Equatorial Ionospheric Scintillation Measurement in Advanced Land Observing Satellite Phased Array-Type L-Band Synthetic Aperture Radar Observations

Yifei Ji; Zhen Dong; Yongsheng Zhang; Feixiang Tang; Wenfei Mao; Haisheng Zhao; Zhengwen Xu; Qingjun Zhang; Bingji Zhao; Heli Gao

doi:10.1016/j.eng.2024.01.027

Engineering ›› 2025, Vol. 47 ›› Issue (4) :76 -92. DOI: 10.1016/j.eng.2024.01.027

Research Precise Positioning and Geoinformation Science—Article

research-article

Equatorial Ionospheric Scintillation Measurement in Advanced Land Observing Satellite Phased Array-Type L-Band Synthetic Aperture Radar Observations

Author information +

History +

PDF (5177KB)

Abstract

Amplitude stripes imposed by ionospheric scintillation have been frequently observed in many of the equatorial nighttime acquisitions of the Advanced Land Observing Satellite (ALOS) Phased Array-type L-band Synthetic Aperture Radar (PALSAR). This type of ionospheric artifact impedes PALSAR interferometric and polarimetric applications, and its formation cause, morphology, and negative influence have been deeply investigated. However, this artifact can provide an alternative opportunity in a positive way for probing and measuring ionosphere scintillation. In this paper, a methodology for measuring ionospheric scintillation parameters from PALSAR images with amplitude stripes is proposed. Firstly, sublook processing is beneficial for recovering the scattered stripes from a single-look complex image; the amplitude stripe pattern is extracted via band-rejection filtering in the frequency domain of the sublook image. Secondly, the amplitude spectrum density function (SDF) is estimated from the amplitude stripe pattern. Thirdly, a fitting scheme for measuring the scintillation strength and spectrum index is conducted between the estimated and theoretical long-wavelength SDFs. In addition, another key parameter, the scintillation index, can be directly measured from the amplitude stripe pattern or indirectly derived from the scintillation strength and spectrum index. The proposed methodology is fully demonstrated on two groups of PALSAR acquisitions in the presence of amplitude stripes. Self-validation is conducted by comparing the measured and derived scintillation index and by comparing the measurements of range lines and azimuth lines. Cross-validation is performed by comparing the PALSAR measurements with in situ Global Position System (GPS) measurements. The processing results demonstrate a powerful capability to robustly measure ionospheric scintillation parameters from space with high spatial resolution.

Graphical abstract

Keywords

Synthetic aperture radar / Ionospheric sounding / Ionospheric scintillation / Amplitude stripes / Global Position System ionospheric measurement

Cite this article

Download citation ▾

Yifei Ji, Zhen Dong, Yongsheng Zhang, Feixiang Tang, Wenfei Mao, Haisheng Zhao, Zhengwen Xu, Qingjun Zhang, Bingji Zhao, Heli Gao. Equatorial Ionospheric Scintillation Measurement in Advanced Land Observing Satellite Phased Array-Type L-Band Synthetic Aperture Radar Observations. Engineering, 2025, 47(4): 76-92 DOI:10.1016/j.eng.2024.01.027

登录浏览全文

4963

注册一个新账户忘记密码

1. Introduction

Low-frequency (L-band or lower) spaceborne synthetic aperture radar (SAR) systems have great advantages in observations of forest, biomass, water vapor, soil moisture, and deformation, but they are more susceptible to ionospheric effects than higher-frequency (S-, C-, and X-band) systems [1], [2], [3], [4]. Various artifacts caused by the large-scale background ionosphere have been captured in the products of the Advanced Land Observing Satellite (ALOS) Phased Array-type L-band SAR (PALSAR), such as polarimetric distortions [5], azimuth displacements [6], [7], interferometric streaks, and phase errors [8], [9].

In particular, the ionospheric scintillation imposed by anisotropic ionospheric irregularities (or turbulence) produces two types of artifacts in SAR images: amplitude stripes and azimuth defocusing [10]. The appearance of ionospheric artifacts is determined by the anisotropic elongation angle (or rotation angle in Ref. [10]), which represents the projected geomagnetic vector [11] or the orientation of the strongest correlation in the horizontal phase screen (PS) [10], [12], [13], [14], [15]. When the anisotropic elongation angle is small, amplitude stripes appear in SAR images accompanied by good imaging quality and interferometric coherence [10]. As the angle increases, the stripes gradually vanish and are replaced by another artifact, azimuth defocusing, which signifies serious imaging and interferometric degradation and is derived from the azimuth decorrelation induced by phase scintillation [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26].

This paper focuses on the artifact of amplitude stripes, whose formation cause, morphology, and negative influence have been investigated in sufficient detail. A SAR scintillation simulator (SAR-SS), comprising a two-dimensional (2D) PS generator and a 2D ionospheric transfer function (ITF) propagator, was developed to simulate this ionospheric artifact in SAR images [27]. By comparing the morphology of the ionospheric amplitude stripes in simulated SAR images and PALSAR real images, the validity of the SAR-SS was confirmed [27]. A statistical model was established to investigate the effect of amplitude scintillation on SAR imagery, and the results indicated that the amplitude stripes could enhance both the radar cross-section (RCS) and image contrast [28]. The appearance probability of amplitude stripes in PALSAR images over the South American continent during October 2010 was statistically analyzed, and it was found that 14% of the surveyed acquisitions and 74% of the surveyed days suffered from visible stripes [10]. The effects of anisotropic ionospheric scintillation on imaging and interferometric performances were simulated and examined in Ref. [10]. Stripe heading could be modeled as a function of the geomagnetic inclination, geomagnetic declination, geographic heading, look-down angle, squint angle, and PS height [10], [11], [12]. Geomagnetic inclination is a dominant factor that changes the stripe heading along the satellite track near the equator [12]. Furthermore, the amplitude stripes in L-band SAR images can induce polarimetric decomposition distortions and impede the terrain classification [29], bringing about serious interferometric streaks [30].

Scholars have attempted to mitigate the ionospheric amplitude stripes in SAR images [31], [32], [33]. A frequency domain approach was first proposed to identify and separate the spectral energy contributed by the amplitude stripes from the dominant energy of the surface backscatter using a spectral filter, followed by producing a stripe-corrected SAR image [31]. Using this approach to correct the amplitude stripes, the processing results of the surface classification of PALSAR full-polarimetric images were improved [32]. A combined approach using multilevel 2D discrete wavelet transform (DWT) and nonlinear Fourier transform (FT) was further proposed for polarimetric SAR images [33], which outperformed the prototype approach in Ref. [31]. An automatic procedure was devised for detecting the stripes based on prior information of the stripe orientation [34].

Based on the principle of RCS and image contrast enhancement induced by amplitude stripes, several approaches for measuring the scintillation index (S₄) were suggested, all of which required a comparison of disturbed and undisturbed images [28]. Using these approaches, applications for measuring ionospheric scintillation were further tested on PALSAR and PALSAR-2 images [35], [36]. An azimuth sub-band analysis method was proposed to detect ionosphere dynamics in sublooks [37]. The stripe drifting in azimuth sublooks was attributed to imaging geometry and ionospheric drifting; therefore, it could be utilized to estimate the ionospheric altitude and range-projected drifting velocity [11], [37], [38]. An interesting and useful conclusion was drawn in Ref. [11]: Namely, that the amplitude stripes could be sharpened by means of sublook processing, which was beneficial for ionospheric measurement.

