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  • View in gallery

    The (a) mean RASS Tυ (solid line) and mean radiosonde Tυ (dashed line) and (b) their difference. (c) The mean RASS N2 profile (solid line) and radiosonde N2 profile (dashed line).

  • View in gallery

    The spectral width obtained with the (0°, 10°) radar beam.

  • View in gallery

    The derived energy dissipation rate ε.

  • View in gallery

    Contour plot of the virtual Brunt–Väisälä frequency squared N2 up to 8 km, with 6-h high-pass-filtered temperature perturbations T ′υ. Missing N2 values are colored white. Numbers on the plot are referred to in the text.

  • View in gallery

    Contour plot of the virtual Brunt–Väisälä frequency squared N2, with 6-h high-pass-filtered vertical velocity w′ perturbations. Numbers on the plot are referred to in the text.

  • View in gallery

    The 30-min low-pass-filtered virtual Brunt–Väisälä frequency squared N2 with (a) the horizontal wind variance overplotted, (b) the vertical wind variance, and (c) the temperature variance.

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    Covariances for the 12-h interval of 0800–2000 LT 13 October at nine heights as indicated in the titles.

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    Heat flux calculated from the covariance of temperature and vertical wind. Most of the heat flux is associated with the 13 October disturbance.

  • View in gallery

    Wavelet energy spectrum of the 3.00-km altitude vertical wind velocity. The dominant wave component between 1600 and 2000 LT of about 60 min is clearly apparent. Waves with periods close to the Brunt–Väisälä period are visible between 0000 and 0400 LT 14 October.

  • View in gallery

    Area-preserved wavenumber spectra at four different hour-long times as annotated in the titles. The u′ spectra are marked by the solid lines, υ′ spectra by the dashed lines, w′ spectra by the dotted lines and ((g/N))2(T ′/T) by the dash–dot lines. The saturated model spectral slope of temperature with gradient −2 is marked by the dash–dot line, while the saturated model spectral slope of horizontal wavenumber is marked by the solid line.

  • View in gallery

    Fig. 1. Horizontal wind velocity field below 8 km. The scale to the top right shows a 40 m s−1 wind vector in the zonal (horizontal) and meridional (vertical) directions.

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Effects of Atmospheric Stability on Wave and Energy Propagation in the Troposphere

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  • 1 Research Institute for Sustainable Humanosphere, Kyoto University, Kyoto, Japan
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Abstract

The very high frequency (VHF) middle and upper atmosphere radar radio acoustic sounding system (MU-RASS) in Shigaraki, Japan, is able to provide tropospheric virtual temperature data with high temporal resolution on the order of a few minutes. The objective of this paper is to test the usefulness of MU-RASS as a tool for examining high-frequency changes in atmospheric stability and its effects on wave and energy propagation. For this study, temperature and wind data below 8-km altitude during a 2-day campaign period in October 2001 were used. A long-lasting inversion layer at 3.5-km altitude dominated the observation period. Large vertical wind perturbations with periods of less than 30 min were observed inside this inversion layer. Wavelet analysis was used to identify the dominant wave period for calculating the wind and temperature variances. The temperature variance characteristics exhibited a combination of the horizontal and vertical wind variance characteristics. In conclusion, the high temporal resolution of the MU-RASS enabled the study of short time-scale wind and temperature perturbations. These perturbations were related to the atmospheric stability, wave propagation, and energy in the troposphere, demonstrating the usefulness of the MU-RASS for this kind of study.

Corresponding author address: Simon Alexander, Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho, Uji 611-0011, Japan. Email: alexander@rish.kyoto-u.ac.jp

Abstract

The very high frequency (VHF) middle and upper atmosphere radar radio acoustic sounding system (MU-RASS) in Shigaraki, Japan, is able to provide tropospheric virtual temperature data with high temporal resolution on the order of a few minutes. The objective of this paper is to test the usefulness of MU-RASS as a tool for examining high-frequency changes in atmospheric stability and its effects on wave and energy propagation. For this study, temperature and wind data below 8-km altitude during a 2-day campaign period in October 2001 were used. A long-lasting inversion layer at 3.5-km altitude dominated the observation period. Large vertical wind perturbations with periods of less than 30 min were observed inside this inversion layer. Wavelet analysis was used to identify the dominant wave period for calculating the wind and temperature variances. The temperature variance characteristics exhibited a combination of the horizontal and vertical wind variance characteristics. In conclusion, the high temporal resolution of the MU-RASS enabled the study of short time-scale wind and temperature perturbations. These perturbations were related to the atmospheric stability, wave propagation, and energy in the troposphere, demonstrating the usefulness of the MU-RASS for this kind of study.

