent episodes of large temperature changes (the largest being the one at 0230 LT). Therefore the lapse rate with values almost persistently close to neutral static stability preconditions the atmosphere between 60 and 70 km as a “surf zone” so that waves in that region are more likely to break due to convective instability. The intermittent large temperature changes may be a manifestation of the breaking of sporadic waves.
 In this section, we will analyze the two scenarios mentioned in the previous section and investigate how they may be related to the observations, especially the significant temperature change at 0230 LT. A numerical model will be used for this analysis. Details of the model can be found in the work of Liu et al.  and a brief overview is given here. The model solves the two dimensional, nonlinear Navier-Stokes equations in a nonrotational system. A turbulence model is used for its closure and a time varying wind and temperature can be imposed as its background. For this study, the vertical range of the model is from 20 to 85 km with the top 15 km as the wave absorbing layer, and the horizontal range is one horizontal wavelength. The background wind and temperature are taken from the TIME-GCM November simulation as mentioned above, and the diurnal tides are taken from the same simulation. As shown in Figure 4, the temperature profile used in the numerical simulation is stable. Therefore the analysis will focus more on the onset of the instability in an originally stable atmosphere. Wave breaking in an environment preconditioned to neutral or negative stability by previous wave breaking has been discussed in the work of Liu et al. . It should be pointed out, though, that no relaxation process (e.g., radiative) on the mean wind or temperature was considered in these numerical experiments.
3.1. Inertial-Gravity Wave
 The heating rate in a region where an internal gravity wave breaks due to convective instability, with wave and turbulent heat flux and dissipative heating considered, is found to be [Liu, 2000]
with linear saturation assumptions [Lindzen, 1981], where κ = R/cp with R as the gas constant for dry air and cp the specific heat of dry air under constant pressure, Prt is the turbulence Prandtl number, η is the turbulence localization measure [Fritts and Dunkerton, 1985], zb the altitude of wave breaking, and is the mean eddy diffusion coefficient. Below the breaking region the convergence of heat flux causes heating
where λz is the vertical wavelength. These equations are used here to estimate the heating rate near a region where the inertial-gravity wave breaks due to convective instability. For the case of a small projected background wind, say U = 20 ms−1, k can be found to be 2π/1110 km−1 from Figure 3 with intrinsic frequency of 2π/6.9 h−1. The eddy diffusion coefficient given by Lindzen  is then ∼150 m2s−1. By assuming Prt = 1 and η = 0.2, it can be calculated from equations (3) and (4) that the cooling rate in the breaking region is about 0.5°Kh−1. The heating rate below the wave breaking region is about 1.6 Kh−1, which are much smaller than that derived from the observed temperature change between 0100 LT and 0200 LT. Therefore even if the inertial-gravity wave grows to an amplitude large enough to cause wave breaking, the associated heating rate is not large enough to account for the observed value. This is also confirmed by numerical experiments done with an internal gravity wave with low intrinsic frequency and large horizontal wavelength. It is an internal gravity wave because the numerical model is a two dimensional model without Coriolis force included. The details of the model is given in the work of Liu et al. .
 Even though the breaking of the long period wave itself can not produce heating rate as large as the observed value, it may modulate the stability of internal gravity waves in a fashion similar to the modulation of internal waves by diurnal tides [Liu and Hagan, 1998; Liu et al., 2000]. The internal waves with large horizontal wave number and large intrinsic phase speed can generate strong turbulent mixing and therefore a large and heating rate.
