AmmrtpkrL hdnwmm Vol 12. pp. 1951-1956. 0 Rrprnon Rcu Ltd. 1978. Printed in Gmt Britain.

A COMPARISON OF ACOUSTIC DOPPLER VERTICAL VELOCITY POWER SPECTRA

WITH DIRECT MEASUREMENTS

D. N. A~IMAKOP~ULC~* and R. S. CoLEt

Department of Electronic and Electrical Engineering, University College London, Tonington Place, London W.C. 1

and

B. A. CREASE and S. J. CAUGHEY

Meteorological Research Unit, R.A.F. Cardington, Bedford, U.K.

(First received 11 November 1977 and infinal form 17 March 1978)

Ahatract - Power spectra of vertical wind velocity obtained using a monostatic acoustic sounder are compared with directly measured spectra at heights of 56 m, 86 m and 124 m in the planetary boundary layer. Encouraging agreement is found hctween the two methods of measurement, under conditions of low horizontal wind speed. Variancs of the vertical velocity estimates are within 300/, across the height range of

INTRODUCJ’ION

In recent years, acoustic echo-sounders have provided valuable qualitative and quantitative information on the structure of the first few hundred metres of the boundary layer by the display and analysis of the echo strength, (McAllister et al., 1969; Asimakopoulos et al., 1975 and Crease et al., 1977). The monostatic acoustic echo, however, contains Doppler information on the vertical air motion (Kelton and B&out, 19&l), and this could prove of great use in the specification of further important boundary layer statistics such as ah the variance of the vertical wind speed, and E, the rate of dissipation of turbulent kinetic energy. Furthermore the technique of monitoring Doppler derived wind- speed could be of potential use at airports since strong wind shears, resulting either from a change in wind speed and/or direction with height, remain a potential hazard for aircraft.

Recent experiments on the measurement of vertical wind speed have given very encouraging results, (Beran et al., 1971; Caughey et al., 1976). However, the range of scales over which useful information may be obtained acoustically is at present uncertain. In an attempt to investigate this matter further a joint experiment was carried out by the Meteorological Research Unit, Cardington and the Department of Electronic and Electrical Engineering, University Col- lege London. In a previous paper (Caughey et al., 1976), comparisons were presented of acoustically and directly measured vertical velocities at a single level

*Now with Department of Meteorology, University of Athens, Greece.

t Author to whom correspondence should he addressed.

which showed encouraging agreement. This paper presents the results of a quantitative comparison between acoustic Doppler derived vertical velocity spectra and direct estimates measured at three different heights in the atmosphere.

THEORGTICAL BACKGROUND

For wind speed measurements using a vertically directed monostatic acoustic sounder the radial va locity (v) of a scattering eddy is given by (Beran et al., 1971):

(1)

where& is the transmitted carrier frequeticy,fd iS the frequency of the scattered signal and c is the velocity of sound in the atmosphere. This expression is approx- imate and can only be used for relatively low radial velocities of up to 2 m s-‘.

In determining the Doppler shift from a spectrum, three kinds of error should be considered (Spizzichino, 1974), instrumental errors, refraction elfects and ap parent vertical velocities introduced by horizontal wind components due to the finite beamwidth of the acoustic antenna.

The relationship which describes the instrumental error (A,) is given by Spizzichino

A2 J5J2B “=ziq (2)

where N is the number of pulses averaged, rG is the actual width of the sampling gate, B is the bandwidth of the Doppler spectrum and 1 the wavelength of the

1951

1952 D. N. ASIMAKOF-OLJLOS, R. S. COLE, B. A. CREASE and S. J. CAUGHEY

sound. For this experiment with a sampling gate of 18Oms and a Doppler bandwidth of 10 Hz the in- strumental error was estimated to be, for N = 1, 4,~ lms-‘andN= 50, A, ‘Y 0.14 m s - ‘. Evidence for the validity of these estimates of the error was obtained by plotting scatter diagrams for direct and acoustically derived velocities averaged over various numbers of pulses.

The refraction effect is potentially serious even for short ranges for the acoustic wave case, being mainly caused by the wind velocity. The systematic error introduced by the refraction effect is given by :

pw,+!$& (3)

where II,, is the averaged total horizontal wind speed between the ground and the altitude z and u”(z) is the total horizontal wind at altitude z. Typical values for runs taken in conditions of relatively low wind speeds @H(Z) = Is, = 3 m s-l) give a value of 1 Aw,l of O.O3ms-’ while for higher wind speeds (u”(z) = tin =10ms-1),~Aw,~isoftheorderof0.3ms-1.