Corresponding author address: Simon Alexander, Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho, Uji 611-0011, Japan. Email: alexander@rish.kyoto-u.ac.jp

1. Introduction

With a pulsed Doppler wind-profiling radar; wind velocities, echo power, and spectral width can be measured with high temporal and spatial resolution. The addition of RASS enables virtual temperature profiling. Since virtual temperature is proportional to the square of acoustic velocity, virtual temperature profiles can be obtained from measurements of the Doppler velocity of artificially induced acoustic waves (e.g., May et al. 1989; Tsuda et al. 1994). If the acoustic wavelength is half of the radar wavelength, then Bragg scattering results and a return signal can be detectable. Frequency sweeping is necessary to satisfy this condition over a range of heights (Adachi et al. 1993).

With the inclusion of an accurate, high-resolution temperature dataset, additional atmospheric parameters to those calculable using only wind data can be investigated. The atmospheric stability, quantified by the Brunt–Väisälä frequency squared N2, can be calculated and compared with changes in the wind and temperature fluctuations and their variances. Calculation of the turbulent energy dissipation rate is also possible. Temperature frequency and wavenumber spectra were contrasted with wind spectra (Yamamoto et al. 1996). Collocated radiosonde derived N2 were compared with MU radar echo power and aspect sensitivity. Rapid increases in the echo power and aspect sensitivity near the tropopause corresponded with stepwise enhancements of N2 (Hermawan et al. 1998). Heat fluxes can be derived by studying the covariance relationship between temperature and vertical wind (Peters et al. 1985; Tsuda et al. 1994).

The MU radar (location 34.85°N, 136.10°E, 370 m MSL) is a VHF radar, operating at 46.5 MHz (Fukao et al. 1985). MU-RASS tropospheric temperature perturbations and spectra have been previously analyzed (Tsuda et al. 1994; Yamamoto et al. 1996). Campaign based measurements of tropospheric humidity are now possible, using data from the MU-RASS (Furumoto et al. 2003). Previous MU-RASS analyses have not studied small-scale changes in atmospheric stability. Therefore, in this paper we present an analysis of the effects of changes in atmospheric stability on wind and temperature perturbations during a campaign period.

Section 2 describes the observational technique, the datasets collected with the MU-RASS and comparisons with collocated radiosonde data. The MU radar spectral width and turbulent energy dissipation rate are also studied. A detailed analysis of atmospheric stability and its relation with temperature and vertical wind velocity perturbations is presented in section 3. Wind and temperature variances and their relation to stability are discussed in section 4. Results from heat flux calculations are described in section 5. Fourier and wavelet spectral analyses of the wind and temperature components are presented in section 6. Results are discussed in section 7, with conclusions presented in section 8.

2. MU radar RASS observations

The MU radar RASS system is capable of measuring high-resolution profiles of wind and virtual temperature Tυ. Thirty-nine hours of wind and RASS temperature data were obtained with the MU radar on 13–14 October 2001. Both the wind and temperature datasets have a time resolution of 3 min and a height resolution of 150 m. The operational parameters are summarized in Table 1 for the MU-RASS radar, Table 2 for the acoustic speaker parameters, and Table 3 for the clear- air observations. The experiment sequence was RASS low mode, RASS high mode, wind low mode, and wind high mode. Five beam directions were used for measurements of the clear-air echoes: vertical, north, east, south, and west. The last four beams were directed 10° off zenith. Four fixed beam directions were used for the RASS experiment (Az, Ze): (270°, 30°), (285°, 30°), (285°, 32°), and (300°, 32°). These RASS beam directions were determined by using a ray-tracing algorithm of acoustic wave fronts, which took into account the background wind profile (Masuda 1988). Twenty hyperbolic horn speakers located around the MU radar array were used to provide the acoustic pulses. An FM chirped acoustic wave was emitted at varying frequencies (72.3–109.2 Hz) in order to satisfy the Bragg condition at different heights. Temperature data were routinely collected up to 8 km. Sporadic temperature measurements were obtained above this height, but data below 8 km only were analyzed. Horizontal wind data were available up to 20 km and vertical wind data w up to 24 km.

The two-hourly averaged zonal eastward u and meridional northward υ wind vectors below 8 km are displayed in Fig. 1. Weak winds occurred close to the surface, with increasingly strong eastward winds at higher altitudes. The wind speed regularly exceeded 30 m s−1 above 7 km. The wind flow is generally eastward, although a short-lived southward wind change of up to 15 m s−1 is apparent between 1600 and 2000 LT 13 October, between 3 and 5 km. The wind vectors above 8 km are not shown, but we note that the zonal wind continued strengthening, reaching a maximum at 13 km of 50 m s−1 eastward. The maximum meridional wind was observed at 11.5 km, with a speed of 20 m s−1 northward. Both horizontal wind components decreased above these altitudes.

