Slant Path Research Articles

Propagation of auto-focusing hypergeometric Gaussian beams along a slant path in oceanic turbulence

Compared to horizontal transmission, the oceanic dissipation rate and temperature-salinity distribution ratio are no longer constant but vary with depth, imposing greater complexity on oceanic turbulence when beams propagate through a slant path and resulting in more limitations on the performance of underwater wireless optical communication (UWOC) links. This study focuses on investigating the performance, especially the auto-focusing characteristic, of auto-focusing hypergeometric Gaussian (AHGG) beams propagating along slant paths in oceanic turbulence. We theoretically derive the spatial coherence radius and the relative probability of the orbital angular momentum (OAM) mode for AHGG beams passing through such links. Numerical simulations reveal that AHGG beams exhibit superior propagation performance compared to hypergeometric Gaussian beams. Lower beam orders and OAM numbers contribute to improved performance, while careful selection of auto-focusing length can tangibly enhance detection performance as well. Additionally, tidal velocities and wind speeds have nonnegligible effects on OAM signal probability. Our results further demonstrate that surface buoyancy flux, temperature gradients, and waterside friction velocity significantly affect beam transmission under varying wind conditions. These findings, particularly controlling the auto-focusing length of AHGG beams to match the transmission distance, provide valuable insights for enhancing the quality of UWOC links.

Modulation effect of focusing mirror on beam propagation through anisotropic turbulence

In this study, we modulated the Bessel-Gaussian (BG) beam using a focusing mirror to enhance the performance of wireless optical communication (WOC) while considering the angles between turbulence cells and the transmitted direction when beams propagate through anisotropic atmospheric turbulence along a slant path. Numerical results reveal that when the BG beam is modulated by a focusing mirror with a focusing length of 1 km, the detection probability of orbital angular momentum (OAM) is increased by 9.06% compared with the unmodulated BG beam when the OAM quantum number is 1. Simultaneously, this modulation method effectively reduces the bit error rate and enhances the channel capacity in OAM-based WOC. Furthermore, we observed that the smaller the OAM number, the better the effect of the modulation. Through our analysis, we identified that the most significant distortions in OAM mode propagation occur at the exponential parameter approximately 3.1 in the modified von Karman spectrum. Moreover, we demonstrated that the effects of the anisotropic tilt angle can not be negligible for beams through a slant path. Therefore, the modulation of the focusing mirror, in combination with a well-designed propagation direction that takes appropriate angles into account, can significantly improve the overall quality and performance of optical communication systems.

Improving urban CO2 spatial distribution modelling using multi-source data

Urban areas contribute approximately 70% of the total anthropogenic CO2 emissions, making them the primary focus of global carbon monitoring. However, accurate modelling of urban meteorology is challenging because of complex artificial landscapes. Reducing errors in urban meteorological simulation and improving the accuracy of modelling the spatial distribution of urban CO2 is of great significance for the “top-down” CO2 emissions estimation in urban areas. In this study, local urban datasets were constructed based on multiple data sources to overcome the limitation of insufficient information from a single data source. In the development of urban datasets, grid-by-grid data processing is realized, and the evaluation results show that the developed urban datasets are greatly improved compared with the default. The developed urban datasets were applied to WRF-Chem with 1-km spatial resolution, and the simulated column-averaged dry air mole fraction of CO2 (XCO2) was verified with the EM27/SUN observed data considering the slant observation path. The results show that urban datasets strongly influence the spatial distribution modelling of XCO2, depending on the state of the atmosphere near the surface, especially wind velocity. Accurate local urban datasets can effectively reduce the bias in urban XCO2 spatial distribution modelling and improve the capability of the atmospheric CO2 transport model in urban carbon emission estimation.

An initial investigation of the non-isotropic feature of GNSS tropospheric delay

Tropospheric delay is a significant error source in Global Navigation Satellite Systems (GNSS) positioning. Slant Path Delay (SPD) is commonly derived by multiplying Zenith Tropospheric Delay (ZTD) with a mapping function. However, mapping functions, assuming atmospheric isotropy, restrict the accuracy of derived SPDs. To improve the accuracy, a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations, treating the atmosphere as anisotropic. This study uncovers that, amidst atmospheric dynamics and spatiotemporal changes in moisture content, the SPD deviates from that based on traditional isotropy or anisotropy assumption. It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles. Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service (IGS) stations, referencing the SPD with the ray-tracing method. It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3 (VMF3) estimation. Lastly, the non-isotropic of SPD is analyzed through the ray-tracing method. The results indicate the smallest residual (1.1–82.7 mm) between the SPDs with VMF3 and those with the ray-tracing. However, introducing horizontal gradient correction yields no significant improvement of SPD accuracy. Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles, a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling. This finding provides vital support for future high-precision tropospheric delay modeling.

