Range-imaging observations of cumulus convection and Kelvin-Helmholtz instabilities with the MU radar



[1] In the present work, we report observations of cumulus convection and Kelvin-Helmholtz (KH) instabilities in the troposphere at high vertical and time resolution with the middle and upper atmosphere (MU) radar (46.5 MHz, 34.85°N, 136.10°E, Japan). A detailed morphology of the structures could be obtained through application of range-imaging technique (called frequency radar interferometric imaging (FII) or range imaging (RIM)) with the Capon processing method. The usefulness of this work lies in the demonstration of the performance of the MU radar in range-imaging mode for investigating various atmospheric phenomena at small scales. As one case study, we describe the high-resolution echo pattern during a convective event. It is found that the convective cells formed in the early afternoon and reached a maximum altitude of about 3.5 km. The high-resolution images revealed thin layers above this altitude, unresolved at the standard 150-m low-resolution mode, associated with vertical oscillations possibly due to gravity waves generated by the convective cells through the mechanism of “obstacle effects.” As a second case study, two clear images of KH billows and waves are shown. The KH billows were observed in the troposphere in regions of strong vertical shear of the horizontal wind and persisted for at least 20 min in both cases. The horizontal wavelengths of the KH waves were estimated to be about 2.5 and 5.7 km, according to the magnitude of the horizontal wind in the altitude range where the dynamic shear instabilities were observed.

1. Introduction

[2] VHF stratosphere-troposphere radars are used for monitoring atmospheric dynamics down to the Bragg (half-wavelength) scale, i.e., a few meters. They are mainly sensitive to clear-air irregularities which are dominantly distributed into horizontally stratified layers in the free atmosphere in the absence of convection. However, because of their lack of radial resolution (typically 75–150 m), these radars only provide a coarse image of the true vertical distribution of the atmospheric scatterers. Palmer et al. [1999, 2001], Luce et al. [2001a, 2001b], Chilson et al. [2001, 2003], Smaïni et al. [2002], Yu and Brown [2004], Chilson [2004], Fernandez et al. [2005], and recently Luce et al. [2006], for example, have theoretically and experimentally shown that range imaging (called frequency radar interferometric imaging (FII) and range imaging (RIM)) with various processing methods can significantly improve the range resolution of the mesosphere-stratosphere-troposphere (MST) radars and UHF wind profilers. Among various processing methods, the nonparametric adaptive filter bank Capon method [e.g., Stoïca and Moses, 1997], is most often used. Indeed, its application does not require any a priori information about the vertical distribution of the atmospheric scatterers and its performance in range resolution is much better than the Fourier method when signal-to-noise ratio (SNR) typically exceeds 0 dB [e.g., Palmer et al., 1999; Luce et al., 2001a]. According to radar balloon data comparisons shown by Chilson et al. [2001] and performed in November 2005 with the MU radar [Luce et al., 2007], the Capon method provides a range resolution of several ten meters or better for high SNR (>0 dB).

[3] The MU radar system was upgraded in March 2004 for being operated with five frequencies switched pulse to pulse within an increased receiver bandwidth of 2 MHz around a carrier frequency of 46.5 MHz (see G. Hassenpflug et al., System description and demonstration of the new middle and upper atmosphere radar imaging system: 1-D, 2-D and 3-D imaging of troposphere and stratosphere, submitted to Radio Science, 2006, for more detail). In imaging modes, the covariance matrix of the received signals is first estimated (see Luce et al. [2006] for more detail on the implementation). This matrix is an input to the Capon method, which provides the so-called range brightness (or power) distribution. The method has already been described in the aforementioned papers and the reader should refer to these works for the practical procedures.