 The numerical experiment conducted to test this possibility is similar to that described by Liu et al. , except that a background temperature modulation due to the inertial-gravity wave is considered in addition to tides. The diurnal tidal amplitudes of wind and temperature are relatively small below 70 km (the tidal wind is less than 5 ms−1 and the tidal temperature perturbation is less than 3°K) as shown in Figure 7. The tidal results are again taken from the same TIME-GCM run for November. Because of the large variations of temperature amplitude of the wave at higher altitudes, the modulating “inertial-gravity wave” in the numerical model is assumed to have a constant amplitude of about 5°K and a phase progression similar to the observation to simplify the analysis and to demonstrate the mechanism. The wind perturbation related to the modulating inertial-gravity wave is not considered either (thus the inertial-gravity wave only modulate the static stability of the mean flow). We quite arbitrarily choose the internal gravity wave characteristics with horizontal wavelength of 100 km, wave period of 2860 s, and a vertical wind perturbation at 20 km altitude of 0.29 ms−1 (corresponding to ∼1.3°K temperature perturbation). The vertical wavelength of this wave is about 10 km and its breaking amplitude would be at about 65 km in a windless and isothermal atmosphere. The wave is launched from 20 km at 2300 LT and ramps up to a constant amplitude after one wave period.
 The numerical model shows that between 60–70 km this internal gravity wave becomes unstable about 4 hours after the simulation starts (it already begins to break at higher altitudes before this). The breaking also occurs later between 40–60 km, below the breaking altitude for this wave if no modulating “inertial-gravity wave” is present. The wave breaking causes large changes in the temperature, as shown in Figure 8. The temperature perturbation field in this figure has been averaged over an hour to provide results that are similar to the processing of the observational data as in Figure 2. Large temperature changes occur after about 0300 LT not only around 60 km but also between 40–50 km. Near the end of the simulation, the temperature increase is about 25°K and 15°K at 55 km and 45 km, respectively, and the temperature decrease is about 15°K at 50 km. This plot shows the temperature structure change in qualitative agreement with the observation (Figure 2), though the amplitude may not be as large.
Figure 9 shows the modeled temperature profiles at 0300, 0400, and 0500 LT (dotted, solid, and dash lines, respectively). The temperature near 60 km increases by about 10°K from 0230 to 0330 and more than 5°K from 0330 to 0430, and the temperature decreases by similar amount above. As a result, the lapse rate around 60 km is approximately equal to the dry adiabatic lapse rate suggesting turbulent mixing after wave breaking. These characteristics are similar to those of the observed temperature changes shown in Figure 6, though the heating rate derived from the observed temperature change is larger and the exact time and altitude of its occurrence are different from the simulation. These could be related to the very small lapse rate as shown in Figure 6. According to linear saturation theory [Lindzen, 1981] and equations (3) and (4) the heating rates are inversely proportional to N, therefore the heating rates associated with the observed temperature profile may be larger. Factors that have been ignored or not known concerning both the background state and the wave characteristics may also contribute to the differences.
 The mean heating rate at 0330 LT is shown in Figure 10. The peak heating rate at 60 km is about 20°Kh−1 and the cooling rate aloft is 20–30°Kh−1. Both the wave heat flux divergence and turbulence heat flux divergence are large in the wave breaking region while dissipative heating is relatively small, as found in previous studies. These values also agree with the heating rates given by equations (3) and (4). According to linear saturation theory, the eddy diffusion coefficient due to the breaking of the aforementioned internal gravity wave is about 2600 m2s−1 (assuming N = 0.022s−1). With the temperature modulation by the assumed inertial-gravity wave, it can be found that N varies between 0.019 to 0.024 s−1. The corresponding are 3800 and 1975 m2s−1. Using the former to estimate the cooling rate near 65 km (where the lapse rate is small) and the latter for the heating rate near 60 km, and assuming Prt = 1 and η = 0 (uniform modulation by the large-scale waves lead to a more uniform turbulence density in the horizontal direction), the rates of cooling and heating are about 18°Kh−1 and 33°Kh−1, respectively. The actual hourly mean temperature change in Figure 9 is smaller probably due to the cancellation of heating and cooling caused by the downward progression of the breaking level.
