Propagation modeling of ocean-scattered low-elevation GPS signals for maritime tropospheric duct inversion

The maritime tropospheric duct is a low-altitude anomalous refractivity structure over the ocean surface,and it can significantly affect the performance of many shore-based/shipboard radar and communication systems.We propose the idea that maritime tropospheric ducts can be retrieved from ocean forward-scattered low-elevation global positioning system(GPS) signals.Retrieval is accomplished by matching the measured power patterns of the signals to those predicted by the forward propagation model as a function of the modified refractivity profile.On the basis of a parabolic equation method and bistatic radar equation,we develop such a forward model for computing the trapped propagation characteristics of an ocean forward-scattered GPS signal within a tropospheric duct.A new GPS scattering initial field is defined for this model to start the propagation modeling.A preliminary test on the performance of this model is conducted using measured data obtained from a 2009-experiment in the South China Sea.Results demonstrate that this model can predict GPS propagation characteristics within maritime tropospheric ducts and serve as a forward model for duct inversion.     

Anomalous propagation conditions of electromagnetic wave observed over Bosten Lake,China in July and August, 2014

Atmospheric duct is a common phenomenon over large bodies of water, and it can significantly affect the performance of many radio systems. In this paper, a two-month(in July and August, 2014) sounding experiment in ducting conditions over Bosten Lake was carried out at a littoral station(41.89°N, 87.22°E) with high resolution GPS radiosondes, and atmospheric ducts were observed for the first time in this area. During the two months, surface and surface-based ducts occurred frequently over the Lake. Strong diurnal variations in ducting characteristics were noticed in clear days. Ducting occurrence was found at its lowest in the early morning and at its highest(nearly 100%) in the afternoon. Duct strength was found increasing from early morning to forenoon, and reaching its maximum in the afternoon. But contrarily, duct altitude experienced a decrease in a clear day. Then the meteorological reasons for the variations were discussed in detail, turbulent bursting was a possible reason for the duct formation in the early morning and the prevailing lake-breeze front was the main reason in the afternoon. The propagation of electromagnetic wave in a ducting environment was also investigated. A raytracing framework based on Runge–Kutta method was proposed to assess the performance of radio systems, and the precise critical angle and grazing angle derived from the ray-tracing equations were provided. Finally, numerical investigations on the radar performance in the observed ducting environments have been carried out with high accuracy, which demonstrated that atmospheric ducts had made great impacts on the performance of radio systems. The range/height errors for radar measurement induced by refraction have also been presented, too, which shows that the height errors were very large for trapped rays when the total range was long enough.     

Observationally constrained modeling of sound in curved ocean internal waves: examination of deep ducting and surface ducting at short range

A study of 400 Hz sound focusing and ducting effects in a packet of curved nonlinear internal waves in shallow water is presented. Sound propagation roughly along the crests of the waves is simulated with a three-dimensional parabolic equation computational code, and the results are compared to measured propagation along fixed 3 and 6 km source/receiver paths. The measurements were made on the shelf of the South China Sea northeast of Tung-Sha Island. Construction of the time-varying three-dimensional sound-speed fields used in the modeling simulations was guided by environmental data collected concurrently with the acoustic data. Computed three-dimensional propagation results compare well with field observations. The simulations allow identification of time-dependent sound forward scattering and ducting processes within the curved internal gravity waves. Strong acoustic intensity enhancement was observed during passage of high-amplitude nonlinear waves over the source/receiver paths, and is replicated in the model. The waves were typical of the region (35 m vertical displacement). Two types of ducting are found in the model, which occur asynchronously. One type is three-dimensional modal trapping in deep ducts within the wave crests (shallow thermocline zones). The second type is surface ducting within the wave troughs (deep thermocline zones).     

Microwave scattering by tropospheric fluctuations in an evaporation duct

Numerical analysis of the centimeter wave propagation in an evaporation duct with allowance for scattering by correlated turbulent fluctuations of the tropospheric refraction index is carried out. It is shown that energy leakage from the duct leads to an additional decrease in the average wave power. The amplitude of random power variations above the duct turns out to be significantly higher compared with the variations inside the duct. An increase in the vertical correlation radius of refraction-index inhomogeneities leads to an increase in the vertical correlation radius of the radio-wave intensity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 307–317, April 2009.     