A work by one of the authors of Ref. [34] presented the interesting idea of further applying the estimated stripe pattern to measure ionospheric scintillation parameters; this approach does not require an undisturbed reference SAR image and can extract more ionospheric scintillation parameters. This idea was briefly realized on several ALOS PALSAR images but was not fully validated using sufficient PALSAR data and exterior ionospheric measurements. Furthermore, the procedure did not consider sublooking processing, which demanded further consideration.

In this paper, a methodology is proposed for extracting the amplitude stripe pattern from sublook observations and further measuring ionospheric scintillation parameters, including the scintillation strength C_kL, spectrum index p, and scintillation index S₄. The steps of sublook processing and measuring the stripe heading from SAR images are specified and highlighted by comparison with the former work in Ref. [34]. Moreover, the methodology is fully examined on two sets of PALSAR data and is fully validated by comparing the measured and derived S₄ with in situ Global Position System (GPS) measurements.

This paper is organized as follows. It starts with a brief introduction of the theoretical background in Section 2. In Section 3, the principle of the proposed methodology is discussed in sufficient detail. Experiments on PALSAR data are conducted and validated in Section 4. We further discuss the experimental results in Section 5. Finally, the conclusion and prospect are presented in Section 6.

2. Theoretical background

2.1. PS theory

Based on the PS theory for weak scatter, ionospheric irregularities can be generally considered as a thin screen that changes the phase of propagating electromagnetic signals, and both multi-scattering and diffraction within the PS layer can be ignored [39], [40], [41]. Therefore, the phase fluctuation can be modeled as follows:

(1)

δ ϕ_{0} = - r_{e} λ \int δ n d l

where r_e is the classic electron radius, λ is the wavelength, and δn is the perturbation component of the local electron density, integrated along the propagating path l.

After passing through the ionosphere, the signals propagate in free space with decorrelated phase terms and mutually interfere, which generates a diffraction pattern in their arrivals at the surface. This procedure can be described by Kirchhoff’s diffraction formula. Under the forward scattering assumption, the received wave field (E(ρ)) can be modeled as follows [42]:

(2)

E (ρ) = \frac{j k E_{0}}{2 π ρ_{z}^{*}} \iint exp [j δ ϕ_{0} (ρ^{'}) - \frac{j k}{2 ρ_{z}^{*}} {|ρ - ρ^{'}|}^{2}] d^{2} ρ^{'}

where

E_{0}

is the initial wave electric field;

δ ϕ_{0} (ρ^{'})

is the phase fluctuation distribution versus the spatial vectors

ρ

and

ρ^{'}

in the transverse plane;

ρ_{z}^{*} = H_{i} sec θ_{i} (H_{r} - H_{i}) / H_{r}

signifies the modification factor for the propagation path of a spherical wave,

H_{i}

is the equivalent PS height,

θ_{i}

is the incident angle at the PS height,

H_{r}

is the radar height;

k = 2 π / λ

signifies the signal wavenumber; and j is an imaginary number.

Let Eq. (2) be written as follows [42]:

(3)

E (ρ) = exp [α (ρ) + j δ ϕ (ρ)]

with

(4)

α (ρ) = \frac{k}{2 π ρ_{z}^{*}} \int \int δ ϕ_{0} (ρ^{'}) cos [\frac{k {|ρ - ρ^{'}|}^{2}}{2 ρ_{z}^{*}}] d^{2} ρ^{'}

and

(5)

δ ϕ (ρ) = \frac{k}{2 π ρ_{z}^{*}} \int \int δ ϕ_{0} (ρ^{'}) sin [\frac{k {|ρ - ρ^{'}|}^{2}}{2 ρ_{z}^{*}}] d^{2} ρ^{'}

where

α (ρ)

is the logarithmic amplitude and

δ ϕ (ρ)

is the phase fluctuation after the diffraction. Notably, the diffraction scheme is driven by the phase fluctuation at the PS, inducing amplitude scintillation and changing the phase pattern.

2.2. Spectrum mechanism

The phase pattern on the PS can be generally described by a power law spectrum density function (SDF) with a form like κ⁻^p, where κ is the spatial wavenumber and p is the spectrum index. Rino’s spectrum mechanism is introduced in this paper to describe both the SDFs’ phase and intensity (or square amplitude) scintillations. The one-dimensional (1D) phase SDF (

S_{Φ}

) and 2D phase SDF (

S_{Φ}^{2 D}

) of the PS are modeled as follows [13], [27], [39]:

(6)

S_{Φ} (κ) = \frac{r_{e}^{2} λ^{2} sec θ_{i} G C_{s} L Γ (p / 2)}{2 \sqrt{π} Γ [(p + 1) / 2]} \times \frac{1}{{(κ_{0}^{2} + κ^{2})}^{p / 2}}

(7)

S_{Φ}^{2D} (κ_{x}, κ_{y}) = \frac{ab r_{e}^{2} λ^{2} {sec}^{2} θ_{i} C_{s} L}{{[κ_{0}^{2} + (A_{1} κ_{x}^{2} + A_{2} κ_{x} κ_{y} + A_{3} κ_{y}^{2})]}^{\frac{p + 1}{2}}}

where

(κ_{x}, κ_{y})

signifies the 2D wavenumber vector;

Γ (\cdot)

is the Gamma function;

κ_{0} = 2 π / L_{0}

is the wavenumber regarding the outer scale L₀;

C_{s} L = C_{k} L {(2 π / 1000)}^{p + 1}

, and C_kL is the vertical integrated turbulence strength at a 1 km scale; the anisotropic coefficients of A₁, A₂, and A₃ are related to two anisotropic elongation scales a and b, the incident angle

θ_{i}

, the squint angle

ψ_{i}

, the geomagnetic heading

δ_{B}

, and the geomagnetic inclination

θ_{B}

; and G is the geometric factor. Notably, the phase power law index of the 1D in situ SDF is one less than that of the 2D SDF, and the FT of the SDF signifies the spatial autocorrelation function [39]. We next use the 2D SDF to interpret the amplitude stripe morphology and use the 1D SDF for in situ measurement.

The diffraction procedure induces amplitude scintillation and changes the phase pattern on the PS. The 1D in situ SDFs of the phase (

S_{Φ}^{'}

) and amplitude scintillations (

S_{α}

) are modeled as follows [42]:

(8)

S_{Φ}^{'} (κ) = S_{Φ} (κ) {cos}^{2} (κ^{2} ρ_{z}^{*} / 2 k)

(9)

S_{α} (κ) = S_{Φ} (κ) {sin}^{2} (κ^{2} ρ_{z}^{*} / 2 k)

The former equation indicates that the SDF of the final phase pattern is modulated by a square cosinusoid, which implies that the diffraction can only change the higher frequency parts and has negligible influence on the phase pattern [14]. In contrast, the amplitude SDF is modulated by a square sinusoid in the latter equation, and spatial structures larger than the first Fresnel cutting scale become dominant in the amplitude pattern, contributing to the morphology of the amplitude stripes [13].

The scintillation index S₄ represents the fluctuating intensity (amplitude square), which can be modeled as follows [39]:

(10)

S_{4}^{2} = r_{e}^{2} λ^{2} sec θ_{i} C_{s} L {(\frac{λ ρ_{z}^{*}}{4 π})}^{p / 2 - 1 / 2} \frac{Γ (1.25 - p / 4) Γ (p / 2)}{2 π Γ (0.25 + p / 4) (p / 2 - 0.5) (p / 2 + 0.5)}

This formulation is valid for p values such that 1 < p < 5 [39].