 One question arising from this scenario is that the analysis of the observations has not produced clear evidence of a coherent internal gravity wave signature in time or in the vertical direction. It is possible, though, that the internal wave is a wave packet with relatively large horizontal phase speed so that it passed the viewing range of the lidar facility within a relatively short period of time and the temporal structure of the wave is partly or completely integrated out in the data. The mean temperature change will still be observable and the downward progression of such an MIL event will be mostly at the very beginning of its formation and will remain at the same altitude afterward [Liu et al., 2000].
3.2. Internal Gravity Wave
 Now consider the case with a large projected background wind. Let U, the horizontal wind projected onto the wave direction, be 40 ms−1. Then from Figure 3 and its corresponding equations the intrinsic period is determined to ∼2380 s for the horizontal wavelength of 100 km, and the corresponding intrinsic phase speed is ∼42 ms−1. The relative phase speed of the wave with respect to the ground is thus quite small, about 2 ms−1, and within the observation time of about 7 hours the phase front only moves by about 50 km relative to the ground, only half of the horizontal wavelength. Therefore, even though the observed event lasted for a relatively long time, the horizontal extent of the wave does not need to be very large.
 The setup of the numerical experiment is similar to the one as previously described, though no background modulation by tides or inertial-gravity wave is present. The reference frame moves in the “positive” direction with respect to the ground with speed of 40 ms−1 speed. The amplitude of the vertical wind perturbation at the lower boundary at 20 km is set to about 0.2 ms−1 so that its breaking altitude is at ∼65 km in windless and isothermal atmosphere. It should be noted that when comparing with the observations, the sampling of the numerical results should consider the change of the reference frame.
Figure 11 is the hourly mean temperature perturbation field from the numerical simulation in the same format as Figure 8 and sampled in the reference frame fixed to the ground. The vertical wavelength, phase speed, and the wave amplitude are similar to those shown in Figure 2. The wave becomes unstable about 3 hours after the simulation begins at ∼65 km, and the temperature profile changes significantly. Figure 12 shows the hourly mean temperature profiles at two local times of 0200 LT (dotted) and 0300 LT (solid). The temperature increases by about 15°K at ∼64 km and decreases above 67 km. The lapse rate between 64 and 72 km at 0300 LT is approximately equal to the dry adiabatic lapse rate. The temperature changes are similar to those shown in Figure 6d.
 The mean heating rate averaged over one horizontal wavelength after wave breaking is shown in Figure 13. The peak heating and cooling rates are ∼9°Kh−1 near 63 km and 7°Kh−1 at 66 km, respectively. These values agree with the rates given by equations (3) and (4) but are smaller compared with the actual temperature changes as shown in Figure 12. This difference is caused by the nonuniform structure of the wave stability and the associated heating. Over one vertical wavelength, there is a phase where the vertical gradient of the temperature perturbation is negative and a phase where the gradient is positive. The wave breaking occurs mainly in the former phase while the latter one is stable [Fritts and Dunkerton, 1985]. The heating and cooling rates shown in Figure 13 and also those calculated in equations (3) and (4) are mean values averaged over one horizontal wavelength. On the other hand, what is shown in Figure 12 reflects a temperature sampling that is almost “phase locked,” with the wave moving by only ∼7 km within an hour compared with its 100 km horizontal wavelength. This is illustrated by the schematic plot in Figure 14, where the shaded column indicates the horizontal spatial range over which the one hour mean is taken. Therefore the rate of temperature change averaged over the shaded region should be larger than that obtained from the mean value taken over one wavelength λx which includes both stable and unstable regions.
 By comparing Figure 13 with Figure 10, it is also evident that the mean heating/cooling rate averaged over one wavelength is smaller for the internal gravity wave case. This is mainly due to the background modulation by the inertial-gravity wave in the previous case. Because of the stability modulation, the Brunt-Väisälä frequency N is modified as previously discussed. Furthermore, the horizontal turbulence density is more uniform and the localization measure η is much smaller in the breaking region with the background modulation included.
