An eastward propagating two-day wave: Evidence for nonlinear planetary wave and tidal coupling in the mesosphere and lower thermosphere



[1] Temperature observations from the SABER instrument on the TIMED spacecraft are used to investigate the structure and evolution of an eastward propagating zonal wavenumber 2 disturbance with a period near two days. This oscillation obtains a maximum amplitude of nearly 10 K in the southern hemisphere mid-latitudes during late January. The timing and location of this planetary wave is coincident with the regular quasi two-day wave intensification that occurs annually in late January. The period, wavenumber and spatial structure of the eastward propagating two-day wave are consistent with a wave that results from a nonlinear interaction between the quasi two-day wave and the migrating diurnal tide. The existence of an eastward propagating wave with a period near two days coincident with the westward propagating two day wave will have an impact on the interpretation of ground based observations. Analysis of the SABER temperature observations are utilized to determine the structure and evolution of both this eastward propagating two-day wave and the classic westward propagating zonal wavenumber 3 quasi two-day wave during January 2005.

1. Introduction

[2] The quasi-two day wave is a dominant feature of the mid and low latitude mesosphere and lower-thermosphere shortly following the solstices. While it is observed in both the northern and southern hemispheres, the southern hemisphere enhancement in late January is more robust and repeatable than the northern hemisphere enhancement, which occurs sometime between July and August and may also occur at multiple times during the northern hemisphere summer. The southern hemisphere manifestation of the quasi two-day wave typically maximizes in late January with peak meridional wind amplitudes in excess of 50 ms−1 and peak temperature perturbations nearing 15 K. These wind and temperature perturbations maximize in the upper mesosphere at mid and low southern hemisphere latitudes. More details on observations related to the quasi two-day wave can be found in work by Palo and Avery [1995, 1996] and Wu et al. [1993], and references therein.

[3] Both linearized mechanistic [Hagan, 1996] and global circulation models [Norton and Thuburn, 1997; Palo et al., 1998, 1999; Garcia et al., 2005] have been able to reproduce the significant features of the quasi two-day wave. Based upon these results in addition to the theoretical work of Salby and Callaghan [2001, 2003], a robust theory for the source and evolution of the quasi two-day wave exists. It appears that the quasi two-day wave is excited by an instability in the background zonal mean zonal winds. This instability gives rise to a range of westward propagating waves with similar phase speeds. One such wave has a period close to two days and a zonal wavenumber 3. However the atmosphere also has a quasi-resonance, the so-called (3,0) Rossby-gravity mode, near this frequency and wavenumber, which can be easily excited. As a result the period and growth rate of the quasi two-day wave are controlled by the instability, but its spatial structure is largely defined by the normal mode response of the atmosphere. Therefore the wave period, event onset, magnitude and duration of a two-day wave event may vary annually but the vertical and latitudinal structure remains relatively unchanged from year to year.

[4] Because the quasi two-day wave achieves significant amplitudes it has been postulated that it may interact non-linearly with other large-scale waves present in the atmosphere. Palo et al. [1998, 1999] used a global circulation model to show that the quasi two-day wave could interact nonlinearly with both the migrating diurnal and semidiurnal tides, creating a host of secondary and tertiary waves. One of the waves generated in this simulation was an eastward propagating quasi-two day wave with zonal wavenumber 2. In these simulations where only the lower boundary of the model was modified to include a quasi two-day perturbation, Palo et al. [1999] were able to show a cascade of nonlinear interactions between the migrating tides and the quasi two-day wave. Until now, the existence of this wave has not been confirmed observationally. This is because it either requires coordinated measurements from multiple ground-based observatories to separate the different wave components, or both day and night satellite observations are required to resolve potential numerical aliasing issues.

[5] In this paper we present temperature measurements from the SABER instrument on board the TIMED spacecraft that definitively show the existence of an eastward propagating wavenumber 2 quasi two-day wave simultaneously with a westward propagating wavenumber 3 quasi two-day wave during January and February 2005.

2. SABER Measurements

[6] SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) is a limb viewing infrared radiometer that measures the thermal structure and composition of the atmosphere from the upper troposphere (10 km) into the lower thermosphere (120 km). SABER is located on the cold side of the NASA TIMED (Thermosphere Ionosphere Mesosphere Energetics and Dynamics) spacecraft and can view from 52° latitude in one hemisphere to 83° latitude in the other [Remsberg et al., 2003]. Temperature and composition measurements are inferred from infrared radiation measured in the 1.27 μm to 17 μm spectral range. During the observational period from January 5th to February 9th, 2005 SABER was viewing from 52°S to 83°N latitude.