2.3. Amplitude stripes in SAR images

Anisotropic ionospheric irregularities are rod-like (a ≫ b) in equatorial areas and sheet-like (a ≈ b) in auroral areas due to the interaction of the geomagnetic fields [28]. This paper focuses on the amplitude stripe artifact that is frequently observed in low-frequency spaceborne SAR images, which is caused by rod-like ionospheric regularities (typical cases of which occur near the equator); thus, sheet-like irregularities are not involved. As shown in Fig. 1, the amplitude error induced by the rod-like structure is elongated, and the elongation direction displays the strongest correlation, which is called the anisotropic elongation heading. Notably, the phase scintillation has the same elongation direction as the amplitude error.

If the anisotropic elongation angle (normal to the along-track direction) is close to zero, the amplitude errors regarding the ionospheric penetration points (IPPs) within the synthetic aperture tend to be gentle, thereby causing backscatter enhancement or attenuation of the target P₀. Due to the high correlation along the elongation direction, the amplitude errors of the targets along the projected elongation heading versus P₀ have a similar trend, and their backscatter will be uniformly changed. This is the cause of the bright–dark amplitude stripes projected onto SAR images; the stripe elongation angle is magnified due to the across-track extension (see the stripe heading in Fig. 1). When the anisotropic elongation angle increases, the amplitude errors within the synthetic aperture tend to fluctuate more violently with a worse correlation, which can disperse the stripe structure; thus, the stripes in SAR images are sparser than amplitude errors in an ionospheric amplitude screen (Fig. 1). Of course, if this angle continues to increase, the stripe artifact becomes invisible in a single-look-complex (SLC) image. Nevertheless, it is still possible to detect the stripe artifact in azimuth sublook images [11]. Fig. 2 presents two examples of PALSAR SLC and their sublook images, which were acquired across the Amazon on March 26, 2008 and across the South China Sea on March 8, 2011. All data related to the South China Sea and the Philippine Sea used in this study were obtained from non-disputed areas and are utilized exclusively for scientific research purposes. These examples demonstrate that the stripes become more visible and concentrated after sublook processing. According to Ref. [11], eight sublooks are sufficient for detecting the amplitude stripes, and this approach is adopted below.

Anisotropic elongation heading plays an important role in the morphology of amplitude stripes. The heading angle versus the geomagnetic north at the PS height can be modeled by A₁, A₂, and A₃ [15] or by the following [12]:

(11)

ϕ^{'} = \{\begin{matrix} \arccos (C / \sqrt{C^{2} + D^{2}}), D \geq 0 \\ - \arccos (C / \sqrt{C^{2} + D^{2}}), D < 0 \end{matrix}

where

(12)

C = - s i n θ_{i} c o s ψ_{i} s i n θ_{B} + c o s θ_{i} c o s θ_{B}

(13)

D = - s i n θ_{i} s i n ψ_{i} s i n θ_{B}

Accordingly, the anisotropic elongation heading angle (ϕ_a) versus the along-track direction of the SAR satellite (see the stripe heading on the PS denoted in Fig. 1) can be simply calculated by

(14)

ϕ_{a} = ϕ' - δ_{B} = ϕ' - (δ_{0} - ψ_{B})

where

δ_{B}

can be calculated by the difference in the geographic heading δ₀ and the geomagnetic declination angle ψ_B. A cross-track magnification is produced when the elongation heading is projected onto the Earth’s surface. Thus, the anisotropic elongation (ϕ₀) heading in the SAR image (see the stripe heading on the SAR image denoted in Fig. 1) can be derived by the following [12]:

(15)

ϕ_{0} = \arctan [\frac{H_{r}}{H_{r} - H_{i}} \tan (ϕ_{a})]

Fig. 3 describes two example groups of consecutive PALSAR acquisitions and plots the ALOS footprint and the illuminated scope on the ground and on the PS in longitude–latitude grids. The International Geomagnetic Reference Field (IGRF) is used to calculate

θ_{B}

and ψ_B based on the transformed longitudes and latitudes of the center IPPs at an empirical altitude of 350 km [20], [21]. The stripe heading ϕ₀ is then calculated using Eqs. (11), (12) and shown as contours in Fig. 3. It is evident that the calculated ϕ₀ is very consistent with the stripe heading observed in the SAR image; for example, the stripe heading of ALPSRP115537040 and ALPSRP272710270 is close to zero, where the zero contour of ϕ₀ just runs through the two scenes. Furthermore, as the absolute ϕ₀ increases, the amplitude stripes in the SAR image become less pronounced and more widely separated, which is consistent with the description in Ref. [10].

3. Methodology

The artifact of amplitude stripes in PALSAR images has a negative impact on interferometric and polarimetric applications [11], [30], [32], [33]; however, it also has a positive aspect—that of providing an alternative opportunity for measuring ionospheric scintillation parameters from PALSAR images [34]. It was reported that PALSAR images acquired at night around the equator often suffered from visible amplitude stripes [10], indicating that there were thousands of samples available for extracting ionospheric scintillation parameters and investigating equatorial ionospheric scintillation. The key is to extract the amplitude stripe pattern from SAR images and to estimate the scintillation parameters from the stripe pattern using a statistical model. A flowchart of the proposed methodology is shown in Fig. 4 and will be discussed below.

3.1. Extraction of the amplitude stripe pattern

As shown in Fig. 3, the amplitude stripe pattern in SAR SLC images becomes scattered or invisible when ϕ₀ increases, but it can be recovered and highlighted in azimuth sublooks. The appropriate number of azimuth sublooks is dependent on ϕ₀, where a larger ϕ₀ signifies that more sublooks are required. Furthermore, there is a tradeoff between spatial resolution and in-aperture correlation; thus, it is not suitable for the number of azimuth sublooks selected to be too large [11].

The frequency domain approach for correcting amplitude stripes from SAR images, as proposed in Ref. [31], is used to extract the amplitude stripe pattern from the sublook images. However, some important steps must be carefully conducted; otherwise, the ionospheric amplitude error will be poorly estimated. It is necessary to estimate the stripe heading beforehand so that its energy contribution can be automatically recognized in the frequency domain. Even though it can be calculated using Eqs. (11), (12) by means of the IGRF, the estimation accuracy is dependent on the precision of H_i and geomagnetic parameters, which is hardly satisfactory for extracting the amplitude stripe pattern [34]. As shown in Fig. 5(a), the stripe pattern appears as a strong ridge in the frequency domain, with an orientation perpendicular to the stripe heading in the image domain. In order to estimate the stripe heading, the mean power of each line through the zero point with respect to the presumed orientation from −90° to 90° is calculated and described in Fig. 5(b). The stripe heading can be simply determined at the orientation, where the mean power is the maximum (−9.84° estimated for the 1/8 sublook image of ALPSRP115537110). Furthermore, due to the fact that the stripe heading in a single image is not generally a constant, the variation scope of the stripe heading can be estimated according to a power threshold. Therefore, the ridge in Fig. 5(a) mainly occupies the orientation scope from −8.31° to −11.14° under a 5 dB threshold.

