Determination of meteorological quantities and sound attenuation via acoustic tomography. 1 Introduction. 2 The Melpitz experiment

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1 Determination of meteorological quantities and sound attenuation via acoustic tomography Klaus Arnold, Kati Balogh, Astrid Ziemann, Manuela Barth, Armin Raabe, Danny Daniel Institut für Meteorologie, Universität Leipzig, D-13 Leipzig, Stephanstr. 3, Germany, The acoustic travel time tomography is presented as an experimental technique for concurrently monitoring of spatially averaged meteorological quantities and the determination of the atmospheric excess attenuation of sound. This ground-based remote sensing technique uses the nearly horizontal straight-line propagation of sound waves in the atmospheric boundary layer up to several hundred meters. By measuring the elapsed time and the modification of the amplitude of the transmitted signal the acoustic velocity along the propagation paths as well the attenuation of the signal can be determined assuming a straightray sound propagation. This enabled us to determine meteorological data, as the temperature and wind speed, and the influence of the atmospheric conditions on the sound attenuation at the same time. The acoustic measuring system, together with several reference measurements, was applied during a field campaign in autumn. In a meadow, a cross with several sound sources and receivers with an extension of roughly five hundred meters was arranged to measure the travel time and the relative amplitude of sound signals. The main objective of the field experiment was to investigate the spatial structure and statistical characteristics of the wind speed and temperature fluctuations in the surface layer with the space-time scales inherent to atmospheric internal gravity waves. These investigations should lead to a better understanding of the role of the internal gravity waves in the dynamics and turbulent regimes of the stable atmospheric boundary layers. 1 Introduction The acoustic travel time tomography was used as a technique to observe area-averaged air temperature and wind fields in their horizontal and temporal variability [1, ]. This technique utilised the dependence of sound speed on temperature and wind vector to derive the distribution of these quantities within the measuring area. The measuring system consists of several sound transmitters and receivers, which are distributed within a landscape. From the recorded travel times of acoustic pulses the speed of sound is estimated under the precondition of known sound path lengths [3, ]. Outgoing from the speed of sound the temperature as well as the wind speed can be determined under some assumptions [5]. At the same time the acoustic measurements can be used to investigate the turbulent structure inside the near surface layer. Different types of instabilities of internal gravity waves (IGW) could be a source of small-scale turbulence and meso-scale eddy structures in the stable atmospheric boundary layer [6]. Therefore the statistical properties of these waves affect the turbulence statistics and the temperature and wind field inside a stable atmospheric boundary layer. The IGWs generate wind and temperature fluctuations with periods from several minutes (to a few hours) at horizontal scales from hundred metres up to a few kilometres [6]. These fluctuations correspond with the variability of the acoustic signals propagating through the atmospheric boundary laver, such as the travel time, signal amplitude or the angles of arrival. The motivation of this study was the investigation of statistical characteristics of these acoustic parameters to obtain a better appreciation of the influence of IGWs on turbulent regimes inside stable atmospheric boundary layers. The Melpitz experiment The acoustic measuring system, together with several reference measurements, was applied during a field campaign in autumn. Fig. 1: Layout of the experimental setup at the research station Melpitz. The five sources (S) and eight receivers (R) are arranged at a cross with an extension of about 5 m. M stands for the 1 m temperature and wind profile mast and S/R for the SODAR/RASS. N 169

2 Forum Acusticum 5 Budapest The main objective of the field experiment was to investigate the spatial structure and statistical characteristics of the wind speed and temperature fluctuations in the surface layer with the space-time scales inherent to atmospheric internal gravity waves. The travel time of each signal was estimated from the recorded data by cross correlation between the received and the transmitted signal. Each peak of the crosscorrelation is associated with a specific ray path. The time delay corresponds to the travel time of the transmitted signal. The experiment was carried out at the research station of the Institute for Tropospheric Research (IFT) in Melpitz (51 3 N, 1 5 E, 86 m a.s.l.) during October. In the meadow, a cross with five sound sources and eight receivers (see fig. ) with an extension of roughly five hundred meters (see fig. 3) was arranged to measure the travel time and the relative amplitude of acoustic pulses. 