## 2 Materials and Methods  
The sensing path chosen for this work is shown in Figure 1. The 511 m path was chosen for its inhomogeneity, with the first half grass and the second half concrete. The data presented in this study was captured on 25 July 2019 from 17:44 to 21:33 EST (UTC-4). The air temperature during testing was 28 \({}^{\circ}\)C on with wind speeds less than 5 mph and intermittent cloud coverage, which was captured by a net radiometer. Each set of tilt variance data contains 100 background frames with the laser beacons shut off and 1000 data frames with both lasers active. The Hartmann Turbulence Sensor (HTS) is a Shack-Hartmann wavefront sensor based on a 16\" Meade LX200 telescope. It was designed to provide time-efficient and accurate estimates of statistical parameters such as the Fried coherence length, \(r_{0}\), the refractive index structure parameter, \(C_{n}^{2}\), and the Greenwood frequency, \(f_{\text{G}}\), all of which are key characteristics of optical turbulence [11]. The HTS was mounted on a floating suspension system within a trailer to protect the system from vibrations and weather during operation and transportation. A custom optics bench mounted in the sensor's backplane contains a 32 \(\times\) 32 lenslet array, relay optics, and a Vision Research Phantom v7.3 high speed camera capable of capturing up to 8639 frames/s [12]. Four SATI/3A non-orthogonal sonic anemometers were mounted 2.64 m above the ground and distributed evenly along the path at points 100 m, 200 m, 300 m, and 400 m from the HTS. The HTS, laser beacon, and sonic anemometer setups are shown in Figure 2. The anemometers calculate point-like estimates of \(C_{n}^{2}\) over a much smaller volume in space than the HTS technique. The anemometers capture measurements at 10 Hz, which are averaged into 1 min increments for the profile comparisons. The anemometers' accuracy in sonic temperature measurements is \(\pm\)0.1 \({}^{\circ}\)C, which suggests measurement error is low relative to the \(C_{n}^{2}\) estimates. Two of the anemometers measured over grass while the other two measured over concrete to help illustrate the expected local rise in turbulence over the concrete. Past experiments [13] have found a potential relation between the turbulence anisotropy and the wind direction with respect to the sensing path. Since the experimental path was roughly aligned with the prevailing winds, this effect was expected to be minimal. The HTS sensing path was horizontal and 1.5 m above ground level. The sonic anemometers were mounted over a meter higher than the HTS sensing path, and thus, saw weaker turbulence. This height difference was roughly corrected using an \(h^{-4/3}\) conversion factor, where \(h\) is the height from ground [14]. This height correction is an approximation for turbulence variations with respect to altitude during typical daytime conditions (\(C_{n}^{2}\) between 10\({}^{-14}\) and 10\({}^{-13}\) m\({}^{-2/3}\)) when convective forces dominate the surface layer. The prevailing wind during this experiment was from the west and roughly parallel to the sensing path. Therefore, the turbulence that reached the HTS developed for about 250 m above the concrete and then for about 250 m above the grass. This not only emphasized the differences in turbulence strength over both parts, but also made the height correction more applicable over the full path. Two 2 mW 632.8 nm helium-neon laser beacons were mounted with an 11 cm separation at the opposite end of the sensing path from the HTS. The 11 cm separation ensured the laser subimages were roughly centered in the subaperture regions. Each laser was fitted with a beam diverged (with 0.5 inch apertures) for complete illumination of the HTS telescope. The beams are treated as spherical waves after exiting the divergers. The Phantom camera's CCD is typically divided into 18 \(\times\) 18 pixel subaperture regions when using a single beacon.