Research on Radio Wave Propagation Prediction Model using 3-D Parabolic Equation over Rough Sea Surface

The parabolic equation (PE) method is widely used in radiowave propagation predictions. It has the advantages of high efficiency and stability, but it will lead to greater predicting errors in some situations, because the effects of transverse terrain gradients are not modeled. This problem can be solved by extending the 2D PE to the three-dimensional (3D) PE. However, the computing efficiency will degrade because of large scale matrix operations. In this paper, a new method is presented, in which the 3D PE is decomposed into two 2D PEs. It increases the computational efficiency and accuracy effectively. To verify the capability of the proposed method in radiowave propagation prediction, an experiment platform was set up. The computational results using this new method are compared with the experimental and Method of Moment (MoM) numerical computational results. Good agreements are achieved in the comparison. The study of radiowave propagation under complex environments is vitally important for improving the effective signal coverage in wireless communication and television broadcasting with plenty of urban buildings as well as mountainous terrains. It presents a big challenge due to the multiple wave propagation mechanisms involving the line of sight, diffraction and scattering propagation and the characteristic of large scale computation. The major issues refer to how to keep the computational accuracy and conducting the large scale computation at the same time. To meet the request for large scale computation of actual engineering problems, the modified empirical formulas are often used for analysis and computation with the drawback of poor computational accuracy, and the variance of the predicted propagation loss is generally 2 to 5 dB for the flat terrain, but for the complex terrain, the variance of the predicted propagation loss is usually about 5 to 10 dB. Many computational methods have been developed to improve the predicted accuracy. The commonly used methods are geometric diffraction methods, path integration methods and FDTD. It is hard to meet the requirement of engineering computation because these methods are computationally expensive and require high data accuracy of the terrain database at the same time (1). The Parabolic Equation (PE) method is a computational method for radiowave propagation loss besides the full wave method and ray tracing method, and has become a research focus. The PE method has high potential in radiowave propagation of mobile communication and broadcasting and television signal coverage as it can not only deal with complex terrain boundary conditions accurately, but also deal with complex atmosphere waveguide structure. Compared with the full wave method, the PE method deals with an unidirectional wave propagation, in which the equation can be solved by the step marching method in the propagation direction. The PE method can reduce the computational complexity of the full wave equation.

This paper presents the characteristics of radio wave scattering from rough sea surfaces in Ka-band. The physical optics method, which is one of the high frequency approximation algorithm, is employed to calculate radar cross section of electromagnetic simulation models of rough sea surfaces with Ship-EDF software. Rough sea surfaces are divided into six levels according to the wind speed over them. The simulation results show the effection that wind speed, the grazinng angle and frequency of radio wave have on the monostatic radar cross section of rough sea surfaces under the conditions of both horizontal and vertical polarization. With the increase of the roughness of sea surfaces and grazing angle of radio wave, the radar cross section value of rough sea surfaces increase. The frequencies of Ka-band have little contribution to the radar cross section value.

The dawn of the information age brought to light technical and economic challenges in delivering broadband telecommunication services to subscribers in rural and remote areas; challenges created by tiny pockets of subscribers scattered over a vast network service area. Dealing with such challenges calls for an appropriate system engineering approach and the utilisation of suitable network building blocks, which could differ significantly from those of the urban areas. The aim of this thesis, therefore, was to make a distinct contribution of knowledge to enable the delivery of broadband telecommunication services to rural and remote communities in a technically-effective and economically-viable manner. The thesis viewed the customer access line as the crucial network building block in determining the optimal architecture of a telecommunication network, based on the fact that maximising the length of customer access line results in minimising the number of network nodes required to serve a given area. A customer access line utilising wideband VHF radio channels, capable of bridging distances of up to 100 km, would make a significant economic difference in deploying telecommunication services in rural and remote areas. For many years, narrowband VHF radio channels have been used to carry voice and low-speed data over long distances in rural and remote areas, but very little or no data is available on the use of wideband VHF radio channels. Therefore, the research focused on wideband VHF radio channel modelling and characterisation over paths extending beyond line-of-sight, where diffraction is the dominant mode of radiowave propagation. This research was mainly concerned with aspects of radiowave propagation, rather than modulation and coding schemes. Conducting radiowave propagation studies over long distances extending beyond line-of-sight is often time consuming and can be extremely expensive. Traditionally, a powerful radio channel sounder is needed for conducting such studies. In this work, a novel inexpensive wide band VHF radio channel sounding technique was developed by the candidate. The technique makes use of a VHF digital television transmitter as a source for wideband sounding signals. The receiving end of the sounder is a special configuration of two synchronised modern swept-tuned spectrum analysers and a crossed-dipole antenna array. This enables the simultaneous measurement of the co-polarised and cross-polarised components of incident radiowaves. The power spectrum traces obtained from both the analysers were then mathematically processed to produce the channel parameters. A field measurement campaign was staged for collecting primary data for eight case studies using a sma1l4-wheel drive vehicle equipped with a 6 m telescopic antenna mast. A specially developed in-situ terrain path profiling tool played a pivotal role in the investigations. In line with the aim of the thesis, the measurements were conducted over ranges from 10 to 100 km. The signals from two transmitter sites, one transmitting on horizontal and the other on vertical polarisation, were used as sources for wide band sounding signals. Field measurements were conducted using antenna height of 7 m above ground level. In conclusion, using the developed radio channel sounding technique, and under the propagation conditions described in this thesis, showed that diffraction alone has little or no effect on the performance of a 7-MHz wide VHF radio channel. Diffraction by terrain obstacles seemed to reduce the effect of multi path. The investigation showed that low antenna height of approximately 7 m at the customer's premises can be used for distance of up to 100 km from the transmitter. The actual data transmission speed possible over a 7-MHz wide VHF radio channel will depend on the adopted modulation and coding schemes.

