In this study, we devised a constraint method, called multi-model ensemble pattern (MEP), to estimate the refractive index structure parameter ($C_n^2$) profiles based on observational data and multiple existing models. We verified this approach against radiosonde data from field campaigns in China’s eastern and northern coastal areas. Multi-dimensional statistical evaluations for the $C_n^2$ profiles and integrated astronomical parameters have proved MEP’s relatively reliable performance in estimating optical turbulence in the atmosphere. The correlation coefficients of MEP and measurement overall $C_n^2$ in two areas are up to 0.65 and 0.76. A much higher correlation can be found for a single radiosonde profile. Meanwhile, the difference evaluation of integrated astronomical parameters also shows its relatively robust performance compared to a single model. The prowess of this reliable approach allows us to carry out regional investigation on optical turbulence features with routine meteorological data soon.

The tropopause is an important transition layer and can be a diagnostic of upper-tropospheric and lower-stratospheric structures, exhibiting unique atmospheric thermal and dynamic characteristics. A comprehensive understanding of the evolution of fine tropopause structures is necessary and primary for the further study of complex multi-scale atmospheric physical–chemical coupling processes in the upper troposphere and lower stratosphere. A novel method utilizing the bi-Gaussian function is capable of identifying the characteristic parameters of vertical tropopause structures and providing information on double-tropopause (DT) structures. The new method improves the definition of the cold-point tropopause and detects one (or two) of the most significant local cold points by fitting the temperature profiles to the bi-Gaussian function, which defines the point(s) as the tropopause height(s). The bi-Gaussian function exhibits excellent potential for explicating the variation trends of temperature profiles. The results of the bi-Gaussian method and lapse rate tropopause, as defined by the World Meteorological Organization, are compared in detail for different cases. Results indicate that the bi-Gaussian method is able to more stably and obviously identify the spatial and temporal distribution characteristics of the thermal tropopauses, even in the presence of multiple temperature inversion layers at higher elevations. Moreover, 5 years of historical radiosonde data from China (from 2012 to 2016) revealed that the occurrence frequency and thickness of the DT, as well as the single-tropopause height and the first and second DT heights, displayed significant meridional monotonic variations. The occurrence frequency (thickness) of the DT increased from 1.07 % (1.96 km) to 47.19 % (5.42 km) in the latitude range of 16–50° N. The meridional gradients of tropopause height were relatively large in the latitude range of 30–40° N, essentially corresponding to the climatological locations of the subtropical jet and the Tibetan Plateau.

The refractive index structure constant $C_n^2$ near the ocean surface is an important parameter for studying atmospheric optical turbulence over the ocean. The measured refractive index structure constant and meteorological parameters, such as temperature and three-dimensional wind speed, near the sea surface on the South China Sea during the period from January to November 2020 were analyzed. On the basis of Monin–Obukhov similarity theory, the dimensionless temperature structure parameter function $f_T$ near the sea surface was established, and a new parameterized model of the near-sea surface was proposed. The new model improved the error of the widely used model proposed by Wyngaard in 1973 (W73) and better reproduced the daily variation in the measured $C_n^2$. Further analysis of the seasonal applicability of the new model indicated that the correlation coefficients between the estimated and measured $C_n^2$ in the spring, summer, autumn, and winter were 0.94, 0.94, 0.95, and 0.89, respectively, and the root mean square errors were 0.32, 0.41, 0.46, and 0.40 m^−2/3, respectively. Compared with the $C_n^2$ estimated by the W73 model, the correlation coefficient of $C_n^2$ estimated by the new model and measured by the micro-thermometer increased by 0.05–0.27 and the root mean square error decreased by 0.04–0.56. The improved $f_T$ demonstrated higher accuracy than the existing models, which can lay a foundation for estimating turbulence parameters in different sea areas.

The high elevation, complex topography, and unique atmospheric circulations of the Tibetan Plateau (TP) make its optical turbulence characteristics different from those in low-elevation regions. In this study, the characteristics of the atmospheric refractive index structure constant ($C_n^2$) profiles in the Lhasa area at different strength states of the Asian summer monsoon anticyclone (ASMA) are analyzed based on precious in situ sounding data measured over the Lhasa in August 2018. $C_n^2$ in the upper troposphere–lower stratosphere fluctuates significantly within a few days during the ASMA, particularly in the upper troposphere. The effect of the ASMA on $C_n^2$ varies among the upper troposphere, tropopause, and lower stratosphere. The stronger and closer the ASMA is to Lhasa, the more pronounced is the “upper highs and lower lows” pressure field structure, which is beneficial for decreasing the potential temperature lapse rate. The decrease in static stability is an important condition for developing optical turbulence, elevating the tropopause height, and reducing the tropopause temperature. However, if strong high-pressure activity occurs at the lower pressure layer, such as at 500 hPa, an “upper highs and lower highs” pressure field structure forms over the Lhasa, increasing the potential temperature lapse rate and suppressing the convective intensity. Being almost unaffected by low-level atmospheric high-pressure activities, the ASMA, as the main influencing factor, mainly inhibits $C_n^2$ in the tropopause and lower stratosphere. The variations of turbulence intensity in UTLS caused by ASMA activities also have a great influence on astronomical parameters, which will have certain guiding significance for astronomical site testing and observations.

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.

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.