[4] Very detailed images of echoes produced by cumulus convection and Kelvin-Helmholtz instabilities are described in the present paper. Three observation sequences are shown, selected from two periods of radar observations performed on 19 July 2005 and on 13 November 2005. The first sequence of about 65 min reveals convective cells and the second and third sequences of 20 and 32 min show Kelvin-Helmholtz (KH) waves and billows in the troposphere. KH billows in the troposphere have been reported many times from observations using frequency modulated continuous wave (FMCW) radars, acoustic sounders or lidars (e.g., Browning and Watkins [1970] or more recently, Eaton et al. [1995], Chapman and Browning [1997] and İnce et al. [2003]) and using a 915-MHz UHF wind profiler with the range-imaging technique [Chilson et al., 2003] but this work constitutes, to our knowledge, the first direct and unambiguous observation at VHF with the range-imaging technique. Palmer et al. [2001, Figure 3a] showed billow-like structures at 4 km with the VHF SOUSY radar during the SOMARE-99 experiment but, as mentioned by the authors themselves, the observed period of the oscillations did not support the hypothesis of KH billows. Luce et al. [2001b] described an event of KH instability with the range-imaging technique but the structures did not clearly appear after the Capon processing because the technical limitations of the MU radar for range-imaging applications did not permit an optimal utilization of the technique at that time.

[5] The format of this paper is as follows. In section 2, the MU radar configurations used for the range-imaging experiments are described. The observational results for the three atmospheric events are shown in section 3 and concluding remarks are given in section 4.

2. Experimental Configuration

[6] The two experiments in range-imaging mode were conducted from 1303 LT on 19 July until 1342 LT on 20 July 2005 and from 2152 LT on 13 November until 1202 LT on 16 November 2005. The main radar operating parameters for both experiments are summarized in Table 1. Five equally spaced frequencies from 46.0 to 47.0 MHz (i.e., with a frequency spacing of 0.25 MHz) were applied. A four- and sixteen-bit optimal phase coding was used in July and November, respectively. SNR and power after the Capon processing of the truncated range gates (i.e., the first 3 and 15 range gates, respectively) were corrected for attenuation effects as explained by Spano and Ghebrebrhan [1996]. Range sampling was performed from 1.05 km (1.50 km) up to 20.10 km (20.55 km) AGL with a step of 0.15 km in August (July). Two beams, one vertically oriented and one tilted 10° off zenith toward north, were switched pulse to pulse for application of range imaging in both directions. Only the results for the vertical beam are shown in the present paper because further works are needed for interpreting the results when an oblique beam is used. One profile is obtained every 16.38 s and the time resolution is 32.77 s. It is worth noting that this time resolution, even though quite common, is better than the time resolution used for standard observations (i.e., typically 1 or 2 min). A time resolution significantly better than a few minutes is a necessary condition for observing phenomena of similar periods, such as KH instability.

Table 1. Operating Radar Parameters for the MU Radar in Range-Imaging Mode During the July and November Experiments
 July 2005/November 2005
Number of frequencies5
Frequencies, MHz46.00, 46.25, 46.5, 46.75, 47.00
Number of beams2
Beam directions (zenith, azimuth)(0°,0°), (0°, 10°)
Coherent integration number128
Time resolution for one sample, s0.51
Number of samples for one record64
Acquisition time for one record, s32.77
Time sampling, s16.38
Number of records per sequence71/111
Time duration of one sequence, min19.38/30.65

[7] Each sequence of range-imaging observations was separated by two or four records of a standard five-beam Doppler beam swinging (DBS) mode at a range resolution of 150 m, mainly for complementary wind measurements. The reader can refer to Fukao et al. [1990] for more details about this mode. Unfortunately, a technical problem occurred in July, producing clutter-like echoes, and profiles could only be retrieved by hand from a careful inspection of the Doppler spectra. In spite of the poor accuracy, they will be used since they provide important qualitative information on the interpretation of the observations.

