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Estimation of turbulence energy dissipation rate and vertical eddy diffusivity with the MU radar RASS
Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
Estimation of turbulence energy dissipation rate and vertical eddy diusivity with the MU radar RASS Eddy Hermawan*, Toshitaka Tsuda Radio Atmospheric Science Center, Kyoto University, Uji, Kyoto, 611-0011, Japan Received 17 March 1999; received in revised form 30 July 1999; accepted 13 September 1999
Abstract We have conducted RASS (Radio Acoustic Sounding System) observations with the MU (Middle and Upper atmosphere) radar on 28±31 July 1994 at Shigaraki, Japan (34851 ' N, 136806 ' E) and determined the characteristics of turbulence energy dissipation rate (e ) and vertical eddy diusivity (K ) in the troposphere and lower stratosphere. We have ®rst examined the accuracy of the Brunt VaÈisaÈlaÈ frequency squared (N 2) derived from RASS temperature pro®les. Then, e and K are determined by using N 2 and the Doppler spectral width of turbulence echoes (s 2turb). We found that the structures of e and K are sometimes aected by the local variations of N 2. We found that sometimes e became small, even though s 2turb was large, because N 2 was small. On the contrary, K was enhanced due to small N 2, although s 2turb was small. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction It is generally recognized that the detailed time± height variations of turbulence parameters such as the turbulent energy dissipation rate (e ) and vertical eddy diusivity (K ) are very important for studying the mixing of minor constituents (e.g., Patra and Lal, 1997). Therefore, they are one of the key parameters in a numerical model that treats the chemistry and dynamics of the troposphere and the middle atmosphere. Observations of e and K have been extensively conducted by in situ measurements made aboard aircraft (e.g., Lilly et al., 1974) and balloons (Barat and Bertin, 1984; Cohn, 1995). Moreover, the possibility of deducing the turbulence parameters, including e and K, from the Doppler spectrum obtained with wind pro®ler radar has been studied (Gage and Balsley, 1978; Gossard, 1990; Hocking, 1985, 1996; Gage, 1990). In these cases, MST (mesosphere±stratosphere±tropo-
* Corresponding author.
sphere) and MLT (mesosphere±lower-thermosphere) radars have been employed as a powerful measurement technique, allowing the estimation of e and K over a quite broad altitude range with far better temporal resolution than previously done with other techniques. There are two major methods to derive turbulence parameters from radar measurements of turbulence echoes Ð the absolute strength of the backscattered echo power and the Doppler spectral width. The ®rst method was applied by Gage et al. (1980), Weinstock (1981a, 1981b, 1981c), and has been extensively reviewed by Hocking (1985). This method requires, however, an accurate pro®le of N 2, the mean gradient of the refractive index, M, and the fraction of the radar volume ®lled with turbulence, F. Therefore, in addition to the radar results, radiosonde pro®les of temperature and relative humidity are also employed, since they are not determined from the radar measurements. The other method utilizes the spectral width of the Doppler spectra determined by the radar. This method was ®rst introduced by Sato and Woodman (1982)
1364-6826/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 4 - 6 8 2 6 ( 9 9 ) 0 0 0 7 5 - 9
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E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
using the 430-MHz Arecibo radar in Puerto Rico and, since then, it has been intensively used in many studies (e.g., Hocking, 1985, 1988). In this method, N 2 is the other necessary parameter to estimate e and K. However, non-turbulent processes that could broaden the spectral width must be compensated for in order to obtain a reliable estimate of e and K. By applying the RASS (Radio Acoustic Sounding System) technique to the MU radar in Shigaraki, Japan (34851 ' N, 136806 ' E), we have successfully measured temperature pro®les simultaneously with the turbulence echoes in the troposphere and lower stratosphere. In this paper, we aim at deriving e and K using N 2 from the RASS pro®les. We carried out the RASS campaign measurement during 28±31 July 1994 and studied the eect of the detailed structure of N 2 on e and K. A similar study has been done by Low et al. (1998), from observations on 30 July 1996, who found that K was high when e was also high. However, they also found that if N 2 was small then K could be large even if e was moderate, indicating that the region was well-mixed due to low stability rather than by active turbulence. We start with a brief review on estimating e and K using the Doppler spectral width, together with a description of the MU radar RASS experiment. We further discuss the detailed structure of N 2 observed by RASS, investigate the accuracy by comparing with the radiosonde data, and then the ®ne structures of e and K are presented.