Image processing is further carried out. First, the logarithmic amplitude of the sublook image is taken to transform the stripe pattern from a multiplicative error to an additive error. To mitigate the edge effect of the FT, a double-sized image is generated and padded in both dimensions, with the original image and three mirror images in reverse order for all four sides [31], [34]. After conducting a 2D fast FT (FFT), a symmetric ridge appears in the frequency domain (Fig. 6(a)). According to an accurate estimation of the ridges’ orientation, the stripe energy is automatically distinguished in the frequency domain from the energy of the ground surface that is mostly distributed in low-frequency areas. Then, a group of symmetric consecutive Gaussian band-rejection filters can be built along the orientation of two ridges. The wavenumber coordinate of the center of the mth filters in range (

k_{c a}^{m}

) and azimuth (

k_{c r}^{m}

) can be modeled as follows:

(16)

\{\begin{matrix} k_{cr}^{m} = \pm d k_{r} cos {\hat{ϕ}}_{0} [r_{s} + (2 m - 1) r_{f}] \\ k_{ca}^{m} = \pm d k_{a} sin {\hat{ϕ}}_{0} [r_{s} + (2 m - 1) r_{f}] \end{matrix}

where

{\hat{ϕ}}_{0}

is the estimated stripe heading, dk_r and dk_a signify the azimuth and range wavenumber spacing, r_s is the pixel of the first filters apart from the zero point, and r_f is the radius of the band-rejection radius. Notably, the first filters should be separated by several pixels from the zero point, because the energy of the ground surface and objects is mainly distributed in the low-frequency domain. In addition, the filter radius r_f can be selected according to the scope of the stripe heading. More details on constructing band-rejection filters can be found in our former work [25]. The Gaussian band-rejection filter (

H_{gs}

) is then designed as follows:

(17)

H_{gs} (k_{r}, k_{a}) = 1 - \sum_{m = 1}^{M} \{exp [- \frac{{(k_{r} - k_{cr}^{m})}^{2} + {(k_{a} - k_{ca}^{m})}^{2}}{2 r_{f}^{2}}]\}

where M is the number of filters, k_a and k_r signify the azimuth and range wavenumbers of each pixel, respectively. As shown in Fig. 6(b), the scope of two ridges is absolutely masked by the designed filter.

Multiplying the FT of the mirror padding logarithmic amplitude with the designed filter, we finally obtain the amplitude of the striped-corrected sublook image and the extracted stripes after the operational steps of the inverse FFT (IFFT) and image cutting (Fig. 7). Indeed, it is difficult to absolutely separate the amplitude stripe pattern from the ground surface and objects, because the energy of some ground objects (e.g., rivers) blends in with the ridge regions in the frequency domain. As a result, there are still some components of ground objects in the extracted stripe pattern. This indicates that the estimation accuracy of the stripe pattern depends on the type of ground surface, and it is easier to obtain a good performance for scenes with nearly uniformly distributed RCS (e.g., the ocean scenes in Fig. 2(b)).

3.2. Estimation and fitting of the amplitude SDF

To further measure the ionospheric scintillation parameters from the extracted amplitude pattern, it is necessary to artificially select qualified estimates (e.g., the areas below the red line in Fig. 7) and remove unqualified estimates (e.g., the areas above the red line) that are seriously contaminated by ground objects. It is generally reasonable for two-way measurement to be interpreted by means of the reciprocity principle as the square of one-way measurement [43]. Therefore, the selected qualified estimates of the two-way ionospheric scintillation amplitude errors (the equivalent one-way intensity errors) of the range lines can be applied to directly measure the one-way S₄, which can be calculated as follows:

(18)

{\hat{S}}_{4}^{i} = \sqrt{\frac{〈{\hat{I}}_{i}^{2}〉 - {〈{\hat{I}}_{i}〉}^{2}}{{〈{\hat{I}}_{i}〉}^{2}}}

where

〈\cdot〉

is the mathematical expectation;

{\hat{S}}_{4}^{i}

is the measured value from the one-way intensity estimate

{\hat{I}}_{i}

of the ith range line,

i = 1, 2, \dots, N_{eff}

, and

N_{eff}

is the effective number of selected range lines.

Furthermore, the amplitude SDF of the ith range line (

{\hat{S}}_{α}^{i}

) can be estimated from the scintillation amplitude errors using a periodogram [14]:

(19)

{\hat{S}}_{α}^{i} (κ_{e f f}) = |{[FFT (\frac{\ln \sqrt{{\hat{A}}_{i}}}{N_{r}})]}^{2} \frac{2 π}{Δ κ_{e f f}}|

(20)

Δ κ_{e ff} = \frac{2 π}{s_{r}} \times \frac{H_{r}}{H_{r} - H_{i}} \times \frac{1}{cos ϕ_{a}}

where κ_eff is the effective across-track wavenumber on the PS plane spaced by Δκ_eff, which can be estimated based on the PS height H_i and the anisotropic elongation heading ϕ_a; s_r is the ground range size of the SAR image; N_r is the effective range samples; and

{\hat{A}}_{i}

is the estimated two-way amplitude error. The reason for using the range line instead of the azimuth line for the SDF estimation should be particularly emphasized. Due to the fact that the real anisotropic elongation heading is generally close to zero, the effective along-track wavenumber spacing may be infinite or very large due to the factor of

1 / sin ϕ_{a}

; this can cause considerable errors when estimating the amplitude SDF. The factor of

1 / cos ϕ_{a}

in Eq. (20) reflects the effect of anisotropic parameters on the 1D in situ measurement; moreover, cosϕ_a ≈ 1 because the absolute value of ϕ_a is lower than 15° for most PALSAR images suffering from amplitude stripes. Of course, the estimated SDF for a single range line is very sensitive to noise and the components of residual ground objects (Fig. 8(a)). The SDFs can be averaged by all effective range lines to further depress the influence of noise and ground objects (Fig. 8(b)), on the assumption that the ionospheric scintillation parameters do not change significantly.

As shown in Eqs. (6), (9), the theoretical SDF depends on the scintillation strength C_kL, the spectrum index p, and the outer scale L₀. Because the frequency of the outer scale is generally much lower than the Fresnel break frequency, the amplitude SDF is not sensitive to the outer scale. Therefore, it is difficult to estimate L₀ from the extracted amplitude errors, and an empirical value of L₀ = 10 km will be used next. In fact, the spectrum index p determines the descending rate in the higher-frequency areas of the SDF, which has been used to estimate p from the estimated phase SDF [14]. Nevertheless, it can be observed in Fig. 8 that the amplitude SDF in the higher-frequency areas is elevated due to the influence of the residual ground components, which means that the higher-frequency part of the SDF is not suitable for the following fitting. Furthermore, the band-rejection filters can cause a truncation effect on the measured SDF. Finally, a measured amplitude SDF with a frequency lower than the Fresnel break frequency or with a longer wavelength is fitted with the theoretical SDF modeled in Eq. (9) to estimate C_kL and p (

(\hat{C_{k} L}, \hat{p})

), which is presented as follows:

(21)

(\hat{C_{k} L}, \hat{p}) = \arg \min_{C_{k} L, p} ∥\bar{{\hat{S}}_{α}^{i} (κ_{e ff})} - S_{α} (κ_{e ff})∥, \frac{κ_{e f f} ρ_{z}^{*}}{2 k} < \frac{π}{2}

The one-way S₄ can be derived from Eq. (10) based on the estimated C_kL and p, and forms a comparison with the direct measurement using Eq. (18), which is beneficial for realizing self-validation. As shown in Fig. 8, both the fitted SDFs for a single line and those averaged across all effective range lines are perfectly consistent with the measured SDFs in the lower-frequency areas, and the derived S₄ is extremely close to the directly measured S₄. Moreover, the robustness of the SDF estimation is improved by means of the averaging processing because the power of noise and ground objects are greatly suppressed.