Thirteen radiosondes were launched from the MU radar site at 3-h intervals during the RASS experiment. It took approximately 30 min for a radiosonde to ascend to 8 km. Radiosonde temperatures T were converted into Tυ via (Angevine and Ecklund 1994):
i1520-0426-24-4-602-e1
where q is the specific humidity and e = 0.622 is the partial pressure of water vapor.

RASS data were extracted from the time of each radiosonde launch until 30 min after that launch and a campaign mean Tυ formed. The campaign averaged Tυ values are plotted in Fig. 2a. The solid line shows the RASS derived Tυ from data within 30 min of each radiosonde launch, while the dashed line shows the radiosonde Tυ profile. A region of enhanced stability is visible at 3 km. The freezing level was at about 4 km throughout the MU-RASS campaign. Agreement between the two profiles is close at all altitudes. The difference (RASS − radiosonde) between the mean Tυ profiles is displayed in Fig. 2b. The magnitude of the difference at all altitudes is less than 0.5°C. This result is consistent with previous calculations of the accuracy of the MU-RASS (Matuura et al. 1986; Tsuda et al. 1994). Differences between specific radiosonde flights and RASS in the half hour following launch are generally less than 0.5°C, although on occasions the Tυ difference is up to 1.0°C. Standard deviations of the campaign average RASS Tυ were less than 0.2°C at all altitudes below 8 km.

The same procedure was used for calculating a campaign mean Brunt–Väisälä frequency squared N2 profile by only using RASS data obtained within 30 min of each radiosonde launch. The campaign average N2 is displayed in Fig. 2c. Small discrepancies between the RASS and radiosonde mean profiles are evident, for example at 6 km. Two regions of large N2 centered on 2.5 and 6 km are visible in both RASS and radiosonde profiles.

a. Synoptic situation

An analysis of the mean sea level (MSL) weather chart for 0000 UTC (0900 LT) 13 October 2001 revealed the presence of a low pressure system to the north of Japan and a high pressure system over China. This combination of systems resulted in air moving southward over most of Japan. The weather chart for 0900 LT 14 October indicated that the low pressure system north of Japan had moved slightly northeastward, as had the high pressure system over China.

The Japan Meteorological Agency (JMA) operates the Automated Meteorological Data Acquisition System (AMEDAS) surface meteorological network. Surface rain data between 0600 and 1100 LT on 13 October showed a band of surface precipitation moving southeastward toward the MU radar. The precipitation band had largely dissipated before reaching the radar site, although isolated precipitation from convection was observed close to the MU radar at 1200 and 1300 LT. No AMEDAS rainfall was reported on 14 October.

Surface atmospheric measurements were recorded at the MU radar site throughout the campaign. A temperature decrease of about 3°C and a humidity increase of 20% occurred between 1200 and 1400 LT 13 October, which corresponded with the AMEDAS surface precipitation observations around the MU site. No convective effects were visible in the surface data on 14 October.

b. Spectral width and turbulence energy dissipation rate

The precipitating convection measured by the AMEDAS surface network at 1200 LT 13 October corresponded to an increase in MU radar half-power half-width spectral width σ1/2, as illustrated in Fig. 3. Data from the clear-air (0°, 10°) beam were used in order to remove as far as possible specular echoes. The background level is the minimum level of σ1/2 ∼ 0.4–0.5 m s−1. A region of enhanced spectral width is here defined as a place where σ1/2 > 1.0 m s−1, which is more than double the background level. This spectral width enhancement was visible in the MU radar data up to 2.8 km at 1200 LT. A further enhancement in spectral width occurred at 1400 LT, 14 October between 3.5 and 5.5 km. This coincided with a region of statically unstable air (as will be discussed in section 3), but also extended into a stable region above 5 km. This region did not correspond to a period of precipitating convection.

The turbulent energy dissipation rate ε was calculated from:
i1520-0426-24-4-602-e2
where c is a correction factor very close to unity (Hocking, 1999) and Lr(z) is the horizontal distance covered by the radar beam at a certain altitude z. Note that this method of calculating ε is not dependent on N. Errors would result if the Labitt formula ε ≃ 0.45σ21/2N was used to calculate ε, because the MU radar has a beamwidth of 3.6° and a pulse length of 150 m. This combination of narrow beamwidth and short pulse length indicates that the Labitt formula would have an associated uncertainty of ∼10% because of a large buoyancy scale (Hocking 1999). The spectral width obtained with the northward beam at 10° off zenith was used, after effects due to beam broadening and wind shear were removed (Hocking 1985).

