Astrid Ziemann

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion.

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.

Acoustic tomography inside the atmospheric boundary layer

Abstract Acoustic tomography is presented as a technique for remote monitoring of meteorological quantities. This method and a special algorithm of analysis can directly produce area averaged values of meteorological parameters. As a result, consistent data will be delivered for validation of numerical atmospheric micro-scale models. Such a measuring system can complement conventional point measurements over different surfaces. The procedure of acoustic tomography uses the horizontal propagation of sound waves in the atmospheric surface layer. The state of the crossed atmosphere can be estimated from measurements of travel time of acoustic signals between sources and receivers on different points in a tomographic array. Derivation of area averaged values of the sound speed and furthermore of air temperature results from the inversion of travel time values for all possible acoustic paths. Thereby, the applied straight-ray two-dimensional tomography model is characterised as a method with small computational equirements and simple handling, especially, for online work.

Acoustic Tomography as a Remote Sensing Method to Investigate the Near-Surface Atmospheric Boundary Layer in Comparison with In Situ Measurements

Abstract The acoustic tomography method is applied in the atmospheric surface layer to observe near-surface temperature fields. Important advantages of this technique are the remote sensing capacity and the possibility of directly deriving area-average meteorological quantities. Combined observations of the air temperature using an acoustic tomography system and point measurements were carried out to validate the tomographic method. Results were used to compare representativeness for a designated area of direct measurements with the tomographic solution. The results demonstrate agreement between the two different measurement methods, except for some deviations of absolute values mainly caused by an imperfectly sheltered and ventilated thermocouple device.

Recent progress in acoustic tomography of the atmosphere

Acoustic tomography of the atmospheric surface layer is based on measurements of travel times of sound propagation among different pairs of sources and receivers usually located several meters above the ground on a horizontal scale of about 100 m. The measured travel times are used as input data in an inverse algorithm for reconstruction of temperature and wind velocity fields. Improved knowledge of these fields is important in boundary layer meteorology, theories of turbulence, and studies of electromagnetic and acoustic wave propagation in the atmosphere. In this paper, a short overview and current status of acoustic travel-time tomography of the atmosphere are presented. A brief description of a 3D array for acoustic tomography of the atmosphere which is being built at the Boulder Atmospheric Observatory is given. Furthermore, different inverse algorithms for reconstruction of temperature and velocity fields are discussed, including stochastic inversion and a recently developed time-dependent stochastic inversion. The latter inverse algorithm was used to reconstruct temperature and wind velocity fields in acoustic tomography experiments. Examples of the reconstructed fields are presented and discussed.

Observations of area averaged near-surface wind- and temperature-fields in real terrain using acoustic travel time tomography

Any physical description setting for the distribution of momentum, energy and matter within the turbulent boundary layer of the atmosphere is usually made according to models based on the assumption of horizontal homogeneity. However, the earths surface not being homogeneous, the consequence of this approach is that these physical models cannot be transferred nor applied under non-homogeneous conditions. The conventional methods used for observing micro-meteorology data do not appear to be adequate in interpreting data observed on heterogeneous surfaces. In this connection, the method of acoustic travel-time tomography is here introduced. This method uses the variability of the speed of sound according to meteorological quantities such as wind and temperature in order to observe synchronous data of wind- and air-temperature fields under natural conditions in a given area. This allows to shun a main requirement of conventional micro-meteorological experiments - the horizontally homogeneous conditions.

Recent progress in acoustic travel-time tomography of the atmospheric surface layer

Acoustic tomography of the atmospheric surface layer (ASL) is based on measurements of the travel times of sound propagation between sources and receivers which constitute a tomography array. Then, the temperature and wind velocity fields inside the tomographic volume or area are reconstructed using different inverse algorithms. Improved knowledge of these fields is important in many practical applications. Tomography has certain advantages in comparison with currently used instrumentation for measurement of the temperature and wind velocity. In this paper, a short historical overview of acoustic tomography of the atmosphere is presented. The main emphasis is on recent progress in acoustic tomography of the ASL. The tomography arrays that have been used so far are discussed. Inverse algorithms for reconstruction of the temperature and wind velocity fields from the travel times are reviewed. Some results in numerical simulations of acoustic tomography of the ASL and reconstruction of the turbulence fields in tomography experiments are presented and discussed. Zusammenfassung

Time-dependent stochastic inversion in acoustic tomography of the atmosphere with reciprocal sound transmission