Investigation on global positioning system signal scattering and propagation over the rough sea surface

This paper is devoted to the study of polarization properties, scattering properties and propagation properties of global positioning system (GPS) scattering signal over the rough sea surface. To investigate the polarization and the scattering properties, the scattering field and the bistatic scattering coefficient of modified Kirchhoff approximation with using the tapered incident wave is derived in detail. In modeling the propagation properties of the GPS scattering signal in the evaporation duct, the initial field of parabolic equation traditionally computed by the antenna pattern with using fast Fourier transform (FFT) is replaced by the GPS scattering field. And the propagation properties of GPS scattering signal in the evaporation duct with different evaporation duct heights and elevation angles of GPS are discussed by the improved discrete mixed Fourier transform with taking into account the sea surface roughness.     

湍流大气中高斯谢尔光束的波前位错

在Rytov近似下,通过引入短期统计平均位错位置的概念,研究了高斯谢尔光束通过近地面弱湍流大气传播时,波前圆形位错形成和位错位置与湍流大气起伏强度和传播距离等参数间的关系.基于湍流大气中平行和交叉双光束的简化近似传输模型,研究了湍流大气中传播高斯谢尔光束波前位错位置与大气湍流强度、传输距离等参数间的相关机制.在远小于光波位相起伏周期的条件下,分别得出了束径不同同轴双光束和交叉双光束传播情况下波前圆位错位置的湍流系综统计平均理论关系.所得结果表明,同轴平行光束干涉和交叉光束干涉所产生的光束波前位错受大气湍流强度、传输距离等参数调制的规律是不同的.     

Monitoring of the ducting by a ground-based GPS receiver

In this paper, we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays. The vertical structure of the refractive environment is modeled using three parameters, i.e., duct height, duct thickness, and duct slope. The refractivity model is implemented with a priori constraints on the duct height, thickness, and strength, which might be derived from soundings or numerical weather-prediction models. A ray propagation model maps the refractivity structure into a replica field. Replica fields are compared with the simulation observed data using a squared-error objective function. A global search for the three environmental parameters is performed using genetic algorithm. The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated. This technique could provide near-real-time estimation of ducting effect. The results suggest that ground-based GPS provides significant atmospheric refractivity information, despite certain fundamental limitations of ground-based measurements. Radiosondes typically are launched just a few times daily. Consequently, estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates using radiosonde data alone.     

Scattering of sonic booms by anisotropic turbulence in the atmosphere

An earlier paper [J. Acoust. Soc. Am. 98, 3412-3417 (1995)] reported on the comparison of rise times and overpressures of sonic booms calculated with a scattering center model of turbulence to measurements of sonic boom propagation through a well-characterized turbulent layer under moderately turbulent conditions. This detailed simulation used spherically symmetric scatterers to calculate the percentage of occurrence histograms of received overpressures and rise times. In this paper the calculation is extended to include distorted ellipsoidal turbules as scatterers and more accurately incorporates the meteorological data into a determination of the number of scatterers per unit volume. The scattering center calculation overpredicts the shifts in rise times for weak turbulence, and still underpredicts the shift under more turbulent conditions. This indicates that a single-scatter center-based model cannot completely describe sonic boom propagation through atmospheric turbulence.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Monitoring of ducting by using a ground-based GPS receiver

In this paper,we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays.The vertical structure of the refractive environment is modeled using three parameters,i.e.,duct height,duct thickness,and duct slope.The refractivity model is implemented with a priori constraints on the duct height,thickness,and strength,which might be derived from soundings or numerical weather-prediction models.A ray propagation model maps the refractivity structure into a replica field.Replica fields are compared with the simulation observed data using a squarederror objective function.A global search for the three environmental parameters is performed using a genetic algorithm.The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated.This technique could provide near-real-time estimation of the ducting effect.The results suggest that ground-based GPS provides significant atmospheric refractivity information,despite certain fundamental limitations of ground-based measurements.Radiosondes are typically launched just a few times daily.Consequently,estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates caused by using radiosonde data alone.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Propagation and radiation of sound in a finite length duct

An analysis has been carried out to investigate sound transmission in an unflanged circular duct of finite length. A new formulation for calculating the generalized radiation impedance of the opening of a finite length duct with a spinning source inside is presented. The effect of interference between the duct apertures at its two ends is identified in the calculations of radiation impedance, reflection coefficient, and the far field radiation pattern. The results show that the degree of interference between the two ends reduces for high frequency waves and/or for long ducts. Further, the interference effects on the far field for spinning sound are more serious than those for non-spinning sound.     