[7] The data utilized for the analysis presented herein are version 1.06, which includes non-LTE temperature inversions in the upper mesosphere and lower-thermosphere [Mertens et al., 2001, 2006]. Due to the departure from LTE in the vibration-rotation bands of the CO2 molecule observed by SABER for temperature determination, accurate accounting for non-LTE is essential throughout the mesosphere. The SABER algorithms accurately include the effects of non-LTE in order to retrieve the kinetic temperature as a function of altitude throughout the mesosphere and lower thermosphere. These temperatures are blended with stratospheric and upper tropospheric temperature profiles retrieved under the assumption of LTE.

3. Results

[8] The SABER observations were analyzed using both the asynoptic Fourier transform [Salby, 1982a, 1982b] and a two-dimensional linear least-squares fit to time and longitude for each altitude and latitude independently. The results of the asynoptic Fourier transform are shown in Figure 1 and clearly indicate the presence of eastward and westward propagating waves with zonal wavenumbers of 2 and 3 respectively near a period of two-days. This spectrum was computed using both ascending and descending node SABER data for latitudes between 42°S and 46°S and altitudes ranging from 78 to 82 km over the time interval January 22nd to 29th, 2005. The dominant spectral component is the classical two-day wave with a period of 51 hours (0.47 cycles/day) and a zonal wavenumber three (westward). This manifestation of the quasi two-day wave has a period slightly longer than two-days, which is not uncommon [Harris, 1994], and this is believed to be related to the structure of the background zonal mean zonal winds [Salby and Callaghan, 2001, 2003]. A secondary component can also be seen in the spectra with a period of 44 hours (0.54 cycles/day) and a zonal wavenumber two (eastward). We estimate these peaks to be statistically significant at the α = 0.023 level (100 * (1 − α)% = 97.7%) for the eastward component and α < 10−7 (100 * (1 − α)% > 99.99%) for the westward component. These significance levels are based on the assumption that the power spectrum can be modeled as a Chi-square process with 2 degrees of freedom. Numerical simulations (not shown) indicate this is a reasonable approximation.

Figure 1.

Frequency-wavenumber spectrum of the SABER temperature observations between 42° and 45°S latitude, 78 and 82 km from January 22nd to January 29th, 2005. A dominant peak occurs at 0.43 cpd (2.17 days) propagating westward with zonal wavenumber three (s = −3) and a secondary peak at 0.56 cpd (1.85 days) propagating eastward with a zonal wavenumber two (s = +2).

[9] Theory [Teitelbaum and Vial, 1991] predicts that if two waves interact nonlinearly the result will be a combination of the parent and child waves where energy from the parent waves are transferred to the child waves. Additionally, there is a specific relationship between the parent and child waves such that (fc1, sc1) = (fp1 + fp2, sp1 + sp2) and (fc2, sc2) = (fp1fp2, sp1sp2), while f and s denote frequency and wavenumber where s < 0 indicates a westward propagating wave and s > 0 an eastward propagating wave. The subscript p and c indicate parent and child waves while the subscripts 1 and 2 represent the 1st and 2nd waves respectively. Notice that there are two waves interacting and two new waves are created. This is similar to the process of mixing or amplitude modulation. If the quasi two-day wave (f = 0.47, s = −3) is interacting with the migrating diurnal tide (f = 1.0, s = −1) then the expected child waves should appear at (f = 1.47, s = −4) and (f = 0.53, s = +2). Notice the difference component is almost identical in frequency and wavenumber to the secondary peak observed in the spectra (Figure 1) and is likely the result of a nonlinear interaction between the westward propagating quasi two-day wave and the migrating diurnal tide as described above. The second child wave at a period near 16 hours was shown to be significant in the TIME-GCM results [Palo et al., 1999], however it falls outside of the Nyqusit sampling limit for the satellite observations and cannot be unambiguously resolved from the SABER observations.

[10] The temporal evolution of both the westward and eastward propagating two day-waves are shown in Figure 2. The top plots show the structure of the westward (left plot) and eastward (right plot) propagating wave components as a function of time and latitude at 80 km. The bottom plots show the same two components over the same time interval but as a function of altitude at 40°S. All of these results were determined by fitting the two observed wave components using both the ascending and descending node SABER observations for a 6 day interval. The center of this interval is used for temporal referencing and the interval is stepped by one day for each calculation of the wave amplitudes and phases. The wave periods used for the fits were determined from the asynoptic Fourier analysis (see Figure 1). The westward propagating two-day wave peaks with an amplitude in excess of 12 K around January 25th at a latitude of 40°S and altitude of 80 km. However amplitudes in excess of 4 K are observed for nearly a month from January 10th to February 4th, 2005. The vertical structure of the westward propagating two-day wave is clearly bimodal with one peak near 80 km and a second peak near 110 km that exceeds 16 K and is roughly out of phase with the lower peak. This bimodal structure in temperature can be explained by a perturbation geopotential field with a single distinct maximum at 87 km (not shown), which was computed using the following relationship where the perturbation geopotential is assumed to be zero at an altitude of 20 km. By noting that the perturbation geopotential (Φ′(z)) is related to the perturbation temperature (T′(z)) by the relationship T′(z) = equation imageequation imageΦ′(z), where H is the atmospheric scale height and R is the gas constant for dry air [Sassi et al., 2002], it can be seen that the temperature perturbation will be zero near the altitude where the perturbation geopotential field maximizes while out-of-phase above and below this altitude.