Time-dependent stochastic inversion (TDSI) was recently developed for acoustic travel-time tomography of the atmosphere. This type of tomography allows reconstruction of temperature and wind-velocity fields given the location of sound sources and receivers and the travel times between all source–receiver pairs. The quality of reconstruction provided by TDSI depends on the geometry of the transducer array. However, TDSI has not been studied for the geometry with reciprocal sound transmission. This paper is focused on three aspects of TDSI. First, the use of TDSI in reciprocal sound transmission arrays is studied in numerical and physical experiments. Second, efficiency of time-dependent and ordinary stochastic inversion (SI) algorithms is studied in numerical experiments. Third, a new model of noise in the input data for TDSI is developed that accounts for systematic errors in transducer positions. It is shown that (i) a separation of the travel times into temperature and wind-velocity components in tomography with reciprocal transmission does not improve the reconstruction, (ii) TDSI yields a better reconstruction than SI and (iii) the developed model of noise yields an accurate reconstruction of turbulent fields and estimation of errors in the reconstruction.

STINHO - Structure of turbulent transport under inhomogeneous surface conditions. Part 1: The micro-α scale field experiment

A micrometeorological field experiment was performed within the frame of the STINHO-project (structure of turbulent transport under inhomogeneous conditions) at the boundary layer field site of the Meteorological Observatory Lindenberg of the German Meteorological Service (Deutscher Wetterdienst) in the summer of 2002 in order to investigate the interaction of thermally heterogeneous surfaces with the turbulent atmosphere. The intention was to compare conventional meteorological point and vertically integrated measurements with area-covering air flow observations and numerical simulations. To observe horizontally variable flow and temperature fields above a heterogeneous land surface, simultaneous acoustic methods (travel time tomography), optical observation methods (IR-camera and line-integrated scintillometer-measurements), as well as the airborne measurement system Helipod were used. The data set will be applied in future to validate large-eddy simulations adjusted to the area of investigation.

Near surface spatially averaged air temperature and wind speed determined by acoustic travel time tomography

Acoustic travel time tomography is presented as a possibility for remote monitoring of near surface air temperature and wind fields. This technique provides line-averaged effective sound speeds changing with temporally and spatially variable air temperature and wind vector. The effective sound speed is derived from the travel times of sound signals which propagate at defined paths between different acoustic sources and receivers. Starting with the travel time data a tomographic algorithm (Simultaneous Iterative Reconstruction Technique, SIRT) is used to calculate area-averaged air temperature and wind speed. The accuracy of the experimental method and the tomographic inversion algorithm is exemplarily demonstrated for one day without remarkable differences in the horizontal temperature field, determined by independent in situ measurements at different points within the measuring field. The differences between the conventionally determined air temperature (point measurement) and the air temperature determined by tomography (area-averaged measurement representative for the area of the measuring field 200 m x 260 m) were below 0.5 K for an average time of 10 minutes. The differences obtained between the wind speed measured at a meteorological mast and calculated from acoustic measurements are not higher than 0.5 m s -1 for the same averaging time. The tomographically determined area-averaged distribution of air temperature (resolution 50 m x 50 m) can be used to estimate the horizontal gradient of air temperature as a pre-condition to detect horizontal turbulent fluxes of sensible heat.

Acoustic Tomography of the Atmosphere: Comparison of Different Reconstruction Algorithms

Acoustic travel-time tomography in the atmosphere is based on travel-time measurements of sound signals propagating along different known ray paths through a medium. Because the speed of sound mainly depends on temperature and flow properties, an inversion of these travel times allows an estimation of temperature and wind velocity fields. The main reconstruction techniques for solving such inverse problems are least-squares methods and stochastic inversion algorithms. In this study, five representatives belonging to these types of inverse approaches are evaluated by reconstructions of two-dimensional temperature distributions from synthetically generated and experimental data. The comparison of the reconstruction results reveals several differences between the algorithms concerning spatial resolution of the reconstructed image, accuracy, and computational efficiency. The stochastic approach provides accurate reconstructions of spatially highly resolved temperature fields when the turbulence characteristic is chosen carefully. Nevertheless, the choice of suitable turbulence parameters, the determination of measurement errors prior to an experiment as well as comparatively high memory requirements of this method are unfavorable for real-time analysis of measured data although possible. In contrast, fast and simple on-site interpretations of temperature fields with acceptable accuracy are feasible with least-squares methods.