Remote sensing of temperature and wind using acoustic travel-time measurements

Transcription

1 Meteorologische Zeitschrift, Vol. 22, No. 2, (April 2013) Ó by Gebrüder Borntraeger 2013 Open Access Article Remote sensing of temperature and wind using acoustic travel-time measurements Manuela Barth 1,*, Gabi Fischer 1, Armin Raabe 1, Astrid Ziemann 2 and Frank Weiße 1 1 Universität Leipzig, Institut für Meteorologie, Leipzig, Germany 2 TU Dresden, Institut für Hydrologie und Meteorologie, Professur für Meteorologie, Dresden, Germany (Manuscript received April 27, 2012; in revised form November 20, 2012; accepted February 10, 2013) Abstract A remote sensing technique to detect area-averaged temperature and flow properties within an area under investigation, utilizing acoustic travel-time measurements, is introduced. This technique uses the dependency of the speed of acoustic signals on the meteorological parameters temperature and wind along the propagation path. The method itself is scalable: It is applicable for investigation areas with an extent of some hundred square metres as well as for small-scale areas in the range of one square metre. Moreover, an arrangement of the acoustic transducers at several height levels makes it possible to determine profiles and gradients of the meteorological quantities. With the help of two examples the potential of this remote sensing technique for simultaneously measuring averaged temperature and flow fields is demonstrated. A comparison of time histories of temperature and wind values derived from acoustic travel-time measurements with point measurements shows a qualitative agreement whereas calculated root-mean-square errors differ for the two example applications. They amount to 1.4 K and 0.3 m/s for transducer distances of 60 m and 0.4 K and 0.2 m/s for transducer distances in the range of one metre. Keywords: acoustic travel-time measurements, sound propagation in air, temperature, wind, flux estimation. Introduction In-situ measurements of meteorological quantities require an insertion of measurement devices into the area under investigation. In turn, such devices may have an impact on the quantity to be observed which results in an alteration of the measurement results. To minimize such effects, remote sensing techniques are used. Such a remote sensing method to estimate temperature and flow characteristics within an area under investigation is the method of acoustic travel-time measurements (AKU). The measurement principle is based on the fact that the propagation speed of acoustic signals in air mainly depends on temperature and flow properties along the acoustic propagation path (PIERCE, 1989; OSTASHEV, 1997). Thus, measuring the travel-time of an acoustic signal yields information on temperature and flow conditions along the propagation path which has to be known. A combination of travel-time measurements along different paths through the area under investigation allows derivation of spatially averaged values of temperature and flow conditions (wind speed and direction) within the area. Basic principles for the use of acoustic signals for measuring meteorological parameters and first experimental * Corresponding author: Manuela Barth, Universität Leipzig, Institut für Meteorologie, Stephanstr. 3, Leipzig, Germany, mbarth@ uni-leipzig.de investigations can already be found in the middle of last century (BARRETT and SUOMI, 1949; SCHOTLAND, 1955). Besides the beneficial remote sensing properties of the method, a further advantage is its scalability: The method is applicable for investigation areas with an extent of some hundred square metres as well as for investigation areas in the range of only one square metre. In the next subsection, a short overview on the theoretical background is given. After that, two measurement examples are presented which demonstrate the potential of the method to simultaneously detect area-averaged temperature and flow properties. Concluding remarks and an outlook are given in the last paragraph. Theoretical Background The effective sound speed c eff depends on the travel-time s of acoustic signals which propagate along a ray path of length d. As good approximation for moderate wind speeds, c eff is composed of a temperature-dependent portion, namely the Laplace s or adiabatic sound speed c L (LAPLACE, 1816), and a flow-dependent portion v s,the wind component in the direction of sound propagation c eff ¼ d s ¼ c p L þ v s ; where c L ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c a R a T av and T av ¼ ð1 þ 0:51qÞ: ð1þ DOI / /2013/ /2013/0385 $ 3.15 Ó Gebrüder Borntraeger, Stuttgart 2013

