Abstract Understanding and modeling snow particle dynamics in the atmosphere remains a significant challenge for atmospheric scientists, hydrologists, and glaciologists. Temporally and spatially varying rates of snow transport, deposition, and erosion are driven by atmospheric turbulence and further complicated by inertial particle dynamics. The present research takes a modern approach to predict snow particle motion with model order reduction tools from nonlinear dynamical systems. A modified Maxey–Riley equation with nonlinear drag is introduced that faithfully provides terminal particle velocities and the characteristic sweeping and loitering particle behavior as seen in decades of hydrometeor studies. A geometric model order reduction of this equation is derived and provides up to 100 times more efficient Lagrangian snow particle trajectory simulations with comparable accuracy. Lastly, novel accumulation diagnostics based on the reduced‐order model provide a simplified framework of snow transport with well‐defined simplification errors and rigorous physical meaning. The accuracy of these diagnostics is verified both numerically and in large‐eddy simulations against terrestrial laser scans at an Arctic‐alpine study site.

In adaptive optics systems, high spatial resolution detection is a core prerequisite for achieving accurate wavefront correction. High spatial resolution wavefront measurement based on the traditional Shack-Hartmann technique is limited by the density of the microlens array. In contrast, off-axis digital holography technology is applied in wavefront measurement systems of adaptive optics systems due to its advantages of high spatial resolution, non-contact measurement, and full-field measurement. However, during the demodulation of its interference fringes, the accurate extraction of the complex amplitude of the +1st-order diffraction order directly determines the precision of wavefront reconstruction. Traditional frequency-domain filtering methods suffer from drawbacks such as reliance on manual threshold setting, poor adaptability to irregular spectra, and localization deviations caused by multi-region interference, making it difficult to meet the dynamic application requirements of adaptive optics. To address these issues, this study proposes a spectrum extraction method based on the Canny operator for adaptive edge extraction and centroid localization. The method first locks the rough range of the +1st-order spectrum through multi-stage peak screening, then achieves complete segmentation of spectrum spots by combining adaptive histogram equalization with edge closing and filling, resolves centroid indexing errors via maximum connected component screening, and ultimately accomplishes accurate extraction through Gaussian window filtering. Simulation experimental results show that, in comparison with two classical spectrum filtering methods, the centroid estimation error of the proposed method remains below 0.245 pixels under different noise intensity conditions. Moreover, the root mean square error of the residual wavefront corresponding to the reconstructed wavefront of the proposed method is reduced by 89.0% and 87.2% compared with those of the two classical methods, respectively. We further carried out measurement experiments based on a self-developed atmospheric turbulence test bench. The experimental results demonstrate that the proposed method exhibits higher-precision spectral centroid localization capability, which provides a reliable technical support for the high-precision measurement of dynamic distortion induced by atmospheric turbulence.

Wavefront estimation under long-distance, strong atmospheric turbulence remains a critical challenge in free-space optical communication (FSOC). Conventional approaches always suffer from high computational cost and latency. To address this issue, we proposed a lightweight high-precision neural network (LHP-Net), a compact yet accurate model that directly predicts Zernike coefficients from single-frame distorted images under long-distance, strong atmospheric turbulence. The architecture combines an optimized convolutional backbone with a lightweight Zernike-aware attention (LZA) module, enhancing the sensitivity to turbulence-induced aberrations while minimizing computational cost. To rigorously evaluate performance, a large-scale dataset using spectral phase screen simulations was obtained, covering propagation distances up to 10 km and turbulence intensity ranging from weak to strong. Simulation results indicate that LHP-Net achieves up to 92.4% lower prediction error and 37.5% faster inference, exhibiting better performance than a conventional convolutional neural network (CNN). Furthermore, our hybrid training strategy significantly enhances the generalization across different turbulence intensities. Remarkably, LHP-Net maintains robust performance even under extreme turbulence, exhibiting minimal prediction error, providing potential for real-time adaptive optics in next-generation free-space optical systems.

ABSTRACT State‐of‐the‐art free‐space continuous‐variable quantum key distribution (CV‐QKD) protocols use phase reference pulses to modulate the wavefront of a real local oscillator at the receiver, thereby compensating for wavefront distortions caused by atmospheric turbulence. It is normally assumed that the wavefront distortion in the phase reference pulses is identical to the wavefront distortion in the quantum signals, which are multiplexed during transmission. However, in real‐world deployments, there can exist a relative wavefront error (WFE) between the reference pulses and quantum signals, which, among other deleterious effects, can severely limit secure key transfer in satellite‐to‐Earth CV‐QKD. In this work, we introduce machine learning‐based wavefront correction algorithms, which utilize multi‐plane light conversion for decomposition of the reference pulses and quantum signals into the Hermite‐Gaussian (HG) basis, then estimate the difference in HG mode phase measurements. Through detailed simulations of the Earth‐satellite channel, we demonstrate that our algorithm can identify and compensate for any relative WFEs that may exist. We quantify the gains available in our algorithm in terms of the CV‐QKD secure key rate. We show channels where positive secure key rates are obtained using our algorithms, while information loss without wavefront correction would result in null key rates.

