DOPPLER SODAR MEASUREMENTS OF VERTICAL WIND VELOCITY

Russian Meteorology and Hydrology No. 7, pp. 28-36, 2003 Meleorologiya i Gidrologiya UDC 551.558:551.501.796 DOPPLER SODAR MEASUREMENTS OF VERTICAL WIND VELOCITY M. A. Lokoshchenko*, V. G. Perepyolkin**, and N. V. Semyonova* A method for Doppler measurements of the vertical wind velocity W and the corresponding technique based on the ECHO-1 vertical sodar are described. The main difference from analogous designs is the principle of noise filtering from the useful signal by means of analysis of the received sound wave phase (not amplitude). Results are presented of comparison of sodar and direct (contact) measurements of the radial wind velocity at the meteorological tower in Obninsk. In 2000, at Moscow State University (MSU), continuous recording of W started, with a m easurement threshold limit of 0.01 m/s. The diurnal cycle of this quantity at levels up to 200-300 m is discussed using measurement data for one month. At midday, there is a general tendency to lifting motions with acceleration, supposedly associated with movements of separate thermals under buoyancy. In the evening, as free convection decays, the tendency to weak sinking motions prevails. The am plitude of the vertical wind velocity gradually grows with height up to a 150-m level. The methodological basis of sodar data analysis is discussed. 1. INTRODUCTION The vertical wind velocity W is an important quantity in fluid dynamics equations. Information about W is necessary for a number of purposes, from weather forecasting to air pollution model estimations. Vertical motions determine water vapor condensation, which gives rise to convective clouds and precipitation. Usually, W values are very small and cannot be measured accurately by contact methods. In the large-scale flows, W can be 2-3 orders of magnitude smaller than the horizontal wind velocity V. This allows one, in many cases, to neglect the terms with W in the equations governing the flow motion. For example, the equation of motion with respect to the vertical coordinate can be replaced by the hydrostatic equation with a good accuracy. However, in consideration of meso- and microscale processes, information on W field has to be taken into account. Therefore, because of the absence of direct measurements of W, indirect estimates of VT are in common use in the mesoscale models. To improve the efficiency of these models, it is important to obtain reliable W measurements. In this connection, remote sensing approaches, particularly acoustic sounding of the atmosphere, are the most promising. In this paper, the design of a method of W sodar measurements, testing of its efficiency, and preliminary analysis of IT are presented. The vertical sodar ECHO-1, produced in Germany, has been operating at the Meteorological Observatory of Moscow State University since 1988. Its working frequency is 1666.7 Hz, pulse length is 75 ms, sample period is 10 s, and the height range of sounding varies from 38 to 800 m, taking into account lags * Lomonosov Moscow State University ** Oboukhov Institute of Atmospheric Physics, Russian Academy of Sciences - 28-

due to loudspeaker switching into the microphone regime. The vertical resolution of sodar data is 12.5 m. These characteristics are rather typical of most sodars of an ordinary range of measurements (e.g., [1] and others). In 2000, a new block for measurements of the Doppler shift of the echo-signal frequency was added to the sodar equipment, and continuous observations of the vertical wind velocity started. 2. METHOD OF DOPPLER MEASUREMENTS OF VERTICAL WIND VELOCITY The frequency of the input signal, subject to the Doppler effect, is f = f 0(c + W)/(c-W), where f0 is the output signal frequency, c is the sound velocity, and W is the projection of the airflow velocity on the beam axis. The numerator and denominator reflect the fact that the Doppler shift of the signal frequency takes place twice, that is, during its way upward and when the echo signal returns back to the antenna. It is well known that the sound scattering strictly backward, that is, for an angle of 180, is caused only by turbulent inhomogeneities of scalar fields of meteorological elements, mainly of temperature [1]. These small-scale inhomogeneities within the scattering volume act as a kind of buoy in the wind field, passive transporters of its velocity. A characteristic feature of sodar measurements is the absence of a constant echo signal in the whole height range, because the upper bound of wind data floats depending on the vertical development of thermal turbulence. From the formula above, it follows that W = c(l -f0/f) /( 1 + f0/f), implying that to measure the radial (in our case, vertical) wind velocity, it is sufficient to determine the ratio of frequencies of output and input signals. The designed device for measuring W from Doppler shifts of the input signal frequency is one of the simplest types and is known as the method of zero counting [1]. In our case, this means measuring the time during which the signal crosses the zero level a given number of times, that is, measuring an average period of the echo signal. When used without special technical tools, this method leads to large errors. A special scheme was designed for signal processing, based upon the principle of automatic phase-regulation of frequency (APRF). It provides efficient suppression of noises as well as the rejection of a heavily noised signal. It is known that the sodar provides a moving averaging of the echo signal from separate inhomogeneities within the pulse scattering volume. The latter is determined by the direction diagram and the pulse length t. During time At = l/fq, equal to the output signal period, the averaging zone will move very little, less than 2%. In other words, at the time tq+ At, 98% of the echo signal will be formed by scattering at the same inhomogeneities as at the time t0. The influence of the lateral entrainment of the inhomogeneities by horizontal wind V from the scattering volume is also extremely small due to low Mach numbers in the atmosphere: V «c. Therefore, the frequency of the useful part of the signal, taking into account low real values of IV, cannot significantly change for the time comparable with the signal period. In the case of a random signal (noise), its frequency is also random and, within the permitted band, changes arbitrarily fast. Figure 1 shows the block-diagram of the device for Doppler measurements of W based on the phase method of the useful signal selection. The device is represented as a branch in the general diagram of the sodar, outlined by a dashed line. The quartz generator signal, frequency-synchronized with the input pulse, comes to a multiplier of the initial frequency f 0 (1) and then to the measuring counter (8). Part of the echo signal on its way from the antenna switcher to the general amplifier and receiver also comes to the Doppler device, which has its own amplifier (2). Then, in the amplified echo signal, a 100-Hz-wide band is cut out by the filter (3), the band center corresponding to the initial frequency f Q. The amplified narrow-band signal comes to the noise-suppressing scheme (4-6) working on the basis of - 29-