2 104 M. Barth et al.: Remote sensing of temperature and wind using acoustic travel-time measurements Meteorol. Z., 22, 2013 Figure 1: Scalar influence of temperature and vectorial influence of wind on the effective speed of sound for bidirectional sound propagation. The Laplace s sound speed depends on temperature T and properties of the medium (specific gas constant for dry air R a = J kg 1 K 1 and specific heat at constant volume over specific heat at constant pressure ratio for dry air c a = 1.4). For tropospheric research the composition of dry air is constant. The only constituent whose concentration may differ considerably is water vapour. To allow for humidity effects, acoustic virtual temperature T av is introduced which is linked with the air temperature T by specific humidity q (LAUBACH et al., 1994). By measuring the effective sound speed in opposite directions it is possible to separate the scalar temperature and the vector wind influence (figure 1). By adding and subtracting the effective sound speeds measured in the forward (index 1) and backward (index 2) direction, c L and v s can be separated from each other c L ¼ 1 ð 2 c eff;1 þ c eff;2 Þ ¼ d 1 þ 1 2 s 1 s 2 v s1 ¼ 1 ð 2 c eff;1 c eff;2 Þ ¼ d 2 1 s 1 1 s 2 : ð2þ In fact the method of acoustic travel-time measurements is used to detect line averaged data of temperature and wind speed along a sound ray path. From a combination of travel-time measurements along at least two bidirectional sound ray paths which intersect each other, properties of the wind field (horizontal components u and v) within the area which is traversed by the sound rays and a temperature value which approximates the area average can be deduced. An arrangement of acoustic transducers at two height levels z 1 and z 2 enables estimation of vertical profiles of temperature and wind. Experimental application of the method The acoustic travel-time measurement technique has already been used under different conditions and for several inquiries. A main advantage of the method is its scalability. It can be used for differently sized measuring areas. It only has to be ensured that the acoustic signals sent by the speakers can properly be detected at the receivers. The two following example applications demonstrate the potential of the measurement method but also reflect some of its limitations. The first example shows an application where acoustic path lengths extend to several decametres. In the second example, the distances between sound sources and receivers extent to only about one metre. In both cases spatially averaged meteorological conditions at two height levels are measured. In addition, results from acoustic travel-time measurements are compared with data from alternative sensors. Example 1: sound ray path lengths in decametre range The purpose of the measurement was to estimate spatially averaged temperature and flow properties at two heights (z 1 =0.5m and z 2 = 2.7 m) above flat grassland in Fuhrberg, Germany. Hereby, the spatial extent of the acoustic measurements corresponds to the spatial extent of spectrometer measurements (line measurements with a path length of 98 m) which, in turn, were designed to record trace gas concentrations at the two heights z 1 and z 2 (SCHÄFER et al, 2012). To capture flow components in the range of the optical measurements it was necessary to arrange the acoustic transducers in such a way that the sound paths intersect each other at one level. Furthermore, a transducer arrangement was chosen which ensures bidirectional sound propagation to enable a separation of temperature and flow along the acoustic path. For these reasons, eight acoustic transducer-pairs (each consisting of one loudspeaker and one microphone, see figure 2) were arranged at the corners of an imaginary cuboid, whose lower and upper boundary surfaces are at the heights z 1 and z 2.The horizontal extent of the measurement area was 60 m in direction of the optical paths and 12 m normal to them. For travel-time analyses, crossing sound paths at each of the two height levels have been considered (figure 3). In addition, ultrasonic anemometers (USAs) were installed on tripods at the same heights as the acoustic source-receiver-pairs (z 1 = 0.5 m: USA of company Young; z 2 = 2.7 m: USA of company METEK). They were mounted at the edge of the cuboid spanned by the acoustic sound paths and the data served as comparative measurements (figures 2, 3). For travel-time measurements, acoustic signals with a special signature and a frequency of 7 khz were used. The time interval between successive measurements (estimation of travel-time data along all relevant sound paths) amounted to 20 s. From these data temperature and horizontal wind speed values have been calculated. For subsequent analyses, all meteorological parameters have been averaged over 10 min intervals. The same time averaging was performed for the USA-data (temperature and horizontal wind speed, measurement interval: 0.1 s). A comparison between acoustic virtual temperature values at the one hand and horizontal wind speeds