We present a year-long experiment using a pinhole camera to determine the Sun's angular size, employing a flat mirror to project large-scale solar images of about 50–60 cm in diameter. Our analysis resolves the annual angular variation of 65 arc sec, reflecting Earth's elliptical orbit. Additionally, we observed atmospheric seeing effects (the effects of atmospheric turbulence) and sunspots visible with the naked eye. The project offers an accessible platform for high school and undergraduate students to engage in scientific inquiry.

In this work, a satellite cluster–to–ship free space optical (FSO) system model over the composite doubly inverted gamma-gamma (IGGG) atmospheric turbulence channel has been proposed, considering the effects of path loss and ship mobility for what we believe is the first time. To quantify the impacts of satellite cluster orbital configurations, minimum separation distance (MSD), and ship velocity in different atmospheric turbulence regimes, the closed-form expressions of outage probability (OP), average bit error rate (ABER), and ergodic capacity (EC) have been derived and verified by Monte Carlo simulations. Results show that although the OP, ABER, and EC performances of both linear and circular orbital configurations will deteriorate as the atmospheric turbulence worsens, the circular orbital configuration consistently outperforms the linear orbital configuration. Besides, reducing the MSD of the satellite cluster will further enhance the system performances while it would be degraded as the ship velocity increases. Specifically, one communication experiment between a low Earth orbit (LEO) satellite and a ground station is carried out under pointing correction and fine-tracking closed-loop control, in which the received signal-to-noise (SNR) logs are recorded to obtain the practical downlink OP, therefore verifying the proposed theoretical OP model.

The degradation of classical and quantum structured light induced by complex media, such as atmospheric turbulence, constitutes a critical barrier to its practical implementation in communication, energy transport, imaging and sensing. Here we construct both classical and quantum optical skyrmions and transmit them through experimentally simulated atmospheric turbulence, revealing the embedded topological resilience of their structure. For nonlocal quantum skyrmions, we show that although photon entanglement rapidly degrades, the topological characteristics of the states remain stable. Similarly, while the vectorial structure of local classical skyrmions is strongly distorted by the medium, their topology is preserved across a wide range of turbulence strengths. Our experimental results are supported by rigorous analytical and numerical modelling, validating that the quantum-classical equivalence of the topological behaviour is due to the non-separability of the states and the one-sided nature of the channel. This equivalence enables robust information transport in noisy environments, opening pathways for resilient terrestrial and satellite-to-ground communication.

This paper introduces a novel statistical model for the performance analysis of hybrid RF/FSO (radio frequency/free-space optics) communication systems. The RF channel is modeled using the Nakagami-m fading distribution, while the FSO channel is characterized by a Chi-square–inverse Gamma distribution to account for atmospheric turbulence and pointing errors. A closed-form expression for the cumulative distribution function (CDF) of a one-hop hybrid RF/FSO system is derived under a selective combining scheme, formulated as a function of the average signal-to-noise ratio (SNR). The resulting CDF is expressed in terms of the extended generalized bivariate Meijer-G function (EGBMGF). Furthermore, new analytical expressions for the average bit error rate (ABER) are obtained for both the hybrid RF/FSO system and its FSO-only counterpart under coherent binary phase-shift keying (CBPSK) modulation. A detailed comparative analysis is performed across varying channel parameters and turbulence conditions. Numerical results, presented graphically, demonstrate the superior robustness of the proposed hybrid scheme under severe turbulence and misalignment effects.

The spectral change properties of coherently combined diffracted chirp Gaussian pulse array (CCDCGPA) beams in turbulent atmosphere are studied in comparison with those of spectrum in free space. The analytical expression for spectral intensity of CCDCGPA beams propagating in turbulent atmosphere is derived based on the extended Huygens-Fresnel principle. Numerical results show that the on-axis and off-axis spectra of CCDCGPA beams propagating in turbulent atmosphere are changed into Gaussian-like profile more quickly compared to those propagating in free space, and these spectra for free space and turbulent atmosphere are almost superposed at the sufficiently far propagation distance. The results also indicate that the spectral changes are connected with the propagation distance in the given condition, the size of aperture, the array parameters (N,d) and beam parameters (C,T). Our research results will be helpful for comparing with spectral measurements, and can find applications in free space and atmospheric optical communication.

