Atmospheric Turbulence Model Research Articles

A physical stochastic model of near-surface fluctuating wind fields

Modeling and simulation of atmospheric turbulence in coastal areas has emerged as a prominent area of research in recent years. This study presents a physical stochastic model to describe the horizontal coherence of fluctuating wind fields within the physical stochastic modeling frame. Based on the one-dimensional stochastic Fourier spectrum and isotropic turbulence theory, the horizontal coherence for fluctuating wind fields is expressed as a random function, with its probability information determined by the physical mechanism/background. The proposed physical stochastic model directly depicts the stochastic time series thereby enabling it to capture all probability information in detail comprehensively. The proposed model is numerically validated with the measured data obtained from an observation array constructed in Southeast China. This investigation holds significant potential for its application in wind-resistance design and reliability assessment of long-span structures.

Real time simulation of atmospheric turbulence based on GPU

Simulated turbulence phase screens have been widely used in a series of optical experiments, but their speed and accuracy still need to be improved. Because of that, We use sparse spectral models for atmospheric turbulence simulation, and we use the Computational Unified Device Architecture (CUDA) to accelerate the calculation process. Finally, we load the calculated turbulence model onto the Liquid Crystal Atmospheric Turbulence Simulator (LC-ATS). The atmospheric turbulence model was used as a wavefront phase screen, and that model was deployed to the Liquid Crystal Spatial Light Modulator (LC-SLM). In 512 × 512 resolution, it takes 1.36 ms per frame, and it reaches 423 Hz on the liquid crystal on silicon (LC-OS).

Stable flight control of UAV under atmospheric turbulence

Unmanned aerial vehicles will be subjected to various environmental disturbances such as atmospheric turbulence during the execution of tasks, which will seriously affect the flight safety of UAV. By establishing UAV flight dynamics model and atmospheric turbulence model, and using PID algorithm to design controller, this paper studies the attitude and altitude control effect of UAV under atmospheric turbulence disturbance. The simulation results show that PID algorithm can effectively control the UAV's stable flight under atmospheric turbulence and ensure the safety of UAV.

A Combined Approach for Predicting the Distribution of Harmful Substances in the Atmosphere Based on Parameter Estimation and Machine Learning Algorithms

This paper proposes a new approach to predicting the distribution of harmful substances in the atmosphere based on the combined use of the parameter estimation technique and machine learning algorithms. The essence of the proposed approach is based on the assumption that the concentration values predicted by machine learning algorithms at observation points can be used to refine the pollutant concentration field when solving a differential equation of the convection-diffusion-reaction type. This approach reduces to minimizing an objective functional on some admissible set by choosing the atmospheric turbulence coefficient. We consider two atmospheric turbulence models and restore its unknown parameters by using the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm. Three ensemble machine learning algorithms are analyzed for the prediction of concentration values at observation points, and comparison of the predicted values with the measurement results is presented. The proposed approach has been tested on an example of two cities in the Republic of Kazakhstan. In addition, due to the lack of data on pollution sources and their intensities, an approach for identifying this information is presented.

The Modeling and Simulation of Turbulence for Civil Aircraft Compliance Verification Test

For the airworthiness compliance verification of civil aircraft, the response of the aircraft in turbulence is one of the most important tests. Turbulence is mentioned in many airworthiness regulations for civil aircraft, but there are no clear requirements. To study the compliance of civil aircraft response in an atmospheric turbulence environment, the airworthiness requirements of civil aircraft were analyzed. The turbulence model that can be used for airworthiness compliance of civil aircraft was determined for the first time. In this paper, the principle of the atmospheric turbulence model is studied. The evaluation process of the model is proposed, which indicates that the turbulence model meets the airworthiness requirements. At the same time, the model was integrated on a certain simulator, and the correctness of the integration was proved through integration testing. The modeling, evaluation, and integration process of the turbulence model proposed in this paper can be used for the airworthiness verification of civil aircraft.