It should be noted that the extracted amplitude errors are useful for SAR radiation calibration and for ionospheric scintillation measurement, where the latter is highlighted in this paper. It should be further clarified that the extracted amplitude errors cannot be further utilized for correcting imaging and interferometry phase errors, because the transformation from the amplitude stripe to the phase pattern is not yet fully formulated and realized.

The PS height is assumed to be 350 km, and ϕ_a is about 4.92°, as calculated using Eq. (15). The blue dashed line refers to the Fresnel break frequency, where

κ_{e f f} ρ_{z}^{*} / 2 k

in Eq. (9) equals π∕2, and the green dashed line refers to the truncated frequency due to the band-rejection filters.

4. Experimental results and validation

4.1. Extraction and correction of amplitude stripes

The procedure described above for measuring ionospheric scintillation parameters from SAR images is fully examined in this section using the two groups of ALOS PALSAR acquisitions mentioned in Fig. 3. Sublook processing is implemented to recover scattered stripes with a large ϕ_a from the SLC images. For the convenience of subsequent processing, a 1/8 sublook image is uniformly produced for each PALSAR SLC image. As shown in Fig. 9, both the SLC and sublook consecutive images are jointed in the satellite along-track direction, and the sublook images (especially the two sides) show more visible and concentrated stripes. It is notable that bright streaks arise in a range of sea areas after sublook processing, and we suppose that these originate from the backscatter of sea waves fluctuating in different visual angles (or sublooks). Because these streaks have almost no influence on scintillation measurement, we provide no further details on them. The jointed pattern of the amplitude stripes seems to be similar to the simulation result of the equatorial plasma bubbles environment studied in Refs. [44], [45].

Through the steps of estimating the stripe heading, transforming into a mirror-padding logarithmic amplitude, and constructing a band-rejection filter along two ridges in the frequency domain, the stripe-corrected sublook images are largely isolated from the stripe pattern (the third and bottom maps in each sub-part of Fig. 9). However, the components of some rivers and islands blend with the extracted stripe patterns of the Amazon and ocean scenes, respectively. This case is addressed carefully later for its significant influence on ionospheric scintillation measurement.

4.2. Estimation of the PS height

The amplitude SDF estimation is conducted once the amplitude stripe pattern is extracted from each sublook image. However, determining the effective wavenumber κ_eff demands knowledge of the PS height H_i and the anisotropic elongation heading ϕ_a, according to Eq. (20); ϕ_a is also related to H_i, so the key is to estimate H_i. Using the empirical value of 350 km is a possible compromise for simplified operation, but it may produce extra errors in estimated SDFs and measured results [14]. The drifting characteristic of the amplitude stripe pattern in different sublooks has been utilized to estimate H_i, but both the principle and operation procedure are rather complicated, and the estimates lose robustness just before the stripe pattern disappears [11].

In this paper, a novel strategy is devised for estimating H_i. Its principle is based on the relationship between the stripe heading and the anisotropic elongation angle shown in Eq. (15). The stripe heading accompanied by the distributed scope can be accurately estimated from each sublook image; the results, which are shown in Fig. 10, have also been used for stripe extraction and correction. The anisotropic elongation angle ϕ_a at the PS height can be derived using IGRF but requires an initial value of H_i to determine the illuminated center on the PS. Here, we adopt an empirical value to calculate ϕ_a (blue circles in Fig. 10). Because the PS height within a reasonable range will not significantly change the value of ϕ_a, H_i can be determined by a fitting process in which the parameter-constrained ϕ₀ mostly approximates to the estimated stripe heading

{\hat{ϕ}}_{0}

for all sublook images.

(22)

{\hat{H}}_{i} = \min_{H_{i}} ∥ϕ_{0} (H_{i}, ϕ_{a}) - {\hat{ϕ}}_{0}∥

In practice, only the variation tendency of ϕ₀ and

{\hat{ϕ}}_{0}

regarding the scene number is compared, and the constant components of ϕ₀ and

{\hat{ϕ}}_{0}

should be dropped in the fitting process. For the two groups of PALSAR images, H_i is first estimated as 312 and 346 km, respectively; both are physically adequate values, which can be iterated as the second initial value for calculating ϕ_a. The second estimates of H_i are 309 and 345 km, respectively, which achieve convergence if given a deviation threshold of 5 km. The fitted ϕ₀ (red lines in Fig. 10) are very consistent with the averages and variation scopes of the stripe heading measured from the PALSAR images, which confirms the effectiveness of the estimated results. It should be noted that the

{\hat{H}}_{i}

estimated in this paper is an equivalent global estimate for one group of SAR images, while the method in Ref. [11] measures it for each SAR image.

4.3. Ionospheric scintillation measurement in the along-track direction

Once H_i and ϕ_a are determined, the amplitude SDF can be estimated in the range lines using Eq. (19), and those range lines that are seriously contaminated by the residual ground energy need to be artificially removed. The SDF averaged across qualified range lines is used to measure C_kL and p using the fitting process in Eq. (21) and to further derive S₄ using Eq. (10). Furthermore, the selected range lines can be employed to directly measure the one-way S₄ based on Eq. (18).

Therefore, a set of ionospheric scintillation parameters (C_kL, p, and S₄) can be measured for each sublook image; the measurement results for the two groups of PALSAR images are presented in Fig. 11, Fig. 12. For the acquisitions across the South China Sea and Philippine Sea on March 8, 2011, log₁₀(C_kL) and S₄ range from 33.8 to 35.4 and from 0.05 to 0.32, respectively, which implies a much stronger scintillation event than the Amazon acquisitions on March 26, 2008. It can be observed that C_kL has a similar variation trend as S₄ on the whole, and that p ranges from 3.2 to 4.5 for both datasets. Evidently, there is a visible inverse correlation between the estimated p and C_kL, and this phenomenon might align well with the conclusion drawn in Ref. [46]. More importantly, the derived one-way S₄ maintains remarkable consistency with the directly measured average and scope (Fig. 12), which verifies the validity of the proposed methodology from the first level.

4.4. Comparison of ionospheric scintillation measurement without sublook processing

It is notable that the above results from the ionospheric scintillation measurement are extracted from the PALSAR 1/8 sublook images, instead of from the SLC images. In order to further highlight the importance of sublook processing, we also perform ionospheric scintillation measurement on the SLC images with regard to the ocean scene; the measured results for C_kL, p, and S₄ are presented in Fig. 13.

It can be observed that the measured p values are saturated to infinitely approach the boundary of p < 5 for the images with a larger stripe heading, such as the example image of Fig. 2(b). Furthermore, the measured S₄ values are consistent with the derived S₄ only when the scene numbers are around ALPSRP272710400, where the stripe heading is nearly zero, whereas they are no longer consistent for these images with a larger stripe heading. This finding indicates that measuring the ionospheric scintillation parameters from the stripe pattern without sublook processing on SAR images will lose validity as the stripe heading increases. The main reason for this is that the stripe pattern will be scattered and sometimes even vanish (Fig. 2) in SLC images due to azimuth decorrelation as the stripe heading increases. As a result, the stripe pattern extracted from SLC images is not the real pattern imposed by amplitude scintillation and thus does not satisfy the theoretical spectrum mechanism presented in Eqs. (6), (7), (8), (9), (10) any longer. The purpose of sublook processing is to retrieve the real stripe pattern from SLC images so as to make the subsequent procedure meaningful. A comparison between the results of Fig. 13 and those of Figs. 11(b) and 12(b) shows that the methodology with sublook processing is obviously more robust and effective, thereby demonstrating its significance.