In Fig. 4, ε is plotted. The precipitating convection on 13 October is visible in the ε data below 3 km, between 1100 and 1300 LT. A second event, centered on 1400 LT 14 October above 4 km and mentioned in the σ1/2 analysis above, is clearly visible in the ε data centered on 1400 LT 14 October above 4 km.

The ε of over 0.02 m2 s−3 were observed during these two enhanced σ1/2 regions and were confined within regions of σ1/2 > 1.0 m s−1. The enhanced dissipation rate on 14 October decreased to be close to the background level of under ∼10−3 m2 s−3 by 6 km.

Large σ1/2 and subsequent large ε were observed above 5.5 km. A possible cause of the large σ1/2 is the wind shear. The campaign average rate of change of u with height was 5 m s−1 km−1 above 5.5 km. Large wind shear normally produces an unstable region, which tends to generate turbulence. Shear broadening effects may also cause a larger spectral width.

3. Atmospheric stability

The high-resolution nature of this MU-RASS dataset permitted a detailed examination of the stability in the lower troposphere during a period when there was an absence of major convection or cold fronts. The virtual Brunt–Väisälä frequency squared N2 is given by
i1520-0426-24-4-602-e3
where the gravitational acceleration g = 9.81 m s−2 and Γ = 9.76 K km−1 is the dry adiabatic lapse rate. From the polarization relation and for wave periods of less than several hours, temperature perturbations T ′ are proportional to changes in Brunt–Väisälä frequency N (Fritts et al. 1988):
i1520-0426-24-4-602-e4
where u′ is the horizontal wind perturbation. Thus, we expect that an increase in atmospheric stability should correspond to an increase in T ′. Van Zandt and Fritts (1989) suggested that an increase in wave amplitude will occur as a gravity wave encounters a region of enhanced stability.

The vertical wind and virtual temperature data were 6-h high-pass filtered before being overplotted on a contour plot of N2, as shown in Fig. 5 for the 6-h high-passed T ′υ and Fig. 6 for the 6-h high-passed w′. Note that in these and subsequent figures, data gaps are marked by white regions.

Nearly all of the time, N2 is positive, although a few small statically unstable places occurred for example at 1400 LT 13 October around 3 km and at 1400 LT 14 October between 4.5 and 5.0 km. Regions of enhanced stability are apparent throughout the observation period below 4 km and correspond to inversion layers. The first of these regions is between 2 and 3 km at the start of the observation period, before descending to 2.2 km at 1500 LT. A second layer was observed from 1300 LT 13 October at 3.5 km, after which time it descended to be at about 2.7 km by 1600 LT. It remained at this height throughout the night before ascending again until 1000 LT 14 October, after which it disappeared. The region immediately above this layer was a region of low N2.

A period of enhanced N2 is visible at 5.7–6.0 km for the first 4 h of the observation interval. Further patchy increases in N2 occurred at this altitude until 2000 LT. Smaller enhancements in N2 centered on 7 km were visible between 2000 and 0800 LT.

Increases in T ′υ in Fig. 5 generally corresponded to increases in N2, as expected from the polarization relation. Large T ′υ occurred during the inversion at 6.0 km during the first 4 h of observation [marked by (1) in Fig. 5], as well as intermittently inside the regions of large N2 below 3 km (2, 3). Large T ′υ were visible at 1400 LT 14 October (4), which were associated with the enhanced σ1/2 observed in the MU radar data at this time. Increased T ′υ also occurred above 6 km around 0000 LT 14 October (5).

The changes in w′ in Fig. 6 were not so strongly related to changes in N2 as was T ′υ. Large oscillations of approximately one hour period were observed between 1400 LT and 2000 LT 13 October below 4 km [marked by (1) in Fig. 6]. The amplitude of these waves decreased with height. High frequency w′ with periods of less than one hour were also observed during the times of the two large σ1/2 events (2, 3) and are most clearly visible during the 14 October event. High-frequency w′ with periods of 7–11 min also occurred inside the 2.5–3.0-km inversion layer (4). The Brunt–Väisälä period in this region was 6 min.

In summary, several evolving inversion layers were observed on 13 and 14 October. An inversion layer occurred below 3.5 km. Temperature perturbations were enhanced during periods of large N2. A region of high amplitude w′ occurred in the late afternoon and early evening of 13 October, which appeared to originate from a source in the lower troposphere.

