A theory of scintillation for two‐component power law irregularity spectra: Overview and numerical results

Carrano, Charles S.; Rino, C. L.

doi:10.1002/2015rs005903

Cited by 52 publications

(98 citation statements)

References 40 publications

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“…To complete the scintillation model Φ Δ ϕ ( q y ) must be specified. Following Carrano and Rino, we hypothesize a two‐component power‐law model with the implicit assumption that specifying the defining parameters compensates for the relation between the one‐dimensional phase SDF and the path‐integrated in situ electron density SDF. Formally,

Φ_{normalΔ ϕ} false(q_{y} false) = C_{p} ({, \begin{matrix} array q_{y}^{- p_{1}} & array for q_{y} \leq q_{0} \\ array q_{0}^{p_{2} - p_{1}} q_{y}^{- p_{2}} & array for q_{y} > q_{0} \end{matrix}),

where q 0 is the spatial frequency at which the power‐law index changes from p 1 to p 2 , and

C_{p} = \frac{4 π^{2} r_{e}^{2}}{k^{2}} false[l C 1 false] .

The meaning of the [ l C 1] parameter will be discussed in a later section.…”

Section: Phase‐screen Realizationsmentioning

confidence: 99%

“…The two‐dimensional theory admits a complete analytic characterization. From Carrano and Rino, the intensity SDF can be computed as follows:

I false(μ false) = 2 \int_{0}^{\infty} \exp ({}, - γ false(η, μ false)) \cos false(η μ false) d η,

where

γ false(η, μ false) = 16 true \int_{0}^{\infty} P false(χ false) \sin^{2} false(χ η false/ 2 false) \sin^{2} false(χ μ false/ 2 false) \frac{d χ}{2 π} .

Carrano and Rino developed a highly efficient algorithm for evaluating I ( μ ) as a function of the universal strength parameter

U = C_{p p} ({, \begin{matrix} array 1 & array for μ_{0} \geq 1 \\ array μ_{0}^{p_{2} - p_{1}} & array for μ_{0} < 1 \end{matrix}),

and p 1 , p 2 , and μ 0 .…”

Section: Phase Screen Theorymentioning

confidence: 99%

“…Recent results reported by Ghafoori and Skone show that physics‐based models can be used effectively for GNSS performance analysis. The GNSS scintillation model introduced in this paper uses a highly efficient implementation of the two‐dimensional phase‐screen theory described in Carrano and Rino . In the following sections, we summarize the essential results from the two‐dimensional phase‐screen theory and then derive the efficient GNSS model formulation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A compact multi‐frequency GNSS scintillation model

et al. 2018

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We present a scintillation model that generates complex scintillation realizations using two‐dimensional phase‐screen calculations. A compact parameter set simplifies the model. The parameters can be adjusted to reproduce statistically equivalent realizations of target multi‐frequency GNSS intensity and phase scintillation time series or defaulted to representative values. Geometric range and TEC inputs can be incorporated to generate realizations of baseband GNSS signals for processor performance evaluation. Selecting model parameters is guided by an efficient encapsulation of the two‐dimensional phase‐screen theory. Motion of the propagation path through ionospheric structure generates temporal variation. The phase‐screen theory incorporates space‐to‐time conversion via a ratio of the Fresnel scale to an effective scan velocity. A universal strength parameter adjusts the strength of the scintillation. The model is an encapsulation of results that have been used for GPS performance analysis work that is cited in the paper. A MATLAB implementation of the model with examples has been made available.

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Φ_{normalΔ ϕ} false(q_{y} false) = C_{p} ({, \begin{matrix} array q_{y}^{- p_{1}} & array for q_{y} \leq q_{0} \\ array q_{0}^{p_{2} - p_{1}} q_{y}^{- p_{2}} & array for q_{y} > q_{0} \end{matrix}),

where q 0 is the spatial frequency at which the power‐law index changes from p 1 to p 2 , and

C_{p} = \frac{4 π^{2} r_{e}^{2}}{k^{2}} false[l C 1 false] .

The meaning of the [ l C 1] parameter will be discussed in a later section.…”

Section: Phase‐screen Realizationsmentioning

confidence: 99%

“…The two‐dimensional theory admits a complete analytic characterization. From Carrano and Rino, the intensity SDF can be computed as follows:

I false(μ false) = 2 \int_{0}^{\infty} \exp ({}, - γ false(η, μ false)) \cos false(η μ false) d η,

where

γ false(η, μ false) = 16 true \int_{0}^{\infty} P false(χ false) \sin^{2} false(χ η false/ 2 false) \sin^{2} false(χ μ false/ 2 false) \frac{d χ}{2 π} .