3 Meteorol. Z., 22, 2013 M. Barth et al.: Remote sensing of temperature and wind using acoustic travel-time measurements 105 Figure 2: Positioning of ultrasonic anemometers (USAs) at two heights (left); Arrangement of acoustic transducers for travel-time measurements at telescope tripods at the corners of the measurement area (centre) and close up view of source-receiver-pairs in z 1 = 0.5 m and z 2 = 2.7 m (speaker of company Visaton, 1/4 inch microphone with wind screen) at a tripod (right). Figure 3: Arrangement of acoustic transducers for travel-time measurements (grey dots: sensor-pairs at the corners of a phantom cuboid) as well as positions of two ultrasonic anemometers (black triangles). The upper measurement plane is at 2.7 m height, the lower one is at 0.5 m. Horizontal grey lines indicate sound paths which have been analysed to estimate meterological parameters. on the other hand are shown in figure 4. Averaged meteorological quantities from travel-time measurements are only printed for those cases where at least 2/3 of the maximum possible individual measurements (30 individual measurements for intervals of 10 minutes) were available for averaging. As can be seen, temporal courses of meteorological quantities agree qualitatively for both measurement techniques. A closer look at acoustic virtual temperatures reveals that USA-data in z 2 = 2.7 m exceed data from acoustic travel-time measurements up to 0.5 K during night-time. During daytime USA-data are up to 1.3 K lower compared to AKU-data in z 2. For the whole experiment (a total number of 169 averaged data sets are available at z 2 ) the root mean square error (RMSE) between USA- and AKU-temperatures amounts to 0.7 K at the upper level. At the lower level, z 1 = 0.5 m, temperature values of AKU are up to 2.5 K higher than USAtemperatures. The RMSE = 1.4 K at z 1 for the whole experiment is remarkably higher than RMSE at z 2.Furthermore, it is evident that there are no AKU-data during daytime (only minute averages are available for the lower level due to bad signal to noise ratio). Reason for that is a strong heating at ground level which is caused by solar radiation. This heating results in a strong temperature decrease with height which yields to a decrease of the sound speed with height. This in turn causes sound Figure 4: Time dependent acoustic virtual temperature (left) and horizontal wind speed (right) calculated from acoustic travel-time measurements (AKU) as well as measured by utrasonic anemometers (USA) at two heights.

4 106 M. Barth et al.: Remote sensing of temperature and wind using acoustic travel-time measurements Meteorol. Z., 22, 2013 rays to be refracted upwards. As a consequence, a region exists where no sound rays arrive which is called shadow zone (SALOMONS, 2001). Horizontal wind speeds differ between USA and AKU at the lower height level up to 0.5 m/s during nighttime, where lower values are detected by the USA (RMSE = 0.3 m/s for the whole experiment). At the upper height level USA-data are lower as well compared to AKU-wind speeds but only up to 0.3 m/s. During daytime USA-wind speeds and AKU-wind speeds differ up to 0.6 m/s. However, during this time, absolute wind speeds are about 3.5 m/s which is clearly more than during night. For the whole experiment the RMSE between AKU- and USA-data at z = z 2 is 0.2 m/s. The above example has shown, firstly, that area-averaged values of temperature and horizontal wind speed in homogeneous terrain (grassland) differ only slightly from point measurements at the same height. But it has also shown, that is has to be ensured that the sound speed does not decrease too strongly with height. Otherwise, sound rays are refracted upwards which results in a development of sound shadow zones. These, in turn, cause that the acoustic signals cannot be properly detected at the receiver so that no travel-time data can be recorded. Furthermore, refraction of sound rays affect uncertainties of estimated meteorological quantities even if the sound signals are properly detected at the receiver. This effect is addressed in the following section. Estimation of errors due to refraction of sound rays Spatial variations of sound speed cause a refraction of sound rays towards regions where the sound speed is low. Due to the fact that sound speed mainly depends on temperature and wind speed (eq. 1) along the path of acoustic signals spatial gradients of these quantities influence the course of sound propagation. Particularly strong gradients of meteorological quantities are to be found in the vertical next to the Earth s surface. In general, wind speed logarithmically increases with height. Thus, in case of a strong temperature decrease with height (strong heating of the surface due to solar radiation on clear days) sound speed decreases with height in upwind direction which results in an upward refraction of sound rays. On the other hand for a strong increase of temperature with height (in cases of strong emittance on clear nights) the speed of sound increases with height in downwind direction, which results in a downward refraction of sound rays. The propagation path of sound rays in a stratified medium (horizontal homogeneous conditions, sound speed c only depends on height z) can be described using Snell s