Investigations of the convective planetary boundary layer using a multiple frequency sodar

Atmospheric Research, 20 (1986) 225--233 Elsevier Science Publishers B.V., Amsterdam - - P r i n t e d in The Netherlands

225

INVESTIGATIONS OF THE CONVECTIVE PLANETARY BOUNDARY LAYER USING A MULTIPLE FREQUENCY SODAR .1

R.L. COULTER and T.J. MARTIN

Environmental Research Division, Argonne National Laboratory, Argonne, Ill. (U.S.A.) (Accepted for publication May 1, 1986)

ABSTRACT

Coulter, R.L. and Martin, T.J., 1986. Investigations of the convective planetary boundary layer using a multiple frequency sodar. Atmos. Res., 20: 225--233. A multifrequency bistatic Doppler sodar has been used to document the mixing effect associated with thermal plumes. The convergence effect has been studied. It has been shown values of convergence associated with plumes near .001 s-~ . RI~SUMI~ U n minisodar Doppler bistatique multifr6quence a ge6 utilis6pour l'6tude des panaches convectifs afin d'estimer leur rSle dans le m~lange turbulent. L'effet de convergence horizontal associ6 aux panaches a 6t6 6tudi6. Des valeurs de convergence ~gale ~ .001 s-~ ont 6t6 observ~es.

INTRODUCTION

Investigations of the planetary boundary layer (PBL) have been enhanced, indeed made possible in some cases, over the past several years through the use of remote sensing devices such as radar, lidar, and sodar that can provide investigators with continuous profiles of wind speed through and above the PBL. Continued advancement in this field requires more and better estimates of mean values on short time scales, and accurate and reliable estimates of second m o m e n t s o f the wind components. Mean and variance estimates made with Doppler sodar result from measurements of the three independent components of the total wind field at a rate that is a fraction of the pulse repetition rate of the system. Since the transmitters are not pointing solely along each of the wind direction components, it is necessary to sample at least one return from each transmitter before estimating either of the horizontal wind components. In conventional systems this results in only one third the sample rate that is possible if all

,i W o r k supported by the U.S. Department of Energy, Office of Health and Environmental Research under Contract W-31-109-Eng-38.

0169-8095/86/$03.50

© 1 9 8 6 Elsevier S c i e n c e Publishers B.V.

226 components could be sampled simultaneously. The so-called triple monastic configuration used by conventional systems, i.e., three centrally located transmitter-receivers that point in three different directions, results in estimates of any one c o m p o n e n t being derived from information separated in both space and time. For example, the length of time necessary to make a single three-component estimate is approximately 10 to 20 s and the separation in space is a b o u t 50% of the representative height of the measurement. These separations may be unacceptable for short averaging times or nonhomogeneous conditions. The sodar system at Argonne National Laboratory (ANL) alleviates the problem of spatial separation of samples by use of a bistatic system that employs two transmitters separated from a centrally located transmitterreceiver. This results in all estimates being made from a single vertical " c o n e " directly above the receiver. The system has been modified to operate at three different frequencies and thus lessen the problem of time separation of samples. All three transmitters transmit simultaneously and the three velocity components are derived in real time from a single signal through use of spectral analysis techniques. This has resulted in the ability to make wind profile estimates on short time intervals with no loss in accuracy. The relatively good spatial and temporal resolution of this three-dimensional Doppler sodar system has proved very useful in studies of flow over complex terrain and of the structure of the convective boundary layer. Of the various types of studies, examination of thermal plumes in the convective boundary layer is discussed later in this paper. SYSTEM DESCRIPTION The ANL three-axis sodar has evolved in recent years into a multifrequency system capable of collecting wind information along all three spatial coordinates simultaneously. This has been accomplished with relatively minor modifications to the existing ANL bistatic system. The previous system has been described earlier (Coulter and Martin, 1980), and uses a central, vertically-pointing monostatic antenna with two separated bistatic horns. The bistatic transmitters are typically placed at right angles to, and a distance of 150 m to 300 m from, the receiver antenna. Bistatic signals, necessary for computation of horizontal wind profiles, are usually collected for heights up to 8 0 0 m. Analog signal processing is achieved with a modified Quan-Tech .1 Transponder and Clock and Timing Generator. Multifrequency operation requires the generation o f two additional frequencies for use by the bistatic horns. The transmit frequencies for the bistatic antennae (fl, f2) are created with a phase-locked loop, frequency-

,i This does not imply approval or recommendations of the product by Argonne National Laboratory or sponsors, to the exclusion of others that might be suitable.