4. Wind and temperature variances

The horizontal wind variance + and vertical wind variance , averaged over the dominant 1-h wave period (as will be determined in section 6), are now compared with the atmospheric stability profile. Spurious data points were manually removed. Data outside two standard deviations from the subsequent mean at each height were then excluded from further analysis.

Figure 7 shows the 30-min low-pass-filtered contour plot of N2. The horizontal wind variance is overplotted as the line contours in Fig. 7a, with each line representing a 3 m2 s−2 increase. Large horizontal wind variances often occurred in regions of small or negative N2, for example at 5.0 km 1600–2200 LT 13 October. The original 3-min meridional wind profiles at 5.0 km showed that at 2000 LT 13 October, υ = −14 m s−1 but by 0200 LT 14 October, υ = 9 m s−1. This synoptic-scale large change of wind speed, during a time of reasonably constant u, was responsible for the enhanced + observed during the night in the weakly stable region.

A region of large + was also observed at 0800 LT 13 October, centered on 6.0 km, which is located in a region of large N2. Small, patchy enhancements in + are also apparent inside the 3-km inversion layer between 0500 and 1000 LT 14 October.

The vertical wind variances are plotted in Fig. 7b, with each line marking an increase of 0.05 m2 s−2. The largest were observed between 1400 and 2000 LT 13 October. This region of large vertical wind variance corresponded to large w′ of approximately 1-h period, where the amplitudes exceeded 1 m s−1 below 3.5 km. The amplitudes of these waves rapidly decreased above this altitude and were no longer visible at 4.5 km. The vertical wind variances show that most of the variance of these waves was below the top of the inversion layer, with significant confined below the inversion layer as well.

Other are apparent above 5.0 km between 1200 and 2200 LT 13 October. Some of these occur in similar positions as horizontal wind variances and may therefore be related to the synoptic-scale changes in horizontal wind direction and gravity wave emission. A small peak in occurred at 0800 LT at 6.0 km, centered on the inversion layer in this region, as was also observed in the + data. Increases in were visible during the times of the two enhanced σ1/2, at 1200 LT 13 October below 3.0 km, and at 1400 LT 14 October centered on 4.5 km.

Here, T ′υ were normalized by the mean virtual temperature at each height before calculation of the virtual temperature variance :
i1520-0426-24-4-602-e5
The temperature variances are shown in Fig. 7c, with each contour line marking an increase of 10−5 K2. The temperature variance characteristics exhibited a combination of the horizontal and vertical wind variance characteristics. Increases in below 4 km on 13 October occur at similar times to increases in , with local maxima of inside stable regions. Large temperature variances above 5 km between 1600 LT 13 October and 0400 LT 14 October appear related to the synoptic changes in the horizontal wind field that occurred at this time. Further are visible inside the 3-km stable layer around 0800 LT 14 October, which also corresponded to increases in + at this time.

5. Heat flux

The heat flux Q was calculated via the eddy correlation method (Peters et al. 1985):
i1520-0426-24-4-602-e6
where Cp is the specific heat at constant pressure (1004 J kg−1 K−1) and ρ is the atmospheric density. The argument of the covariance is the lag between T ′υ and w′. The atmospheric density was calculated using ρ = (P/RTυ), where P is the model tropospheric pressure and R = 287 J kg−1 K−1.

The covariances between T ′υ and w′ at nine altitudes are illustrated in Fig. 8 for the 12-h period of 0800–2000 LT 13 October. The plots are between 1.50 and 7.50 km and show different features at different heights. Figure 8a, at 1.50-km altitude, shows in-phase waves with a 2-h period, which decreased in amplitude in the next two range gates (not shown). At 1.95 km (Fig. 8b), little evidence of wave activity was apparent but between 2.55 and 3.75 km (Figs. 8c–e), wavelike behavior was again visible; T ′υ and w′ show an anticorrelation at 2.55 km, with no phase delay but become correlated at 3.00 km, although still with no phase delay. The covariance at 5.25 km is shown in Fig. 8g, where a wave period of about 2 h was observed. Above this altitude, waves with periods of 8 h or greater were observed. At 6.45 km (Fig. 8h), the lag is 2–3 h, which is approximately one quarter of a wave cycle (with T ′υ leading). A similar situation is observed in Fig. 8i, at 7.50 km, although the lag between T ′υ and w′ was less.

In summary, the lower regions, below about 4.35 km, were characterized by having a maximum covariance at or close to zero lag. This is consistent with convective processes lifting the air. On the other hand, the higher altitudes seem to exhibit more of a tendency for phase shifting, which follows from gravity wave activity and the previous observation that was largely confined below 4.0 km.