Fig. 1. Block-diagram of Doppler measurements of the vertical wind velocity at Moscow State University. (1) Multiplier of frequency f 0 of the input signal; (2) signal amplifier; (3) band Filter; (4) phase detector; (5) low-pass filter; 6) generator governed by voltage; (7) frequency divider; (8) measuring counter; (9) phase capture indicator. APRF. The scheme contains a phase detector (4) which compares the phases of the echo signal and of a standard generator (6), whose frequency can be manipulated by means of the corresponding input voltage. The phase detector output (4) is connected with the regulating input of the generator through a special filter (5) limiting the maximum rate of the generator frequency change. On the whole, this noise suppressor represents a feedback system whose output is the signal of the generator (6). It repeats the output signal; however, the filter (5) smoothes out fast changes of its frequency. In the normal regime, the feedback equals the phases of the input and output signals ( phase capture ). If the input signal frequency changes too fast under strong noises, the signal of the generator (6), due to additional inertia of the filter (5), starts lagging, and a mismatch signal appears at the output of the phase detector (4). In this case, the phase capture indicator (9) sends the counter (8) a command to stop the computation of W because of non-reliability. The reliable signal comes from the output of the noise suppressor to the frequency divider (7). The low-frequency signal thus obtained governs the measuring counter (8). The latter counts the high-frequency pulses coming from the output of the multiplier o f/0 (1) during the time determined by the period of the low-frequency pulse coming from the divider output /(7 ). It can be easily seen that the number of pulses collected by the counter will be proportional to the frequency ratio f 0 If. Coefficients of multiplication o f/0 and division o f/are selected so as to provide the dynamic range of measurements of W within ±5.5 m/s and a speed resolution of 0.01 m/s. The entire cycle is repeated separately for each height with a 12.5-m step, after receiving the echo signal from the preceding level. An important criterion of the efficiency of a Doppler device is a percentage of the W profiles subjected to a multistep logic reliability test, first by means of two ordinary filters (one is shown in Fig. 1) and then by means of the device (4-6). According to our data, under well-developed convection at midday in the lower layer (from the boundary of the dead zone to 106 m), individual measurements of W correspond to about 45% of the whole time. This is almost every second possible case if a reliable signal were always - 30 -