3. Observational Results

[8] Time-altitude plots of SNR at a height resolution of 150 m revealing the convective cells and the two KHI events are shown in Figures 1a, 1c, and 1e, respectively. The corresponding images of power after the Capon processing are shown in Figures 1b, 1d, and 1f. Note that the altitude ranges and periods have been chosen specifically for the events discussed in the present work. The corresponding time-altitude plots of radial velocity and spectral width at a height resolution of 150 m calculated from the Doppler spectra measured by the vertical beam are shown in Figure 2. The wind profiles estimated from the DBS data before and after the selected sequences are presented in Figures 3a, 3b, and 3c.

Figure 1.

(a, c, e) Time-altitude plots of SNR (dB) measured vertically with the MU radar at a vertical resolution of 150 m for the three periods discussed in the text. (b, d, f) Corresponding images of Capon power (dB).

Figure 2.

(a, c, e) Time-altitude plots of radial velocity measured vertically corresponding to the plots shown in Figure 1. (b, d, f) Corresponding plots of raw spectral width of the Doppler spectra. The vertical resolution is 150 m.

Figure 3a.

Zonal and meridional components of wind profiles obtained from the five-beam DBS mode at 1434 LT (thick lines) and at 1457 LT 19 July 2005 (thin lines).

Figure 3b.

Same as Figure 3a at 1845 LT (thick lines) and 1908 LT 19 July 2005 (thin lines).

Figure 3c.

Same as Figure 3a at 2148 LT (thick lines) and 2234 LT 13 November 2005 (thin lines).

3.1. Case of Cumulus Convection

[9] As reported by Sato [1992] and Sato et al. [1995], cumulus convection is often observed with the MU radar during midsummer afternoons, after the maximum of solar heating. The convection can show (1) large updrafts and downdrafts (sometimes with peaks up to 10 m s−1) measured by a VHF radar at a vertical incidence, (2) large (vertical beam) spectral widths, resulting from both clear air turbulence and transient effects due to the nonstationarity of the nonturbulent wind component during the observation time, (3) strong enhancement of the radar reflectivity, resulting from clear-air turbulence and possibly Rayleigh scattering from hydrometeors [e.g., Hooper et al., 2005]. Because of its small spatial scale, cumulus convection is also associated with strong horizontal inhomogeneity of turbulence and wind fields, producing large errors when estimating wind components with the classical DBS method.

[10] All the features of cumulus convection described above are found in the radar observations from 1351 LT until 1456 LT on 19 July 2005 shown in Figures 1a, 1b, 2a, and 2b at the standard resolution and after the Capon processing, respectively. Convective cells can be easily distinguished in Figure 1a and even more easily in Figure 1b and the top of the cumuli does not exceed the altitude of 3.5 km around 1400 LT. However, the available scanning weather radar plots did not reveal precipitation during this period. Infrared or visible satellite images of Southeast Asia do not seem to indicate the presence of cumulus at 1300 LT and 1500 LT suggesting a very short-time and localized event. These structures are associated with large values of SNR, especially near their top. Figure 2a shows a time-altitude plot of radial velocities measured with the vertical beam. Quite large updrafts and downdrafts are observed with peaks of ±2.5 m s−1. Fluctuations are not only observed in the altitude range associated with the strong echoes but also above, with decreasing intensity, at least up to about 5 km around 1410 LT. Figure 2b shows the corresponding raw spectral width (i.e., the spectral width not corrected for beam broadening, expected to be small here since the wind speed did not exceed 10–20 m s−1 in the considered altitude range). The spectral width is strongly enhanced (up to about 4 m s−1) in the region associated with the cumulus convection, while it is quite small for the thick horizontally stratified echoing layer around 3 km, seen before and after the convective cells, and for the poorly organized echoing structures observed between 3.5 and 5 km (Figure 1a). In contrast, the Capon image in Figure 1b nicely delimits the convective cells with a quite uniform spread of the intensity within the structures. Thus it is confirmed that the Capon processing does not produce artifacts when scatterers are expected to fill the whole radar volume. On the contrary, the Capon image reveals several peaks distributed in altitude of power around 3 km while the structure appeared as the thick and single layer at the standard resolution in Figure 1a. Even more striking are the thin layers with wavelike appearance above 3.5 km in Figure 1b, while the same structures appeared more or less sporadic with the standard 150-m resolution (Figure 1a). Contrary to the echoes associated with the convective cells, these thin echoing layers are strongly aspect sensitive (i.e., echo power in the oblique is much smaller than in the vertical direction, not shown), indicating that they likely result from partial or diffuse reflection from thin stable layers. Some of these echoes are associated with vertical displacements which appear to be nearly sinusoidal (giving credence to their reality) in the high-resolution image and are impossible to distinguish in the standard pattern.