The value of 〈T ′υw′〉 in Eq. (6) was obtained by taking the average of the covariance at +1 and −1 lag. At zero lag, contamination from the vertical wind measurement may occur. A sharp negative peak in the covariance was noticed on occasions by Peters et al. (1985), who used a 15-s resolution dataset. A MU-RASS dataset with 90-s time resolution did not reveal any zero lag contamination (Tsuda et al. 1994). Negative peaks were not observed in the covariance data of Fig. 8. However, interpolation across zero lag was still used in the present study in order to remove measurement errors resulting from one sample period (Angevine et al. 1993).

The magnitude of the covariance is around a factor of 10 larger than the covariance estimates of Peters et al. (1985). This may be due to different atmospheric sampling regions, different data sampling rates and different atmospheric conditions. Figure 8 revealed covariances exceeding 0.1 between 2 and 4 km. This translates into regions of heat flux in the inversion layer exceeding 100 W m−2, as displayed in Fig. 9.

The heat flux Q in Fig. 9 shows similar characteristics to the in Fig. 7b. Essentially all of the heat flux occurred before 0000 LT 14 October and was associated with the afternoon disturbance on 13 October. Large positive (upward propagating) values of Q are visible below 1.8 km, and in two separate peaks centered on 3.0 and 3.2 km. Large positive Q are associated with a low stability environment, with N2 occasionally negative at these times. The upward heat flux propagation is halted at the inversion layer. A large negative heat flux is apparent in a small region between 2.5 and 3.0 km at 1200 LT. This corresponds to the top of the enhanced σ1/2 observed at this time. Smaller heat fluxes are observed above 4 km during the same period, although the relationship between the sign of Q and the stability is less clear.

Peters et al. (1985) applied the eddy-correlation method for calculating Q to a sodar–RASS boundary layer dataset with 15-s resolution. Later studies used data with coarser resolution to study the heat flux. Angevine et al. (1993) used 60-s resolution data from a boundary layer radar to record a 14-day averaged heat flux below 450 m. The peak flux average was reported as 120 W m−2 so in the boundary layer, Q on individual days often exceeded this level. Measurements of Q in the free troposphere of up to 10 W m−2 were reported using RASS data with a time resolution of 90 s (Tsuda et al. 1994). The free troposphere heat fluxes reported here are larger than the results of Tsuda et al. (1994). Different meteorological conditions and a coarser resolution dataset may explain some of the differences between Q.

6. Spectral characteristics

The raw wind and temperature datasets were interpolated to 162-s resolution, with gaps in the data linearly interpolated. After removal of the mean at each height, the datasets were Welch windowed (Press et al. 1992) and then the power spectra determined.

a. Wavelet analysis

While Fourier analysis permits no temporal indication of when certain frequencies dominate, wavelet analysis allows the signal to be localized in time and frequency. Wavelet analysis thus provides a way of determining the dominant frequencies at different temporal locations (Torrence and Compo 1998). A Morlet wavelet was used as the necessary orthonormal wavelet, since the wind perturbation data are amplitude-modulated sine waves. The Morlet wavelet ψ0(t) is a plane-modulated Gaussian function:
i1520-0426-24-4-602-e7
where i = −1. Note that the Morlet wavelet is complex, allowing amplitude and phase information to be extracted from a one-dimensional time series. The two-dimensional wavelet spectrum is constructed by modifying the scale of the Morlet wavelet. High-frequency versions of the wavelet enable temporal analysis, while low-frequency versions enable frequency analysis. Other orthornormal wavelets can also be used instead of the Morlet wavelet, for instance, Sato and Yamada (1994) used a Meyer wavelet for an analysis of radiosonde data.

The area-preserved (energy density) w wavelet spectrum at 3.00 km is shown in Fig. 10. Only wave periods of less than 600 min (10 h) are displayed in the wavelet plot since progressively less energy was associated with the long period vertical velocity components. The dominant energy at this height was associated with the activity between 1600 and 2000 LT 13 October. The peak period of this disturbance was between 50 and 70 min. Analysis of the wavelet spectra above and below 3.00 km showed that the peak period increased from 50–60 min at 2.10 km to 70–80 min at 3.60 km. Above 4.50 km, the fluctuations decreased in amplitude significantly and were not resolvable.