In this section we brie¯y review the procedure to estimate e and K from the Doppler spectral width. Provided that the spectral broadening is completely due to turbulent processes, a relation between e and spectral width, s 2turb, can be expressed as (e.g., Hocking, 1985) W kgÿ1
1
However, the observed spectral width, s 2obs, contains not only turbulence eects, but also contributions of non-turbulent processes which modify the shape of the spectrum. Under such conditions, the spectral width induced by turbulence alone is given by s2turb s2obs ÿ s2beam ÿ s2shear ÿ s2trans
sbeam 1 d1=2 j u h j
2
where, s 2beam, s 2shear and s 2trans denote non-turbulent processes, the beam broadening eect, shear broadening eect and contamination due to transient atmospheric motions, respectively. The beam broadening eect arises because the radial wind velocity is slightly
3
where d1/2 (11.38 1 0.023 rad for the MU radar) is the half-power half width of the eective (two way) radar beam, and u h is the background horizontal velocity (Hocking, 1990; Nastrom, 1977). For typical MST radar observations with suciently small zenith angle, this eect produces the largest contamination. For a known horizontal wind shear, the shear broadening eect can be evaluated (Nastrom, 1977) as du h Dz sin 158 sshear 10:5 4 dz for an antenna at a zenith angle of 158, and Dz is the sample volume thickness which is 150 m for the present observation with the MU radar RASS. Finally, the contamination due to transient atmospheric motions is estimated by 0 2 strans 14 u2t
2. Estimation of e and K from spectral width
e10:38 Ns2turb
dierent for dierent parts (dierent line-of-sight directions) within a ®nite beam width. The shear broadening occurs when the radial component of the wind changes along the range within the sample volume. The last broadening eect is caused by the wind variations during the interval used for incoherent integration (see Hocking (1985) and (1988) for more detail). In order to estimate s 2turb from s 2obs correctly, we need to remove the contributions of the non-turbulence eects. The beam broadening eect can be quanti®ed as
5
0 where u 2t is the variance of the radial velocity for the integration interval t (Hocking, 1988). After non-turbulence eects have been removed, the turbulent energy dissipation rate can be properly estimated from Eq. (1) and the vertical eddy diusi®ty, K is de®ned as (e.g. Lilly et al., 1974; Weinstock, 1978)
K10:38
s2turb N
m2 sÿ1
6
High time-resolution N 2 pro®les derived from the MU radar RASS experiment are used in Eqs. (1) and (6).
3. MU radar RASS experiments In this section, we brie¯y review the basic principle of RASS, including a ray tracing of acoustic wave fronts for determining an appropriate beam direction of the MU radar. RASS is a ground based remote sensing technique for measuring the height-pro®le of the atmospheric virtual temperature in the troposphere
E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
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Table 1 Observation parameters on 28±31 July 1994 MU radar Height range (km) IPP (ms) Sub-pulse length (ms) Number of beams Number of Rx channels Coherent integration Sample height Sample rate (ms) Time series Incoherent integration Observation time (s) Maximum Doppler shift (m sÿ1)
1.20±10.65 402 2 6 2 30 6 72.4 128 4 37.0 222.3
5.10±14.55 432 2 6 2 22 6 57.0 128 5 36.5 228.3
Accoustic source Transmitter Waveform Pulse length (s)
Loudspeaker CW No
Pulse interval (s) Repetition period (s) Chirped frequency (Hz)
No 3.0 85±115
Number of pulses
No
Pneumatic transducer Pulse 0.4 (1.20±10.65 km) 0.4 (5.10±14.55 km) 0.5 (10.50±19.95 km) 10 No 85±115 (1.20±10.65 km) 93±103 (5.10±14.55 km) 87±97 (10.50±19.95 km) 4
and lower stratosphere, with good time-resolution of a few minutes and moderate height-resolution of about 150±300 m. Acoustic waves emitted from a high-power transmitter on the ground produce sinusoidal variations of atmospheric density, resulting in radio refractive index perturbations. A radar tracks the acoustic wave fronts, and strongly scattered radio waves (RASS echo) can be received. However, there are two necessary conditions to detect RASS echoes: the wave number vector of the incident radio wave must be perpendicular to the acoustic wave fronts, and the acoustic wavelength must be half the radar wavelength for optimum Bragg resonance. The Doppler velocity of the RASS echo corresponds to the apparent sound speed, from which the radial wind velocity of the ambient atmosphere, available from simultaneous MU radar measurements, must be subtracted. Then, the obtained true sound speed cs, can be related to the virtual temperature Tv as Tv
cs kd
1=2
7
where kd=20.046 for a dry atmosphere. Estimation of Tv pro®les with the RASS technique can be simpli®ed by using a vertically pointing beam.
10.50±19.95 414 2 6 2 24 6 59.6 128 5 38.2 2 27.0
However, RASS echo detection will fail under strong background horizontal winds due to advection of the acoustic wave front. Therefore, we use real time acoustic wave ray tracing, and steer the antenna appropriately as described by Masuda (1988). The eective echoing range largely depends on the background wind structure, but it is not so sensitive to the temperature pro®le. Thus, for the ray-tracing computation we use temperature pro®les taken from a previously launched radiosonde, while wind velocity pro®les are updated from time to time by using simultaneous MU radar data. In this study, we used data collected from 23:00 LT on 28 July to 16:00 LT on 31 July 1994. The observation parameters are shown in Table 1, which indicates three height ranges (1.20±10.65, 5.10±14.55 and 10.50±19.95 km), and three acoustic transmissions with chirped frequency of 85±115, 93±103 and 87±97 Hz, respectively. Between pulses the beam was switched to the next direction, so that six directions were covered in sequence, i.e. the vertical, four oblique directions at a zenith angle of 158 in the North, South, East and West azimuths, and the sixth direction was appropriately changed by considering the real-time ray tracing of the acoustic wave fronts in order especially to detect RASS echoes. Both radial wind velocity and sound speed in each
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Fig. 1. Comparisons between RASS and radiosonde measurements in determining the virtual temperature (left-panel), (centerpanel) N 2 pro®les and (right-panel) accuracy of N 2 RASS for observation on 29 July 1994 from 02:41 to 03:41 LT. Triangle marks denoted RASS experiments.
