Comparison of 2D and 3D Electromagnetic Approaches to Predict Tropospheric Turbulence Effects in Clear Sky Conditions

Fabbro, Vincent; Féral, Laurent

doi:10.1109/tap.2012.2207070

Cited by 18 publications

(35 citation statements)

References 16 publications

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“…The classical assumption is then to consider that the dimensional reduction lies in a cross section of the real medium along the longitudinal plane ℘. From a spectral point of view, this leads to define

S_{normalΔ N_{e}}^{2 normalD} ((), \overset{true\to}{K})

as the integral of

S_{normalΔ N_{e}}^{3 normalD} ((), \overset{true\to}{K})

along the dimension transverse to ℘, i.e., the dimension disregarded by the reduction 3‐D/2‐D [ Fabbro and Féral , ]. As an illustration but without loss of generality, if the dimensional reduction is conducted along the plane ℘ = ( X , Z ) defined in Figure , then

S_{normalΔ N_{e}}^{2 normalD} ((), \overset{true\to}{K}) = S_{normalΔ N_{e}}^{2 normalD} ((),, K_{X}, K_{Z})

is given by

S_{normalΔ N_{e}}^{2 normalD} ((),, K_{X}, K_{Z}) = true {true\int}_{- \infty}^{+ \infty} d K_{Y} S_{normalΔ N_{e}}^{3 normalD} ((),,, K_{X}, K_{Y}, K_{Z}) .

…”

Section: Statistical Description Of Ionospheric Irregularitiesmentioning

confidence: 99%

Validity of 2‐D electromagnetic approaches to estimate log‐amplitude and phase variances due to 3‐D ionospheric irregularities

2017

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To limit the computation time and the computer resource, 2‐D numerical approaches such as 2‐D parabolic wave equation (2‐D PWE) associated with 1‐D multiple phase screens (1‐D MPS) are classically used to estimate ionospheric scintillation effects on radio wave propagation. However, in the ionosphere, the turbulent fluctuations of the electron density responsible for the scintillation effects are clearly a three‐dimensional process. This paper quantitatively assesses the errors potentially induced by the 3‐D to 2‐D dimensional reduction to predict ionospheric effects in terms of log‐amplitude and phase variances. To that purpose, the ionospheric electron density fluctuations are described by an anisotropic turbulent spectrum with three axes of anisotropy. On the one hand, considering four typical configurations (two equatorial and two polar radio links), scintillation effects are evaluated numerically, using 3‐D and 2‐D PWE‐MPS numerical techniques. Some consequences of the dimensional reduction are then qualitatively discussed. On the other hand, an analytical framework that solves the 3‐D and 2‐D propagation equations in the line‐of‐sight coordinate system is proposed. Under weak scattering assumption, it allows assessing analytically the consequences of the dimensional reduction whatever the geometry of the transionospheric radio link and, finally, allows 2‐D numerical schemes to be used advisedly for the prediction of ionospheric scintillation effects.

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S_{normalΔ N_{e}}^{2 normalD} ((), \overset{true\to}{K})

as the integral of

S_{normalΔ N_{e}}^{3 normalD} ((), \overset{true\to}{K})

S_{normalΔ N_{e}}^{2 normalD} ((), \overset{true\to}{K}) = S_{normalΔ N_{e}}^{2 normalD} ((),, K_{X}, K_{Z})

is given by

S_{normalΔ N_{e}}^{2 normalD} ((),, K_{X}, K_{Z}) = true {true\int}_{- \infty}^{+ \infty} d K_{Y} S_{normalΔ N_{e}}^{3 normalD} ((),,, K_{X}, K_{Y}, K_{Z}) .

…”

Section: Statistical Description Of Ionospheric Irregularitiesmentioning

confidence: 99%

Validity of 2‐D electromagnetic approaches to estimate log‐amplitude and phase variances due to 3‐D ionospheric irregularities

2017

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“…The constraint of applying a 2D propagation scheme to predict 3D turbulence effects has been discussed [26]. The phase variance of the 2D model is slightly overestimated.…”

Section: Refractive-index Fluctuationmentioning

confidence: 99%

Ducting and Turbulence Effects on Radio-Wave Propagation in an Atmospheric Boundary Layer

Chou¹,

Kiang²

2014

PIER B

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Abstract-The split-step Fourier (SSF) algorithm is applied to simulate the propagation of radio waves in an atmospheric duct. The refractive-index fluctuation in the ducts is assumed to follow a twodimensional Kolmogorov power spectrum, which is derived from its three-dimensional counterpart via the Wiener-Khinchin theorem. The measured profiles of temperature, humidity and wind speed in the Gulf area on April 28, 1996, are used to derive the average refractive index and the scaling parameters in order to estimate the outer scale and the structure constant of turbulence in the atmospheric boundary layer (ABL). Simulation results show significant turbulence effects above sea in daytime, under stable conditions, which are attributed to the presence of atmospheric ducts. Weak turbulence effects are observed over lands in daytime, under unstable conditions, in which the high surface temperature prevents the formation of ducts.

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“…The PWE-MPS is a resolution of the scalar wave Helmholtz equation only considering forward propagation and taking into account turbulence effect via phase screen generations. For more details, the reader should refer to [10] and [2]. The refractive index is decomposed in n(x, y, z) = n 0 (x, y, z) + n 1 (x, y, z), with n 0 (x, y, z) the stable component of the modified refractive index, and n 1 (x, y, z) the turbulent component of the refractive index.…”

Section: Turbulent Tropospherementioning

confidence: 99%

“…E(x 0 , y, z)e −j(k y y+k z z) e j(k y y+k z z) (2) where along x the range step is δx, y and z are the transverse coordinates, k y and k z are the spatial wave number dual of y and z in Fourier space. For one step forward, the turbulent propagation index n 1 is integrated over the propagation step by generation of a phase screen φ (y, z) [10]:…”

Section: Turbulent Tropospherementioning

confidence: 99%

“…2D and 3D PWE-MPS method allow generating electromagnetic field realisations in terms of amplitude and phase. 2D or 3D fields can be computed but 2D resolution induces a slight underestimation of log-amplitude variance in Fresnel regime [2,10]. The antenna pattern can be considered in the modelling, and variations of C n ² or L o along the propagation path can be taken into account.…”

Section: Turbulent Tropospherementioning

confidence: 99%

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Scintillation modelling in troposphere using Multiple Phase Screen

Fabbro

Jeannin

Djafri

et al. 2013

Space Communications

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Microwaves propagation modelling in clear air troposphere (i.e. without rain) is investigated. Large scale variations of refractivity are computed from mesoscale meteorological modelling. Small scale variations are deduced from large scale considering that the inertial regime of Kolmogorov spectrum is established. The propagation effects are estimated applying launching ray to take into account large scale refractivity effects and resolution of Parabolic Wave Equation with Multiple PhaseScreen technique for small scale. The proposed approach has been evaluated versus earth satellite measurements of log-amplitude scintillation measured at Louvain-la-Neuve.

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Comparison of 2D and 3D Electromagnetic Approaches to Predict Tropospheric Turbulence Effects in Clear Sky Conditions

Cited by 18 publications

References 16 publications

Validity of 2‐D electromagnetic approaches to estimate log‐amplitude and phase variances due to 3‐D ionospheric irregularities

Validity of 2‐D electromagnetic approaches to estimate log‐amplitude and phase variances due to 3‐D ionospheric irregularities

Ducting and Turbulence Effects on Radio-Wave Propagation in an Atmospheric Boundary Layer

Scintillation modelling in troposphere using Multiple Phase Screen

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