A global turbulence model shows excellent atmospheric optical turbulence conditions over the Ethiopian plateau during non-rainy season

ABSTRACT A worldwide search is currently being conducted to determine the most appropriate sites for the next generation of large optical and infrared telescopes. Here, we report a global map of atmospheric optical turbulence-associated parameter (atmospheric coherence length) based on the fifth generation of European Centre for Medium Range Weather Forecasts re-analysis data set and results for atmospheric coherence lengths at European Southern Observatory and Tibetan Plateau locations (all at mid-latitudes). These confirm the accuracy of the global atmospheric optical turbulence model, but also the simulation result reveals that an excellent atmospheric calm site exist at the Ethiopian Plateau (at a latitude of ∼10°N) outside of the rainy season. The Ethiopian Plateau is the highest plateau in Africa, known as the ‘Roof of Africa’, with an average elevation of over 2500 m, and thus potentially provides good opportunities for astronomy and astrophysics. The median atmospheric coherence length at the Ethiopian Plateau was 17.7 cm and approximately 75 per cent of the time above 15.6 cm for dry conditions, indicating a very calm atmosphere. Although favourable atmospheric turbulence conditions at the Ethiopian Plateau were found from the global turbulence model, due to the complete lack of infrastructure it has never been visited, meaning that additional validation experiments are required.

A Method of Superimposing Subapertures for Shark–Hartmann Wave Front Sensing with Faint Objects

Abstract For the astronomical adaptive optics systems, the observation condition is always in a regime of low photon flux. We present a method of superimposing subapertures for the Shark–Hartmann wave front sensing with faint objects. This approach significantly improves the signal-to-noise ratio (S/N) of the spot pattern by superimposing adjacent subapertures, thus circumventing the invalid wave front sensing with faint object, enhancing the accuracy of the wave front detection. In addition, we demonstrate that the validity of this approach is not an incidental result under a specific condition, which can be explained theoretically by exploiting the atmospheric turbulence model. Then we validate the approach with simulations and experimental realization under weak-light and bright-light conditions. Results show that the proposed subaperture superposition approach can achieve accurate wave front reconstruction for low S/N or faint object even in cases beyond the ability of conventional methods. It brings out a new idea, besides long exposure and variable sampling, that comes with a tradeoff between temporal sampling frequency and spatial resolution. In addition, this method is also valid for extended objects; we preliminarily validate this method on a 600 mm aperture solar telescope, achieving stable closed-loop control with lower-contrast objects.

Forecasting atmospheric turbulence conditions from prior environmental parameters using artificial neural networks.

Atmospheric turbulence (C n2) modeling has been proposed by physics-based models, but they are unable to capture the many cases. Recently, machine learning surrogate models have been used to learn the relationship between local meteorological conditions and turbulence strength. These models predict C n2 at time t from weather at time t. This work expands modeling capabilities by proposing a technique to forecast 3h of future turbulence conditions at 30min intervals from prior environmental parameters using artificial neural networks. First, local weather and turbulence measurements are formatted to pairs of the input sequence and output forecast. Next, a grid search is used to find the best combination of model architecture, input variables, and training parameters. The architectures investigated are the multilayer perceptron and three variants of the recurrent neural network (RNN): the simple RNN, the long short-term memory RNN (LSTM-RNN), and the gated recurrent unit RNN (GRU-RNN). A GRU-RNN architecture that uses 12h of prior inputs is found to have the best performance. Finally, this model is applied to the test dataset and analyzed. It is shown that the model has generally learned the relationship between prior environmental and future turbulence conditions.

Statistical modeling of atmospheric turbulence based on a low-cost experimental setup for measuring C n2 over water.

The performance of communication systems based on free-space optical links depends on external factors such as weather conditions. Among many atmospheric factors, turbulence can be the greatest challenge to performance. The characterization of atmospheric turbulence usually involves expensive equipment known as a scintillometer. This work presents a low-cost experimental setup for measuring the refractive index structure constant over water, which results in a statistical model based on weather conditions. The turbulence variations with air and water temperature, relative humidity, pressure, dew point, and different watercourse widths are analyzed for the proposed scenario.

Experimental free-space continuous-variable quantum key distribution with thermal source.

Passive-state-preparation (PSP) continuous-variable quantum key distribution (CVQKD) protocol explores the intrinsic field fluctuations of a thermal source. Compared with traditional Gaussian-modulated coherent-state CVQKD, it does not need active modulations and has promising applications in chip integration and portable free-space quantum key distribution. In this Letter, we propose and experimentally realize a PSP CVQKD scheme with transmitted local oscillator (LO) through fluctuating transmittance free-space channel using an off-the-shelf amplified spontaneous emission source for the first time. By proposing thermal-state polarization multiplexing transmitted LO, synchronized channel transmittance monitoring and fine-grained phase compensation techniques, secure keys within -15 dB transmittance of simulated free-space channel with turbulence are generated, with a final average secure key rate of 1.015 Mbps asymptotically. Equivalent atmospheric turbulence model analysis shows that the free-space PSP CVQKD scheme provides a promising outlook for high-speed and chip-based CVQKD for kilometer-level atmospheric channel networks.