The error due to the finite antenna beamwidth (approx 10’) is a function of the horizontal wind. Hence the relative error for the vertical wind measure ments can be much larger than for horizontal wind measurements, since vertical velocities are in general smaller than the horizontal velocities. According to Spizzichino (1974) this error is given by :

Aw, = [u(z)cos tj + v(z)sin $]&I (4)

where $ is the azimuth of any transmitted ray within the antenna beamwidth, 68 is the angle subtended by a scattering centre at the acoustic array (the upper bound of 60 is the beamwidth semiangle) and u(z), V(Z) are the horizontal wind speed components at height z, in the same reference frame as the angle JI. Again, for relatively low wind cases u(z) = v(z) = 3 m s- ’ and for 60 d 5”, the absolute error varies between 0 and 0.3ms-‘, while for higher wind cases u(z) = D(Z) = 10 m s- 1 the absolute error ranges from 0 to 0.9 m s- ‘. Equation (4) indicates two possible effects. Firstly when the observation time is long enough for the reflectivity to be considered statistically uniform within the scattering volume, the error is reflected in a spectral broadening. This is already represented by the term B in Equation (2) and hence should not be included in the Aw, errors. If the relIectivity is not uniform, systematic errors will occur for which cor- rection is very difficult. The relIectivity may well have many maxima in the scattering volume which will be represented in the echo spectrum by an equal number of maxima. Therefore a narrow beamwidth and a low horizontal wind, together with a high time resolution will greatly improve the accuracy of the results.

A further source of error is in the determination of the position of the peak of the power spectrum, necessary for the measurement of the frequent shift. This error was estimated to be of the order of 0.1 m s - ’ for a single spectral photograph. The accuracy of the

AF L’,

-F 40 2u 0 20 40 tF(M)

I I 1 I -F 40 20 0 20 40 tFlHz)

(b)

Fig. 1. Examples of two types of spectra ruxived by the sounder. (a) Transmitted spectrum (dashed line) and received spectrum (solid line). AF represents the frequency shift. The vertical scale is arbitrary. (b) Example of a received spectrum when more than one scattering region is present in the

scattering volume.

Doppler measurements decreases with height because the signal to noise ratio of the scattered signal worsens, resulting in the deterioration of the spectrum of the Doppler signal.

INSTRUMENTATION

The acoustic sounder used in this experiment has been described in detail elsewhere (Asimakopoulos and Cole, 1977). In the present case a pulse repetition frequency of 1 Hz (to increase the time resolution) and a pulse length of 50ms (equivalent to a height resolution of 9 m) were used. The transmit pulse was used to synchronise a gating system which controlled the selection of the signal received from any chosen height for Doppler shift determination. This system provided five gates of variable width hence allowing the signal to be analysed at up to five different heights. A Hewlett-Packard spectrum analyser with an 8553B radio frequency section was used to produce the frequency spectrum of the received echo. The oscillo- scope display was automatically photographed using a tine camera triggered by the same gating circuit. The photographed power spectra were subsequently anal- ysed to determine the frequency shift of the signal. Figure l(a,b) shows two examples of the received

Acoustic Doppkr vertical velocity power spectra 1953

spectra. With a distribution of velocities within the scattering volume a spectrum of Doppler frequencies occurs in the scattered signal which is considerably broader than that transmitted. The Doppler spectrum represents the distribution of radial velocities within the resolution cell. Spectra similar to that in Fig. l(a) were observed approx 95% of the time and permitted a fairly ~arn~g~o~ estimation of the Doppler fre- quency shift. Spectra of the type illustrated in Fig. l(b) occurred the remainder of the time and a meaningful extraction of the Doppler shift in these cases was not possible. These spectra probably reflect the presence of several distinct scattering centres within the scattering volume. The amount of data lost in this way compares favourably with that reported by Caughey et al. (1976).

birect estimates of the vertical velocity at three different heights were made using a “reduced” version of the turbulence probe described by Readings and Butler (1972). Three of these probes were attached to the tethering cable of a large kite balloon (1300m3) and measurements made at heights of 56, 86 and 124 m. Average vertical velocities (G) over time periods corresponding to fifty sounder pulses were then ob- tained from the ~lationship:

ti;= Vrsin#-f$f (5)

since the probe only measures the variability about 4. V, is the total wind speed, I#J is the inclination of the

wind vector to the local horizontal (as seen by the

Fi. Z(a& E&o intensity as a function of height and time. Recorded during convaxive conditions bctwam 13.59 and 15.14 GMT 0x1 April 29 1976, with the corresponding sounder estimates of vertical velocities (averaged over 100 puIsc@ at X24 m height (The dotted line is drawn by the instrtmtimt to indicate the 100 m

heigbt.)