Fig. 2. Comparison of sodar and direct measurements of wind velocity (m/s) at 73-m level under sloped antenna, Obninsk, August 2001. The horizontal axis is the radial component of horizontal wind velocity from the tower vane data on the sodar antenna axis; the vertical axis is the radial component of wind velocity from sodar data on the antenna axis. present in all the height ranges. With height, this percentage decreases and makes up only every 5th case, or 19%, in the 206-m layer. 3. TESTING OF RELIABILITY OF SODAR MEASUREMENTS The sodar data obtained with the proposed phase scheme, are compared with direct measurements of the horizontal wind velocity V aloft. For this purpose, a special experiment was carried out in August 2001. During 6 days, the sodar operated at Obninsk, 150 m distant from the meteorological tower, with the sloped antenna (zenith angle of 30 ). Hourly averaged values of V measured by tower wind vanes at 73 and 121 m were compared against the sodar data, i.e., the radial projection of the wind on the antenna beam axis in the height ranges close to the tower levels (81 and 144 m, respectively, along the sloped axis). As the antenna was sloped to the southeast, winds from south and east were interpreted by the sodar as sinking motions, and those from north and west were identified as lifting motions. With the same signs, projections of V on the antenna axis from the vane data were calculated taking into account wind direction. An example of a similar comparison for the first half of the experiment is given in Fig. 2 at the 73-m level. A certain spread in the values is inevitable, because the vertical motions contribute to sodar measurements (as the tangent component along the beam axis), but they do not affect horizontal vanes at the tower. In any event, the linear correlation coefficient R (the relationship is evidently close to the linear one) was found to be very high: 0.85 for the sample volume of 66 h. The estimate bias was comparatively low. During the same period at 121 m, R was equal to 0.81. Throughout the experiment, the values of R were always within the limits from 0.7 to 0.9. This implies that the statistical relationship between the data from two sources is more than statistically significant, it is very close. The vertical velocity is a particular case of any radial velocity along the beam axis. Therefore, it can be concluded that the proposed method is also efficient for the vertical position of the antenna and the sodar data are reliable, at least when their values are not very small. 4. OBSERVATIONS Preliminary data on the vertical wind velocity W were obtained from measurements during one month, from 28 September to 25 October 2000. In total, there were 520 hours of sodar measurements during 27 days, -31 -

Fig. 3. Hourly profiles of the vertical wind velocity, Moscow State University, 28 September to October 25 2000. The дг-axis is vertical velocity (m/s), and the y-axis is height (m). both complete and incomplete, with four short pauses. As a result, 520 hourly averaged profiles of W were calculated, each derived from 360 individual measurements. Figure 3 shows the average profiles of W for every hour of the day for one month. Positive direction is upward, which corresponds to lifting airflows from the surface. Lateral lines show confidence intervals with 0.95 probability. It must be noted that at the lowest point, i.e., in the calculation range centered at the 56-m level, the data could be slightly distorted by locals (multiple reflections from nearby buildings). Up to 100-120 m, the samples of W for each of 24 profiles include all the days of sodar operation. Above, thermal turbulence was not always developed enough for a confident detection of the echo signal against the background of noises. Therefore, in the upper parts of the profiles in Fig. 3, each upper point is obtained from a smaller number of observations. - 32-

