The relationship between the non-Kolmogorov refractive-index structure constant and the Kolmogorov refractive-index structure constant is derived by using the refractive-index structure function and the variance of refractive-index fluctuations. It shows that the non-Kolmogorov structure constant is proportional to the Kolmogorov structure constant and the scaling factor depends on the outer scale and the spectral power law. For a fixed Kolmogorov structure constant, the non-Kolmogorov structure constant increases with a increasing outer scale for the power law less than 11/3, the trend is opposite for the power law greater than 11/3. This equivalent relation provides a way of obtaining the non-Kolmogorov structure constant by using the Kolmogorov structure constant.

Optical turbulence strongly affects different types of optoelectronic and adaptive optics systems. Systematic direct measurements of optical turbulence profiles [$C_n^2\left(h\right)$] are lacking for many climates and seasons, particularly in marine environments, because it is impractical and expensive to deploy instrumentation. Here, a backpropagation neural network optimized using a genetic algorithm (GA-BP) is developed to estimate atmospheric turbulence profiles in marine environments which is validated against corresponding [$C_n^2\left(h\right)$] profile datasets from a field campaign of balloon-borne microthermal measurements at the Haikou marine environment site. Overall, the trend and magnitude of the GA-BP model and measurements agree. The [$C_n^2\left(h\right)$] profiles from the GA-BP model are generally superior to those obtained by BP and the physically-based (HMNSP99) models. Several statistical operators were used to quantify the GA-BP model performance on reconstructing the optical turbulence profiles in marine environments. The characterization of vertical distributions of optical turbulence profiles and the main integral parameters derived from [$C_n^2\left(h\right)$] profiles are presented. The median Fried parameter, isoplanatic angle, and coherence time are 9.94 cm, ${0.69}^{″}$, and 2.85 ms, respectively, providing independent optical turbulence parameters for adaptive optics systems. The proposed approach exhibits potential for implementation in ground-based optical applications in marine environments.

Since systematic direct measurements of refractive index structure constant ( $C_n^2$) for many climates and seasons are not available, an indirect approach is developed in which $C_n^2$ is estimated from the mesoscale atmospheric model outputs. In previous work, we have presented an approach that a state-of-the-art mesoscale atmospheric model called Weather Research and Forecasting (WRF) model coupled with Monin-Obukhov Similarity (MOS) theory which can be used to estimate surface layer $C_n^2$ over the ocean. Here this paper is focused on surface layer $C_n^2$ over snow and sea ice, which is the extending of estimating surface layer $C_n^2$ utilizing WRF model for ground-based optical application requirements. This powerful approach is validated against the corresponding 9-day $C_n^2$ data from a field campaign of the 30th Chinese National Antarctic Research Expedition (CHINARE). We employ several statistical operators to assess how this approach performs. Besides, we present an independent analysis of this approach performance using the contingency tables. Such a method permits us to provide supplementary key information with respect to statistical operators. These methods make our analysis more robust and permit us to confirm the excellent performances of this approach. The reasonably good agreement in trend and magnitude is found between estimated values and measurements overall, and the estimated $C_n^2$ values are even better than the ones obtained by this approach over the ocean surface layer. The encouraging performance of this approach has a concrete practical implementation of ground-based optical applications over snow and sea ice.

Ground-based remote observation systems are vulnerable to atmospheric turbulence, which can lead to image degradation. While some methods can mitigate this turbulence distortion, many have issues such as long processing times and unstable restoration effects. Furthermore, the physics of turbulence is often not fully integrated into the image reconstruction algorithms, making their theoretical foundations weak. In this paper, we propose a method for atmospheric turbulence mitigation using optical flow and convolutional neural networks (CNN). We first employ robust principal component analysis (RPCA) to extract a reference frame from the images. With the help of optical flow and the reference frame, the tilt can be effectively corrected. After correcting the tilt, the turbulence mitigation problem can be simplified as a deblurring problem. Then, we use a trained CNN to remove blur. By utilizing (i) a dataset that conforms to the turbulence physical model to ensure the restoration effect of the CNN and (ii) the efficient parallel computing of the CNN to reduce computation time, we can achieve better results compared to existing methods. Experimental results based on actual observed turbulence images demonstrate the effectiveness of our method. In the future, with further improvements to the algorithm and updates to GPU technology, we expect even better performance.

Cloud occurrences, vertical structures, and along-track horizontal scales over East Asia are studied using four years (2007–2010) of CloudSat 2B-CLDCLASS-LIDAR data. The CloudSat 2B-CLDCLASS-LIDAR data employs combined CloudSat radar and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) measurements to provide by far the most accurate detections of cloud boundaries and their vertical structures. The mean cloud occurrence frequency over East Asia is 66.3%, which is 13.8% and 21.6% higher than that from the Cloud–Aerosol LIdar with Orthogonal Polarization (CALIOP) level 2 5-km cloud layer product and the CloudSat 2B-GEOPROF product, respectively. Cloud-top heights over East Asia show three local peaks at approximately 1.5 km, 10 km, and 15 km above ground level (AGL), indicating different mid-altitude cloud formation mechanisms from those over the tropics. Significant fractions of low-level cloud, mid-level cloud, and high-level cloud have thicknesses smaller than 0.5 km, indicating that models with vertical resolutions lower than 0.5 km have difficulties resolving those clouds. The average cloud along-track horizontal scale over East Asia is 82.0 km. Probability distribution functions (PDFs) of cloud along-track horizontal scales suggest that approximately 81.2% of the clouds over East Asia cannot be resolved by climate models with a grid resolution of 1°. The results from this study can be used to improve cloud parameterizations in climate models and validate model simulations of clouds over East Asia.