Cooperative Institute for Research in Environmental Sciences

A winning proposal for the Innovative Research Program, 2009:

Measurements of the area averaged vertical heat flux with acoustic tomography

Investigators: Vladimir Ostashev (CU/CIRES), Jesse Leach (NOAA/ESRL/PSD), and Sergey Vecherin (NMSU)

Objective
Study a feasibility of measurements of the area averaged vertical sensible heat flux with the array for acoustic tomography of the atmosphere at the Boulder Atmospheric Observatory (BAO).

Background and Importance
The vertical sensible heat flux Q_s is one of the most important parameters in the boundary layer meteorology. It is needed in the weather forecast, studies of the climate change, etc. Currently, conventional meteorological devices are used for point measurements of this flux. However, such point measurements might not be representative due to horizontal variations in the flux. At present, there is no remote sensing technique for measurements of the area averaged values of Q_s. The main goal of this proposal is to study a feasibility of such measurements with acoustic tomography of the atmosphere. The proposed approach is outlined in section Research Plan. Below we explain acoustic tomography of the atmosphere, which is a relatively new technique.

The idea of acoustic tomography of the atmosphere is similar to that in medicine where electromagnetic or ultrasound waves probe a particular organ of a human body resulting in an “image” of that organ. In the case of acoustic tomography of the atmospheric surface layer (ASL), sound waves are used as a probe and, then, the temperature T and wind velocity v fields within a tomographic volume or area are reconstructed using different inverse algorithms, e.g. see [1]. We have started theoretical and experimental studies of acoustic tomography of the ASL in 2004. (Since then, we have published 15 papers with five of them in peer reviewed journals.) We have built an array for acoustic tomography of the atmosphere at the BAO. A schematic of the BAO tomography array is shown in Fig. 1. The array consists of three speaker and five microphone towers located along the perimeter of a square with the side length L = 80 m. Speakers and microphones are located on the towers at three levels ranging from about 3 to 9 m. Speakers and microphones are connected via underground cables with a central command and data acquisition computer. The computer and some other equipment of the array (power amplifiers for speakers, A/D cards, microphone filters, etc.) are located inside the BAO Visitor Center. The BAO array allows us to measure the travel times of sound propagation between different pairs of speakers and microphones. The temperature T and wind velocity v fields are then reconstructed using the time-dependent stochastic inversion (TDSI) algorithm [2]. The tomography array became operational in March of 2008. This is the only acoustic tomography array in the U.S. Speakers and microphones at the upper level of the array have been used so far in transmission and reception of acoustic signals thus enabling 2D, horizontal slice tomography. Transducers at the other two levels of the BAO array are proposed to be employed latter. Then, 3D tomography of the ASL will be feasible.

In our theoretical studied of acoustic tomography of the ASL, we developed the TDSI algorithm for reconstruction of T and v fields. We did many numerical simulations of acoustic tomography of the ASL. The results obtained clearly showed that TDSI yields the best reconstruction of T and v fields among known inverse algorithms. The TDSI algorithm was used in reconstruction of Tand v fields in acoustic tomography experiments with the BAO array and also in those carried out by scientists from the University of Leipzig, Germany with their portable tomography array. Also the TDSI was used extensively in 2D and 3D numerical simulations of the BAO tomography array. The results obtained showed that the temperature and horizontal components of the wind velocity can be reconstructed reliably (with accuracy of about 0.2 K and 0.2 m/s). However, so far in numerical simulations, we have not been able to reliably reconstruct the vertical component of the wind velocity, which is needed in measurements of Q_s. The reason for that is that the BAO tomography array is highly anisotropic, with the vertical dimension being much smaller than the horizontal. Therefore, a different approach for measurements of Q_s is proposed below.

What makes this innovative?
For the first time, we propose a method for remote sensing of the area averaged vertical sensible heat flux Q_s, which is one of the most important parameters in the boundary layer meteorology.

Expected outcome and impact
So far our theoretical and experimental studies of acoustic tomography of the ASL have been funded by the Army Research Office. However, measurements of the area averaged heat flux are of primary importance to NOAA and the Weather Service. We anticipate to demonstrate a feasibility of such measurements with acoustic tomography. Then, this relatively inexpensive technique might become a component of a very wide net of sensors to be installed within the U.S. for measurements of atmospheric parameters for improvement of the weather forecast and studies of the climate change. Furthermore, acoustic tomography would allow measurements of the area averaged heat flux over a complex terrain (e.g. over a river, lake, or polynya), where point measurements of the heat flux are difficult or infeasible.

Research Plan
The 2D BAO acoustic tomography array (with transducers at one level only) allows us to measure the covariance (u′T′) between the longitudinal velocity fluctuations, u′ (i.e., the velocity fluctuations in the direction of the mean wind) and the temperature fluctuations, T′. In an unstable atmospheric boundary layer, the following relationship is commonly used (u′T′) =αu_*T_*, where α is an empirical constant, u_* the friction velocity, and T_* the temperature scale. By definition, the vertical heat flux is: Q_s ≡(w′T′) = -u_*T_*, where w′ stands for the vertical velocity fluctuations. Hence, the heat flux Q_s = -(u′T′) /α. Note, that acoustic tomography allows us to measure the point and area averaged values of (u′T′). Then, the point and area averaged values of Q_s can be obtained with the equation above.

To implement this approach, the following steps will be done. First, we will develop computer programs for calculating the point and area averaged values of Q_s. Then, already existing acoustic tomography data will be used to test the programs and to make sure that the values of Q_s make sense. Second, we will carry out new experiments with the 2D BAO tomography array and simultaneously will make point measurements of the heat flux with sonic anemometers/thermometers inside the array. These point measurements will be compared with point measurements of Q_s with the acoustic tomography. Finally, point measurements of Q_s will be compared with area averaged values of Q_s to study a difference between the two.

References
¹ V. E. Ostashev, S. N. Vecherin, D. K. Wilson, and A. Ziemann ”Recent progress in acoustic tomography of the atmosphere,” IOP Conf. Series: Earth and Environmental Science 1 (2008) 012008 doi:10.1088/1755-1307/1/1/012008.
² S. N. Vecherin, V. E. Ostashev, A. Ziemann, D. K. Wilson, K. Arnold, and M. Barth, ”Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion,” J. Acoust. Soc. Am. 122 (3), 1416-1425 (2007).