4.5. Refined 2D measurement with higher resolution

The above experiments produce a group of equivalent global estimates for a SAR image, which is based on the premise that C_kL, p, and S₄ will not significantly change within a single observation. However, the scintillation parameters actually fluctuate dramatically within some individual scenes; for example, the variation scope of S₄ even reaches 0.07 with a fiducial probability of 68.3% (green blocks of ALPSRP272710370 in Fig. 12).

Thus, refined measurement must be further carried out for a more detailed and higher-resolution distribution of the ionospheric scintillation parameters in 2D space. A block strategy is adopted for the 2D image. Given that the amplitude SDF estimation is conducted using range lines, the sub-block image demands sufficient range samples—that is, sparse blocks and measurements in range. Three of the above PALSAR acquisitions are selected for refined 2D measurement, all of which have a wide variation scope of S₄ and a nearly uniformly distributed RCS. The extracted stripe patterns of the three scenes are presented in the left column of Fig. 14; they are further separated into 16 × 4 subblocks in the azimuth and range, respectively, and each is used for measuring C_kL, p, and S₄. The measurement results after the 2D interpolation processing are presented in the right four columns of Fig. 14, depicting more detailed characteristics. It can be observed that C_kL and S₄ mostly decline in the line of sight and in the along-track direction for ALPSRP115537130 and ALPSRP272710370, and rise in the along-track direction for ALPSRP272710330, on the whole. Similar to the 1D results shown in Fig. 12, the derived and measured 2D S₄ has a consistent spatial distribution. Furthermore, the variation range of C_kL, p, and S₄ in Fig. 14 contains the corresponding 1D results of three scenes in Fig. 11, Fig. 12.

Refined 2D measurement is carried out for the whole group of ocean scenes (28 consecutive images). However, some scenes with islands require special processing because the extracted stripe pattern of some sub-blocks is seriously contaminated, indicating that bad estimates of the ionospheric scintillation parameters will be achieved. These bad estimates can be easily detected by setting a basic threshold and substituting by the mean of the qualified estimates in neighboring subblocks. Fig. 15 compares the S₄ curves in the along-track direction of the 1D and 2D measurements (from four range sub-blocks), indicating the consistency of the overall variation tendency. The results of the 2D measurement of the derived one-way S₄ after the along-track splicing and 2D interpolation are presented in Fig. 16, providing more details both along track and across track; the variation tendency in the along-track direction is similar to the results in Fig. 12(b).

4.6. Self-validation using measurements of azimuth lines

Ionospheric scintillation measurement based on the extracted amplitude pattern can also be conducted in azimuth lines; the corresponding SDF estimation (

{\hat{S}}_{α}^{q}

) is presented as follows:

(23)

{\hat{S}}_{α}^{q} (κ_{e ff}^{'}) = |{[FFT (\frac{\ln \sqrt{{\hat{A}}_{q}}}{N_{a}})]}^{2} \frac{2 π}{Δ κ_{e ff}^{'}}|

(24)

Δ κ_{e f f}^{'} = \frac{2 π}{s_{a}} \times \frac{v_{i}}{v_{g} sin ϕ_{a}}

where

κ_{e ff}^{'}

is the effective across-track wavenumber at the PS plane spaced by

Δ κ_{e ff}^{'}

, N_a is the effective azimuth samples, s_a is the azimuth size of the SAR image, v_i is the beam-scanning velocity at the PS, v_g is the ground velocity, and

{\hat{A}}_{q}

signifies the qth azimuth lines. For the low-Earth-orbit SAR system, the condition v_g ≈ v_i is satisfied. The fitting process of azimuth lines is similar to that of range lines shown in Eq. (21).

According to Eq. (24), when ϕ_a is close to zero,

Δ κ_{e ff}^{'}

becomes very large or even infinite, which causes a condition in which the estimated SDF is moving and mainly distributed in the high-frequency domain. Given that the high-frequency part of the estimated SDF is not suitable for the fitting process, due to the considerable residual ground components, measurements of azimuth lines are limited on the condition of ϕ_a ≈ 0, but they can still be used for self-validation despite this defect.

The SDF estimation and fitting results of range and azimuth lines for the two images are presented in Fig. 17. The usable part of the estimated SDF in the low-frequency domain of the azimuth lines is shorter than that of the range lines, which fits with the theoretical analysis. Furthermore, the fitted SDF and measurement results for the C_kL, p, and C_kL of the azimuth lines are similar to those of the range lines. Measurement experiments of azimuth lines are further conducted for the two groups of PALSAR acquisitions; the results for the one-way S₄ are presented in Fig. 18. The results indicate that the measurements of azimuth lines are extremely consistent with those of range lines, unless ϕ_a is close to zero, which verifies the validity of the proposed methodology from the second level.

4.7. Cross-validation using GPS measurement

Two comparison experiments of the derived and measured S₄ and of measurements of range lines and azimuth lines were designed above for self-validation based on SAR images, which largely confirmed the validity of the proposed methodology. Comparing the measurement results with those from traditional ionospheric scintillation measurement based on ground GPS receivers is beneficial for both cross-validation and highlighting the advantages of our methodology. Here, the measurement results of the Haikou Station (20°N, 110°E) of the China Research Institute of Radiowave Propagation are compared with those from the PALSAR acquisitions of the ocean scene. The one-way S₄ of different GPS satellites, along with both GPS and SAR satellite footprints on the PS at the equivalent height of 345 km, is depicted in Fig. 19. Considering that the SAR images were acquired from 22:37 to 22:41 local time (LT), the GPS measurements within the two hours from 22:00 to 24:00 LT are displayed, which include nine sets of consecutive measurements from different GPS satellites. It should be noted that the footprints of the GPS satellite “⑨” highlighted by a red dashed rectangle just passed through the SAR footprints on the PS. Thus, this set of consecutive measurements is analyzed in particular; the variation curves of the measured S₄ and elevation angle versus the LT are presented in Fig. 20. It can be observed that the time windows of the GPS measurements and SAR acquisitions do not overlap but are very close, with an interval of less than 10 min. The measured one-way S₄ from the GPS receiver reaches about 0.7, which on the whole seems larger than that from SAR images.

Nevertheless, GPS measurements cannot be directly used for comparison with the PALSAR measurements due to the system difference. According to Eq. (10), the theoretical one-way S₄ is also related to the wavelength λ, the incident angle θ_i on the PS, and the modified propagation path

ρ_{z}^{*}

in addition to C_kL and p, and

ρ_{z}^{*}

depends on θ_i, H_i, and the satellite height H_r. Therefore, λ, θ_i, and H_r should be uniformized in order to realize a comparison of the S₄ measured by different systems. These related parameters of GPS and PALSAR are summarized in Table 1. Although the height of the GPS satellite “⑨” in a high Earth orbit is not accurately calculated, its

ρ_{z}^{*}

can be approximated as follows:

(25)

ρ_{z}^{*} = \frac{H_{i} (H_{r} - H_{i}) cos θ_{i}}{H_{r}} \approx H_{i} cos θ_{i}, if H_{i} ≪ H_{r}

This approximation is also valid for other GPS satellites. Therefore, the one-way S₄ measured by GPS satellites (

{\tilde{S}}_{4}^{GPS}

) can be adjusted to the wavelength (λ^PALSAR), incident angle (θ_i^PALSAR), and radar height (H_r^PALSAR) of the PALSAR, as well as the wavelength of GPS satellites (λ^GPS), which is derived by the following:

(26)