3 Observations at the test side A stable stratification of the atmospheric boundary layer is one necessary presupposition for buoyancy waves, therefore the following investigations concentrates on nighttimes, were these conditions dominate. As an example, the first hours of a clear night of 8 October with very stable conditions were selected here. 3.1 Meteorological sound attenuation temperature [ C] All sound sources transmit the same signal simultaneously (sine double burst with frequency of 1 Hz). The individual signals were received by the eight microphones with a time offset depending on their spacing (see fig. 3). R/1 1. amplitude S1 S S amplitude S : 3: : Fig. : Evaluation of the air temperature and wind speed on 8th October, between : and :3. The acoustic derived values were compared with the profile mast data at the according height of m above ground surface. For the temperature and wind calculation the bi-directional sound propagation between in each case two receivers was used : travel time [ms] 1. temperature acoustic temperature profile mast wind speed acoustic wind speed profile mast 33 3 travel time [ms] Fig. 3: Example of the recorded signal, above: the complete signal after filtering at the receiver R/1, below: zoom of the signal from source S5, a double peak with a short intermission. This leads to four bi-directional measuring paths for the searched meteorological quantities [5], whereas the amount of the wind speed was determined from the orthogonal wind components. In figure the averaged values for the wind speed and temperature of these four : wind speed [ms ] S S5 8 and From the measured travel times between each source and receiver the speed of sound was calculated knowing the exact sound path length under assumption of straight-line sound propagation [3]. The special configuration of the sound sources and receivers enabled us to determine the temperature-sensitive sound speed and wind components between in each case two receivers autonomous (e.g. R1/1 and R1/, see fig. 1). Fig. : On the left: the receiver set, a microphone with a windscreen and on the right the sound source: three loudspeakers (compression drivers), all devices were mounted on tripods at about m above the ground. 1. quantities

3 Forum Acusticum 5 Budapest paths were compared with the profile mast data. This figure demonstrates, that generally, the measurements agree very well. The observed discrepancies in the air temperature are due to the differences of the measuring systems and the unequal spatial footprint range of the point and area-averaged measurements. The observed variances in the wind speed mainly arise from the error due to inertia of the cup anemometer at low wind speed conditions. Besides the meteorological parameters, also the atmospheric excess attenuation of sound due to absorption, refraction and turbulence is detectable with the acoustic measurements. If we have a straight line with two sound sources and receivers inside, the change of the signal amplitude provides information about an attenuation additionally to the geometrically caused decrease of sound level Outgoing from the recorded signal amplitude at each receiver, the relative change of the sound pressure level between each receiver pair (e.g. R1/1 and R1/ an so on) was calculated [7]. excess attenuation [db] S1 - R1(/1) S5 - R1(1/) wind direction -1 :3 1: 1:3 : :3 3: 3:3 : :3 Fig. 5: Evaluation of the excess attenuation depending on the wind direction on 8 th October, between :3 and :3 (1 min averaged values). As an example the excess attenuation between the sources S1 and S5 the receivers R1/1 and R1/ (see fig. 1) are displayed (positive values: noise reducing, negative values: increasing sound immission). In fig. 7 the excess attenuation of sound due to the atmospheric influence is shown. Depending on the prevailing wind direction, a different excess attenuation at the considered propagation paths was observed. During the observation time the wind direction primarily varies between southwest and northwest. Therefore at the propagation path from source S5 to the receivers R1/1 and R1/ downwind conditions predominates and at the opposite direction (S1 to the receivers R1/ and R1/1) upwind conditions accordingly (see fig 1). This leads to different excess attenuation of sound depending on the angle between the wind direction and the sound propagation. During crosswind conditions (southern directions at about 3: and :1 a.m.) at both directions nearly the same sound attenuation was wind direction [deg] observed. However, it has to take into account, that during this night only low wind conditions dominates (1- ms -1, see fig. ) and therefore only unconfident conclusions are possible. The wind influence is superposed by the vertical temperature profile (see fig. 8), which causes significant changes of the excess attenuation independent of the direction of sound propagation. 3. Internal gravity waves Since internal gravity waves significantly contribute to the variability of the wind speed and temperature fields in stable atmosphere, they may cause variations of acoustic waves parameters propagating through the atmospheric surface layer [6] Vertical profiling and air pressure heigth above ground [m] ,,,,,6,8,1 N BV Buoyancy - Frequency squared [s - ] : 1: : 3: : Fig. 6: Variation of the Brunt-Vaisala Frequency (squared) with height on 8 th October, between : and : (1 min averaged values). The values above 7 m were calculated from the SO- DAR/RASS, the bottom value from the 1 m profile mast. The wave frequencies for the IGW at any altitude must be less then the Brunt-Vaisala Frequency, N BV at that height: N BV g θ = θ z (1) where g is the gravity acceleration, and θ is the potential temperature. In figure 6, the Brunt-Vaisala Frequency is plotted as a function of height for the first hours of 8 October. The vertical temperature profiles were estimated from the 1 m profile mast (bottom value) and the SODAR/RASS (heights above 7 m). Fig. 6 shows a notably strong stable stratification between the ground and approximately 1 m. Therefore the propagations of vertically waves is supported in particular between the ground and the neutral layers aloft. Between mid- 171