law of refraction which states that the angle of a sound ray measured to the normal of the boundary a varies in such a way that the ratio sin (a)/c (z) is constant. As an example to illustrate the effect of refraction due to vertical gradients of meteorological quantities a ray path is calculated for the conditions observed on :50 CEST. This time is characterized by a strong temperature increase with height and the availability of surface temperature data (measured with an infrared camera). Meteorological data (temperature and wind speed) are obtained from the ultrasonic anemometers at two heights (z 1 =0.5m, z 2 = 2.7 m) averaged over a time interval of 10 minutes (see table 1). The surface temperature measured by the infrared camera was temporally (9 single pictures were taken during the 10 minutes interval) and spatially averaged over the measurement area. From measured data a vertical profile of horizontal wind is estimated in the form of vh (z) =A ln (z/z 0 ) with A and z 0 being constants (A = m/s, z 0 = 0.15 m). For the vertical temperature change a profile in the form of T (z) =T inf + BC z has been chosen where T inf, B, andc are constants (for z in m and T in K: T inf = , B = -4.22, and C = ). Calculated vertical profiles for temperature and wind as well as measured values are plotted in figure 5. The estimated profiles of temperature and wind (vertical resolution: Dz = 1E-04 m) are used to estimate vertical profiles of effective sound speed which, in turn, are the starting point for sound ray estimation according to Snell s law (refraction at boundaries between layers with different effective sound speeds which are assumed to be constant within each height layer). The coordinates of the turning point of the sound ray (x t, z t ) are estimated according to Table 1: Values for temperature (T) and horizontal wind speed (vh) at two heights (z 1 and z 2 ), and vertical gradients of these quantities. Data are obtained from measurements of an ultrasonic anemometer (USA), and estimated from acoustic travel-times assuming straight ray propagation (SR) and considering a refracted ray path (RR), and for interpolated profile data estimated from USA-measurements (PR). Values of temperature and horizontal wind speed for SR and RR are both calculated using simulated travel-time estimates for the refracted ray (data correspond to measured travel-time data), but different lengths of the sound ray path (direct line for SR and curved line for RR). Furthermore, heights for RR represent median heights (half of the ray path is located below and the other half above this height) averaged for up- and downwind condition. z 1 in m T(z 1 )in C vh(z 1 ) in m/s z 2 in m T(z 2 )in C vh(z 2 ) in m/s DT/Dz in K/m Dvh/Dz in m/s/m USA SR RR PR

5 Meteorol. Z., 22, 2013 M. Barth et al.: Remote sensing of temperature and wind using acoustic travel-time measurements 107 Figure 5: Vertical profiles of horizontal wind speed (top left), temperature (top center) and effective sound speed in upwind (c L - vh) and downwind (c L + vh) direction (top right). Profiles (lines) are estimated from measured data (circles) on at 04:50 CEST (for details on profile estimation see text). The lower figure shows sound rays which are calculated for the profiles above (assuming horizontal homogeneous conditions) using ray tracing (heights of speakers and microphones are 0.5 m and 2.7 m). SAGER (1974) with x t =cota 1 /m, z t = 1/m(1/sin a 1 1), and m =1/c 1 (dc/dz). a 1 denotes the incident angel normal to the boundary (in the layer where c = c 1 ), and dc/dz represents the vertical gradient of the sound speed. Sound rays are calculated assuming source and receiver heights of 0.5 m and 2.7 m and a horizontal distance of 60 m which is in accordance with the experimental set-up. Resultant sound rays for up- and downwind conditions are plotted in figure 5. Particularly for the lower level (0.5 m) a strongly refracted sound ray is estimated. For downwind conditions the ray which is emitted at a height of 0.5 m travels up to a maximum height of m before it returns to 0.5 m. The median height of this sound ray (half the ray path is below this height) is m. Besides the course of the sound ray path, travel-times are calculated depending on the sound path and the effective sound speed for each section of the sound ray. These travel-times correspond to measured values (sound propagation along the curved ray path as it is observed in nature). From estimated sound ray properties and calculated travel-times, temperature and wind values are estimated using equations (1) and(2) and are compared to the predetermined profile data. Properties of the sound rays as well as derived and measured meteorological quantities and gradients are listed in table 1. The effect of sound refraction is especially apparent at the lower height level which is characterized by strong temperature increase with height. The median height of the curved sound ray (1.139 m) is clearly above the height of the acoustic transducers (0.5 m). Thus, estimated temperature for the curved ray is higher than the temperature measured at transducer height. The temperature difference for the refracted sound ray and the estimated profile data at the median height (1.139 m) is only 0.14 K whereas the estimated temperature difference between the assumption of a direct sound path and the USA measurements in 0.5 m is 0.76 K. The same statement can be given for wind speed values. The highest difference is estimated for USA-data in comparison to the straight ray assumption in 0.5 m (Dvh = 0.06 m/s). As for temperature differences a lower difference is obtained for the refracted sound ray in comparison with the profile data (Dvh =0.01m/s).Atthe upper level, differences due to refraction of the sound ray are lower due to weaker vertical gradients of temperature and wind speed. The preceding remarks show that calculations which account for a refraction of sound rays result in lower differences of temperature and wind speeds calculated from travel-time estimations in comparison to profile data

6 108 M. Barth et al.: Remote sensing of temperature and wind using acoustic travel-time measurements Meteorol. Z., 22, 2013 (especially with respect to the height to which the estimated data are assigned). This is particularly valid for large source-receiver distances as well as for conditions with strong sound speed gradients. The second condition especially occurs near to a surface (for low source-receiver heights). Furthermore, the example calculations well correspond to the differences estimated for the measured data. From this it can be concluded that parts of the differences between measured USA- und AKU-data are due to sound refraction which has not yet been considered during analysis of measured travel-time data. Example 2: sound ray path lengths in metre range The second sample application used a transducer arrangement where sound rays covered a horizontal area of 1.4 m 1.4 m. This measurement was carried out in order to investigate the capability of the acoustic traveltime method to detect micrometeorological data in the vicinity of a surface without the need to place sensors Figure 6: Close-up view of a source-receiver unit (left) and arrangement of devices for acoustic travel-time measurements (AKU) on a meadow of the Institute for Meteorology of Universität Leipzig (Germany). Acoustic travel-time measurements are performed at two heights (z 1 = 0.2 m und z 2 = 0.7 m), analysed sound paths are marked as white arrows. For comparison data from an ultrasonic anemometer (USA) are recorded which is positioned at a height of z 3 = 0.5 m. directly on the surface. For comparison, an ultrasonic anemometer (USA from company METEK) next to the AKU-measurements and a meteorological station in the surrounding were used. Acoustic travel-time measurements took place on a meadow of the Leipzig Institute for Meteorology. The meadow is bordered by a hedge, trees, buildings and a wall (1.5 m high). The lower level for acoustic travel-time measurements to estimate temperature and wind was z 1 = 0.2 m, the upper level was z 2 = 0.7 m. The USA was positioned at an intermediate height (z 3 = 0.5 m) very close to the travel-time measurements but outside the volume which was spanned by the sound paths (figure 6). Due to the shorter propagation distances, the demands on the accuracy of travel-time measurements increase. This requirement was accounted for by using smaller acoustic transducers. In addition, signal frequency was shifted into ultrasonic range (40 khz). The repetition rate for single measurements was 1 s. As in the first example, USA-data are recorded every 0.1 s. For comparison of meteorological values, all data are averaged over a period of 10 minutes again. Figure 7 shows the time series of acoustic virtual temperature and horizontal wind speed detected by all devices mentioned above. All measurement methods detect similar courses of air temperature and wind speed. Largest deviations occur for the data of the meteorological station which is located most distant from the other measurement locations. In particular, measurements obtained by the meteorological station are not representative for the location of the acoustic transducers, especially with respect to the flow. Differences between AKU-measurements and USA-measurements are comparatively low (RMSE(z 1, z 3 )=0.4K and 0.2 m/s and RMSE(z 2, z 3 )=0.3K and 0.1m/s). However it is evident, that the area-averaged data from AKU-measurements differ between the two height levels. USA-measurements most resemble AKU-measurements Figure 7: Time dependent acoustic virtual temperature (left) and horizontal wind speed (right), calculated from acoustic travel-time measurements (AKU), measured by an utrasonic anemometer (USA) as well as recorded by a meteorological station of the Leipzig Institute for Meteorology (LIM) at the surrounding of the acoustic measurements (temperature sensor: PT100-resistance thermometer, wind sensor: cup anemometer).