{\tilde{S}}_{4}^{GPS} = {(\frac{λ^{PALSAR}}{λ^{GPS}})}^{\frac{p + 3}{4}} {(\frac{sec θ_{i}^{PALSAR}}{sec θ_{i}^{GPS}})}^{\frac{p + 1}{4}} {(\frac{H_{r}^{PALSAR} - H_{i}}{H_{r}^{PALSAR}})}^{\frac{p - 1}{4}} S_{4}^{GPS}

The average of the measured spectrum index (

\bar{p} \approx 4

) shown in Fig. 11(b) will be adopted for the calculation of

{\tilde{S}}_{4}^{GPS}

. The adjusted GPS S₄, which is lower than the original results, is presented in Fig. 21, where the derived PALSAR S₄ measured in the along-track direction and 2D space is depicted. It can be observed that the adjusted S₄ of the GPS satellite “⑨” is broadly comparable with the PALSAR S₄ near the GPS footprints. Fig. 22 gives a description of the adjusted S₄ of the GPS satellite “⑨” versus the LT; the average of the later 14 measurements is very close to the derived S₄ from the three PALSAR images. The slight difference mainly originates from the varying p and from the fact that the measured time of the GPS and PALSAR is not exactly coincident. Therefore, the drifting and temporally varying characteristics of the ionospheric irregularity structures can differentiate the measurement results. The results in both Fig. 21, Fig. 22 confirm the validity of the proposed methodology from the third level.

Furthermore, compared with traditional GPS measurement, three advantages of the SAR-based measurement should be emphasized. Firstly, the variation tendency of the derived S₄ from PALSAR images is much smoother in the along-track direction (Fig. 12, Fig. 21), while the GPS-measured S₄ fluctuates dramatically in the along-track direction (Fig. 20, Fig. 22). This indicates that the proposed methodology can realize more robust ionospheric scintillation measurement. Secondly, it takes a longer time (a minute) to accumulate enough GPS signals contaminated by ionosphere scintillation for each calculation of S₄, whereas the rate of the PALSAR-derived S₄ is less than 10 s per measurement, which can be further improved by adopting an azimuth block for SAR images. The spatial resolution of the measurements can also be refined by means of the 2D block strategy (Fig. 16). The above two points demonstrate that the SAR-based measurement provides a higher spatial resolution. Thirdly, ionospheric irregularities are actually drifting with a velocity of up to 100 m∙s⁻¹ near the equator [22], which implies that the drifting distance reaches about 6 km for the duration of each GPS measurement (60 s) and more than 200 km during a set of consecutive measurements (36 min for the GPS satellite “⑨”). Thus, the GPS-measured S₄ reflects the spatiotemporal coupling ionospheric irregularities. Compared with high-Earth-orbit GPS satellites, the beam-tracking velocity of the low-Earth-orbit ALOS PALSAR, of up to several kilometers per second, is much greater than the drifting velocity of ionospheric irregularities [22]. The drifting distance is about 1 km during a single PALSAR scene, which satisfies the “frozen field” assumption. As a result, the SAR-based measurement decouples the drifting and spatially distributed ionospheric irregularities, and the measured parameters simply reflect the spatial distribution of ionospheric irregularities. Of course, the temporal variation of the ionospheric irregularities can be detected from the drifting stripe pattern of different sublooks [11].

5. Discussion

5.1. Overview of the experimental procedure and results

A methodology for measuring ionospheric scintillation parameters (C_kL, p, and S₄) from PALSAR images with stripe amplitudes is proposed. Sublook processing is the first key step, which aims to recover the scattered or invisible stripes from the SLC image. By searching the direction with the maximum power in the frequency domain, the stripe heading is estimated from each sublook image. A group of band-rejection filters is constructed and implemented, based on the estimated stripe heading, to separate the stripe pattern from the ground surface and objects. Qualified amplitude estimates of the range lines are selected to directly measure the one-way S₄ and estimate the amplitude SDF; the averaged SDF is then further applied to a fitting procedure to estimate C_kL and p. Finally, the one-way S₄ can be calculated based on the estimated C_kL and p.

Two groups of the consecutive PALSAR images, acquired across the Amazon and ocean scenes, respectively, are used to sufficiently examine the validity of the proposed methodology. The stripe pattern is successfully detected in the sublook images and is mostly estimated, except for river and island areas. Based on the estimated along-track stripe heading and the anisotropic elongation angle (at the ionospheric PS) derived using IGRF, an iterative fitting processing for measuring the PS height is designed and tested, finally achieving convergence at 309 and 345 km for the two groups of PALSAR images. The estimated PS height is a key for the SDF estimation. The curves of the variation tendencies of C_kL, p, and S₄ are depicted in the along-track: C_kL reaches a maximum of 34.3 and 35.3 for the two groups and has a similar variation trend as S₄, which reaches a maximum of 0.12 and 0.33, respectively; p ranges from 3.2 to 4.5, and its variation tendency presents an inverse correlation with C_kL. In comparison with the measurement results from the SLC images, the significance of the sublook processing and the great superiority of the proposed methodology are emphasized. Refined 2D measurement with higher resolution is realized by the sub-block measurements and interpolation, providing more details in both the along track and the across track direcctions.

All estimates of H_i, C_kL, p, and S₄ are physically adequate values. The measurement validity has been sufficiently confirmed from the three levels. Firstly, the derived S₄ from the estimated C_kL and p is perfectly consistent with the directly measured S₄, both in along-track and 2D measurements. Secondly, these parameters can be theoretically measured in azimuth lines, and the measurement results are extremely consistent with those of the range lines, except for the case in which the anisotropic elongation angle is close to zero. Thirdly, GPS measurements of S₄ from the Haikou Station are applied and modified to adjust to the carrier frequency, radar height, and incident angle of ALOS PALSAR. The adjusted S₄ from the closest GPS satellite “⑨,” with an average value of 0.1532, is broadly comparable with the derived S₄ of 0.1616, 0.1439, and 0.1908 from ALPSRP272710380, ALPSRP272710390, and ALPSRP272710400. The former two levels refer to the self-validation using the PALSAR image itself, whereas the last level refers to the cross-validation using exterior measurements.

5.2. Highlight of the proposed methodology

Compared with traditional GPS measurement, SAR-based measurement has the advantages of greater robustness and higher spatial resolution. In detail, our methodology produces more stable measurements, whereas GPS results violently fluctuate even after a smoothing operation. Furthermore, the rate of SAR-based measurement can reach an order higher than per second using the azimuth block, which is much higher than the rate of GPS measurement (i.e., per minute). Moreover, SAR-based measurement can even achieve across-track resolution using the 2D block, and the along-track resolution can be further improved using an azimuth block. In addition, the SAR payload operating in the low-Earth orbit tracks much faster than the GPS satellite, so it takes less than 10 s to illuminate a single belt, during which ionospheric irregularities can be reasonably considered as a frozen structure. Therefore, the proposed methodology has the great advantages of decoupling spatially distributed and temporally drifting characteristics and of providing a simple description of spatially distributed and temporally frozen ionospheric irregularities.

6. Conclusion and prospect

Spaceborne L-band SAR systems, such as ALOS PALSAR and ALOS-2 PALSAR-2, have exhibited great advantages in disaster monitoring, natural resource exploration, and global forest surveys. At the same time, however, the carrier frequency of the L-band brings about the adverse factor of significant ionospheric effects. Amplitude stripes are one of the significant ionospheric artifacts frequently observed in many of the PALSAR equatorial nighttime acquisitions and can hamper high-precision imaging and the polarimetric and interferometric measurements of geographic and geophysical processes. Nevertheless, thousands of PALSAR images suffering from the artifact of amplitude stripes carry a wealth of ionospheric scintillation information, making ionospheric scintillation detection and measurement feasible.