 We have found that with both scenarios, namely one for which the Doppler effect by the background wind is small and conversely, one for which this effect is large, temperature changes similar in magnitude to the observation can be reproduced from the numerical experiments, but with mechanisms that are considerably different. With the former scenario, the observed wave would be an inertial-gravity wave. However, even if this wave could break, the induced temperature change is much smaller than the observed value. On the other hand, the inertial-gravity wave can modulate the stability of an assumed internal gravity wave or wave packet and the consequent internal gravity wave breaking can produce the large temperature changes observed. With the latter scenario, the observed wave should be an internal gravity wave but with a very small apparent phase speed. The breaking of this wave can produce apparent heating/cooling rates comparable to the observed value. Therefore this study shows that both mechanisms are capable of producing large temperature changes that appear as MIL events while driving the lapse rate to the dry adiabatic value. Specific to this measurement, it is difficult to determine which gives a better explanation to the observation solely from the current data or the modeling results. The ambiguity comes from the lack of knowledge of the background wind velocity as well as the direction of the wave propagation. For the upper mesosphere, this problem could be solved with data derived from simultaneous lidar or radar wind and all sky airglow imaging measurements [e.g., Collins et al., 1997; Huang et al., 1998]. For the lower mesosphere, this issue may be addressed with data derived from simultaneous Rayleigh wind and temperature measurements. Such measurements can be achieved for the region of the lower MIL between 60 to 80 km but would require a narrowband laser transmitter and a high resolution detector such as the Fabry-Perot interferometer [e.g., Nardell and Hays, 2001].
 It should be noted that the approximate 12 hour period of the wave may also suggest the possibility of a semidiurnal tide. Its amplitude, however, is much larger than the semidiurnal tidal amplitude calculated from the Global Scale Wave Model (GSWM) [Hagan et al., 1999] at these altitudes. Furthermore, if it is a migrating semidiurnal tide, the ∼12 km vertical wavelength would suggest a very high order mode which would be vulnerable to severe damping. The possibility of a nonmigrating semidiurnal tide should be investigated elsewhere, but it will not affect our discussion of the modulation of the internal gravity waves by large-scale waves. Owing to their global nature, the possibility of tidal waves may be further investigated in future studies by comparing observations at different sites.
 Recently, numerical experiments conducted by Sassi et al.  using the NCAR Whole Atmosphere Community Climate Model (WACCM) demonstrated convincingly that the interaction between planetary wave and mesospheric surf zone in the winter hemisphere can produce temperature inversion layer peaking near 80–85 km at a certain phase of the planetary wave. However, this mechanism may not apply to the type of MIL events studied here which (1) are transient and in some cases have downward vertical phase progression, (2) have lapse rate near or less than the dry adiabatic value above the MIL temperature maximum, and (3) have peaks between 60–70 km.
 As mentioned earlier, the numerical simulations are intended to study the formation of the MIL and the negative vertical temperature gradient that is close to the dry adiabatic value. On the other hand, the presence of the dry adiabatic lapse rate at certain altitudes between 60 and 70 km throughout the observational period with intermittent large temperature changes may indicate recurring wave breaking events in the region. The adjustment process of the unbalanced flow associated with the frontal system at the lower atmosphere is probably the source of these waves. This interesting prospect will be further investigated in future studies.
 The authors thank Ray Roble for providing the TIME-GCM output. We also acknowledge the comments by four anonymous reviewers. HLL wants to thank Maura Hagan, Jens Oberheide, Dorothy Gibson-Wilde, and Biff Williams for helpful discussions. HLL is supported in part by the NASA Sun Earth Connection Theory Program. JWM is pleased to acknowledge the support that he received from Chet Gardner and Bob States at the University of Illinois Electro-Optics Systems Laboratory for the acquisition of the measurements reported in this paper. His work was supported by a grant from the National Science Foundation CEDAR program, ATM-98-73179. The UIUC lidar is supported by the National Science Foundation. The National Center for Atmospheric Research is sponsored by National Science Foundation.