Figure 2.

(top) Time/latitude and (bottom) height/latitude cross-sections of the (left) 2.17 day, s = −3 wave and (right) 1.85 day, s = +2 wave at 80 km (top plot) and for 40°S (bottom plot).

[11] The eastward propagating two-day wave exhibits a structure similar to the westward propagating two-day wave with a peak near 80 km in the southern hemisphere mid-latitudes. There is also indication of a bimodal structure in altitude but this feature is less organized in the eastward propagating two-day wave. The peak response for the eastward propagating two-day wave exceeds 8 K for a short time between January 20th and 25th but is in excess of 4 K for nearly a month.

[12] The vertical and latitudinal structure of both the eastward and westward wave components are shown in Figure 3 for the 6 days around January 25th, when the maximum amplitudes are observed. The westward propagating component exhibits a clear maximum response near 40°S that extends to lower latitudes. Evidence for a low latitude response in the northern hemisphere tropics is also seen above 80 km. The eastward propagating component maximizes at a slightly higher latitude than the westward component and it also exhibits the same extension to lower latitudes. There is a slightly enhanced response in the northern hemisphere tropics between 80 and 110 km with amplitudes approaching 10 K.

Figure 3.

Vertical and latitudinal structure of the (top) 2.17 day, s = −3 wave and (bottom) 1.85 day, s = +2 wave determined using observations from January 23rd to 28th, 2005.

[13] Figure 4 shows vertical profiles for each of the two wave components at 40°S and 45°S. The amplitude structure, shown in the left plots, is similar for both of the wave components with the mesospheric peak (80 km) largest in the westward component but the lower-thermospheric peak (110 km) is similar in amplitude for both components. The vertical phase structure, shown in the right plots, indicates a similar vertical wavelength of 60 km for both components below 95 km with a divergence from this structure above. The phases of the wave components are reported as the phase offset computed relative to 0° longitude at 0 UT on January 1st 2005.

Figure 4.

Vertical (left) amplitude and (right) phase profiles for the 2.17 day, s = −3 wave (red) and 1.85 day, s = +2 wave (blue) at (top) 40°S and (bottom) 45°S. Profiles are determined using observations from January 23rd to 28th, 2005.

[14] The existence of both an eastward and westward propagating component will have an impact on the perturbation amplitudes observed from the perspective of a ground based observer. The superposition of these two waves will create an interference pattern with regions of enhanced and suppressed amplitudes that will depend upon the longitude of the observer. As a result, observations from a single ground based site could be biased depending upon the phases of the eastward and westward propagating waves and should be considered when interpreting such observations.

[15] Finally, one must consider the possibility that aliasing could impact these results because the Nyquist limit for a satellite taking single node (either ascending or descending only) measurements is approximately 2 days [Salby, 1982a, 1982b]. In such cases energy from the westward propagating wave could appear as an eastward propagating wave. Since SABER only takes a single measurement at the “turning latitudes” of 52°S and 83°N, this effect would be most pronounced at the orbit extrema. Simulations (not shown) indicate that such aliasing effects are negligible for latitudes equatorward of 50°S where sufficient longitudinal separation is achieved between the ascending and descending nodes. Therefore, we consider our results to be robust, and not an effect of aliasing.

4. Conclusions

[16] Evidence for the existence of an eastward propagating quasi-two day wave has been presented. During 2005 this eastward propagating two day-wave had a frequency of 0.53 cycles/day and was propagating eastward with a zonal wavenumber 2. It was observed coincidentally with the semiannual enhancement of the classical quasi-two day wave shortly following the solstice. This component had a frequency of 0.47 cycles/day and was propagating westward with a zonal wavenumber 3. A similar eastward propagating two-day wave was observed in a global circulation model simulation and was interpreted as the result of a nonlinear interaction between the westward propagating two-day wave and the migrating diurnal tide. The frequency and wavenumber of the observed eastward propagating two-day wave agrees with this supposition. Furthermore, the period of the westward propagating wave was slightly longer than 48 hours while the eastward propagating two-day wave was slightly shorter than 48 hours. This is what one would expect if the eastward propagating two-day wave was the result of a nonlinear interaction between the westward propagating two-day wave and the migrating diurnal tide.


[17] This material is based upon work supported by the NASA TIMED Program under grant NAG5-5028 and the National Science Foundation grant ATM-0228026. Support for MGM is provided by the NASA Science Mission Directorate and the NASA Langley Science Directorate. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflected the views of the National Science Foundation.