# Re-Visiting Acoustic Sounding to Advance the Measurement of Optical Turbulence
## 2 Materials and Methods
### Field Test Description: Propagation Path and Instrumentation Bed-Down  
Section 3 below presents optical turbulence profiles derived by in situ micro-meteorological point measurements recorded using two time-synchronized sonic anemometers, one designated as primary and the other secondary, installed at arbitrary heights, \(z_{1}\) and \(z_{2}\), vertically  
Figure 1: DELTA turbulence profiling system. Figure 2: Differential tilt variances. (**a**) DELTA target board; (**b**) Weighting functions (dimensionless) for 4 different feature point separations. z = 0 at the DELTA location. one above the other. Being vertically stacked, the associated sonic anemometer stations are hereafter referred to as stacked sonic anemometer masts. Subsequently, a diurnal, temporally varying optical turbulence profile at a primary point and height of interest is derived using Equation (5) above. Namely, the profile is arrived at by combining the wind velocity and calculated small scale fluctuations of the index of refraction gradients between the secondary and primary level with the velocity structure constant as derived using the primary instrument's measurements. As the sonic anemometers are installed one directly above the other to ensure there is no lateral offset, the gradients essentially are with respect to the vertical direction. As reference, the primary sonic anemometer's recorded temperature fluctuations are used to calculate the temperature structure function at the primary point of interest, and hence profile optical turbulence using the standard approach through the application of Equation (3). Given the 10 Hz sampling rate of the sonic anemometers, a 90-second ensemble averaging time was largely utilized for the presented results because \(C_{n}^{2}\) profiles obtained via Equation (5) and those obtained via optical methods and \(C_{T}^{2}\) converged best in terms of variability and magnitude. It is also close to the 100-second ensemble averaging time suggested in [5]. The selection of optimum ensemble averaging times, especially when pursuing the technique presented here, would likely benefit from further investigation. The field measurements were conducted at Wright Patterson AFB, Ohio during the summer of 2020 and the height of the COVID-19 pandemic. Atmospheric micrometeorological as well as soil measurements were recorded at multiple points along a 1.9-kilometer propagation path. While the slant path traversed many types of soil/canopy cover and topographical features, equipment and personnel availability limited the deployment of stacked sonic anemometer masts to two locations along the path. An aerial view of the slant path and surrounding area is shown in Figure 3 along with the locations of the stacked sonic anemometer mast stations. A portion of the propagation path was situated alongside the quasi-active runway-taxiway used to fly in aircraft for display at the National Museum of the United States  
Figure 3: Propagation Path. Left: the 30-meter mast and locations of the sonic anemometers. Upper right: aerial view of the optically sampled 1.9-kilometer turbulence path and location of the 30-meter sonic anemometer mast station as well as the DELTA system (Telescope/Camera Receiver and Target Board). The 6-meter sonic anemometer mast station was co-located with the DELTA target board. Lower right: Schematic (looking south) showing the propagation path topographical elevation change. Elevations are shown in meters above mean sea level (MSL). Air Force. The topography, a portion of which is level and open, can lead to strong wind shears, and indeed one of the Dayton area tornados of May 2019 had passed through this area. Sonic anemometry continues to benefit from a strong vendor base, which makes high-quality instrumentation and a wide variety of probe array configurations available, many optimized according to one's application (e.g., optical imaging and communication, near-surface fundamental eddy covariance flux assessments, or canopy wind effects and simulations).