Joint channel model for fog and atmospheric turbulence and performance analysis of unmanned aerial vehicles’ free-space optical communication

To study the joint effects of turbulence and fog on free-space optical (FSO) communication, a joint fog-turbulence-pointing error probability model for FSO is derived based on the random fog channel, Malaga turbulence model, and pointing error model. The closed-form expressions for the average signal to noise ratio (SNR), outage probability, average bit error rate (BER), ergodic channel capacity, and moment generating function in FSO communication under intensity modulation/direct detection are derived based on the joint model. Based on the unmanned aerial vehicle (UAV) working scenario, applying these expressions, the performance analysis of the inter-UAVs optical wave communication is implemented under the conditions for different beam widths, turbulence intensity and fog density and the pointing error caused by position, orientation, and jitter deviations. The calculated results are in good agreement with the Monte Carlo simulations. The analytical results for the average BER and outage probability show that the increase in beam width can significantly degrade the BER and outage probability, for the UAVs optical communication link. The analysis for the ergodic channel capacity shows that it increases with the increase of average transmission power; however, it increases slowly with the increase of beam width. And the increase in turbulence intensity, fog density, and drone jitter will degrade the communication performance of the system. Our study lays an important theoretical foundation for the development of FSO communication and UAV communication performance improvement in joint fog and turbulent environment.

Multistep ahead atmospheric optical turbulence forecasting for free-space optical communication using empirical mode decomposition and LSTM-based sequence-to-sequence learning

Although free-space optical communication (FSOC) is a promising means of high data rate satellite-to-ground communication, beam distortion caused by atmospheric optical turbulence remains a major challenge for its engineering applications. Accurate prediction of atmospheric optical turbulence to optimize communication plans and equipment parameters, such as adaptive optics (AO), is an effective means to address this problem. In this research, a hybrid multi-step prediction model for atmospheric optical turbulence, EMD-Seq2Seq-LSTM, is proposed by combining empirical mode decomposition (EMD), sequence-to-sequence (Seq2Seq), and long short-term memory (LSTM) network. First, using empirical mode decomposition to decompose the non-linear and non-stationary atmospheric optical turbulence dataset into a set of stationary components for which internal feature information can be easily extracted significantly reduces the training difficulty and improves the forecast accuracy of the model. Second, sequence-to-sequence is combined with LSTM networks to build a prediction model that can eliminate time delay and make full use of long-term information and then use the model to predict each component separately. Finally, the prediction results of each component are combined to obtain the final atmospheric turbulence forecasting results. To validate the performance of the proposed method, three comparative models, including WRF, LSTM, and sequence-to-sequence-LSTM, are demonstrated in this study. The forecasting results reveal that the proposed model outperforms all other models both qualitatively and quantitatively and thus can be a powerful method for atmospheric optical turbulence forecasting.

Analysis of atmospheric optical turbulence model— methods and progress

Stratification is a significant characteristic of atmospheric turbulence, especially high-altitude turbulence. At a fixed height, the real optical turbulence value fluctuates by 1–2 orders of magnitude or even greater on the average value. The turbulence profile model based on the observed data is a statistical average result. It can neither represent the stratification characteristics of an actual atmospheric turbulence profile nor have the prediction function, and can not fully meet the demand of optical engineering. Owing to the limitation of the capacity and speed of the computer, it is impossible to solve the Navier Stokes equation through direct numerical simulation (DNS) and large eddy simulation (LES) to predict the optical turbulence. The solution is to predict the conventional gas parameters through the mesoscale weather numerical prediction model MM5/ WRF, and then calculate the turbulence parameters through the turbulence parameterization scheme. In this paper, the prediction methods and research results of <inline-formula><tex-math id="M6">\begin{document}$ C_n^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221986_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221986_M6.png"/></alternatives></inline-formula> in surface layer,boundary layer and free atmosphere layer are introduced. Tatarski formula is derived in detail from the turbulence kinetic energy prediction equation and the temperature fluctuation variance prediction equation, and the physical meaning and applicable conditions of the formula are summarized. The latest research progress of neural network prediction and Antarctic astronomical site selection is mainly introduced. The characteristics and differences among different models, such as the empirical model fitted with experimental data, the parameter model with conventional meteorological parameters based on Kolmogorov turbulence theory, the prediction model related to mesoscale meteorological model, and the neural network method based on data driving and so on, are analyzed. It is emphasized that Kolmogorov turbulence theory is the theoretical basis of the existing atmospheric optical turbulence parameter models.