[11] Cumulus convection is one of the sources of atmospheric gravity waves, in particular in tropical regions. Since these waves can transport momentum far away in altitude, they can strongly contribute to the momentum budget of the stratosphere, for example. For this reason, many results of numerical simulations have been recently published for estimating the parameters of gravity waves generated by mesoscale convective systems [e.g., Song et al., 2003; Lane and Knievel, 2005].

[12] Our experimental observations seem to support the presence of gravity waves generated by the convective cells.

[13] 1. As already reported by Sato et al. [1995] with the MU radar, the presence of vertical wind disturbances well above the top of the cumuli can be explained by the propagation of gravity waves.

[14] 2. The clear, nearly sinusoidal, oscillations of the thin aspect sensitive layers revealed in the high-resolution image of Figure 1b above the top of the cumuli may result from distortions of the isentropic surfaces due to the propagation of gravity waves. Indeed, since the analysis of the 24-hour data set we performed did not reveal similar oscillations in the absence of cumulus convection, the simultaneous observations of convection with the above wave disturbances of thin layers may not be fortuitous.

[15] 3. The vertical structure of the horizontal wind could be favorable to the generation of gravity waves by “obstacle effects” [e.g., Kuettner et al., 1987]. The convective cells or turrets can act as mountains in the atmosphere since the horizontal displacement of the turrets is governed by the wind near the ground, usually much weaker than the wind near the top of the cumuli. Figure 3a shows the vertical profiles of meridional and zonal wind components and horizontal speed at 1434 and 1457 LT up to about 7 km as deduced from DBS-mode data. The zonal component is weak (except below 2.5 km at 1434 LT but the estimates can also be affected by the strong inhomogeneity of the wind field in the convective clouds) and the southward meridional component shows a significant increase with altitude from a few m s−1 around 1.5 km to about 15 m s−1 around 5 km (corresponding to a mean vertical shear on the order of 3–5 m s−1 km−1). The observed vertical shear of the horizontal wind can be a factor in gravity wave generation by obstacle effects since a vertical shear as small as 3 m s−1 km−1 may be sufficient according to the observations shown by Kuettner et al. [1987]. Thus the available wind profiles seem to suggest that the mechanism of “topographic effects” may have been possible during the period of observations in addition to or instead of thermal forcing or “mechanical oscillator effects” [e.g., Alexander et al., 1995].

3.2. Cases of Kelvin-Helmholtz Instability

[16] KH billow structures were frequently observed in the atmospheric boundary layer using lidars [e.g., Blumen et al., 2001; Newson and Benta, 2003], or meteorological FMCW decimeter radars [e.g., Gossard, 1990, and references therein; Metcalf, 1975; Eaton et al., 1995; Chapman and Browning, 1997; İnce et al., 2003], but also at higher altitudes, in the troposphere [Browning and Watkins, 1970] or up to the tropopause in upper level frontal zones [e.g., Reed and Hardy, 1972]. These structures result from a dynamic instability produced by a sufficiently strong wind shear in a statically stable flow. They can be described as growing waves oriented perpendicular to the direction of the wind shear and can possibly break into 3-D turbulence at smaller scales. Their crest-to-trough amplitudes do not usually exceed a few hundred meters. Because of the lack of vertical resolution of the ST VHF radars, only indirect observations could be made, usually via velocity measurements [e.g., Klostermeyer and Rüster, 1980; Rüster and Klostermeyer, 1983]. In case of KH instability, the vertical velocities show large fluctuations resulting from vertical motions of the wave. More details on the morphology of the structures have been obtained using the dual FDI technique [Chilson et al., 1997] and “cat's eye” structures have been revealed using another high-resolution technique by Röttger and Schmidt [1979]. Braided structures resulting from a KH instability has been successfully reported using the Capon method with a 915-MHz radar [Chilson et al., 2003].