Oscillations close to the Brunt–Väisälä period dominated the wavelet spectra in Fig. 10 between 0200 and 0600 LT 14 October. At 3.00 km, this time interval corresponded to the main inversion layer. These oscillations had periods of 7–11 min, during which time the Brunt–Väisälä period was 6 min. Another time when high-frequency oscillations contributed significantly to the energy was at 1400 LT 14 October. During this time, the Brunt–Väisälä period was about 10 min. This time of enhanced energy coincided with observations of large σ1/2 although this was only visible in the spectral width plot at altitudes above 3.5 km. The vertical N2 profile at this time showed statically unstable conditions at several altitudes from 3.2 km upward, suggesting that the observed high-frequency waves at 3.0 km are related to the large σ1/2 higher in the atmosphere. Oscillations of periods less than 10 min in w and Tυ were observed up to 6.0 km in different wavelet spectra.

The effects of the precipitating convective cell at 1200 LT 13 October were not visible in the 3.00-km wavelet analysis as this was above the enhanced σ1/2 region. In the 2.10-km spectrum, a dominant period of 55 min was observed, which was weakly visible at 2.55 km (near the top of enhanced σ1/2). Energy from this convection did not propagate above the limits of the spectral width increase.

b. Wavenumber domain

Four area-preserved wavenumber spectra are displayed in Fig. 11. The mFu(m) spectrum is marked by the solid line, the mFu(m) spectrum by the dashed line, the mFw(m) spectrum by the dotted line and the ((g/N))2(T ′/T) spectrum by the dash–dot line. A model of area-preserved saturated temperature wavenumber spectrum of (Tsuda et al. 1991):
i1520-0426-24-4-602-e8
with a Brunt–Väisälä period of 10 min used is also marked by the dash–dot straight line. A model area-preserved saturated horizontal wavenumber spectrum is given by
i1520-0426-24-4-602-e9
and is displayed by the solid straight line in Fig. 11. For each case, the spectral data were averaged over an hour-long interval. Only tropospheric wind data between 2 and 15 km were included because the inclusion of stratospheric data would result in incorrect spectra. Because of large data gaps at higher altitudes, only temperature data between 2 and 8 km were used. Figure 11a shows the wavenumber spectra from 1130 until 1230 LT 13 October, which corresponded in time with the observation of the precipitating convection below 3 km. The spectra in Fig. 11b corresponded to the time of large vertical motion below 4-km altitude. An inversion layer at 3-km altitude was present at 0300–0400 LT 14 October, with the spectra at this time shown in Fig. 11c. Figure 11d corresponded to the region of enhanced σ1/2 on 14 October, between 1330 and 1430 LT.

In each case, the horizontal wind and temperature spectra were similar in energy and showed that longer wavelengths were associated with more energy. The horizontal wind spectra at all times except Fig. 11b exhibited gradients less than the model predictions. This was most notable during the precipitating convection time of Fig. 11a. Temperature spectral gradients were consistently less than the universal spectra model predictions. This may be due to the atmospheric conditions such as the temperature inversion layer and convective effects. Noise contamination may also exist at the higher wavenumbers, thus also producing a shallower slope than the model predicts.

The vertical wind wavenumber spectra also showed that longer wavelengths were associated with increased energy, which may be due to the presence of nearby mountains as well as synoptic-scale processes. An increase in spectral energy around 2-km wavelength associated with gravity waves was previously reported at the MU radar site (Fritts et al. 1988; Tsuda et al. 1989, 1991). However, 2-km peaks were not visible in Fig. 11, perhaps because of the availability of longer datasets in previous analyses.

7. Discussion

The dominant feature of the campaign period was the presence of a stable temperature inversion layer at 2.5–3.0 km. This layer split in the afternoon of 13 October, with an unstable layer between two regions of enhanced stability. This split may be related to the southward airflow over Japan and the AMEDAS observations, which showed a southward-moving rainband. As expected from Eq. (4), temperature perturbations increased inside regions of enhanced stability. Inside the nocturnal 3-km layer, high-frequency vertical velocity perturbations w′ were noticed. Wavelet analysis revealed their periods to be 7–11 min, which was slightly longer than the Brunt–Väisälä period of 6 min.

Another important feature during this relatively calm observation period was the presence of vertical velocity perturbations on the afternoon of 13 October, which had a period of about 1 h. The amplitudes of these waves decreased with altitude. The vertical wind variance associated with these perturbations was largest below 2 km and decreased to a negligible level at the top of the 3.5-km inversion layer. Corresponding calculations of the heat flux showed that most Q was confined below the top of the inversion as well. The inversion layer at 3.5 km acted to inhibit significant upward heat flux propagation. A covariance analysis of this period below the inversion top was consistent with convective lifting of the air.

