Interannual variability of the 5-day wave in the stratosphere is examined by the use of National Center for Environmental Prediction reanalysis data. Quasi-biennial variation of the 5-day wave amplitude is clearly seen in the stratosphere. This quasi-biennial variation is closely related to the zonal wind variation associated with the equatorial quasi-biennial oscillation in the stratosphere. We give a short description of the mechanism bringing about the relationship.
 The 5-day wave is one of normal mode Rossby waves (or free oscillations of the atmosphere). It is well recognized that the 5-day wave frequently appears in the troposphere and stratosphere [Madden, 1978; Hirota and Hirooka, 1984] (hereinafter referred to as HH84). Recently, the Upper Atmosphere Research Satellite (UARS) observations reveal the global appearance of the 5-day wave in the mesosphere and lower thermosphere [Wu et al., 1994; Hirooka, 2000].
Ahlquist  investigated seasonal variability of the 5-day wave in the troposphere to show that the 5-day wave has maximum amplitudes in the equinoctial season. However, there are only a few studies dealing with interannual variability of the 5-day wave. Hamilton  examined the relationship between the 5-day wave component of the sea surface pressure and interannual variation of the sea surface temperature (SST) in the tropics. He obtained a significant correlation between the 5-day wave amplitude and the SST in the tropics. Hirooka and Hirota  showed interannual variation of appearance periods of various normal modes, including the 5-day wave, in the stratosphere. However, no plausible mechanisms causing it have been presented as yet. Hence we examine the interannual variability of the 5-day wave in the stratosphere and discuss the causing mechanism from the viewpoint of excitation sources of the 5-day wave.
2. Data and Analysis Method
 For this study, we used daily zonal wind and geopotential height data of the National Center for Environmental Prediction (NCEP) reanalysis [Kalnay et al., 1996] with 2.5° × 2.5° latitude-longitude grid spacing and 17 vertical levels up to 10 hPa. The analysis period is 1980 through 2000.
 The global grid point data are expanded into zonal Fourier harmonics at each latitude and each vertical level to obtain the wave component of zonal wavenumber 1. On the basis of a space-time Fourier transform [Hayashi, 1971], a westward moving component is extracted. Next, a numerical bandpass filter with a period from 4.5 to 5.9 days is used to separate dominant frequency component of the 5-day wave. This procedure is similar to that in HH84.
 First, the behavior of the 5-day wave in the stratosphere is examined. We present the result in years of 1984 and 1994 which correspond to typical years of strong and weak wave activity, respectively. Figure 1 shows the time-latitude section of the amplitude of the 5-day wave at 10 hPa in 1984. The 5-day wave amplitude increases simultaneously in both hemispheres except for the winter season of the northern hemisphere, appearing rather irregularly with a lifetime of 20–40 days. The latitudinal phase structure shows that the wave is symmetric in respect to the equator (not illustrated). The maximum amplitude exists around 40°–50° latitude and the value is 20–70 m. These features are basically the same as those in HH84. Note that the localized amplitude at high latitudes in the winter season of the northern hemisphere is considered to be a 5-day portion of wave variance with wide period range related to stratospheric sudden warming events and is not due to the normal mode Rossby wave.
Figure 2 shows the time-latitude section of the 5-day wave amplitude at 10 hPa in 1994. The 5-day wave amplitude from June to December is extremely weak. The overall 5-day wave amplitude is smaller in 1994 than in 1984. Thus it is clear that the 5-day wave activity shows significant interannual variation.
 Next, interannual variability of the 5-day wave activity during the full analysis period is examined. As shown in Figures 1 and 2, the 5-day wave amplitude has maxima in 40°–50°, and the 5-day wave component poleward of 60° is contaminated by other wave components during the stratospheric sudden warming. Hence we discuss time series of the 5-day wave amplitude averaged over 40°–50°N and 40°–50°S at 10 hPa (Figure 3 (top)). The quasi-biennial variation of the 5-day wave amplitude for 360-day filtering is clearly seen. Similar quasi-biennial variation is also seen at other vertical levels of the stratosphere (not shown). In the troposphere, however, the quasi-biennial variation of the 5-day wave becomes unclear. It is difficult to extract the 5-day wave component without the contamination of other waves, because the typical amplitude of the 5-day wave in the troposphere is only 5–8 m in the most predominant case.