beam direction were measured every 3.2 min. Although the range resolution was 300 m, data were oversampled with a height interval of 150 m from 1.67 to 19 km altitude. Our analysis concentrates on heights of 2±13 km where the quality of the RASS data is best. During the experiment, we also launched nine radiosondes which made measurements of pressure, temperature and water vapor mixing ratio.
with those derived from a radiosonde. Statistics of the normalized dierence are used to assess the accuracy of N 2 obtained with the RASS technique. Fig. 1 illustrates an example of the discrepancy between individual pro®les taken on 30 July 1994, where the left, center and right panels show the virtual temperature pro®le, Tv, N 2 and the normalized dierence (DN 2) between RASS and radiosonde measurements de®ned as
4. Pro®les of from the MU radar RASS observations DN 2
2
In this section, we compare RASS-derived N values
N 2RASS ÿ N 2sonde 100% N 2sonde
8
Table 2 Results of statistical analysis for observations on 29±31 July 1994 Launch time of radiosonde (LT)
Height of analysis (km)
Number of data points
DN2 (%) Mean value
Standard deviation
29 July 02:41 08.39 14:46 20:49
2.3±11.3 2.3±11.3 2.3±11.3 2.3±11.3
61 61 61 61
18.2 18.0 18.4 18.2
10.8 13.8 17.9 11.6
July 30 02:32 14:34 23:54
2.3±11.3 2.3±11.3 2.3±11.3
61 61 61
15.1 13.0 14.5
12.0 9.6 11.0
July 31 08:34 14:48
2.3±11.3 2.3±11.3
61 61
13.8 15.0
8.9 7.6
61
16.0
11.5
Average
E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
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Fig. 2. Time±height section of Brunt VaÈisaÈlaÈ frequency squared, N 2 observed with the MU-RASS on 28±31 July 1994.
The RASS temperature pro®le was averaged for one hour from 14:34 to 15:34 LT. Since the sampling interval of the RASS measurements is approximately 150 m, we have 61 data points in this altitude range. The mean value and standard deviation of DN 2 are about 13.0 and 9.6%, respectively. We have repeated a similar analysis for all of the available radiosonde data, and summarize the results in Table 2. Average values for the mean and standard deviation of DN 2 are about 16.0 and 11.5%, respectively, where the average number of data analysis points is 61. We present, in Fig. 2, the detailed time±height sec-
tion of N 2 observed with the MU radar RASS during the observation period from 23:00 LT on 28 July to 16:00 LT on 31 July 1994. The RASS pro®les were averaged for 60 min so that Fig. 2 consists of 66 pro®les of N 2. Although some data are missing, from 06:55 to 10:09 LT on 30 July 1994, we mostly obtained continuous pro®les of N 2 between 2 and 13 km. Large variations are seen in the rapid increase of N 2 from minimum to maximum close to 18 10ÿ5 rad2 sÿ2 between 6.5 and 9 km from 15:42 LT on 29 July to 06:28 LT on 30 July, and from 10:09 LT on 30 July to 04:09 LT on 31 July 1994. Small variations are seen by the rapid decrease of N 2 from maximum to minimum
Fig. 3. The same as Fig. 2, but observed with the radiosonde.
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E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
Fig. 4. The same as Fig. 2, but for the turbulent spectral width, s 2turb.
close to 2 10ÿ5 rad2 sÿ2 on 29 July, from 09:55 to 15:14 LT between 10.6 and 12.3 km, and from 12:00 to 21:55 LT on 29 July 1994. We can also see strong stable layers close to 3 and 4.5 km from 23:00 LT on 28 July to 05:46 LT on 30 July 1994. Also occurring are downward phase progressions of N 2 close to 0.88 m sÿ1 between 5.8 and 8.7 km from 12:29 LT on 30 July to 07:12 LT on 31 July 1994 and 0.99 m sÿ1 between 2 and 5.5 km during 10:05 LT on 30 July to 09:07 LT on 31 July 1994. We also plot the time±height variations of N 2 using nine radiosonde pro®les in Fig. 3, which shows that
the radiosonde misses much of the dynamical variation. Thus, it is obvious that radiosondes are not well suited to provide detailed time variations of N 2. 5. Time±height variations of e and K In this section we discuss the characteristics of the turbulent energy dissipation rate, e, and vertical eddy diusivity, K. Particular emphasis will be directed here towards eects of N 2 on e and K. We start this section by showing time variations of the turbulent spectral
Fig. 5. The same as Fig. 2, but for the turbulent energy dissipation rate, e.