[17] Figures 1c and 1d show similar information as Figures 1a and 1b for another selected period from 1847 LT until 1907 LT on 19 July 2005. Also, Figures 2c and 2d show time-altitude plots of (vertical beam) radial velocity and Doppler spectral width, respectively. The SNR plot at a 150-m vertical resolution only reveals, roughly, three echoing layers around 2.4 km, 2.8 km and 4 km. The radial velocities (Figure 2c) around 2.5 km show rapid oscillations over a height range of about 1.5 km with a maximum peak to peak amplitude of about 1.3 m s−1 around minute 14. A period of the fluctuations of about 2.5 min can be deduced from the plots and has been confirmed from a spectral analysis (not shown). A phase offset can be ascertained just below 3 km indicating the presence of a possible critical level. Figure 2d reveals a significant enhancement of the spectral width with a maximum at the altitude range where the vertical velocity disturbances are large. These characteristics reveal the presence of a KH instability associated with turbulence, as shown, for instance, by Klostermeyer and Rüster [1980] and Chilson et al. [1997]. The morphology of the KH waves cannot be observed in Figure 1c because of the lack of vertical resolution. In the Capon image of Figure 1d, the KH instability pattern is now clear, especially between minutes 12 and 18 where a breaking wave structure is recognized around 2.7 km. The KH wave breaking seems to be responsible for the apparent distortion of the top of the thick echoing layer about 300 m below, around 2.3 km, and, especially between 12 and 18 min, in agreement with the vertical extent of the vertical wind disturbances (Figure 2d). It is interesting to note that the horizontal scales of the disturbances at the top of the thick layer correspond to the horizontal scale of the KH wave and are in phase, indicating a possible direct influence of the KH wave on its stable environment. Even more evident examples of this phenomenon will be shown when analyzing the second KHI case. Such detailed information cannot be obtained with standard VHF range resolutions, but becomes possible with the range-imaging technique.

[18] The time lag between two crests of the well-defined structures centered around 15 min is about 170 s, i.e., close to the 2.5 min period obtained from the velocity measurements at this time. According to the wind profiles derived from the DBS mode at 1845 LT and 1908 LT (Figure 3b), it is found that the prevailing wind was mainly southward, typically 15 m s−1 in the altitude range where the KH instability was observed, with a significant vertical shear of the horizontal wind of about 25 m s−1 km−1. Since the zonal wind component is much weaker, the shear direction is also southward, compatible with the orientation of the breaking wave as suggested by the high-resolution image in Figure 1d. Considering that the sheared layer thickness is about 400 m (i.e., approximately the crest-to-trough amplitude of the KH instability), it is expected from theory that the most rapidly growing unstable disturbance has a horizontal wavelength 7.5 times larger [e.g., Fritts and Rastogi, 1985], i.e., about 3000 m in the present case. If we consider that the structure is indeed advected by the wind, it can be deduced that the horizontal scale is 15 × 170 = 2550 m, i.e., close to the expected value.