Propagation properties of the vortex beam in the slant path of ocean turbulence under weak wind model

Propagation properties of the vortex beam in the slant path of ocean turbulence under weak wind model

Twelve years of rain attenuation statistics of Earth–space propagation experiment at Ka band in Toulouse

SummarySince 2009, ONERA has been running Ka band propagation experiments in Toulouse (France, latitude 43.57°N, longitude 1.47°E). A rain gauge was also deployed on site to collect rainfall rate measurements concurrently to beacon data. Since April 2011, the beacon receiver has been recording the 20.2 GHz (vertical polarisation) Astra 3B beacon signal along a slant path of 35.1° of elevation angle. All years of the experiment had excellent data availability, hence giving 12 years of data at Ka band. First, the propagation experiment and the data processing methodology are described. Second, a statistical analysis of rain attenuation and rainfall rate is conducted. Comparisons are then performed with the prediction methods of Recommendations ITU‐R P.837‐7 (rainfall rate), P.618‐13 (rain attenuation) and P.678‐3 (variability of propagation phenomena).

Wave structure function, spatial coherence radius, and Fried parameter of optical wave propagating through ocean turbulence with a slant path.

The analytical formula for characteristic parameters of optical wave (wave structure function, spatial coherence radius, and Fried parameter) in the slant path of ocean turbulence are derived and analyzed. Under the Rytov approximation, the wave structure function derived by the oceanic power spectrum of the refractive index of optical turbulent fluctuations in the slant path still complies with the five-thirds power law of the Kolmogorov spectrum in the inertial subregion, and the relationship between spatial coherence radius and Fried parameters satisfies 2.1 times. The correctness of analytical formulation of the wave structure function is demonstrated by comparing the numerical results of the original integral formula with the analytical formula of the derived in this paper.

Total column ozone retrieval from a novel array spectroradiometer

Abstract. This study presents a new total column ozone (TCO) retrieval from the Koherent system, developed at the Physikalisch-Meteorologisches Observatorium Davos, World Radiation Center (PMOD/WRC). The instrument is based on a small, cost-effective, robust, low-maintenance and state-of-the-art-technology array spectroradiometer. It consists of a BTS-2048-UV-S-F array spectroradiometer from Gigahertz-Optik GmbH, coupled with an optical fibre to a lens-based telescope mounted on a sun tracker for measuring direct UV irradiance in the ultraviolet wavelength band between 305 to 345 nm. Two different algorithms are developed for retrieving TCO from these spectral measurements: (1) TCO retrieved by a least-squares-fit algorithm (LSF) and (2) a custom-double-ratio (CDR) technique using four specifically selected wavelengths from the spectral measurements. The double-ratio technique is analogous to the retrieval algorithm applied for the Dobson instruments and the Brewer instruments but is adopted here for TCO retrieval with Koherent. The instrument was calibrated in two different ways: (a) absolute calibration of the spectra using the portable reference for ultraviolet radiation QASUME for the LSF retrieval and (b) relative calibration of the extraterrestrial constant (ETC) of the CDR retrieval by minimising the slope between air mass and the relative differences of TCO from QASUME and Koherent. This adjustment of the ETC allows the instrument to be calibrated with standard TCO reference instruments during calibration campaigns, such as a double-monochromator Brewer. A 2-year comparison in Davos, Switzerland, between Koherent and the Brewer 156 (double monochromator) shows that TCO derived from Koherent and the Brewer 156 agree, on average, over the entire period within 0.7 % for all retrievals in terms of offset. The performance in terms of slant path depends on the selected retrieval and the applied corrections. The stray-light-corrected LSF retrieval exhibits a smaller slant path dependency than the CDR retrieval and performs almost as well as a double-monochromator system. The slant path dependency of the CDR is comparable to the slant path dependency of a single Brewer monochromator. The combination of both retrievals leads to performance with an offset close to zero compared to Brewer 156, a seasonal amplitude of the relative difference of 0.08 % and a slant path dependency of maximum 1.64 %, which is similar to other standard TCO instruments such as single Brewer or Dobson. Applying the double-ratio technique by selecting the wavelengths and slit functions from Brewer and Dobson, respectively, allows for the determination of the effective ozone temperature with an uncertainty of 3 K in terms of daily averages. With the improved TCO retrieval, Koherent serves as a new low-maintenance instrument which could also be used to monitor TCO at remote sites. The TCO retrieval presented here may be applied to other array-based spectroradiometers, providing direct spectral measurements in the ultraviolet wavelength band.