Performance of Reconfigurable-Intelligent-Surface-Assisted Satellite Quasi-Stationary Aircraft–Terrestrial Laser Communication System

This paper proposes the use of quasi-stationary aircraft and reconfigurable intelligent surfaces (RIS) to improve the system performance in satellite–terrestrial laser communication downlink. Single-input multiple-output (SIMO) technology is applied to the relay node of a quasi-stationary aircraft. The closed expression of the bit error rate (BER) of an RIS-assisted satellite quasi-stationary aircraft–terrestrial laser communication system (RIS-SHTLC) is derived under the M-distributed atmospheric turbulence model while considering the influence of atmospheric turbulence and pointing errors caused by RIS jitter. The effects of coherent binary frequency shift keying (CBFSK), coherent binary phase-shift keying (CBPSK), non-coherent binary frequency shift keying (NBFSK), and differential binary phase-shift keying (DBPSK) on the performance of an RIS-SHTLC system are simulated and analyzed under weak turbulence. The results show that the RIS-SHTLC system with CBPSK modulation has the best communication performance. Simultaneously, the relationships between the average signal-to-noise ratio (SNR) and BER of the RIS-SHTLC system under different RIS elements are simulated and analyzed, and compared with the traditional SHTLC system. In addition, the influence of the zenith angle, receiving aperture and divergence angle on the performance of the system is studied. Finally, Monte Carlo simulations are used to validate the analytical results.

Fuzzy Neural Network Dynamic Inverse Control Strategy for Quadrotor UAV Based on Atmospheric Turbulence

Quadrotor UAV is vulnerable to external interference, which affects search and rescue. In this paper, a fuzzy neural network dynamic inverse controller (FNN-DIC) is designed to eliminate the instability of the attitude angle caused by atmospheric turbulence. Considering the complexity of atmospheric turbulence, the component model of atmospheric turbulence is obtained firstly based on the Dryden model, using Gaussian white noise as a random input signal and a designed shaping filter. Combined with the Newton-Euler equation, a nonlinear dynamic model for the quadrotor UAV with atmospheric disturbance is established. While the traditional nonlinear dynamic inverse cancels the nonlinearity of the controlled object, it relies on precise mathematical models. The fuzzy neural network can adaptively compensate for the inaccurate part of the model and the inverse error of the model caused by the external disturbance, and the stability of the control system is strictly proved by using the Lyapunov function. The experiments are carried out on the simulation platform, and the results show that the FNN method can ensure that the quadrotor UAV can still fly smoothly against strong disturbances, and that robustness of the system is significantly improved.

Signal Space Diversity-Based Distributed RIS-Aided Dual-Hop Mixed RF-FSO Systems

Reconfigurable intelligent surface (RIS) is a recently emerged promising technology for beyond-5G (B5G)/6G wireless networks. In this letter, we propose to employ a signal space diversity (SSD) technique to improve the performance of distributed RIS-aided dual-hop mixed radio frequency (RF)-free-space optical (FSO) communication systems. The source-relay, source-RIS, and RIS-relay links are assumed to undergo independent but not identically distributed (i.n.i.d.) Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading. The destination node is equipped with multiple FSO apertures and the relay-destination links follow Gamma-Gamma (GG) distributed atmospheric turbulence (AT) model with pointing errors (PEs). Novel approximate closed-form expressions for the system’s symbol error rate (SER) are derived for both the exhaustive RIS-aided (ERA) and opportunistic RIS-aided (ORA) configurations. The numerical results show that using the SSD technique at both the RF and FSO links significantly improves the spectral efficiency and the diversity order of the system considered.

Atmospheric turbulence effects on shaped and unshaped sonic boom signatures.