7 Meteorol. Z., 22, 2013 M. Barth et al.: Remote sensing of temperature and wind using acoustic travel-time measurements 109 from the upper height level which corresponds to the fact that the USA-height is closer to the upper height of travel-time measurements. The second example application of acoustic traveltime measurements has shown that the method is able to detect area-averaged values of temperature and wind speed in direct vicinity of a surface, with the area under investigation being no more than 2 m 2. Measurements were performed without the need to place additional sensors directly on the surface. By minimizing the size of the acoustic transducers as well as the mounting, disturbances of the flow field to be measured by the instrumentation are as low as possible and much less than they would be by using in-situ sensors. Conclusions and outlook The acoustic travel-time measurement method presented here provides area-averaged values of temperature and flow within an area under investigation. For this purpose, acoustic transducers (speakers and microphones) are positioned around the measurement area and no sensors have to be installed within the area. The small size of the acoustic components compared to the extent of the measurement area results in minimum disturbances of the flow field to be measured. The measurement method is scalable. To estimate temperature and wind velocities properly it is only necessary to ensure that the acoustic signals are clearly detectable at the receivers. In this context, larger sound path lengths very close to a surface could be precarious. This is due to the fact that near to a surface strong vertical gradients of temperature and wind may occur, which cause a refraction of the acoustic sound ray paths. This, in turn, leads to an enlargement of the sound path length and a change of the average sound path height. Thus, especially for such conditions (large distances between sources and receivers and heights close to a surface) a ray tracing algorithm has to be introduced in data analysis in order to reduce errors for estimated temperature and wind speed values due to the refraction of sound rays. Furthermore, refraction could also cause a formation of sound shadow zones where no proper measurements of acoustic travel-times are possible. This effect can occur for decreasing sound speeds with height (strong decrease of temperature with height due to a strong heating at the lowest atmospheric layer) which causes sound rays to be refracted upwards. References BARRETT, E.W., V.E. SUOMI, 1949: Preliminary report on temperature measurement by sonic means. J. Meteor. 6, LAPLACE, P.S., 1816: Sur la Vitesse du son dans l air et dans l eau. Ann. Chem. Phys. 3, LAUBACH, J., M. RASCHENDORFER, H. KREILEIN, G. GRAVENHORST, 1994: Determination of heat and water vapour fluxes above a spruce forest by eddy correlation. Agric. For. Meteor. 71, OSTASHEV, V.E., 1997: Acoustics in Moving Inhomogeneous Media. E & FN Spon, London, Weinheim, New York, Tokyo, Melbourne, Madras, 259 pp. PIERCE, A.D., 1989: ACOUSTICS. An Introduction to its Physical Principles and Applications. Acoustical Society of America, Melville, New York, 678 pp. SALOMONS, E.M., 2001: Computational Atmospheric Acoustics. Kluwer Academic Publishers, Dordrecht. SAGER, G., 1974: Eine Methode zur Bestimmung der Schallausbreitung in quasiruhender Atmosphäre. Z. Meteorol. 24, SCHÄFER, K., R.H. GRANT, S. EMEIS, A. RAABE, C. VON DER HEIDE, H.P. SCHMID, 2012: Areal-averaged trace gas emission rates from long-range open-path measurements in stable boundary layer conditions. Atmos. Meas. Tech. 5, DOI: /amtd SCHOTLAND, R.M., 1955: The measurement of wind velocity by sonic means. J. Meteor. 12,