Data Assimilation for the Two-Dimensional Ambipolar Diffusion Equation in Earth’s Ionosphere Model

The problem of variational data assimilation for the INM RAS two-dimensional diffusion model of the Earth’s ionosphere F region is considered. Total integral electron contents along given paths are used as observation data. The general statement of the problem in differential form is formulated, and its solvability is analyzed. Based on a regularized statement, an iterative algorithm for solving the assimilation problem is constructed, and its convergence is demonstrated. A finite-dimensional approximation is constructed, the numerical solution of the problem is implemented, and the stability and convergence of the difference scheme are proved. The quality of the reconstruction of electron concentration fields is examined in test numerical experiments. It is shown that a weakly perturbed solution is reconstructed with acceptable accuracy for both stationary and evolutionary statements in the case of vertical and slant integration paths.

Elevation angle effect on slant path attenuation along earth-space paths: A Northern Nigeria perspective

In the network planning and design of terrestrial and earth-space communication links, the slant path attenuation caused by rain and its associated strong winds is of interest. Rain causes severe link degradation to radio links by absorbing parts or the whole signal during propagation. This study predicts slant path attenuation by rain in three (3) Northern Nigerian zones using the International Telecommunications Unions (ITU-R) model for 10 to 40 GHz. The effect of specific attenuation, rain attenuation, and elevation angle on the received signal strength is analyzed. The ITU-R model suggests rain attenuation values ranging from 4.26 dB to 31.67 dB for Jaji, Wudil, and Potiskum. The results further indicate a decrease in rain attenuation with an increase in elevation angle up to 50.1° elevation for the three (3) monitored stations, which starts to decrease steadily after this threshold. Results from this study can aid the network engineer in anticipating network changes and planning fade mitigation techniques where necessary.

Effect of Self-Focusing on Propagation of a Laser Beam in the Atmosphere Along a Slant Path

The equivalent B-integral phase screen (EBPS) method of numerical simulation is proposed to study the propagation of a high-power laser beam in the atmosphere along a slant path, and the computational accuracy and efficiency of the EBPS method are confirmed. It is shown that a decrease of the self-focusing caused by the atmosphere refraction effect. However, the refraction correction for the elevation angle is hardly affected by the self-focusing effect. On the other hand, the analytical expressions of the B integral and the optimal initial beam power of a high-power laser beam propagating in the atmosphere along a slant path are derived. It is found that the optimal beam power and the target maximum intensity decrease as the apparent elevation angle decreases, while the optimal beam power decreases but the target maximum intensity increases as the wavelength decreases. A method to optimize the beam quality on the target is presented.

An evaluation of scintillation index in atmospheric turbulent for new super Lorentz vortex Gaussian beam

Super Lorentz vortex Gaussian beam (SLVGB) is propagated via the turbulent atmosphere parameters. The benefit key of the SLVGB wave model is that the unlimited bandwidth wave and a spherical wave are involved. Additionally, Huygens Fresnel integral was used for schoolwork to study the propagation of SLVGB in a slant direction via a moderate turbulent medium. On the other hand, applying the crude international telecommunication union (ITU-R) model possible. Moreover, the Kolmogorov turbulent power spectrum model is applied, and the source field is dispersed by the zenith angle to the receiver plane. Additionally, examine the contour of the source field and the SLVGB intensity. To investigate various parameters such as source size, mode, scintillation index, topological charge, and others that are associated with the beam of super Lorentz vortex Gaussian are entirely understood, the outcomes were examined, and obtained other references to build the beam of slant path propagation in turbulent; the form constants are especially in comparison and matching. Our graphical findings indicate that the parameters happened randomly in the scintillation index and intensity of the SLVGB, resulting in a novel beam technical configuration. To summarize, this article is advantageous for remote sensing and uses an optical communications system and laser applications.