Atmospheric turbulence is known to randomly distort the "N-wave" sonic boom signature emitted by conventional, unshaped supersonic aircraft. To predict the effect of turbulence on the signature from shaped aircraft, a numerical model has been developed based on the nonlinear Khokhlov-Zabolotskaya-Kuznetzov (KZK) propagation equation coupled with an approximate atmospheric turbulence model. The effects of turbulence on an archetypal N-wave and a shaped signature are compared via a series of numerical experiments propagating the signatures through multiple random realizations of turbulence in varying atmospheric and propagation conditions. The simulated results generally show that the variance of the Stevens Mark VII perceived level metric related to loudness is decreased by boom shaping and that the shocks in the shaped signature are less distorted than for the N-wave. Additionally, the probabilities of high-level and high-amplitude signatures are decreased for the shaped signature. Thus, the model predicts that boom shaping results in a signature with more consistent loudness and amplitude after propagation through turbulence.

Examination of the Performance of a Three-Phase Atmospheric Turbulence Model for Line-Source Dispersion Modeling Using Multiple Air Quality Datasets

One of the weaknesses of current line-source models for predicting downwind concentrations from mobile sources is accounting for the dispersion of effluents. Most of the investigators in the field have taken different approaches over the last 50 years, ranging from the use of Pasquill–Gifford (P-G) dispersion curves to the use of equations based on atmospheric turbulence for point source dispersion. Madiraju and Kumar (2021) proposed a three-phase turbulence (TPT) model using the key features of mobile source dispersion that appear in the existing literature. This paper examines the performance of line-source models using an updated TPT model. The generic dispersion equations were considered from the SLINE 1.1, CALINE 4, ADMS, and SLSM models. Multiple air quality field data sets collected by other investigators near the roadways were used during this study. These include field data collected from the Idaho Falls Tracer Experiment 2008 (used as the dataset to compare with the initial model), the CALTRANS Highway 99 Tracer experiment, and the Raleigh 2006 experiment. The predicted concentrations were grouped under unstable and stable atmospheric conditions. The evaluation of the model was performed using several statistical parameters such as FB, NMSE, R2, MG, VG, MSLE, and MAPE. The results indicate that the ADMS and SLINE 1.1 models perform better than CALINE4 and SLSM. SLINE 1.1 tends to overpredict for stable atmospheric conditions and underpredict for unstable atmospheric conditions. A trial test was performed to implement the TPT model in the basic line-source model (SLSM). The results indicate that the majority (FB, NMSE, R2, and MSLE) of the indicators have improved and are in the satisfactory range of a good model performance level.

Stable propagation of Ince–Gaussian vector beams through atmospheric turbulence

In this paper, we investigate the propagation properties of the Ince–Gaussian​ vector beams through atmospheric turbulence. For this type of generalized fundamental vector beams, the spatial structures of intensity and polarization are demonstrated to have the stability of transmission over kilometers. Analysis of scintillation index and spot centroid drift also supports this view. The von Kármán type index power spectrum and the resulting random phase screens are used to simulate the atmospheric turbulence model. Owing to the strong quantum-like correlation between polarization and the spatial components, the Ince–Gaussian vector beams exhibit stable photon entanglement and high inseparability. In particular, the increasing complexity of light field structure will enhance this stability of structure transmission. Higher-order Ince–Gaussian vector beams have the longer decoherence time and longer identified distance. The fourth-order Ince–Gaussian vector beams have stronger transmission stability than the third-order Ince–Gaussian vector beams. Our work contributes to the understanding of the stable propagation of the vectorial structured light and improves imaging and free-space optical communication in perturbing media.

Application limitations of a laser guide star in adaptive optoelectronic systems caused by its jitter in the atmosphere

Application limitations caused by the jitter of a laser guide star used for the compensation of atmospheric phase distortions are considered for Earth-based adaptive optoelectronic systems for the observation of natural and artificial space objects. The spatial coherence radii (Fried parameter) for which a laser beam remains within the isoplanatic angle under the jitter effect during guide star formation are estimated using locally homogeneous and isotropic atmospheric turbulence models. Beam deflections in two mutually orthogonal directions are considered to be distributed normally, and the probability of the beam remaining within the isoplanatic angle is considered to be subject to the Rayleigh law. The angular divergence of the deflected beam is estimated for a short exposure with a duration less than the atmosphere freezing time for the far and near fields of the emitting laser aperture.