UAV-Based Estimation of the Two-Dimensional Spatial Distribution of the Refractive Index Structure Constant

The refractive index structure constant (Cn2) is a crucial parameter for quantifying the intensity of atmospheric optical turbulence. However, directly measuring its two-dimensional (2D) spatial distribution remains a significant challenge. In this study, we propose a novel unmanned aerial vehicle (UAV)-based method to estimate the 2D spatial distribution of near-surface Cn2. This approach integrates a semi-empirical triangular method with the Monin–Obukhov similarity theory (MOST) for the atmospheric surface layer. Utilizing the customized UAV system, we conducted flight experiments on 12 October 2024 over a heterogeneous surface of farmland and grassland in Shouxian, Anhui Province, China. A total of 144 sets of imagery with a high spatial resolution of 0.045 m were acquired to map the planar-scale Cn2 across the study area. To improve the accuracy of model estimation, observational data were used to fit similarity functions tailored to the complex underlying surface of the study area. Compared with the traditional W73 model, the newly fitted functions improved the estimation accuracy by 8.8%. The UAV-derived estimates were validated at the pixel scale against in situ measurements from a micro-thermometer mounted on a meteorological tower. The results demonstrate that the UAV estimated Cn2 captures the diurnal variation trends of the ground-based measurements, with magnitudes ranging from 10−15 to 10−12. Statistical analysis yields a strong correlation coefficient (r) of 0.85 and a root mean square error (RMSE) of 0.44. By overcoming the limitations of traditional single-point measurements, in this study, we successfully characterize high-spatial-resolution Cn2 distributions and offers an effective technical framework for areal-scale turbulence estimation.