E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
1129
Fig. 6. The same as Fig. 2, but for vertical eddy diusivity, K.
width, s2turb in Fig. 4 as the key parameter necessary to estimate e and K. Then, we show e and K in Figs. 5 and 6, respectively. Fig. 4 shows large variations of s 2turb, especially from 12:42 to 20:14 LT on 29 July 1994 between 7 and 9 km and a large value between 21:11 LT on 29 July and 07:04 LT on 30 July between 6 and 10 km, close to 0.3 m2 sÿ2. Small variations appeared between 6 and 10 km from 23:00 LT on 28 July to 14:00 LT on 29 July, and from 19:23 LT on 30 July to 06:28 LT on 31 July, close to 0.02 m2 sÿ2. The time±height variations of e on 28±31 July 1994 are presented in Fig. 5. By comparing Figs. 4 and 5, we can see the similarity of the structure indicating that e is mostly determined by s 2turb rather than by N 2. However, a discrepancy between the structure of e and s 2turb can be recognized during 09:55±15:14 LT on 29 July between 10.6 and 12.3 km. For this exceptional case, N 2 was very small, although s 2turb was moderately large. As a result, e became small, as suggested by Eq. (1). We present in Fig. 6 time±height variations of K for 28±31 July 1994, whose pattern shows some dierences from that in Fig. 4. We can see an enhancement of K on 29 July from 12:00 to 21:55 LT between 6.7 and 9 km. Considering Eq. (6), K can become large (1.8 m2 sÿ1), when N 2 is small (0.2 m2 sÿ1), even though s 2turb is small. That is, the region is well-mixed due to low static stability rather than by active turbulence.
MU radar RASS technique for determining ®ne structure of the turbulent energy dissipation rate, e, and the vertical eddy diusivity, K, in the troposphere and lower stratosphere with good time and spatial height resolution. First, we have applied the RASS technique to obtain detailed time±height variations of N 2, which is one of the important parameters needed to estimate e and K. The ®ne structure of N 2 was investigated from 23:00 LT on 28 July to 16:00 LT on 31 July 1994. We have validated the RASS results comparing them with radiosonde pro®les and shown that the normalized dierence was about 16%, with a standard deviation of 11.5%. We have simultaneously analyzed the spectral width, s 2turb, of Doppler spectra from the turbulence echo measurements made with the MU radar, and determined the ®ne structures of e and K, using N 2 from the RASS pro®les. We have investigated e and K, focusing on the eects of N 2. We found that the ®ne structures of e and K were sometimes aected by the local variations of N 2, which was more evident for K than for e. When local N 2 was small, K became large, although s 2turb was small. Local variations of N 2 should be considered in order accurately to determine the ®ne structure of e and K in the troposphere and lower stratosphere.
Acknowledgements 6. Concluding remarks This study is concerned with the application of the
The authors are deeply indebted to Drs D. Riggin and T. Nakamura and Mr T.W. Hadi for helpful comments and suggestions. Special thanks are given to Dr
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T. Adachi for his support to improve the MU radar RASS data. The data used in this study were collected with the MU radar operated by Radio Atmospheric Science Center (RASC) of Kyoto University, Japan. References Barat, J., Bertin, F., 1984. Simultaneous measurements of temperature and velocity ¯uctuations within clear air turbulence layers: analysis of the estimate of dissipation rate by remote sensing. J. Atmos. Sci. 41, 1613±1618. Cohn, S.A., 1995. Radar measurements of turbulence eddy dissipation rate in the troposphere: a comparison of techniques, J. Atmos. Oceanic Technol., 85±95. Gage, K.S., 1990. Radar observations of the free atmosphere: structure and dynamics. In: Atlas, D. (Ed.), Radar in Meteorology. American Meteorol. Soc, Boston, pp. 534± 565. Gage, K.S., Balsley, B.B., 1978. Doppler radar probing of the clear atmosphere. Bull. Amer. Meteorol. Soc. 59, 1074± 1093. Gage, K.S., Green, J.L., Vanzandt, T.E., 1980. Use of Doppler radar for the measurement of atmospheric turbulence parameters from the intensity of clear-air-echoes. Radio Sci. 15, 407±416. Gossard, E.E., 1990. Radar research on the atmospheric boundary layer. In: Atlas, D. (Ed.), Radar in Meteorology. American Meteorol. Soc, Boston, pp. 477± 527. Hocking, W.K., 1985. Measurement of turbulent energy dissipation rates in the middle atmosphere by radar techniques: a review. Radio Sci. 20, 1403±1422. Hocking, W.K., 1988. Two years of continuous measurements of turbulence parameters in the upper mesosphere and