Nevertheless, up to 200 m, the number of individual observations is 10 or more (except a few hours in the afternoon, when the number is lower). That is, starting at the second point up to 200 m, the hourly averaged profiles are statistically reliable. The uppermost points of the profiles are represented by at least three different days of observations. Note that at night in the stable atmosphere, the range of W is usually larger than in the evening when stratification is close to neutral. As can be seen, the values of W show a well-pronounced diurnal cycle. At midday, above 80-100 m, there is a tendency to lifting motions. Moreover, starting from this level, within at least 50-70 m, the value of the vertical velocity increases, that is, the air lifting accelerates (particularly from 13:00 to 16:00). Evidently, the dominant process at this time is the ascent of warmer-than-ambient thermals under the action of the buoyancy force. This force is able to generate a real acceleration of lifting air parcels on the time scale of the order of several minutes (the ascent of a single thermal). Furthermore, the accelerating ascent itself shows that the buoyancy effect is the main cause determining the shape of the daytime profiles of W. The increase in W with height in the daytime is clearly seen from the sodar data not only in Fig. 3 but also in Fig. 4a, where the diurnal cycle of monthly averaged W at three levels is displayed. It can be seen that from 13:00 to 16:00, minimum positive values of W occur at the lowest level of 69 m, and maximum values are at 106 and 144 m. Daytime W profiles similar in sign and shape were obtained from sodar data in [1, 3]. It is natural that lifting areas in the convective cells alternate with zones of mainly sinking motions (in the areas between individual convective clouds if the convection level is above the condensation level). The question arises as to why, from the sodar data, the sinking in the daytime does not fully compensate the lifting of separate thermals. This strange effect can be explained both by stable convergence of the wind field in the lower layer and by the limitations of sodar measurements causing a partial loss of real sinking flows. This loss can have two causes: asymmetry of sodar measurements in the flows with varying direction and very low velocities of sinking, below the detection threshold (in our case, 0.01 m/s). As to the first of the possible causes, it must be noted that thermal turbulence in the lifting areas, which generates the sodar echo signal, is developed more strongly. According to our data, in daytime convection in the lower 206-m layer, the ratio of numbers of individual measurements in the thermals and in the sinking areas between them is about 6 : 4. In periods with high turbulence, this ratio reaches 55 : 45%. Unfortunately, this asymmetry of the measurements in the airflows with different directions is always present in the sodar data. It can lead to certain overestimation of averaged W under convection. The standard deviation a(w) in the daytime is usually 0.5 m/s, sometimes increasing to 1.0 m/s [2,4]. Taking into account the proportion of 6 : 4, it is evident that, under convection, the measurement bias toward overestimation is, on average, about 0.05 m/s and does not exceed 0.10 m/s. Note that, as shown in Fig. 3, positive values of W in the daytime reach 0.3 to 0.5 m/s and, thus, cannot be explained by the asymmetry alone. In the evening, as convection decays, there is an opposite tendency to weak sinking. In Fig. 4a it can be seen that at 19:00-20:00, the proportion of W at three levels is mirror-opposite to that observed in the daytime. That is, the sinking (not lifting) speed increases with height, the air parcels being subject to dynamic drag near the surface. A general sinking tendency remains all night. It is also possible that at this time there exist compensating lifting motions, too slow to be detected by the sodar. According to our data, the amplitude of the diurnal cycle of W gradually increases with height, up to 150 m. For example, the monthly average difference of W values at 15:00 and 20:00 is below 0.1 m/s at 69 m; between 0.1 and 0.2 m/s at 81 and 94 m; between 0.2 and 0.3 m/s at 106 m; about 0.5 m/s at 119 m; about 0.6 m/s at 131 and 144 m; and as large as 0.9 m/s at 156 m, i.e., an order of magnitude greater than the value in the surface layer. The amplitude of growth with height is a result of both the accelerated lifting of heated thermals in the daytime and dynamic drag of sinking motions at the surface. - 33-

ir m/s Fig. 4. (a) Diurnal cycle of monthly averaged vertical wind velocity (m/s) and (b) an example of the diurnal cycle of vertical velocity for 2 8-29 September 2000 at 69 (1), 106 (2), and 156 m (3). 5. ESTIMATION OF MEASUREMENTS OF THE VERTICAL WIND VELOCITY As noted above, measurements of W have large errors due to the generally small values of IV in comparison with horizontal wind V. Thus, it is necessary to carefully control the vertical orientation of the beam for IV measurements. In our case, the correspondence of the antenna beam to the true vertical was tested by a mechanical bubble level placed at the loudspeaker head surface. The level accuracy is about 1 of deviation of this surface from the horizontal position. As sinl = 0.017, the value of V must not exceed IV more than tenfold. In this case, the contribution of V to the measured IV will be less than 0.2 and, thus, will be an order of magnitude lower than the real W. Then, when individual measurements are considered, we must select cases of calm weather or very slight wind at levels up to 300 m, from which a reliable signal can be obtained. Often, this type of weather is associated with central parts of anticyclones, with axes of vast ridges, or with any low-gradient field with high background pressure. Theoretically, calm weather can be associated with cyclone centers as well. However, horizontal pressure gradients here are usually higher than in the anticyclones, and one can rarely get to the center of this eddy. Also, precipitation, which is frequent in these areas, produces noise in the sodar data. An example of the calculation of IV for one day (from 19:00 28 September to 18:00 29 September), i.e., at the beginning of the study period, is shown in Fig. 4b. At that time, Moscow was situated at the center of a vast high extending across the whole of eastern Europe (Fig. 5). According to three radiosonde ascents and vane data from Dolgoprudnyi (a town near the northern boundary of Moscow), in the daytime of 28 September and nighttime of 29 September, the wind speed in the layer from the surface to the 300-m - 34-