227 ratio circuit that produces bistatic frequencies with integer ratio relationships to the monostatic transmit frequency (fro), i.e.:

f~ = fmj/k f2 = fro j~ l

I [ (1)

where j, k, l, and m are integers. All frequency analysis is performed relative to the monostatic frequency, and it is important to maintain a known relationship among the three values. This can be accomplished through use of a frequency-translation loop. However, a frequency-ratio circuit was found to be more stable and reliable in achieving the desired phase-locking condition. With the frequency-ratio technique, a small drift in the monostatic reference frequency results in an acceptably small error about the desired frequency difference (1.0 Hz drift in the monostatic reference frequency results in bistatic frequencies that are in error by about 0.1 Hz). There is, of course, little error in the vertical velocity determination due to drift in the monostatic transmit frequency since the monostatic frequency is used as the reference frequency in heterodyning. The frequency-ratio circuitry produces square wave signals, whose odd harmonic content is acceptably filtered by a single pole RC low-pass filter prior to amplification and use by each bistatic horn. The received signal contains contributions from all three wind compponents, separated in frequency and well suited for spectral analysis. A microcomputer is used for much of the system control as well as data acquisition, analysis, and display. In order to accommodate the larger range of frequencies, the sample rate is increased to 333 s -1 and bandwidth increased to 300 Hz (previously it was 100 Hz). An integer fast Fourier transform (FFT) routine is used for spectral analysis of the digitized signal. A 64 complex point transform that executes in about 50 ms, has typically been used. The Doppler spectrum associated with the signal along each axis is determined and a frequency estimate is produced for each by averaging a selectable number of FFT bins about each peak using a modification of the technique described by Mastrontonio and Fiocco (1982). The signal-tonoise ratio (SNR) is also estimated from the spectrum. Signal amplitude and SNR are used in quality control o f Doppler estimates. Data are displayed and stored by a number of devices. A color map of vertical velocity profiles as well as the current running-mean horizontal wind profile are displayed on a CRT monitor during operation of the sodar system. A separate small microcomputer system and dot matrix printer produces a continuous facsimile-type display of monostatic signal strength with height versus time (Martin, 1981). A floppy disk system is used for storage of averaged wind and amplitude information and a high capacity (44 Mbyte) tape cartridge system can store about 9 h of the 333-Hz, raw, digitized data for later detailed analysis. System performance is aided by the practice of precomputing and storing, at start time, tabulated values of the Doppler frequency-to-velocity factors as determined by the system

228

geometry (transmitter separation, orientation, elevation angle and height) for each range gate. In addition the data are " d o u b l e buffered" so that data analysis is performed on one complete sodar return signal while another signal is being collected. SYSTEM ADVANTAGES AND DISADVANTAGES

The principal advantages of the multifrequency system are an increase in sample rate by a factor of three and the simultaneity of the estimates of horizontal and vertical wind components. This results in spectra that include more high-frequency wind components and the ability to observe PBL develo p m e n t on a finer time and space scale. In addition, of course, long-term averages are enhanced by the increased number of samples included in the estimate. The simultaneity of wind c o m p o n e n t estimates implies that eddycorrelation estimates of fluxes of m o m e n t u m , obtained as the covariance of the vertical and horizontal wind components, are potentially available under the appropriate conditions (fetch, height above the surface, wind speed, for example). A less obvious advantage inherent to multifrequency operation is a reduction in the computation necessary to maintain proper system operation. Since all three components are present in the signal at any one time, it is not necessary to treat return signals separately. This carries over into the logic controlling the transmitters as well, since all three transmit simultaneously, There is another inherent bistatic-system problem that is reduced considerably by use of the multifrequency technique. The incident pulse from separated transmitters arrives .33 s to 1.0 s after initial transmission from the transmitters. Refraction and reflection of the incident pulse from nearby objects can result in degradation of signal quality for a short time period after the arrival of the initial pulse. The result may be biased estimates of vertical velocity in the lower levels unless special measures are taken to " b l o c k " the incident pulse. With a multi-frequency system, however, it is a straight forward matter, in principle, to remove this component. Multifrequency operation is not free of problems, however. In conditions of very high wind speeds, the Doppler shift of the horizontal components can be large enough to affect the adjacent frequency c o m p o n e n t estimate. For example, if the system geometry is such that the vertically pointing antenna has the center frequency, large wind speeds along one baseline can cause Doppler shifts large enough to produce false vertical velocity estimates. This can be alleviated by recognizing these conditions and interchanging the frequency assignments of the two bistatic transmitters. This problem is most severe at low altitudes because the effect of the geometry upon the sensed Doppler shift from the bistatic transmitter is to increase the magnitude of the shift for returns from lower altitudes. A second potential problem is drift of the three frequency sources with respect to one another, which can be interpreted erroneously as wind speed.