lower thermosphere made with a 2-MHz radar. J. Geophys. Res. 93, 2475±2491. Hocking, W.K., 1990. Turbulence in the region 80±120 km. Adv. Space Res. 10 (12), 153±161. Hocking, W.K., 1996. An assessment of the capabilities and limitations of radars in measurements of upper atmosphere turbulence. Adv. Space Res. 17, 37±47. Lilly, D.K., Waco, D.E., Adelfang, S.I., 1974. Stratospheric mixing estimates from high-altitude turbulence measurements. J. Appl. Meteor. 13, 488±493. Low, D.J., Adachi, T., Tsuda, T., 1998. MU radar-RASS measurements of tropospheric turbulence parameters. Meteorol. Zeitschrift 7 (6), 345±354. Masuda, Y., 1988. In¯uence of wind and temperature on the height limit of a radio acoustic sounding system. Radio Sci. 23, 647±654. Nastrom, G.D., 1977. Doppler radar spectral with broadening due to beamwidth and wind shear. Ann. Geophys. 15, 786±796. Patra, P.K., Lal, S., 1997. Variability of eddy diusivity in the stratosphere deduced from vertical distributions of $Nÿ{2}$O and CFC-12. J. Atmos. Terr. Phys. 59, 1149± 1157. Sato, Woodman, R.F., 1982. Fine altitude layers by Arecibo 430 MHz radar. J. Atmos. Sci. 39, 2546±2552. Weinstock, J., 1978. Vertical turbulent diusion in a stably strati®ed ¯uid. J. Atmos. Sci. 35, 1022±1027. Weinstock, J., 1981a. Energy dissipation rates of turbulence in the stable free atmosphere. J. Atmos. Sci. 38, 880±883. Weinstock, J., 1981b. Vertical turbulence diusivity for weak or strong stable strati®cation. J. Geophys. Res. 86, 9925± 9928. Weinstock, J., 1981c. Using radar to estimate dissipation rates in this layers of turbulence. Radio Sci. 16, 1401±1406.
Estimation of turbulence energy dissipation rate and vertical eddy diusivity with the MU radar RASS Eddy Hermawan*, Toshitaka Tsuda Radio Atmospheric Science Center, Kyoto University, Uji, Kyoto, 611-0011, Japan Received 17 March 1999; received in revised form 30 July 1999; accepted 13 September 1999
Abstract We have conducted RASS (Radio Acoustic Sounding System) observations with the MU (Middle and Upper atmosphere) radar on 28±31 July 1994 at Shigaraki, Japan (34851 ' N, 136806 ' E) and determined the characteristics of turbulence energy dissipation rate (e ) and vertical eddy diusivity (K ) in the troposphere and lower stratosphere. We have ®rst examined the accuracy of the Brunt VaÈisaÈlaÈ frequency squared (N 2) derived from RASS temperature pro®les. Then, e and K are determined by using N 2 and the Doppler spectral width of turbulence echoes (s 2turb). We found that the structures of e and K are sometimes aected by the local variations of N 2. We found that sometimes e became small, even though s 2turb was large, because N 2 was small. On the contrary, K was enhanced due to small N 2, although s 2turb was small. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction It is generally recognized that the detailed time± height variations of turbulence parameters such as the turbulent energy dissipation rate (e ) and vertical eddy diusivity (K ) are very important for studying the mixing of minor constituents (e.g., Patra and Lal, 1997). Therefore, they are one of the key parameters in a numerical model that treats the chemistry and dynamics of the troposphere and the middle atmosphere. Observations of e and K have been extensively conducted by in situ measurements made aboard aircraft (e.g., Lilly et al., 1974) and balloons (Barat and Bertin, 1984; Cohn, 1995). Moreover, the possibility of deducing the turbulence parameters, including e and K, from the Doppler spectrum obtained with wind pro®ler radar has been studied (Gage and Balsley, 1978; Gossard, 1990; Hocking, 1985, 1996; Gage, 1990). In these cases, MST (mesosphere±stratosphere±tropo-
* Corresponding author.