We investigate the structure of correlation singularities for the Laguerre–Gauss beam of order n=0 and m=2 in the transverse plane during the propagation of the beam in the beam-wander model. We explicitly derive analytical expressions for the cross-spectral density of the corresponding beam order and the analytic expressions representing the singular behavior. We also verify that the singular points disappear at certain z values and reappear at other z values as shown in the previous numerical study. We investigate the dependence of the absolute value of the complex degree of coherence μ on the parameter δ of the beam-wander model during the propagation of the Laguerre–Gauss beam in the corresponding order. The complex degree of coherence depends not only on δ but also on the relative positions of two transverse observation points ρ1 and ρ2, as well as on the propagation variable z for the fixed values of the beam waist and the wavelength of the Laguerre–Gauss beam. Experiments on μ can demonstrate the range of the applicability of the beam-wander model in the turbulent atmosphere. Finally, we examine the orbital angular momentum flux density of the beam and confirm that the general behaviors of the previous studies also hold for m=2.

Atmospheric turbulence-induced random fluctuations in the refractive index can lead to the degradation of the polarization of polarized light. In accordance with the unified theory of coherent polarization, a comprehensive investigation was undertaken to explore the variation in the degree of polarization (DOP) of laser beams propagating through atmospheric turbulence channels under diverse weather conditions. This investigation involved both theoretical analyses and experimental validations, providing a multifaceted approach to understanding the dynamics of laser beam propagation in atmospheric turbulence. To this end, numerical simulations were performed to analyze the polarization-maintaining characteristics of laser beams with varying wavelengths, turbulence intensities, and initial DOP values. To validate the simulation results for various weather scenarios, three experimental links with different propagation distances were constructed. The experimental results demonstrated that as the turbulence intensity increased, the average DOP of the beam continuously decreased until it reached a threshold value. Furthermore, the polarization fluctuations exhibited a distance-threshold effect, wherein the polarization parameters tended to saturate beyond a critical propagation distance.

Free-space optical communication (FSO) utilizes laser beams to transmit data through the atmosphere. However, FSO faces significant challenges, including the strict requirement for line-of-sight (LoS) communication and terrestrial obstacles, which limit its scalability to connect multiple users in diverse environments. To address these limitations and enable reliable multi-user connectivity, the integration of high-altitude platforms (HAP) and optical intelligent reflecting surfaces (OIRS) has emerged as a critical solution. To serve multiple users simultaneously, an OIRS is equipped at the HAP to dynamically control the reflected beam from a ground station to the terminals. This study analyzes the proposed FSO system performance through the outage probability. During the analysis, practically influencing factors such as optical crosstalk, i.e., interference between OIRS regions, and atmospheric turbulence, are considered. The numerical results show the feasibility of deploying OIRS on HAP to support multiuser FSO systems. In addition, properly designing the OIRS coverage could improve the overall performance of the multiuser FSO system.

This paper systematically analyzes the propagation, transformation, and accumulation mechanisms of multi-source noise and device non-idealities within the complete signal chain from the transmitter through the channel to the receiver, focusing on wireless optical coherent communication systems from a signal propagation perspective. It establishes the stepwise propagation process of signals and noise from the transmitter through the atmospheric turbulence channel to the coherent receiver, clarifying the coupling mechanisms and accumulation patterns of various noise sources within the propagation chain. From a signal propagation viewpoint, the study focuses on analyzing the impact mechanisms of factors, such as Mach–Zehnder modulator nonlinear distortion, atmospheric turbulence effects, 90° mixer optical splitting ratio imbalance, and dual-balanced detector responsivity mismatch, on system bit error rate performance and constellation diagrams under conditions of coexisting multiple noises. Simultaneously, by introducing differential and common-mode processes, the propagation and suppression characteristics of additive noise at the receiver end within the balanced detection structure were analyzed, revealing the dominant properties of different noise components under varying optical power conditions. Simulation results indicate that within the range of weak turbulence and engineering parameters, the impact of modulator nonlinearity on system bit error rate is relatively minor compared to channel noise. Atmospheric turbulence dominates system performance degradation through the combined effects of amplitude fading and phase perturbation, causing significant constellation spreading. Imbalanced optical splitting ratios and mismatched responsivity at the receiver weaken common-mode noise suppression, leading to variations in effective signal gain and constellation stretching/distortion. Under different signal light power and local oscillator light power conditions, the system noise exhibits distinct dominant characteristics.