229

As previously shown, this problem can be alleviated with appropriate analog techniques. Because the bandwidth of the receiver is broader in order to encompass the range of the three signals, the sample rate of the raw signal must be correspondingly larger. This results in some increase in computer m e m o r y if real-time analysis is being done. In addition, if real-time analysis is being done, it is more economical to perform only a single transform at each range (time) gate. This implies that the three velocity components will be from slightly different heights even after compensating for the delay time for the baselines. This is n o t a serious problem for mean wind profiles because the height differences are small and interpolation to the same height intervals is straightforward. It may be a problem if eddy-correlation estimates of m o m e n t u m flux are attempted. In this case, re-analysis of raw data with three separate transforms can be done or faster real-time methods developed. T H E R M A L PLUMES IN THE CONVECTIVE BOUNDARY LAYER

Several investigations into the nature of thermal plumes in the convective boundary layer have been done with sodar in the past (e.g., Hall et al., 1975, Taconet and Weill, 1982). Our interest lies primarily in the ability of thermal plumes to provide mixing of pollutants within the PBL during daytime conditions, the interaction of thermal plumes with fair-weather cumulus clouds, and the processes by which thermals and clouds can transport mixed-layer air into the free troposphere where it can undergo enhanced long-range transport. The Vertical Observations Involving Convective Exchange (VOICE, in 1982), Boundary Layer eXperiment 1983 (BLX83, in 1983), VENTing Experiments (VENTEX, in 1984 and 1985) were a series of studies by which a large data set on vertical motions in the unstable PBL was collected. During the 1984 and 1985 experimental periods, ANL used its multifrequency sodar to study the horizontal wind field as well as the vertical wind field in and around thermal plumes and cumulus clouds. By use of the horizontal and vertical wind profiles on a short averaging time, it is of interest to calculate the horizontal convergence associated with thermal plumes and to investigate the consistency of the multifrequency sodar results on short time intervals. Thermal plumes are well defined structures consisting of rising air whose lower boundary is often within 50 m of the surface and whose upper boundary m a y be the t o p of the well mixed layer. They may be associated with, or even part of, cumulus clouds whose base is near the inversion capping the mixed layer. Statistically, the diameter o f thermal plumes has been found to increase with the one third p o w e r of height over water (Lenschow and Stephens, 1980). We have found this to be true over land as well; however, large deviations from this mean picture do occur. Vertical velocities within the thermals can be larger than 5 m s -1, depending upon meteorological conditions, and strong downdrafts (greater than 3 m s -1 ) at both the upwind and downwind edges of the thermals often exist.

230

The horizontal dimension of the thermal plumes is usually on the order of 1 km except under special conditions such as streeting (Ferrare, 1984)' With a mean wind speed of 5 m s -1, this implies that the plume is "seen" by the sodar for 3 to 6 min when its center passes over the sodar moving with the mean wind. Therefore, averaging times no longer than 20 s are needed in order to investigate the thermals in detail. Thus one of the advantages of multifrequency operation becomes immediately apparent: the effective sample rate of the wind profile allows three samples per average versus only one for single-frequency operation within the 20 s sampling period, for profiles up to 1000 m. In fact, for this study, only vertical velocities were evaluated to 1000 m; horizontal values were limited to 500 m as a result of baselines being limited to 200 m. We assume the simplest of models for an "average" thermal plume: a circular cylinder of radius R moves with the mean wind at speed S (Fig.l). The continuity equation implies: V.V-

~w

(2)

Oz

~S ( ~ LUIMO)

~s~

Fig.1. Idealized cross-section of a thermal plume.

where w is the vertical velocity, V is the horizontal wind vector, and z is height. Integrating over the area of the plume at constant height and using the divergence theorem, we find:

f(v.V)da= --f(a-~z) da

(3)

Since we are using a thermal with circular s y m m e t r y it is reasonable to expect that the convergence in the horizontal wind field is symmetric, hence the difference between horizontal wind speeds on opposite "sides" of the thermal (AS) is not position dependent. Then

f V~dh~--.RaS,

(4)

231

where V± is the c o m p o n e n t along the radial of Fig.2, and AS is S1--$2 in Fig.2. We estimate AS as: AS ~ 2

R,

(5)

where (aS/al) is the gradient, assumed constant, of the inflow c o m p o n e n t of the horizontal wind speed across the thermal plume. Combining eqs. 4 and 5:

where the overbar indicates an areal average and D is the area averaged vertical velocity gradient over the plume at height z. This can be expressed as:

1 D - ~R 2

R

f

2~ D(r)rdr

(7)

0

Now define D m a s the measured value of the average vertical velocity gradient. This average is not a true area average, but a line average, and may be written as: R --

1

Dm= ~ f D(l)dl

(8)

0

Finally, assume that the vertical velocity gradient is a linear function of radius from the center with maximum value at the center and zero at the edge. Then:

-D 2 :°RD(r)rdr D--~ - R f°R D(l)dl

-

2

(9)

3

Thus: 2~R2

aS = ~R 2 ~ = >

=~D m

010)