sphere) and MLT (mesosphere±lower-thermosphere) radars have been employed as a powerful measurement technique, allowing the estimation of e and K over a quite broad altitude range with far better temporal resolution than previously done with other techniques. There are two major methods to derive turbulence parameters from radar measurements of turbulence echoes Ð the absolute strength of the backscattered echo power and the Doppler spectral width. The ®rst method was applied by Gage et al. (1980), Weinstock (1981a, 1981b, 1981c), and has been extensively reviewed by Hocking (1985). This method requires, however, an accurate pro®le of N 2, the mean gradient of the refractive index, M, and the fraction of the radar volume ®lled with turbulence, F. Therefore, in addition to the radar results, radiosonde pro®les of temperature and relative humidity are also employed, since they are not determined from the radar measurements. The other method utilizes the spectral width of the Doppler spectra determined by the radar. This method was ®rst introduced by Sato and Woodman (1982)
1364-6826/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 4 - 6 8 2 6 ( 9 9 ) 0 0 0 7 5 - 9
1124
E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
using the 430-MHz Arecibo radar in Puerto Rico and, since then, it has been intensively used in many studies (e.g., Hocking, 1985, 1988). In this method, N 2 is the other necessary parameter to estimate e and K. However, non-turbulent processes that could broaden the spectral width must be compensated for in order to obtain a reliable estimate of e and K. By applying the RASS (Radio Acoustic Sounding System) technique to the MU radar in Shigaraki, Japan (34851 ' N, 136806 ' E), we have successfully measured temperature pro®les simultaneously with the turbulence echoes in the troposphere and lower stratosphere. In this paper, we aim at deriving e and K using N 2 from the RASS pro®les. We carried out the RASS campaign measurement during 28±31 July 1994 and studied the eect of the detailed structure of N 2 on e and K. A similar study has been done by Low et al. (1998), from observations on 30 July 1996, who found that K was high when e was also high. However, they also found that if N 2 was small then K could be large even if e was moderate, indicating that the region was well-mixed due to low stability rather than by active turbulence. We start with a brief review on estimating e and K using the Doppler spectral width, together with a description of the MU radar RASS experiment. We further discuss the detailed structure of N 2 observed by RASS, investigate the accuracy by comparing with the radiosonde data, and then the ®ne structures of e and K are presented.
In this section we brie¯y review the procedure to estimate e and K from the Doppler spectral width. Provided that the spectral broadening is completely due to turbulent processes, a relation between e and spectral width, s 2turb, can be expressed as (e.g., Hocking, 1985) W kgÿ1
1
However, the observed spectral width, s 2obs, contains not only turbulence eects, but also contributions of non-turbulent processes which modify the shape of the spectrum. Under such conditions, the spectral width induced by turbulence alone is given by s2turb s2obs ÿ s2beam ÿ s2shear ÿ s2trans
sbeam 1 d1=2 j u h j
2
where, s 2beam, s 2shear and s 2trans denote non-turbulent processes, the beam broadening eect, shear broadening eect and contamination due to transient atmospheric motions, respectively. The beam broadening eect arises because the radial wind velocity is slightly
3
where d1/2 (11.38 1 0.023 rad for the MU radar) is the half-power half width of the eective (two way) radar beam, and u h is the background horizontal velocity (Hocking, 1990; Nastrom, 1977). For typical MST radar observations with suciently small zenith angle, this eect produces the largest contamination. For a known horizontal wind shear, the shear broadening eect can be evaluated (Nastrom, 1977) as du h Dz sin 158 sshear 10:5 4 dz for an antenna at a zenith angle of 158, and Dz is the sample volume thickness which is 150 m for the present observation with the MU radar RASS. Finally, the contamination due to transient atmospheric motions is estimated by 0 2 strans 14 u2t
2. Estimation of e and K from spectral width
e10:38 Ns2turb
dierent for dierent parts (dierent line-of-sight directions) within a ®nite beam width. The shear broadening occurs when the radial component of the wind changes along the range within the sample volume. The last broadening eect is caused by the wind variations during the interval used for incoherent integration (see Hocking (1985) and (1988) for more detail). In order to estimate s 2turb from s 2obs correctly, we need to remove the contributions of the non-turbulence eects. The beam broadening eect can be quanti®ed as
5
0 where u 2t is the variance of the radial velocity for the integration interval t (Hocking, 1988). After non-turbulence eects have been removed, the turbulent energy dissipation rate can be properly estimated from Eq. (1) and the vertical eddy diusi®ty, K is de®ned as (e.g. Lilly et al., 1974; Weinstock, 1978)
K10:38
s2turb N
m2 sÿ1
6
High time-resolution N 2 pro®les derived from the MU radar RASS experiment are used in Eqs. (1) and (6).
3. MU radar RASS experiments In this section, we brie¯y review the basic principle of RASS, including a ray tracing of acoustic wave fronts for determining an appropriate beam direction of the MU radar. RASS is a ground based remote sensing technique for measuring the height-pro®le of the atmospheric virtual temperature in the troposphere
E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
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Table 1 Observation parameters on 28±31 July 1994 MU radar Height range (km) IPP (ms) Sub-pulse length (ms) Number of beams Number of Rx channels Coherent integration Sample height Sample rate (ms) Time series Incoherent integration Observation time (s) Maximum Doppler shift (m sÿ1)
1.20±10.65 402 2 6 2 30 6 72.4 128 4 37.0 222.3
5.10±14.55 432 2 6 2 22 6 57.0 128 5 36.5 228.3
Accoustic source Transmitter Waveform Pulse length (s)
Loudspeaker CW No
Pulse interval (s) Repetition period (s) Chirped frequency (Hz)
No 3.0 85±115
Number of pulses
No
Pneumatic transducer Pulse 0.4 (1.20±10.65 km) 0.4 (5.10±14.55 km) 0.5 (10.50±19.95 km) 10 No 85±115 (1.20±10.65 km) 93±103 (5.10±14.55 km) 87±97 (10.50±19.95 km) 4
and lower stratosphere, with good time-resolution of a few minutes and moderate height-resolution of about 150±300 m. Acoustic waves emitted from a high-power transmitter on the ground produce sinusoidal variations of atmospheric density, resulting in radio refractive index perturbations. A radar tracks the acoustic wave fronts, and strongly scattered radio waves (RASS echo) can be received. However, there are two necessary conditions to detect RASS echoes: the wave number vector of the incident radio wave must be perpendicular to the acoustic wave fronts, and the acoustic wavelength must be half the radar wavelength for optimum Bragg resonance. The Doppler velocity of the RASS echo corresponds to the apparent sound speed, from which the radial wind velocity of the ambient atmosphere, available from simultaneous MU radar measurements, must be subtracted. Then, the obtained true sound speed cs, can be related to the virtual temperature Tv as Tv
cs kd
1=2
7
where kd=20.046 for a dry atmosphere. Estimation of Tv pro®les with the RASS technique can be simpli®ed by using a vertically pointing beam.