On the Impact of GPS Multipath Correction Maps and Post-Fit Residuals on Slant Wet Delays for Tracking Severe Weather Events

Climate change has increased the frequency and intensity of weather events with heavy precipitation, making communities worldwide more vulnerable to flash flooding. As a result, accurate fore- and nowcasting of impending excessive rainfall is crucial for warning and mitigating these hydro-meteorological hazards. The measurement of integrated water vapour along slant paths is made possible by ground-based global positioning system (GPS) receiver networks, delivering three-dimensional (3D) water vapour distributions at low cost and in real-time. As a result, these data are an invaluable supplementary source of knowledge for monitoring storm events and determining their paths. However, it is generally known that multipath effects at GPS stations have an influence on incoming signals, particularly at low elevations. Although estimates of zenith total delay and horizontal linear gradients make up the majority of the GPS products for meteorology to date, these products are not sufficient for understanding the full 3D distribution of water vapour above a station. Direct utilization of slant delays can address this lack of azimuthal information, although, at low elevations it is more prone to multipath (MP) errors. This study uses the convective storm event that happened on 27 July 2017 over Bulgaria, Greece, and Turkey, which caused flash floods and severe damage, to examine the effects of multipath-corrected slant wet delay (SWD) estimations on monitoring severe weather events. First, we reconstructed the one-way SWD by adding GPS post-fit phase residuals, describing the anisotropic component of the SWD. Because MP errors in the GPS phase observables can considerably impact SWD from individual satellites, we used an averaging technique to build station-specific MP correction maps by stacking the post-fit phase residuals acquired from a precise point positioning (PPP) processing strategy. The stacking was created by spatially organizing the residuals into congruent cells with an optimal resolution in terms of the elevation and azimuth at the local horizon.This enables approximately equal numbers of post-fit residuals to be distributed across each congruent cell. Finally, using these MP correction maps, the one-way SWD was improved for use in the weather event analysis. We found that the anisotropic component of the one-way SWD accounts for up to 20% of the overall SWD estimates. For a station that is strongly influenced by site-specific multipath error, the anisotropic component of SWD can reach up to 4.3 mm in equivalent precipitable water vapour. The result also showed that the spatio-temporal changes in the SWD as measured by GPS closely reflected the moisture field estimated from a numerical weather prediction model (ERA5 reanalysis) associated with this weather event.

Propagation Characteristics of Partially-Coherent Radially-Polarized Vortex Beams Through Non-Kolmogorov Turbulence Along a Slant Path

Propagation Characteristics of Partially-Coherent Radially-Polarized Vortex Beams Through Non-Kolmogorov Turbulence Along a Slant Path

On the Quasi-Moment-Method as a Rain Attenuation Prediction Modeling Algorithm

A computationally inexpensive, analytically simple, and remarkably efficient rain attenuation prediction algorithm is presented in this paper. The algorithm, here referred to as the Quasi Moment-Method (QMM), has only two main requirements for its implementation. First, rain attenuation measurement data (terrestrial or slant path) for the site of interest must be available; and second, a model, known to have predicted attenuation for any site to a reasonable level of accuracy (base model), and whose analytical format can be expressed as a linear combination of its parameters, is also required. An important novelty introduced by the QMM algorithm is a normalization scheme, through which a modelling difficulty concerning exceedance probabilities outside a 0.01 to 1.00 range, is eliminated. Model validation and performance evaluation using a comprehensive set of data available from the literature clearly demonstrated that the QMM models consistently improved base model performance by more than 90%; and outperformed all published ‘best fit’ models with which they were compared.

COMPARISON OF MEASURED SLANT PATH ATTENUATION AT 10.982 GHZ WITH LARGE-SCALE PREDICTION MODELS IN A TROPICAL CLIMATE

Rain-induced attenuation above 10 GHz can be severe at heavy rain rates resulting in deep fading, which can negatively impact the quality of receive signal level at the Earth station receiver. The dearth of direct measurement data in most of the tropical and equatorial climates has motivated the campaign for collection of rain attenuation data on slant paths in these regions. This is mainly due to a huge receiver margin required for such measurement, and which is very difficult to obtain by using a spectrum analyzer. The measurement results of rain rates and rain-induced attenuation in vertically polarized signals propagating at 10.982 GHz in a tropical Malaysian climate are presented in this study. The measured attenuation is compared with large-scale prediction models. As shown in the statistically-tested results, the Bryant model yields the best overall fit, while the Crane model yields the worst overall fit. The results show that the models have relatively good prediction capabilities in the Malaysian tropical climate; however, their prediction errors still need to be minimized. Therefore, in this study, a correction factor is proposed to enhance their predictions.