An improved fractal sea surface model, which can describe the capillary waves very well, is introduced to simulate the one-dimension rough sea surface. In this model, the propagation of electromagnetic waves (EWs) is computed by the parabolic equation (PE) method using the finite-difference (FD) algorithm. The numerical simulation results of the introduced model are compared with those of the Miller-Brown model and the Elfouhaily spectrum inversion model. It has been shown that the effects of the fine structure of the sea surface on the EWs propagation in the introduced model are more apparent than those in the other two models.

The problem of very high frequency (VHF) radiowave propagation over the sea surface at low grazing angles is of a great interest for a lot of applications including radar backscattering at different polarizations. Existing theoretical approaches predict much bigger backscattering cross section for vertical polarized (TM) waves as compared to horizontal polarized (TE) waves, and are unable to give satisfactory explanation of experimental results showing that these two values occasionally can be of the same order. In this paper two main features are taken into account in a theoretical investigation of the processes of VHF radiowave backscattering by the rough sea surface at low grazing angles: a) distortion of the incident plane wave by diffraction effects at the sea wave crests prior to scattering by smallscale roughness; b) the concave form of the most part of the visible undulating sea surface. The incident wave diffraction caused by sea wave crests is considered using the simplest model of the crest shape, i.e. a perfectly conducting wedge. It is shown that the diffraction in forward direction at low grazing angles increases the strength of the horizontal polarized field as compared to the vertical polarized one just near the boundary between shadowed and illuminated parts of the surface. Back scattering of electromagnetic waves from cylindrical impedance concave statistically rough surface is studied analytically by the small perturbation method.

The emissivity model for rough sea surface [Remote Sensing Environ. 24, 313-329 (1988)] is inspected in light of the measured surface emissivity. In the presence of moderate wind (5 m/s or less), the emissivity model is found to be adequate for small to moderate view angles. For large view angles, the discrepancy between the computed and the measured emissivity is large, but one can reduce this considerably by incorporating the reflected sea surface emission into the emissivity model. In addition, examination of the spectral variation of the observed and computed emissivity suggests the need for refined measurements of the complex refractive index. An improved model is constructed to calculate the rough sea surface emissivity that can be used to provide accurate estimates of sea surface skin temperatures from remotely sensed radiometric measurements. An important feature of the improved model is that the computed sea surface emissivity is only weakly dependent on wind speed for most view angles used in practice.

Plasma bubbles are large‐scale irregular structures that often occur at equatorial latitudes, equatorial plasma bubbles (EPBs) affect the propagation of high‐frequency (HF) radio waves. Based on their main observational characteristics, a three‐dimensional (3D) model of EPBs was established, and a preliminary simulation of EPBs was performed. Three‐dimensional ray tracing can be used to simulate HF radio wave propagation. In this study, we consider EPBs at different scales, appearing at different times and different heights, and investigate the influence of EPBs on the propagation path of radio waves at low latitudes. The simulation results show that when they propagate through EPBs of different scales, the propagation paths of radio waves are completely different. Radio waves at 6, 8, and 10 MHz show obvious refraction; With an increase in EPB scale, the focusing effect of radio waves will diminish, and the focusing height will increase. The propagation of HF radio waves through EPB change with time as follows: partial penetration, partial reflection, and total penetration, the refraction effect of EPB on radio waves gradually decreases over time. When radio waves propagate through EPB at different heights, the simulation results show that EPB at an altitude of 200 km makes little impact on the radio waves. As the height of EPB increases, the radio waves will exhibit significant refraction, showing an obvious focusing effect.

ARMA based approaches for forecasting the tuple of wind speed and direction

Study of RF waves on plasma

The optical detection accuracy of ship wakes strongly depends on the precision of wake–sea surface coupling modeling. Most existing studies ignore the energy interaction between the two and adopt a direct superposition approach, which results in significant deviation from the actual marine environment. This paper focuses on the research framework of “wake distribution characteristics–sea surface modeling–coupling superposition–detection impact.” First, the three-dimensional distribution characteristics of ship wakes in length, width, and depth are systematically reviewed, and the quantitative relationships between key parameters such as total wake length, effective detection length, diffusion angle, and ship type (length, draft), as well as sailing speed, are clarified. Second, a three-dimensional sea surface geometric model is constructed based on the Elfouhaily spectrum and the Longuet-Higgins directional distribution function, revealing the modulation patterns of wind speed and fetch on sea surface roughness. Third, to overcome the limitations of existing superposition methods, a Gaussian-energy-based wake–sea coupling modeling method is proposed, in which each wake point is regarded as an energy source, and a Gaussian function is used to describe its influence weight on the surrounding sea surface. Finally, multi-case simulations verify that this method can accurately reproduce the modulation effect of the sea surface on wake wave height—the larger the ship speed and hull size, the more significant the wake fluctuations; meanwhile, increasing sea surface wind speed enhances background interference to the wake signal. The results provide theoretical support and a modeling method for improving the anti-interference capability and target recognition accuracy of ship wake optical detection.