10.50±19.95 414 2 6 2 24 6 59.6 128 5 38.2 2 27.0
However, RASS echo detection will fail under strong background horizontal winds due to advection of the acoustic wave front. Therefore, we use real time acoustic wave ray tracing, and steer the antenna appropriately as described by Masuda (1988). The eective echoing range largely depends on the background wind structure, but it is not so sensitive to the temperature pro®le. Thus, for the ray-tracing computation we use temperature pro®les taken from a previously launched radiosonde, while wind velocity pro®les are updated from time to time by using simultaneous MU radar data. In this study, we used data collected from 23:00 LT on 28 July to 16:00 LT on 31 July 1994. The observation parameters are shown in Table 1, which indicates three height ranges (1.20±10.65, 5.10±14.55 and 10.50±19.95 km), and three acoustic transmissions with chirped frequency of 85±115, 93±103 and 87±97 Hz, respectively. Between pulses the beam was switched to the next direction, so that six directions were covered in sequence, i.e. the vertical, four oblique directions at a zenith angle of 158 in the North, South, East and West azimuths, and the sixth direction was appropriately changed by considering the real-time ray tracing of the acoustic wave fronts in order especially to detect RASS echoes. Both radial wind velocity and sound speed in each
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Fig. 1. Comparisons between RASS and radiosonde measurements in determining the virtual temperature (left-panel), (centerpanel) N 2 pro®les and (right-panel) accuracy of N 2 RASS for observation on 29 July 1994 from 02:41 to 03:41 LT. Triangle marks denoted RASS experiments.
beam direction were measured every 3.2 min. Although the range resolution was 300 m, data were oversampled with a height interval of 150 m from 1.67 to 19 km altitude. Our analysis concentrates on heights of 2±13 km where the quality of the RASS data is best. During the experiment, we also launched nine radiosondes which made measurements of pressure, temperature and water vapor mixing ratio.
with those derived from a radiosonde. Statistics of the normalized dierence are used to assess the accuracy of N 2 obtained with the RASS technique. Fig. 1 illustrates an example of the discrepancy between individual pro®les taken on 30 July 1994, where the left, center and right panels show the virtual temperature pro®le, Tv, N 2 and the normalized dierence (DN 2) between RASS and radiosonde measurements de®ned as
4. Pro®les of from the MU radar RASS observations DN 2
2
In this section, we compare RASS-derived N values
N 2RASS ÿ N 2sonde 100% N 2sonde
8
Table 2 Results of statistical analysis for observations on 29±31 July 1994 Launch time of radiosonde (LT)
Height of analysis (km)
Number of data points
DN2 (%) Mean value
Standard deviation
29 July 02:41 08.39 14:46 20:49
2.3±11.3 2.3±11.3 2.3±11.3 2.3±11.3
61 61 61 61
18.2 18.0 18.4 18.2
10.8 13.8 17.9 11.6
July 30 02:32 14:34 23:54
2.3±11.3 2.3±11.3 2.3±11.3
61 61 61
15.1 13.0 14.5
12.0 9.6 11.0
July 31 08:34 14:48
2.3±11.3 2.3±11.3
61 61
13.8 15.0
8.9 7.6
61
16.0
11.5
Average
E. Hermawan, T. Tsuda / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1123±1130
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Fig. 2. Time±height section of Brunt VaÈisaÈlaÈ frequency squared, N 2 observed with the MU-RASS on 28±31 July 1994.