4 Forum Acusticum 5 Budapest night and 3 a.m. the stratification is nearly unchanged, at a.m. close to the ground a change to lower stabilities was observed. Fig. 7 shows an example of the SODAR observations during night time. The Doppler SODAR (METEK GmbH) consists of three antennas whose signal reflectivity was analysed. In the raw data modus, values at the range between 7 m and 63 m above the ground ( m height resolution) were recorded approximately every seconds. In fig. 8 the time series of the psychrometer temperatures between.5 m and m above the ground are shown. The vertical temperature profile shows some potential signatures of IGW events. Several temperature drops (e.g. around 1: or 1:5 ) can be a result of the passage of internal gravity waves. If the turbulent mixing event propagated downward, warmer air is mixed down into the cold air below, which generated a reduction of the thermal stability. Some remarkable leaps are also visible in the air pressure registration. The installed Vaisala sensor (PTB) has a pressure resolution of.1 hpa (at an time resolution of 1 Hz). The abrupt changes of the atmospheric pressure (in fig. 9) correspond partially with the temperature drops in fig 8, which is a hint on the IGW events. 18,5 18, Fig. 7: Evaluation of the SODAR signal reflectivity as a function of height. The three radial wind components were averaged for the 8 th October, between : and 5:. In figure 7 the averaged values of the three radial wind components are plotted. A significant change of the reflectivity was observed at a height range between roughly 5 m and 5 m. Starting at approximately 3 a.m., a downward motion of this sharp transition is visible. The contribution of the IGW is also visible in the variability of the temperature vertical profile close to the ground. temperature [ C] : 1: : 3: :.5 m.8 m.1 m 5.3 m 7.8 m m Fig. 8: Evaluation of the air temperature, measured at the profile mast at different heights above the ground on 8 th October, between : and : local time (3 s values). atmospheric pressure [hpa] 18,3 18, 18,1 18, 17,9 17,8 17,7 17,6 17,5 : 1: : 3: : Fig. 9: Time series of the air pressure (sensor: Vaisala PTB ) on 8 th October, between : and :. 3.. Horizontal acoustic sounding To characterise the statistical properties of gravity waves in the stable atmospheric boundary layer, the horizontal acoustic pulse propagation was used. For each sound source (except S5) the travel times to twice-three receivers that spanned a triangle (e.g. S1: R3/1, R/1, R/1 and S1: R3/1, R/, R/ and so on) were estimated (see fig 1). As a result, we get eight triangles with travel time series of the acoustic pulses (repetition period of 3 s). These are the basic data for the following determination of the statistical characteristics of the travel time fluctuations, such as frequency spectra, coherences and horizontal phase speeds. In fig. 1 an example for the variability of the pulse travel time fluctuations is given. Here the temporal variations of the travel time difference between two receivers τ ij () t relative to its mean value ( hours) were considered: 17

5 Forum Acusticum 5 Budapest τi() t τ j() t τ ij() t = τ τ i j () where τ is the travel time and i, j = 1,, 3. In fig. 1 this temporal variation for a triangle, which consists outgoing from the source S1 of the three receivers R/, R3/1 and R/, is shown. For all three considered travel time differences nearly the same variation was observed during this examined nighttime period. The variation of the travel times was compared with the wind component along the path between the two receivers R1/1 and R1/. It is discernable, that the modifications of the travel time differences are almost independent from the fluctuations of the wind field and therefore they are mainly affected by the temperature variability. An indication for the occurrence of organised wave structures inside the considered time interval is that at the same time K = 1 (which is given for K 1 = K 3 = K 31 = 1) and Σ ϕ =. Therefore the calculated coherences and phase spectra has to be checked for the maximum of the coherence function with the additional condition that sum of the phase differences is zero [8]. The coherence and phase spectra for the travel time differences were calculated for each transmitter-receiverreceiver pair about one hour (6 min) period (18 values) for the eight triangles. In figure 11 an example of the coherence and the corresponding phase spectra is shown for a one hour time period for the triangle (R3/1, R/ and R/) on 8 October. travel time difference [s*1-3 ] - - R3/1 R/ R/ R/ R/ R3/1 wind speed -6 - : 1: : 3: : Fig. 1: Evaluation of the difference between the travel times compared to the mean difference on 8 th October, between : and :. Here three paths from the source S1 were selected. This difference was compared with the wind component along the path R1/1 and R1/ (see fig. 1). A comparison of the times with abrupt modifications of the travel time differences with the changes in the vertical temperature profile (see fig. 8) demonstrates, that time intervals almost corresponds with each other. As well as the peak of the atmospheric pressure