A small precipitating convective cell passed above the MU radar at 1200 LT 13 October. While no precipitation radar was operational at the MU radar site, information about the convection was deduced concurrently with the examination of the whole campaign dataset. Analysis of the Doppler spectral width and turbulent energy dissipation rate revealed significant enhancements associated with the precipitating convection. The top of the ε enhancement corresponded with the top of the temperature inversion layer. The wavelet energy spectrum at 2.10 km revealed the dominant wave period associated with this precipitating convection to be 55 min. Increases in the vertical wind variance during the event were confined below 3 km. Heat fluxes were negligible during the precipitating convection.

8. Conclusions

MU-RASS data were analyzed during a 39-h campaign on 13–14 October 2001 with the objective of studying tropospheric stability and its relation to other atmospheric parameters. The MU-RASS provided an excellent dataset with which to study atmospheric phenomena and its relation to stability. The high temporal resolution permitted a detailed analysis of atmospheric stability and its effects on wave propagation and energy in the troposphere of a kind not previously performed with the MU-RASS. Study of processes on the scale of a few minutes is not possible using coarse temporal resolution radiosondes. However, the collocated radiosonde launches during the campaign allowed direct comparison between MU-RASS and radiosonde parameters, which showed good agreement.

Wavelet analysis of the vertical wind velocity data was shown to be useful in isolating the dominant wave periods at different times and heights. This assisted in the calculation of the wind and temperature variances.

While no meteorologically significant phenomena such as cold fronts or large convection occurred during the campaign period, the stability profiles were not constant. A small precipitating convective event was identified and studied using the MU-RASS data, despite the lack of a precipitation radar for direct observations. Larger atmospheric phenomena would be expected to transmit energy and momentum flux into the lower stratosphere and as such future work will focus on isolating these events.

Acknowledgments

This research was supported by the Kyoto University Active Geosphere Investigations for the 21st Century COE (KAGI21) Grant 15216301, which was approved by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The study was partially supported by Grants-in-Aid for Scientific Research (B) 14340140 and 18340140 and partially supported by a Grant-in-Aid for Scientific Research on Priority Area-764 (A04) 13136203. We thank two anonymous reviewers whose valuable comments improved earlier versions of this manuscript.

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Fig. 2.
Fig. 2.

The (a) mean RASS Tυ (solid line) and mean radiosonde Tυ (dashed line) and (b) their difference. (c) The mean RASS N2 profile (solid line) and radiosonde N2 profile (dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 3.
Fig. 3.

The spectral width obtained with the (0°, 10°) radar beam.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 4.
Fig. 4.

The derived energy dissipation rate ε.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 5.
Fig. 5.

Contour plot of the virtual Brunt–Väisälä frequency squared N2 up to 8 km, with 6-h high-pass-filtered temperature perturbations T ′υ. Missing N2 values are colored white. Numbers on the plot are referred to in the text.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 6.
Fig. 6.

Contour plot of the virtual Brunt–Väisälä frequency squared N2, with 6-h high-pass-filtered vertical velocity w′ perturbations. Numbers on the plot are referred to in the text.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 7.
Fig. 7.

The 30-min low-pass-filtered virtual Brunt–Väisälä frequency squared N2 with (a) the horizontal wind variance overplotted, (b) the vertical wind variance, and (c) the temperature variance.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 8.
Fig. 8.

Covariances for the 12-h interval of 0800–2000 LT 13 October at nine heights as indicated in the titles.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 9.
Fig. 9.

Heat flux calculated from the covariance of temperature and vertical wind. Most of the heat flux is associated with the 13 October disturbance.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 10.
Fig. 10.

Wavelet energy spectrum of the 3.00-km altitude vertical wind velocity. The dominant wave component between 1600 and 2000 LT of about 60 min is clearly apparent. Waves with periods close to the Brunt–Väisälä period are visible between 0000 and 0400 LT 14 October.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Fig. 11.
Fig. 11.

Area-preserved wavenumber spectra at four different hour-long times as annotated in the titles. The u′ spectra are marked by the solid lines, υ′ spectra by the dashed lines, w′ spectra by the dotted lines and ((g/N))2(T ′/T) by the dash–dot lines. The saturated model spectral slope of temperature with gradient −2 is marked by the dash–dot line, while the saturated model spectral slope of horizontal wavenumber is marked by the solid line.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

i1520-0426-24-4-602-f01

Fig. 1. Horizontal wind velocity field below 8 km. The scale to the top right shows a 40 m s−1 wind vector in the zonal (horizontal) and meridional (vertical) directions.

Citation: Journal of Atmospheric and Oceanic Technology 24, 4; 10.1175/JTECH2046.1

Table 1.

MU-RASS observational parameters.

Table 1.
Table 2.

Acoustic speaker parameters.

Table 2.
Table 3.

Clear-air echo observational parameters.

Table 3.
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