The RASS temperature pro®le was averaged for one hour from 14:34 to 15:34 LT. Since the sampling interval of the RASS measurements is approximately 150 m, we have 61 data points in this altitude range. The mean value and standard deviation of DN 2 are about 13.0 and 9.6%, respectively. We have repeated a similar analysis for all of the available radiosonde data, and summarize the results in Table 2. Average values for the mean and standard deviation of DN 2 are about 16.0 and 11.5%, respectively, where the average number of data analysis points is 61. We present, in Fig. 2, the detailed time±height sec-
tion of N 2 observed with the MU radar RASS during the observation period from 23:00 LT on 28 July to 16:00 LT on 31 July 1994. The RASS pro®les were averaged for 60 min so that Fig. 2 consists of 66 pro®les of N 2. Although some data are missing, from 06:55 to 10:09 LT on 30 July 1994, we mostly obtained continuous pro®les of N 2 between 2 and 13 km. Large variations are seen in the rapid increase of N 2 from minimum to maximum close to 18 10ÿ5 rad2 sÿ2 between 6.5 and 9 km from 15:42 LT on 29 July to 06:28 LT on 30 July, and from 10:09 LT on 30 July to 04:09 LT on 31 July 1994. Small variations are seen by the rapid decrease of N 2 from maximum to minimum
Fig. 3. The same as Fig. 2, but observed with the radiosonde.
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Fig. 4. The same as Fig. 2, but for the turbulent spectral width, s 2turb.
close to 2 10ÿ5 rad2 sÿ2 on 29 July, from 09:55 to 15:14 LT between 10.6 and 12.3 km, and from 12:00 to 21:55 LT on 29 July 1994. We can also see strong stable layers close to 3 and 4.5 km from 23:00 LT on 28 July to 05:46 LT on 30 July 1994. Also occurring are downward phase progressions of N 2 close to 0.88 m sÿ1 between 5.8 and 8.7 km from 12:29 LT on 30 July to 07:12 LT on 31 July 1994 and 0.99 m sÿ1 between 2 and 5.5 km during 10:05 LT on 30 July to 09:07 LT on 31 July 1994. We also plot the time±height variations of N 2 using nine radiosonde pro®les in Fig. 3, which shows that
the radiosonde misses much of the dynamical variation. Thus, it is obvious that radiosondes are not well suited to provide detailed time variations of N 2. 5. Time±height variations of e and K In this section we discuss the characteristics of the turbulent energy dissipation rate, e, and vertical eddy diusivity, K. Particular emphasis will be directed here towards eects of N 2 on e and K. We start this section by showing time variations of the turbulent spectral
Fig. 5. The same as Fig. 2, but for the turbulent energy dissipation rate, e.
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Fig. 6. The same as Fig. 2, but for vertical eddy diusivity, K.
width, s2turb in Fig. 4 as the key parameter necessary to estimate e and K. Then, we show e and K in Figs. 5 and 6, respectively. Fig. 4 shows large variations of s 2turb, especially from 12:42 to 20:14 LT on 29 July 1994 between 7 and 9 km and a large value between 21:11 LT on 29 July and 07:04 LT on 30 July between 6 and 10 km, close to 0.3 m2 sÿ2. Small variations appeared between 6 and 10 km from 23:00 LT on 28 July to 14:00 LT on 29 July, and from 19:23 LT on 30 July to 06:28 LT on 31 July, close to 0.02 m2 sÿ2. The time±height variations of e on 28±31 July 1994 are presented in Fig. 5. By comparing Figs. 4 and 5, we can see the similarity of the structure indicating that e is mostly determined by s 2turb rather than by N 2. However, a discrepancy between the structure of e and s 2turb can be recognized during 09:55±15:14 LT on 29 July between 10.6 and 12.3 km. For this exceptional case, N 2 was very small, although s 2turb was moderately large. As a result, e became small, as suggested by Eq. (1). We present in Fig. 6 time±height variations of K for 28±31 July 1994, whose pattern shows some dierences from that in Fig. 4. We can see an enhancement of K on 29 July from 12:00 to 21:55 LT between 6.7 and 9 km. Considering Eq. (6), K can become large (1.8 m2 sÿ1), when N 2 is small (0.2 m2 sÿ1), even though s 2turb is small. That is, the region is well-mixed due to low static stability rather than by active turbulence.
MU radar RASS technique for determining ®ne structure of the turbulent energy dissipation rate, e, and the vertical eddy diusivity, K, in the troposphere and lower stratosphere with good time and spatial height resolution. First, we have applied the RASS technique to obtain detailed time±height variations of N 2, which is one of the important parameters needed to estimate e and K. The ®ne structure of N 2 was investigated from 23:00 LT on 28 July to 16:00 LT on 31 July 1994. We have validated the RASS results comparing them with radiosonde pro®les and shown that the normalized dierence was about 16%, with a standard deviation of 11.5%. We have simultaneously analyzed the spectral width, s 2turb, of Doppler spectra from the turbulence echo measurements made with the MU radar, and determined the ®ne structures of e and K, using N 2 from the RASS pro®les. We have investigated e and K, focusing on the eects of N 2. We found that the ®ne structures of e and K were sometimes aected by the local variations of N 2, which was more evident for K than for e. When local N 2 was small, K became large, although s 2turb was small. Local variations of N 2 should be considered in order accurately to determine the ®ne structure of e and K in the troposphere and lower stratosphere.
Acknowledgements 6. Concluding remarks This study is concerned with the application of the
The authors are deeply indebted to Drs D. Riggin and T. Nakamura and Mr T.W. Hadi for helpful comments and suggestions. Special thanks are given to Dr
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