Development of mobile lidar for remote sensing of tropospheric ozone on the vertical and horizontal (slant) paths

We present a mobile lidar for measuring, in the ultraviolet (UV) region of the spectrum, the spatial distribution of ozone (O3) in the troposphere on the vertical and horizontal (slant) sensing paths, using the four-channel system of recording the return signals. The lidar operates, based on the lidar differential absorption and scattering method on the wavelength pair of 299 nm and 341 nm. We present a technical description of the lidar developed.

Feasibility demonstration of AO pre-compensation for GEO feeder links in a relevant environment.

Optical technologies are extremely competitive candidates to achieve very-high throughput links between ground and GEO satellites; however, their feasibility relies on the ability to mitigate channel impairments due to atmospheric turbulence. For that purpose, Adaptive Optics (AO) has already proved to be highly efficient on the downlink. However, for the uplink, anisoplanatism induced by point-ahead angle (PAA) compromises AO pre-compensation efficiency to an extent that depends on propagation conditions. The ability to properly assess the anisoplanatism impact in a wide variety of conditions is thus critical in designing the optical ground terminals. In this paper, we demonstrate the consistency of experimental coupled flux statistics with results coming from performance and end-to-end models, on an AO pre-compensated 13 km slant path in Tenerife. This validation is demonstrated in a wide variety of turbulence conditions, hence consolidating propagation channel models that are of critical importance for the reliability of future GEO feeder links. We then compare experimental results to theoretical on-sky performance, and discuss to what extent such slant path or horizontal path experiments can be representative of real GEO links.

A mixed mode phase-field model of ductile fracture

We present the first mixed mode phase-field model of ductile fracture. The contribution of crack opening and shearing deformations to the propagation of a crack is expressed by introducing two phase fields. Constitutive relations are then introduced to couple and distinguish these phase fields. Special attention is given to the maximum shear stress and its effect on the development of fractures. The proposed model is validated by tensile testing experiments found in the literature on Al 2024 T-351. Model predictions of the crack path and load-displacement response are compared to a plane-strain tension experiment, a round bar tension experiment and a notched round bar tension experiment. The model is shown to accurately capture the slant and cup-cone crack paths as well as force-displacement curves.

Threshold sensitivity of staring thermal imaging devices operating in slant atmospheric paths

Subject of study. A method for predicting threshold sensitivity, i.e., the resulting noise equivalent temperature difference of modern air- or ground-based staring thermal imaging devices, was considered. Aim of study. The study aimed to estimate the effectiveness of thermal imaging devices surveying aerial and ground-based objects. Method. The method implied a theoretical computational analysis based on a previously developed model for emission of the atmosphere in arbitrarily oriented paths considering the following: the nominal noise equivalent temperature difference that characterizes the quantum or thermal array photodetectors used in thermal imaging devices; the temperature profile of the atmosphere whose emission, together with background emission of, e.g., the ground surface, significantly affects the external photon noise in thermal imaging devices; elevation of the line of sight of the object; presence and type of clouds; and season. Results. A method was developed for refined calculation of the threshold sensitivity of staring thermal imaging devices determined by photon noise resulting from the radiation of the elements of the thermal imaging device itself, particularly its objective, dark-current noise, readout noise, and spatial (geometric) noise resulting from the residual dispersion of sensitivity of photodetector elements after correction. This threshold sensitivity determines the effectiveness of thermal imaging devices in object detection and recognition against a quasi-uniform background of ground or sky under different conditions, including long slant ground-to-air and air-to-ground atmospheric paths. The investigation results are presented in a form convenient for practical applications, i.e., reduced to equations and illustrated with a calculation example. Practical significance. The engineering method for calculating the resulting noise equivalent temperature difference proposed in this study, which considers the thermal stratification of the atmosphere and corresponds to real operating conditions of thermal imaging devices, is advantageous for adequate assessment of their effectiveness in surveilling ground-based and aerial objects, including low-contrast objects.