Carrano and Rino developed a highly efficient algorithm for evaluating I ( μ ) as a function of the universal strength parameter

U = C_{p p} ({, \begin{matrix} array 1 & array for μ_{0} \geq 1 \\ array μ_{0}^{p_{2} - p_{1}} & array for μ_{0} < 1 \end{matrix}),

and p 1 , p 2 , and μ 0 .…”

Section: Phase Screen Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A compact multi‐frequency GNSS scintillation model

et al. 2018

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show abstract

“…However, configuration space realizations can be constructed by assigning a target one‐dimensional form to

φ_{N_{e}} ((), q_{y})

directly. Following the development in Carrano and Rino (), the following one‐dimensional analytic SDF will be used:

{normalΦ}_{N_{e}} false(q false) = C_{s} ({, \begin{matrix} array q^{- η_{1}} for q \leq q_{0} \\ array q_{0}^{η_{2} - η_{1}} q^{- η_{2}} for q > q_{0} \end{matrix}) .

…”

Section: Introductionmentioning

confidence: 99%

A Configuration Space Model for Intermediate‐Scale Ionospheric Structure

et al. 2018

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Stochastic ionospheric structure is characterized by spectral density functions (SDFs), which are formally the average intensity of Fourier transformations of the electron density structure. Structure elongation along magnetic field lines is typically accommodated by constraining contours of constant spatial correlation to field‐aligned ellipsoidal surfaces. Structure realizations are generated by imposing the square root of the SDF onto uncorrelated random Fourier modes. The approach has been used successfully for interpreting both in situ and remote propagation diagnostics. However, the only connection to the field‐aligned structures generated by the underlying instability mechanism is the correlation scale. This paper introduces a configuration space model that constructs realizations as summations of field‐aligned elemental striations with a prescribed scale and peak electron density. We show that by choosing the contributing scales according to a bifurcation rule and imposing a power law intensity scaling, the corresponding SDF closely approximates an inverse power law. Thus, configuration space realizations can be structured to reproduce prescribed or measured SDFs from one‐dimensional scans. Stochastic variation comes from an imposed random distribution of striation locations, which are defined by their intercept in a reference slice plane. To conform more directly to physics‐based simulations, the striations can be interpreted as voids in the background electron density. The model is designed to support propagation simulations with arbitrary propagation angles relative to the local magnetic field direction. Relations between in situ structure and diagnostic measurements as well as phase screen equivalence can be explored.

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“…For the two‐component spectrum, as R b decreases, n shifts toward the value obtained for a single‐component spectrum with the shallower slope m 1 = 2. This is expected from the variation of S 4 with R b (Carrano & Rino, ). These results show that n is a parameter that can be computed from observations to establish the nature of the irregularity spectra encountered by VHF and L‐band signals recorded at different locations.…”

Section: Theoretical Results For the Frequency Exponentmentioning

confidence: 60%

Signal Frequency Dependence of Ionospheric Scintillations: An Indicator of Irregularity Spectrum Characteristics

et al. 2019

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Multifrequency scintillation observations show that strong amplitude scintillations on very high frequency (VHF) signals are accompanied by weak L‐band scintillations near the dip equator and strong L‐band scintillations in equatorial ionization anomaly (EIA) region. For several decades this has been attributed to higher ambient plasma density in the EIA region. Recent work suggests that occurrence of stronger L‐band scintillations in the EIA region requires that the intermediate‐scale (~100 m to few km) ionospheric irregularity spectrum in this region be significantly shallower than that in the equatorial region. However, this has not been established so far. Signal frequency dependence of amplitude scintillations is characterized by the frequency exponent that determines the dependence on signal frequency of the S4 index: the standard deviation of normalized intensity fluctuations. In this paper, theoretical calculations of the frequency exponent for VHF and L‐band signals are carried out using different irregularity spectra and compared with observations in order to characterize power‐law irregularity spectra in different latitude zones. Intermediate‐scale irregularities in the equatorial and low‐latitude region, which are aligned with the geomagnetic field, are described by a two‐dimensional model. Model simulations show that the frequency exponent derived from S4 indices for VHF and L‐band signals is determined only by the characteristics of the irregularity spectrum and hence can be utilized to identify the nature of the power‐law irregularity spectrum. Frequency exponents computed using VHF and L‐band observations near the dip equator and EIA regions show distinct patterns, which clearly indicate steep and shallow irregularity spectra, respectively, in these regions.

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A theory of scintillation for two‐component power law irregularity spectra: Overview and numerical results

Cited by 52 publications

References 40 publications

A compact multi‐frequency GNSS scintillation model

A compact multi‐frequency GNSS scintillation model

A Configuration Space Model for Intermediate‐Scale Ionospheric Structure

Signal Frequency Dependence of Ionospheric Scintillations: An Indicator of Irregularity Spectrum Characteristics

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