Fig. 5. Fragment of surface pressure analysis at 10:00 Summer Moscow Time 29 September 2000. Moscow is marked by the asterisk. level did not exceed 2 m/s and, the next day, reached 3 m/s at 200 and 300 m only. This weak wind allows us to consider reliable (at least qualitatively) any effect associated with the measured \W\ > 0.2 m/s. As can be seen in Fig. 4b, the main features of the diurnal cycle are similar to those for monthly averaged data: a general tendency to lifting at midday and the compensating sinking in the evening after decay of convection. Note that the daytime lifting developed, evidently, against the large-scale tendency of dynamic subsidence, typical of that deep high. Thus, in analysis of the vertical wind data, one of the two approaches can be used. Averaging over a large sample of data (over the whole month) allows one to expect a mutual compensation of the errors associated with effects of the horizontal wind velocity due to random deviations of the antenna beam from the true vertical. The analysis of individual measurements of W should be limited to cases of calm weather or very slight winds in the whole layer. If V = 3 m/s and W = 0.3 m/s, the measurement error of W due to random deviations is ± 0.05 m/s. In our case, both approaches show similar features of the diurnal cycle of W. The accuracy of W measurements can also be affected by the general slope of the surface in the area of measurements [2,4]. In the vicinity of Moscow State University, the terrain is rather flat. Within the radius of 400 m around the sodar site, the terrain slope in any direction does not exceed 2, with an average of 1-1.5. Therefore, the measurement error of W due to the slope wind effect on the true vertical does not exceed ± 0.08 m/s. 6. DISCUSSION Nonzero values of W, averaged over long periods of measurements, require interpretation from the point of view of fluid mechanics. This interpretation can be ambiguous. First, effects of steady-state mesoscale flows under the conditions of a large city and inhomogeneous terrain cannot be neglected. Thus, positive W in the daytime can be explained by a total convergence of the horizontal wind field in the surface layer in the zone of an urban breeze circulation. In [4], it has been shown for Rome that, in conditions of an urban circulation, the integral estimates of W even over a long period can differ significantly from zero. On the other hand, there can exist very slow motions of opposite sign as compared to the above-mentioned tendencies. For example, the daytime weak sinking of air with velocities of about 1 cm/s or less can represent the general background of the vertical motions compensating the fast lifting of separate thermals. However, this value (1 cm/s) is in our case the lower threshold of detection of vertical motions by the sodar. Remember also that transporters of these motions are only temperature inhomogeneities of a certain size limited by the working frequency of the sodar. Strictly speaking, the proposed method measures not the full vertical velocity itself, but sufficiently rapid movements of fairly large inhomogeneities: - 35 -

W '= W > 1 cm/s. Anyway, our conclusions are absolutely correct with respect to this quantity W\ which is important for many applications. Note also that the measurement of the full integral over all possible values of vertical velocity cannot be done by any existing technique. 7. CONCLUSIONS 1. An original version of Doppler measurements of wind velocity is designed and implemented in a hardware-software complex on the basis of ECHO-1 sodar. The proposed approach consists of the detection of a useful echo signal by means of its phase analysis. 2. The sodar measurements of the radial wind are compared with its direct measurements aloft. A high level of data consistency is obtained. 3. Using the example of measurements during one month, daily variations of vertical velocity not less than 0.01 m/s are analyzed. At midday, the vertical velocity is positive at the levels up to 150-200 m, which indicates a general tendency to lifting motions in developed convection. Positive values of W increase with height. Qualitatively, this increase is similar to the acceleration of an ascending parcel under buoyancy. At night, within the lower 300-m layer, W is negative. The sinking motions at the surface tend to slow down due to dynamic drag. As a consequence of both effects, the amplitude of vertical velocity in the diurnal cycle increases with height up to 150 m. Nonzero values of W averaged over a long period can be caused by neglect of very slow motions as well as by effects of steady-state mesoscale flows over a large city. 4. Methodologically, two approaches can be applied to sodar measurements of vertical wind: either averaging over large data samples or analysis of individual profiles in near-calm conditions. The authors thank M. A. Petrosyants and N. F. Veltishchev for helpful discussion and advice. REFERENCES [1] N. P. Krasnenko, Acoustic Sounding of the Atmosphere [in Russian], Nauka, Novosibirsk, 1986. [2] R. L. Coulter et al., Questions or answers: Sodar observations from the CASES-99 field study, Proc. of the 10th Int. Symp. on Acoustic Remote Sensing, Auckland, New Zealand, 2000. [3] F. F. Hall, J. G. Edinger, and W. D. Neff, Convective plumes in the planetary boundary layer, investigated with an acoustic echo sounder, J. Appl. Meteorol., vol. 14, 1975. [4] G. Mastrantonio et al., The Rome urban heat island effect observed by a network of sodars, Proc. o f the 8th Int. Symp. on Acoustic Remote Sensing, Moscow, Russia, 1996. 30 May 2002-36-