1954 D. N. hI~KOPOuLos, R. S. COLE, 3. A. CnE.4sE and S. J. CAUOHEY

sensor) and 4 is the mean value of inclination over the complete run (typically (~1 1 h) which is taken as the instrumental offset. The overall accuracy of the balloon-borne turbulence instrumentation including the sensitivity of the observations to sensor design, frequency response, data reduction techniques and the influence of probe motion as it sways with the balloon cable is approx 5% for the vertical velocity measure ment (Haugen et al., 1975).

REWLlS

The comparison studies reported here were carried

out on the afternoon of the 29th April 1976, between 13.59 and 16.29 GMT. Surface winds during this period were light (1 - 3 m s-l) and generally from a north easterly direction. Cloud cover was somewhat variable but consisted chiefly of 2/8+8 small cumulus with a base at 2500ft. Shown in Fig. 2(a, b) are the monostatic facsimile recordings for the two runs to be discussed, together with the corresponding sounder estimates at 124 m averaged over 100 pulses. The first run was made during convective conditions in which clearly defined thermal plumes, extending through the first few hundred metres of the boundary layer,

Fig. 2(b). Echo intensity as a function of height and time. Recorded during convective conditions between 15.W16.29GMT on April 29 1976. with the corresponding sounder estimates of vertical velocitiar (averaged over 100 pulses) at 124 m height. (The dotted line is drawn by the instrument to indicate the 100 m

height.)

. . 56m

\ -2/3 “.. ‘c

10-3 I I I 10-4 10-3 lo-2 lo-’

n. HZ

. . t36m

lo-31 I I I

10-e 10-3 lpi? IO”

n. Hz

1c.P

i

. (c) l

. 124m

l

all3 10-4 10-3 lo-2 10-l

In Fig. 3(a, b,c) the power spectra of the time series of the vertical velocities at the three heights are shown. (The solid and open circles represent the sounder estimates for the first and second run respectively.) These estimates form two discrete levels representing the strong convection in the first run and the less turbulent conditions in the second. The peak of the sounder vertical velocity spectra is in fair agreement with the probe spectra for both runs at all three heights. The upper frequency limit for the sounder spectral estimates is set by the need to average over a large number of pulses to obtain a reliable estimate for the vertical velocity since Spixxichino (1974) has shown that single pulse estimates are highly inaccurate (see Equation 2). In the present experiment an average of 25 pulses was used for the calculation of the spectra (corresponding to a theoretical instrument error of 0.2 m s-t). During the first run and at all heights the sounder velocity power spectra shows a loss of spectral density, i.e. falls below the measured value, at a frequencybetween x 10e3upto2 x 10-fHzThis is not present, however, during the second run. The reason for this spectral loss is not clearly understood.

The wavelength, &,, corresponding to the peak of the turbulence probe vertical velocity spectra varies between 250-600 m in the height interval 55-124 m for the first run, which is in fair agreement with that expected from the free convection relationship, d,,, _ We, obtained from other experiments (see e.g. Kaimal et al., 1976). For comparison purposes vertical velocity variances have been computed over the restricted frequency interval 2 x lo-* to 2 x lo-’ Hz (the variance in this bandwidth is approx 70% of the total variance). The upper limit having been set as previously discussed and the lower one determined by the run duration. As expected ut shows a marked increase with height in the markedly convective first run (see Fig. 4(a)). Kaimal ec al. (1976) have recently inv~tigat~ the behaviour of dW in convective boun- dary layers and find (for e/et c 0.1, where et is the boundary layer depth) a variation as (&)2’3. Unfor- tunately neither the parameter e, nor the mixed layer velocity scale are available but it is clear that the data in Fig. 4(a) do vary approx as e2’3.

The second run, carried out in much less convective

n. HZ

conditions, yields markedly different conclusions. Peak wavelengths are substantially shorter, falling in the range 100-200 m and the magnitude of the overall vertical velocity variances also decreases significantly (see Fig. 4(b)), The profile shape now indicates a slow decrease of ai with height and this relates well to the numerical predictions of Deardorff (1972) for neutral

Fig. 3. Comparisons betwea! the vertical velocity powa spectra from the turbulence probe (solid curves) and the acoustic sounder (0. Run 1, 0, Run 2) for heights of (a)

56m.Ibt86mandIcl 124m. . . I . _ and slightly unstable planetary boundary layers.