ABSTRACT The Earth’s atmospheric turbulence degrades the precision of ground-based astrometry. Here, we discuss these limitations and propose that, with proper treatment of systematics and by leveraging the many epochs available from the Korean Microlensing Telescope Network (KMTNet), seeing-limited observations can reach sub-milliarcsecond precision. Such observations may be instrumental for the detection of Galactic black holes via microlensing. We present our methodology and pipeline for precise astrometric measurements using seeing-limited observations. The method is a variant of Gaia’s Astrometric Global Iterative Solution that include several detrending steps. Tests on 6500 images of the same field, obtained by KMTNet with typical seeing condition of 1 arcsec and pixel scale of 0.4 arcsec, suggest that we can achieve, at the bright end (mag $\lesssim$ 17), per-epoch relative astrometric precision of ${\sim }$5 mas and relative proper motion precision of 0.1–0.2 mas yr$^{-1}$ over a baseline of approximately five years, using data from the Cerro Tololo Inter-American Observatory (CTIO) site. Time binning on 5–20 d cadences improves the bright-source precision to $\sim$2 mas per coordinate on astrometric microlensing-relevant time-scales. The precision is estimated using bootstrap simulations and further validated by comparing results from two independent KMTNet telescopes.

An experimental investigation was conducted to evaluate the statistical properties and scintillation mitigation performance of multi-aperture free-space optical transmission under real-measured atmospheric turbulence. Continuous monitoring of turbulence parameters over a 24 h period showed that the atmospheric coherence length ranged from 3 to 29 cm, indicating that the experimental link operated predominantly under weak-to-moderate turbulence conditions, while a limited number of measurement intervals exhibited relatively strong scintillation and were included for statistical modelling analysis. An 865 m four-channel receiving link was constructed under the measured turbulence conditions to acquire irradiance data for analysis. The results show that the multi-aperture reception significantly suppresses scintillation, reducing the scintillation index from 0.36 to 0.04 under moderate turbulence. The irradiance probability density functions were fitted using lognormal, Gamma–Gamma, exponentiated Weibull, and Málaga (M) distributions. The M distribution exhibited superior adaptability, with fitting accuracy improved by 18.75% under weak turbulence and 13.16% under moderate turbulence. Further analysis shows that the shape parameters of the M distribution vary systematically with turbulence strength, effectively capturing the turbulence-induced evolution of irradiance statistics and providing experimental support for turbulence channel modelling and the optimisation of FSO diversity reception architectures.

Robust End-to-End FSO Transmission with Joint Coding Modulation and BiLSTM-Based Channel Modeling under Atmospheric Turbulence

Effects of turbulence inhomogeneity and atmosphere stability on the aeroelastic response of the IEA 22 MW wind turbine

Abstract In this study, we analyzed a Lagrangian data set composed of observations from 15 CARbon Interface OCean Atmosphere (CARIOCA) drifting buoys deployed in the Southern Ocean. These buoys recorded sea surface temperature (SST), sea surface salinity (SSS), fugacity of , and chlorophyll a fluorescence at a 1‐hr temporal resolution between 2001 and 2012. We investigated the scaling properties of these time series and identified two distinct power‐law spectral regimes, separated by a characteristic timescale of approximately 10 days, likely associated with synoptic‐scale processes. In the high‐frequency regime, SST and SSS exhibited spectral scaling exponents close to 2, consistent with theoretical predictions for three‐dimensional Lagrangian turbulence. For and fluorescence, the mean spectral slopes deviated from 2, with and , respectively, suggesting an influence of biological or biogeochemical activity. Additionally, we detected intermittency in all time series within this regime and estimated a Hurst exponent of and an intermittency coefficient of for , corresponding to a correlated and intermittent random walk. The large‐scale regime, for its part, shows slopes close to 1.3 for all scalars. We further analyzed dependencies between and the other variables using Probability Density Function (PDF) quotient analysis. The results revealed that synoptic‐scale variability plays a key role in governing the interdependence among the variables. Stronger dependencies with SST and SSS were observed at timescales shorter than 10 days, while an asymmetric relationship with fluorescence emerged at longer timescales, likely reflecting primary production processes.

Load and response analysis of the IEA 22 MW monopile wind turbine considering marine atmospheric turbulence characteristics

Real-time monitoring of beam wander and angle-of-arrival fluctuation under atmospheric turbulence for efficient laser coupling to single-mode optical fibers