[19] A second KH instability event observed in the troposphere during the November experiment is shown in Figure 1e (at a vertical resolution of 150 m) and Figure 1f (at a better resolution after the Capon processing). The corresponding height-time plots of vertical velocity and spectral width are shown in Figures 2e and 2f, respectively. The KH wave patterns are particularly evident for at least 20 min until 2210 LT. Unfortunately, the range-imaging experiment started at 2152 LT and the beginning of the event could not be observed. Their amplitudes are so large around 5.5 km (about 1 km around min 5) that they can even be distinguished in the initial 150-m resolution plot. The oscillations of the (unfiltered) radial velocities in Figure 2e occur over a height of more than 4 km and their crest-to-trough amplitude exceeded 8 m s−1. The period is about 3 min. Since the mean wind speed was about 30 m s−1 at the altitude of the KH instability (Figure 3c), a horizontal wavelength of about 5.7 km can be deduced. The phase of the oscillations undergoes a clear offset of 90° around 5.5 km, indicating the position of the critical level of the KH instability. The position of the critical level corresponds to the region of strong vertical wind shear exceeding 50 m s−1 km−1, associated with the shear region below the jet stream axis (Figure 4). The wind shear was significantly smaller at 2234 LT than at 2148 LT, compatible with the decay of the KH instability.

Figure 4.

Vertical profiles of horizontal wind shears corresponding to the wind profiles shown in Figure 3c.

[20] Nearly monochromatic wave-like disturbances are observed in the Capon image around 4 km in the absence of significant shear of the horizontal wind at this altitude, indicating again a possible direct influence of the KH instability on its nearby environment. Also, successive dot-like echoes are noticeable between 6 km and 6.7 km during the first 15 min at the crests of the oscillations in Figure 1f. These structures are not detectable in the standard plot (Figure 1e). The Capon processing does not generate “ghost” structures in adjacent gates, as shown in the aforementioned papers on the range-imaging technique. For instance, ghost echoes do not appear in the Capon image at the top of the convective cells in Figure 1b. Thus we believe that the dot-like echoes are really the signature of a backscattering process from atmospheric structures. Their shape and their absence in the image obtained from the oblique beam (not shown) suggest that they may result from a mechanism of partial reflection from thin stable layers distorted by the KH waves. A similar observation near the tropopause was reported by Gage et al. [1981]. They suggested that systematic oscillations of the echo power were due to the effects of gravity waves on specular echoes.

[21] Figure 5 shows that the vertical velocity disturbances around 4.2 km are in harmony with the nearly monochromatic vertical displacements of the layer at this altitude. The vertical velocities deduced from the variations of position of the layer agree well with those directly measured from the Doppler spectra. The peaks of Doppler velocities have smaller amplitudes than the peaks of the reconstructed velocities, possibly due to underestimation when the Doppler shift is near the Nyquist frequency of the Doppler spectra.

Figure 5.

(top) Variations of height versus time of the layer extracted from the Capon image around 4.2 km where nearly monochromatic fluctuations are observed (see Figure 1f). Superimposed are the corresponding variations of vertical velocity at 4.2 km measured from the Doppler spectra. (bottom) Comparison of the vertical velocity measured from the Doppler spectra and the same parameter deduced from the variations of the layer position in the Capon image.

4. Conclusions

[22] In the present work, we have reported observations of the troposphere with high spatial and temporal resolution using the multifrequency range-imaging technique applied on the MU radar. The purpose of this paper was to demonstrate the high performance of the technique for imaging convective structures and billows and waves resulting from shear flow (KH) instabilities more commonly observed with FMCW radars, lidars and acoustic sounders. The better range resolution obtained with the Capon method also permitted us to reveal the disturbances that convection and KH instabilities produced on the nearby thin stratified layers, possibly due to the propagation of gravity waves generated by these instabilities.

[23] The range-imaging technique with a high temporal resolution can thus be useful for studying the atmospheric processes at small scales. With complementary data collected from other instruments (for example, temperature, humidity and wind data measured by balloons, and collocated observations with other remote sensing techniques such as UHF radar or Raman-Mie lidar available at the MU radar site), more thorough scientific interpretations of the observed phenomena would be possible. Also, comparisons with observations of the temperature and humidity fields at a high vertical resolution would help to validate the observations made in range imaging.


[24] The authors wish to thank the anonymous referees for their constructive comments on the present paper.