Acoustic Doppler vertical vdocity power SpeCtm 1955

produce intense aho regions. On the other hand the results of the second run were typical of substantiahy quieter, almost neutral conditions. Although the echo strengths in this run (and in the gaps between thermals in the first run) were week it was found that they were still sufTiciently above noise level to permit Doppler analysis.

19%

ISO-

no- E

B

D. N. ~~SIMAKOPOU~, R. S. COLE, B. A. CRew and S. J. CAUGHEY

estimates obtained with the sounder agree reasonably well with the directly measured values.

Acknowledgements - Thanks are due to the Science Research Council which has provided financial support for the acoustic sounder part of the work described above including the design and building of the sounder at University College London, under a grant to UCL.

Thanks are also due to the staff of the Meteorological Research Unit Cardington for assistance in carrying out these experiments.

5co 0 0.2 0.4 0.6 0.8 2

0, 9 m2 sm2

Fig. 4. Ver&al profiles of the vertical velocity variance within the range 2 x 10 -*<n<2x lo-‘Hz from the turbulence probes (0 -0) and acoustic sounder (O--- @) for (a) 13.59-15.14 GMT and (b) 15.14-1619 GMT on April 29 1976. The line drawn -.-.-.- represents a variation with height of z~‘~. The position of this

line on the at axis is arbitrary.

CONCLNDING REMARRS

The 1OOm spatial separation between the sounder

and the balloon-borne turbulence probes and also the volume average over which the sounder operates because of its finite beamwidth, make it difficult to assess whether the measured difference in variances is real. Evidence from runs in conditions of higher wind speed (- 10 m s-l) showed significant differences be- tween the sounder and the probe time series of vertical velocity estimates, probably indicating contamination from horizontal wind effects in the sounder data. Further comparison studies are clearly required to establish the tolerance and limitations of acoustic Doppler sensing and their dependence on the sounder operating characteristics. However, from the results quoted it is apparent that the magnitude of the spectral

REFERENCES

Asimakopoulos D. N., Cole R. S., Caughey S. J. Moss S. H. and Readings C. J. (1975) A comparison between acoustic radar returns and the direct measurement of the tempera- ture structure of the atmosphere. Armosphedc Environment 9,775-776.

Asimakopoulos D. N. and Cole R. S. (1977) An acoustic sounder for the remote probing of the lower atmosphere. J. Inst. Phys. E. 10,47-M.

Beran D. W., Little C. G. and Willmarth B. C. (1971) Acoustic Doppler measurements of vertical velocities in the atmos- phere. Nature 230, 160-162.

Caughey S. J., Crease B. A., Asimakopoulos D. N. and Cole R. S. (1976) A comparison of acoustic Doppler vertical velocities with direct measurements in the atmospheric boundary layer. Nature 262.274-276.

Crease B. A., Caughey S. J. and Tribblc D. T. (1977) Information on the thermal structure of the atmospheric boundary layer from acoustic sounding. Met. Msg. 106, 42-52.

DeardorffJ. W. (1972)Numerical investigation ofneutral and unstable planetary boundary layers. J. atmos. Sci. 29, 91-115.

Haugen D. A., Kaimal J. C., Readings C. 1. and Rayment R. (1975) A comparison of balloon-borne and tower mounted instrumentation for probing the atmospheric boundary layer. J. appl. Met. 14, 540-545.

Kaimal J. C., Wyngaard J. C., Haugen D. A., Cot6 0. R.. Izumi Y., Caughey S. J. and Readings C. J. (1976) Turbulence structure in the convective boundary layer. J. atmos. Sci. 33, 2152-2169.

Kelton C. qd Bricout P. (1964) Wind velocity measurements using sound techniques. Bull. Am. met. Sot. 45, 571-580.

McAllister L. G., Pollard J., Mahoney A. and Shaw P. (1969) Acoustic sounding - a new approach to the study of atmospheric structure. Proc. IEEE, 57, 579-587.

Readings C. J. and Butler H. E. (1972) The measurement of atmospheric turbulence from a captive balloon. Met. Msg. 101.286-298.

Spiuichino A. (1974) Discussion of the operating conditions of a Doppler radar. J. geophys. Res. 79, 5585-5591.