Inversion for atmosphere duct parameters using real radar sea clutter

This paper addresses the problem of estimating the lower atmospheric refractivity (M profile) under nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled using five parameters and the horizontal structure is modeled using five parameters. The refractivity model is implemented with and without a priori constraint on the duct strength as might be derived from soundings or numerical weather-prediction models. An electromagnetic propagation model maps the refractivity structure into a replica field. Replica fields are compared with the observed clutter using a squared-error objective function. A global search for the 10 environmental parameters is performed using genetic algorithms. The inversion algorithm is implemented on the basis of S-band radar sea-clutter data from Wallops Island, Virginia (SPANDAR). Reference data are from range-dependent refractivity profiles obtained with a helicopter. The inversion is assessed (ⅰ) by comparing the propagation predicted from the radar-inferred refractivity profiles with that from the helicopter profiles, (ⅱ) by comparing the refractivity parameters from the helicopter soundings with those estimated. This technique could provide near-real-time estimation of ducting effects.     

等价分布源方法新发展

本文以广义Lighthill方程和广义Green函数为基础给出任意截面管道声传播计算模型,同时应用等价分布源方法建立了包含声衬影响的声传播模型,该方法避开了复杂的管道特征值计算,并在此基础上以积分变换发展了等价分布源方法,免去了声源及观察点匹配时产生的奇异性,使该方法大大简化,易于工程实际计算.此外,本文还给出了特殊截面管的算例.     

Finite element modeling of reverberation and transmission loss in shallow water waveguides with rough boundaries

A finite element model for the reverberation and propagation in a shallow water waveguide with a sandy bottom was calculated for five different environments at a center frequency of 250 Hz. The various environments included a rough water/sediment interface, a rough air/water interface, roughness at both interfaces and downward and upward refracting sound speed profiles with roughness at both interfaces. When compared to other models of reverberation such as ray theory, coupled modes, and parabolic equations, finite elements predicted higher levels of reverberation. At early times, this is due to the "fathometer" return, energy that is normally incident on the boundaries at zero range. At later times, the increased reverberation was due to high angle scattering paths between the two interfaces. Differences in reverberation levels among the environments indicated that scattered energy from the air/water interface is transmitted into the bottom at steep angles. This led to a large decrease in reverberation for a rough air/water interface relative to a rough water/sediment interface. Sound speed profile effects on reverberation were minimal at this frequency range. Calculations of the scintillation index of the different environments indicated that most of the reverberation was relatively Rayleigh-like with heavier tailed distributions at longer ranges.     

Influence of scattering, atmospheric refraction, and ground effect on sound propagation through a pine forest

Sound propagation through a forest is affected by the microclimate in the canopy, scattering by trunks and stems, and ground reflection. Each of these effects is such a strong contributor to the attenuation of sound that mutual interactions between the phenomena could become important. A sound propagation model for use in a forest has been developed that incorporates scattering from trunks and branches and atmospheric refraction by modifying the effective wave number in the Green's function parabolic equation model. The ground effect for a hard-backed pine straw layer is approximated as a local reaction impedance condition. Comparisons to experimental data are made for frequencies up to 4,200 Hz. Cumulative influences of the separate phenomena are examined. The method developed in this paper is compared to previously published methods. The overall comparison with spectral transmission data is good, suggesting that the model captures the necessary details.     

Optical paths involved in determining the scattering angle for the scattering algorithm developed in LOWTRAN7

This paper presents a part of the complete study [1] of the low-resolution atmospheric propagation model and computer code LOWTRAN7 developed by the U.S. Air Force Geophysics Laboratory [2]. It concerns the new parameters included in LOWTRAN7 to account for scattering when calculating the transmission and luminance.     

非视线散射大气光通信的光学天线

由于大气衰减的影响,非视线散射大气光通信需要使用光学天线以提高对光信号的采集能力,进而增加通信距离。针对非视线大气光通信的需求,利用ZEMAX软件对半球透镜、复合抛物面聚光器（CPC）和卡塞格伦望远镜等光学天线进行了性能分析。分析表明：半球透镜和CPC视场较大,增益值高。利用蒙特卡罗法模拟计算了一定条件下,非视线散射光通信在有无半球透镜或CPC作光学天线时到达探测元件的能量随通信距离的变化。结果表明：CPC聚光能力更强,适合作为非视线散射光通信的光学天线。     

Light scattering in disperse layers with a high concentration of optically soft particles

A model describing the propagation of radiation in disperse close-packed layers of optically soft particles is proposed. The model is based on the radiative transfer equation used for describing a light field in the multiple scattering regime and on the interference approximation for describing collective scattering effects; it also takes into account the Fresnel reflection at the layer boundaries. To describe the single-scattering characteristics, the Mie formulas are used. The model allows one to consider scattering in layers of any optical thickness. Calculations of the angular structure of the radiation leaving the layer and estimates of the errors of the calculations were performed. The possibility of forming a maximum at small scattering angles in media with correlated particles is shown. The theoretical results are in good agreement with the available experimental data.