Changyu Liu

The refractive index structure constant ($C_n^2$) 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 $C_n^2$. 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 $C_n^2$ 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 $C_n^2$ 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 $C_n^2$ distributions and offers an effective technical framework for areal-scale turbulence estimation.

Analysis of turbulent heat fluxes in urban forests is crucial for understanding structural variations in the urban sub-surface boundary layer. This study used data captured by an unmanned aerial vehicle (UAV) and an improved semi-empirical triangle method to estimate small-scale turbulent heat fluxes in the sub-surface of an urban forest. To improve the estimation accuracy, the surface temperature (T_S) of the UAV-based remote sensing inversion was corrected using the hot and cold spot correction method, and the process of calculating ${\varphi }_{max}$ using the traditional semi-empirical triangle method was improved to simplify the calculation process and reduce the number of parameters in the model. Based on this method, latent heat fluxes (LE) and sensible heat fluxes (H) were obtained with a horizontal resolution of 0.13 m at different time points in the study area. A comparison and validation with the measured values of the eddy covariance (EC) system showed that the absolute error of the LE estimates ranged from 4.43 to 23.11 W/m², the relative error ranged from 4.57% to 25.33%, the correlation coefficient (r) with the measured values was 0.95, and the root mean square error (RMSE) was 35.96 W/m², while the absolute error of the H estimates ranged from 3.42 to 15.45 W/m², the relative error ranged from 7.51% to 28.65%, r was 0.91, and RMSE was 9.77 W/m². Compared to the traditional triangle method, the r of LE was improved by 0.04, while that of H was improved by 0.06, and the improved triangle method was more accurate in estimating the heat fluxes of urban mixed forest ecosystems in the region. Using this method, it was possible to accurately track the LE and H of individual trees at the leaf level.

In order to investigate the equivalent complex refractive index of atmospheric aerosols near the Earth’s surface, we conducted measurements in the Hefei region from March to April 2022. These measurements utilized a micro-pulse lidar, an Aethalometer, and a Portable Optical Particle Profiler. These measurements encompassed aerosol particle size distribution as well as standard meteorological parameters including temperature, humidity, atmospheric pressure, and wind speed. Subsequently, this dataset was employed to develop an optimization algorithm for retrieving the equivalent complex refractive indices of near-surface aerosols. The methodology relies on lookup tables containing data for extinction efficiency and absorption efficiency factors. It operates on the premise of aerosol property stability within a defined time frame, utilizing measured extinction and absorption coefficients as simultaneous constraints during this period to inversely derive both the real and imaginary parts of the aerosol complex refractive index. Results from the simulation analysis reveal that the newly optimized retrieval algorithm, which relies on lookup tables, exhibits reduced sensitivity to instrument errors when compared to single-point constraint algorithms. This enhancement results in a more efficient and dependable approach for retrieving the aerosol complex refractive index. Empirical inversion and simulation studies were carried out to determine the aerosol equivalent complex refractive index in the Hefei region, utilizing measured data. This inversion process yielded an average complex refractive index of 1.48-i0.017 for aerosols in the Hefei region throughout the experimental period. Correlation analysis unveiled a positive association between the real part of the aerosol complex refractive index and the single-scattering albedo (SSA), whereas the imaginary part displayed a linear negative correlation with the SSA. The mathematical relationship between the real part and the SSA is $y=0.19x+0.62$, and the corresponding relationship between the imaginary part and the SSA is $y=-5.3x+0.99$. This research offers a novel method for the retrieval of the aerosol equivalent complex refractive index.