A three-dimensional parabolic equation (PE) and perturbation approach is used to invert for the range-dependent geoacoustic characteristics of the seabed. The model assumes that the sound speed profile is the superposition of a known range-independent profile and an unknown depth and range-dependent perturbation. Using a Green’s function approach, the total measured pressure field in the water column is decomposed into a background field, which is due to the range-independent profile, and a scattered field, which is due to the range-dependent perturbation. When the Born approximation is applied to the resulting integral equation, it can be solved for the range-dependent profile using linear inverse theory. For simplicity, the sound speed profile in the water column is assumed to be known, and the range-dependent perturbation is added to the index of refraction n(x,y,z), rather than the sound speed profile c(x,y,z). The method is implemented in both Cartesian (x,y,z) and cylindrical (r,θ,z) coordinates with the forward propagation of the field in x and r, respectively. Synthetic and experimental data are used to demonstrate the validity of the method. Keywords: Three-dimensional parabolic equation method, geoacoustic inversion, range-dependent sound speed profile, linear inversion, Born approximation, and Green’s functions.

Rain cells or convective rain, the dominant form of rain in the tropics and subtropics, can be easy detected by satellite Synthetic Aperture Radar (SAR) images with high horizontal resolution. The footprints of rain cells on SAR images are caused by the scattering and attenuation of the rain drops, as well as the downward airflow. In this study, we extract sea surface wind field and its structure caused by rain cells by using a RADARSAT-2 SAR image with a spatial resolution of 100 m for case study. We extract the sea surface wind speeds from SAR image by using CMOD4 geophysical model function with outside wind directions of NCEP final operational global analysis data, Advance Scatterometer (ASCAT) onboard European MetOp-A satellite and microwave scatterometer onboard Chinese HY-2 satellite, respectively. The root-mean-square errors (RMSE) of these SAR wind speeds, validated against NCEP, ASCAT and HY-2, are 1.48 m/s, 1.64 m/s and 2.14 m/s, respectively. Circular signature patterns with brighter on one side and darker on the opposite side on SAR image are interpreted as the sea surface wind speed (or sea surface roughness) variety caused by downdraft associated with rain cells. The wind speeds taken from the transect profile which superposes to the wind ambient vectors and goes through the center of the circular footprint of rain cell can be fitted as a cosine or sine curve in high linear correlation with the values of no less than 0.80. The background wind speed, the wind speed caused by rain cell and the diameter of footprint of the rain cell with kilometers or tens of kilometers can be acquired by fitting curve. Eight cases interpreted and analyzed in this study all show the same conclusion.

Importance of thermal effects and sea surface roughness for offshore wind resource assessment

The propagation phenomena through 2D surface duct-to-elevated duct transition is described in terms of parabolic equation (PE) method. The split step marching solution of the PE method is first compared with the reference solutions obtained from Helmholtz wave equation in longitudinally invariant surface duct problem and the excellent agreement between the results is presented. Then the PE method is applied to propagation through surface duct-to-elevated duct transition problem which is non-separable in any of the known orthogonal coordinate system. The transformation of the surface trapped modes into propagating elevated beams is shown with the PE method. >

Inadequate representation of the environment is a limitation for prediction of radar system performance as well as for validation of propagation codes. To improve understanding of how different environmental effects/parameters compete and compare, this study examines the sensitivity of radar wave propagation to a suite of environmental parameters for low grazing angle near‐surface radar systems at 3–15 GHz at horizontal and vertical polarizations. A global sensitivity analysis method is used, which accounts for parameter interactions, and propagation is modeled using the parabolic equation method. Environmental parameters examined include eight sea state parameters and eight parameters characterizing the vertical structure and character of range‐independent refractivity profiles. The relative importance of parameters varies more with frequency than polarization, and parameter interactions are found to be significant. Atmospheric mixed layer parameters are found to be the most sensitive, particularly the thickness of the mixed layer. The most significant ocean surface parameter is swell period, although sea directionality is important at 3 GHz and sea surface roughness and salinity are important at 9 and 15 GHz. Because of the spatial variability of sensitivity throughout the domain, regional analysis is performed to determine the most important parameters in different regions of the domain (1000 m in altitude and 60 km in range). These regional sensitivity results, along with those for the whole domain, provide guidance on prioritization of environmental characterization in numerical weather prediction and inversion studies (e.g., refractivity from clutter studies), which are two common methods currently used to address environmental effects on propagation.