variation at around 3 a.m. (fig. 9) conforms to the modification of the travel time differences. For all time series the coherences K ij and the corresponding phase spectra ϕ i -ϕ j where calculated. The coherences K ij and the multi-coherence function were defined after [8] as: K = K + K + K K K K cos ϕ (3) where the sum of the phase differences is [9]: ϕ = ( ϕ 1 ϕ ) + ( ϕ ϕ 3) + ( ϕ ϕ 3 1) () 8 6 wind component [ms -1 ] Fig. 11: Coherence and spectra of the phase differences of the travel time on 8 th October, between :8 and 3:11 (18 values) (triangle: R3/1, R/ and R/). A maximum of the coherence together with a sum of the phase difference equal zero indicates the occurrence of internal gravity waves. Fig. 11 shows several maxima of the sum of the coherence function. One is at the lower boundary of the frequency, two other at about.6 and.1 Hz. However, only at the low frequency range (between and. Hz) at the same time the sum of the phase spectra is also nearly zero. That means, that inside the considered time period only gravity waves with a repetition period of greater than 1 min were observed. That fits to the observations of the atmospheric pressure series (fig. 9) and travel time variations (fig. 1). Results and discussion The acoustic tomography was applied to obtain spatially averaged meteorological quantities, such as temperature and wind speed and the atmospheric excess attenuation of sound at the same time. These data agree very well with the conventionally observed meteoro- 173

6 Forum Acusticum 5 Budapest logical data. As well a correlation between the prevailing wind direction and speed and the excess attenuation of sound was observed. The technique of acoustic sound propagation inside the stable atmospheric boundary layer is also applicable to obtain information about the statistical behaviour of internal gravity waves. This can be realised, if the travel time variances, coherences and phase differences of several sound transmission paths are considered. Some periods (especially 1 min) were detected in the coherences and phase spectra of the travel time fluctuations that contain some typical signatures of internal gravity waves. These periods, and the corresponding travel time fluctuations, agree with the observed time periods of the additional estimated temperature profile and atmospheric pressure measurements and are typically for the internal gravity waves inside a stable lower atmosphere. The existence of the wave guide near ground surface was confirmed by the analysis of the vertical wind speed and temperature profiles (Brunt-Vaisala Frequency) in the atmospheric boundary layer, which were continuously controlled by a SODAR/RASS and a profile mast. Further investigations should be concentrated on the estimation of the confidence interval of the coherence and the spectra of the phase differences. This is necessary for a precise and improved interpretation of the measured data. As well, an expansion of the analysed time periods should be realised for a statistical investigation of the results. Acknowledgements Our special thanks goes to G. Spindler and A. Grüner (Institute for Tropospheric Research, Leipzig) for the data provision and the assistance during the Melpitz field experiment. Many thanks also go to Th. Conrath and H. Siebert (also Institute for Tropospheric Research, Leipzig) for the provision of the SO- DAR/RASS data. We would like to thank F. Weiße and M. Engelhorn for their support in the development and manufacturing of the acoustic measuring system. As well we also like to thank the students from the Institute of Meteorology, P. Achert, J. Stanislawsky and A. Schleichardt for their assistance during the field experiment. The investigations of the IGWs were carried out in cooperation with the colleagues from the Obukhov Institute of Atmospheric Physic in Moscow, I. Chunchuzov, S. Kulichkov and V. Perepelkin. These investigations were supported by the Deutsche Forschungsgemeinschaft under grant RA 569/9-1. Literature [1] K. Arnold, A. Ziemann, A. Raabe, Tomographic monitoring of wind and temperature in different heights above the ground. Acustica Vol. 87, pp (1) [] A. Raabe, K. Arnold, A. Ziemann, Horizontal turbulent fluxes of sensible heat and horizontal homogeneity in micrometeorological experiments. J. Atmos. Oceanic Technol.. Vol. 19, pp () [3] A. Ziemann, K. Arnold, A. Raabe, Acoustic tomography as a method to describe measuring sites. J. Atmos. Ocean. Technol. Vol. 19, pp () [] K. Arnold, A. Ziemann, A. Raabe., G. Spindler, Acoustic tomography and conventional meteorological measurements over heterogeneous surfaces. Meteorol. and Atmos. Physics Vol. 85, pp () [5] K. Arnold, A. Ziemann, A. Raabe, M. Barth, D., Daniel, Acoustic tomographic measurements in the atmospheric surface layer. Proceedings 16 th Symposium on boundary layers and turbulence, AMS, Portland ME. () [6] I. Chunchuzov, Influence of internal gravity waves on sound propagation in the lower atmosphere, Meteorology and Atmospheric Physics, Vol. 3, pp (3) [7] K. Balogh, A. Ziemann, Einfluss von Atmosphäre und Boden auf die Schallausbreitung im Freien. Wiss. Mit. Inst. für Meteorologie Universität Leipzig. Vol. 36, pp (5) [8] I. Chunchuzov, S. Kulichkov, A. Otrezov, V. Perepelkin, Acoustic pulse propagation through a fluctuating stably stratified atmospheric boundary layer. J. Acoust. Soc. Am. Vol. 117, pp (5) [9] J.S. Bendat, A.G. Piersol: Random Data: Analysis and Measurement Procedures. J. Wiley & Sons Inc., New York, 566 p. (1986) 17