 The quasi-biennial variation of the 5-day wave amplitude is intimately connected with the zonal wind oscillations in the equatorial lower stratosphere. Figure 3 (bottom) shows the vertical shear of the zonal mean zonal wind between 70 hPa and 10 hPa, (10 hPa)–(70 hPa), at the equator. There is a good negative correlation between the two: The 5-day wave amplitude during the easterly shear phase of the quasi-biennial oscillation (QBO) (d/dz < 0) is larger than that during the westerly shear phase (d/dz > 0). These results imply that the equatorial QBO influences the 5-day wave activity in the stratosphere.
 If we look at the 5-day wave behavior during the easterly vertical shear phase, the maximum amplitude itself also shows interannual variation. The maximum amplitude of the 5-day wave in 1984, 1991, and 1995–1996 is 18–21 m, while that in 1981, 1986, and 1993 is 15–16 m. The minimum value of the zonal wind shear is about −35 m s−1 and almost unchanged throughout the analysis period. Thus the maximum amplitude of the 5-day wave may be influenced not only by the QBO but also by interannual variations in the tropospheric circulation.
 The zonal phase velocity of the 5-day wave is large, so that the 5-day wave amplitude might be insensitive to the seasonal change of the zonal wind distribution in middle and high latitudes; the 5-day wave appears globally even if the easterly is fairly strong in the summer hemisphere. However, the 5-day wave amplitude would be modulated through the propagating condition accompanied with the zonal wind variation of the QBO.
 By a series of GCM experiments, Miyoshi and Hirooka  showed that heating due to the moist convection in the tropics was essential for excitation of the 5-day wave. By using a mechanistic model, Horinouchi and Yoden  studied excitation characters of the 5-day wave by localized episodic heating in the tropical upper troposphere to show that the 5-day wave suffers from QBO modulation if the 5-day wave is excited in the tropics. The 5-day wave amplitude is larger during the easterly shear phase of the QBO than the westerly shear phase. This result is consistent with the QBO modulation in this study. The most plausible explanation for the correlation between the 5-day wave amplitude and the QBO is as follows: The 5-day wave might be excited by heating due to the moist convection in the tropics and modulated through the propagation condition accompanied with the zonal wind variation of the QBO.
 In Horinouchi and Yoden's model, the magnitude of localized episodic heating is fixed, and effects on the 5-day wave amplitude due to interannual variation of the convective heating magnitude are not taken into account. In the real atmosphere, the convective activity in the tropics changes interannually. Lau and Sheu  showed that the global precipitation pattern fluctuated with a timescale of 2–3 years as well as the Southern Oscillation timescale. This result implies that the magnitude of heating due to the moist convection varies with the same period. As a result, the 5-day wave amplitude may be influenced by variations of the moist convective heating with a period of 2–3 years. However, the details are not well understood, and this is a subject of the future study.
 On the other hand, Talaat et al.  showed that the westward moving wave of zonal wave number 1 with a period from 6.0 to 7.5 days (6.5-day wave hereafter) appeared frequently in the stratosphere. The 5-day and 6.5-day waves have nearby traveling periods each other. Hence it is very interesting to examine interannual variability of the 6.5-day wave and its relationship with that of the 5-day wave. In order to extract the 6.5-day wave component, we used a similar numerical bandpass filter with a period from 5.9 to 7.7 days. Note that the filter for the 5-day wave separates the component with a period from 4.5 to 5.9 days. Figure 4 shows interannual variations of the 5-day and 6.5-day wave amplitudes at 10 hPa. It is found that the 6.5-day wave shows a different character of the interannual variability and no indication of the QBO modulation. Thus the interannual variability of the 5-day wave is clearly distinguishable from that of the 6.5-day wave.
 In this study, by the use of the NCEP reanalysis data, the interannual variability of the 5-day wave in the stratosphere is examined. The quasi-biennial variation of the 5-day wave amplitude is clearly seen and is intimately related to the zonal wind oscillations associated with the equatorial QBO in the stratosphere. The 5-day wave amplitude is larger during the easterly shear phase of the QBO than the westerly vertical shear phase. The plausible explanation of the quasi-biennial variation of the 5-day wave amplitude is that the 5-day wave is excited by heating due to the moist convection in the tropics and the 5-day wave is modulated through the propagation condition accompanied with the zonal wind variation of the QBO.
 We wish to thank Professor S. Miyahara and Dr. K. Nakajima for their helpful discussions throughout this work. Thanks are also due to anonymous reviewers for their suggestions to improve the original manuscript. GFD-DENNOU Library was used for drawing the figures. This research was financially supported by a Grant-in-aid for Scientific Research by the Ministry of Education, Science, Sports and Culture, Japan.