Calculation of Dm and (as/al) was performed with data from August 21--22, 1985. Thermal plumes were selected on a subjective basis to be those whose center appeared to pass over the sodar. The principal requirement for this definition was that a central portion of the thermal evinced positive vertical velocities within 60 m of the surface. The gradient of horizontal wind speed was estimated from the difference in mean values of wind speed in the leading and trailing edge of the thermal plume at each

232 range gate. Vertical wind speed gradients were d e t e r m i n e d by differencing o f the averages o f W at neighboring range gates, where averages were determined f r o m the total time period during which the p l u m e was over the sodar. A l t h o u g h these estimates are relatively u n s o p h i s t i c a t e d t h e y corresp o n d to t h e assumptions o f the m o d e l d e f i n i t i o n o f D m and ~ S / ~ I outlined above. Table I shows that the ratio o f aS/Ol to D m o b t a i n e d with the sodar m e a s u r e m e n t s is .26, surprisingly close to the estimate o f 0.33. We n o t e also that the c o n v e r g e n c e estimates above the vertical velocity m a x i m u m are an o r d e r o f m a g n i t u d e less than those below t h e v e l o c i t y m a x i m u m , in agreem e n t with the picture o f a thermal whose dimensions change o n l y slightly in the u p p e r p o r t i o n o f the m i x e d layer. Values o f c o n v e r g e n c e m e a s u r e d in the lower p o r t i o n s o f the thermals investigated here were a b o u t 0.001 s- 1. A l t h o u g h this is a very limited data set and the m o d e l is crude, it lends c o n f i d e n c e to the use o f the sodar data collected on very s h o r t t i m e scales. F u r t h e r sodar investigations are w a r r a n t e d on e n t r a i n m e n t into thermals and the variability o f the h o r i z o n t a l wind field as a f f e c t e d by t h e r m a l plumes. TABLE I Average vertic~ and horizontal wind field estimatesforeighteenthermalplumeson Aug. 21--22,1985 Mean Duration (s) Length (m) Convergence below, 0S/O l (s ~ ) Convergence below, Dm( W~) Convergence above, oS/Ol (s ~) Convergence above, D~m (s 1) Ratio below, (OS/~I)/D m Ratio above, id.

377 1069 0.0013 0.0057 0.0001 --0.0022 0.26 0.30

Std. dev. (153) (463) (.0017) (.0037) (.0024) (.0027) (0.43) (t.62)

See text for definitions of terms. Values are listed for estimates below and above the maximum in vertical wind speed. CONCLUSION T h e m u l t i f r e q u e n c y , bistatic s o d a r s y s t e m c u r r e n t l y in o p e r a t i o n at A r g o n n e National L a b o r a t o r y has been described. T h e use o f multiple frequencies in c o n j u n c t i o n with a bistatic c o n f i g u r a t i o n has n o t a b l e advantages for e s t i m a t i o n o f variances and s h o r t - t i m e m e a n values o f t h e comp o n e n t s o f t h e wind field. Estimates o f h o r i z o n t a l c o n v e r g e n c e within t h e r m a l p l u m e s m a d e with data o b t a i n e d with this system s h o w g o o d c o n s i s t e n c y b e t w e e n h o r i z o n t a l

233 and vertical wind fields. Values of convergence associated with thermal plumes near 0.001 s -1 were observed, when a circularly symmetric model for the deviation from the mean horizontal and vertical wind fields is assumed. Continued analysis of this data should provide insights into the variability of the horizontal wind field under convective conditions. REFERENCES Coulter, R.L. and Martin, T.J., 1980. Three-dimensional sodar capabilities. Argonne National Laboratory Environmental Research Division, Ann. Rep. ANL-80-115, pp. 11--13. Ferrare, R.A., 1984. Lidar Observations of Organized Convection Within the Atmospheric Mixed Layer. Masters Thesis, University of Wisconsin, Madison, Wisc. Hall, F.F. Jr., Edinger, J.G. and Neff, W.D., 1975. Convective plumes in the planetary boundary layer, investigated with an acoustic echo sounder. J. Appl. Meteorol., 14(4): 513--523. Lenschow, D.H. and Stephens, P.L., 1980. The role of thermals in the convective boundary layer. Boundary Layer Meteorol., 19: 509--531. Mastrantonio, G. and Fiocco, G., 1982. Accuracy of wind velocity determination with Doppler sodars. J. Appl. Meteorol., 21(6): 823--830. Martin, T.J., 1981. Acoustic sounder intensity display techniques. Proc., Int. Acoustic Remote Sensing of the Atmosphere and Oceans, June 22--25, University of Calgary, Calgary, Ala., pp. II-26-29. Taconet, O. and Weill, A., 1982. Convective plumes in the atmospheric boundary layer as observed with an acoustic Doppler sodar. Boundary Layer Meteorol., 25 : 143--158.