This paper provided a reliable technique for ionospheric scintillation measurement based on SAR images with visible amplitude stripes. It also presented an application example of the technique’s capability to provide detailed information of ionospheric scintillation parameters, which grants more robustness and higher spatial resolution than traditional GPS measurement. Furthermore, the paper demonstrated that the SAR-based measurement of ionospheric scintillation is an interesting and promising research subject and a powerful application of space-based microwave remote sensing. In the near future, we will further expand the application and investigate dynamic state of the ionosphere using different sublooks. Once thousands of ALOS PALSAR images with amplitude stripes or other L-band SAR (e.g., ALOS-2 PALSAR-2 and Lutan-1) images are used, global distribution can be achieved in order to depict the situation and variation tendency of ionospheric scintillation on large spatiotemporal scales.

CRediT authorship contribution statement

Yifei Ji initiated the experiments and wrote the manuscript; Yongsheng Zhang and Zhen Dong contributed to the conception of the study; Feixiang Tang conducted the experiments; Wenfei Mao provided revision suggestion; Zhengwen Xu and Haisheng Zhao provided the data and performed the data analyses; Qingjun Zhang, Bingji Zhao, and Heli Gao helped perform the analysis with constructive discussions.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported partly by the National Natural Science Foundation of China (NSFC) (62101568 and 62371460), the Scientific Research Program of the National University of Defense Technology (ZK21-06), and the Taishan Scholars of Shandong Province (ts20190968). The authors would like to thank the Japan Aerospace Exploration Agency for providing the ALOS PALSAR data. The authors are also grateful for the China Research Institute of Radiowave Propagation to provide GPS measurements of ionospheric scintillation from the Haikou Station.

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Ishimaru A, Kuga Y, Liu J, Kim Y, Freeman T.Ionospheric effects on synthetic aperture radar at 100 MHz to 2 GHz.Radio Sci 1999; 34(1):257-268.

[2]	Xu ZW, Wu J, Wu ZS.A survey of ionosphere effects on space-based radar.Waves Random Media 2004; 14(2):S189.

[3]	Belcher DP.Theoretical limits on SAR imposed by the ionosphere.IET Radar Sonar Navig 2008; 2(6):435-448.

[4]	Meyer FJ.Performance requirements for ionospheric correction of low-frequency SAR data.IEEE Trans Geosci Remote Sens 2011; 49(10):3694-3702.

[5]	Meyer FJ, Nicoll JB.Prediction, detection, and correction of Faraday rotation in full-polarimetric L-band SAR data.IEEE Trans Geosci Remote Sens 2008; 46(10):3076-3086.

[6]	Meyer F, Bamler R, Jakowski N, Fritz T.The potential of low-frequency SAR systems for mapping ionospheric TEC distributions.IEEE Geosci Remote Sens Lett 2006; 3(4):560-564.

[7]	Yang Z, Zhang Q, Ding X, Chen W.Analysis of the quality of daily DEM generation with geosynchronous InSAR.Engineering 2020; 6(8):913-918.

[8]	Liao H, Meyer FJ, Scheuchl B, Mouginot J, Joughin I, Rignot E.Ionospheric correction of InSAR data for accurate ice velocity measurement at polar regions.Remote Sens Environ 2018; 209:166-180.

[9]	Zhang B, Ding X, Amelung F, Wang C, Xu W, Zhu W, et al.Impact of ionosphere on InSAR observation and coseismic slip inversion: improved slip model for the 2010 Maule, Chile, earthquake.Remote Sens Environ 2021; 267:112733.

[10]	Meyer FJ, Chotoo K, Chotoo SD, Huxtable BD, Carrano CS.The influence of equatorial scintillation on L-band SAR image quality and phase.IEEE Trans Geosci Remote Sens 2016; 54(2):869-880.

[11]	Kim JS, Papathanassiou KP, Sato H, Quegan S.Detection and estimation of equatorial spread F scintillations using synthetic aperture radar.IEEE Trans Geosci Remote Sens 2017; 55(12):6713-6725.

[12]	Ji Y, Zhang Y, Zhang Q, Dong Z.Comments on “the influence of equatorial scintillation on L-band SAR image quality and phase”.IEEE Trans Geosci Remote Sens 2019; 57(9):7300-7301.

[13]	Ji Y, Zhang Y, Dong Z, Zhang Q, Li D, Yao B.Impacts of ionospheric irregularities on L-band geosynchronous synthetic aperture radar.IEEE Trans Geosci Remote Sens 2020; 58(6):3941-3954.

[14]	Ji Y, Dong Z, Zhang Y, Zhang Q, Yu L, Qin B.Measuring ionospheric scintillation parameters from SAR images using phase gradient autofocus: a case study.IEEE Trans Geosci Remote Sens 2022; 60:5200212.

[15]	Ji Y, Dong Z, Zhang Y, Zhang Q.An autofocus approach with applications to ionospheric scintillation compensation for spaceborne SAR images.IEEE Trans Aerosp Electron Syst 2022; 58(2):989-1004.

[16]	Xu ZW, Wu J, Wu ZS.Potential effects of the ionosphere on space-based SAR imaging.IEEE Trans Antenna Propag 2008; 56(7):1968-1975.

[17]	Wang C, Zhang M, Xu ZW, Chen C, Sheng DS.Effects of anisotropic ionospheric irregularities on space-borne SAR imaging.IEEE Trans Antenna Propag 2014; 62(9):4664-4673.

[18]	Wang C, Zhang M, Xu ZW, Chen C, Guo LX.Cubic phase distortion and irregular degradation on SAR imaging due to the ionosphere.IEEE Trans Geosci Remote Sens 2015; 53(6):3442-3451.

[19]	Hu C, Li Y, Dong X, Wang R, Ao D.Performance analysis of L-band geosynchronous SAR imaging in the presence of ionospheric scintillation.IEEE Trans Geosci Remote Sens 2017; 55(1):159-172.

[20]	Mannix CR, Belcher DP, Cannon PS.Measurement of ionospheric scintillation parameters from SAR images using corner reflectors.IEEE Trans Geosci Remote Sens 2017; 55(12):6695-6702.

[21]	Belcher DP, Mannix CR, Cannon PS.Measurement of the ionospheric scintillation parameter C_kL from SAR images of clutter.IEEE Trans Geosci Remote Sens 2017; 55(10):5937-5943.

[22]	Ji Y, Zhang Q, Zhang Y, Dong Z.L-band geosynchronous SAR imaging degradations imposed by ionospheric irregularities.Sci China Inf Sci 2017; 60:060308.

[23]	Ji Y, Zhang Q, Zhang Y, Dong Z, Yao B.Spaceborne P-band SAR imaging degradation by anisotropic ionospheric irregularities: a comprehensive numerical study.IEEE Trans Geosci Remote Sens 2020; 58(8):5516-5526.

[24]	Ji Y, Dong Z, Zhang Y, Zhang Q, Yao B.Extended scintillation phase gradient autofocus in future spaceborne P-band SAR mission.Sci China Inf Sci 2021; 64:212303.

[25]	Ji Y, Yu C, Zhang Q, Dong Z, Zhang Y, Wang Y.An ionospheric phase screen projection method of phase gradient autofocus in spaceborne SAR.IEEE Geosci Remote Sens Lett 2022; 19:4504205.

[26]	Tang F, Ji Y, Zhang Y, Dong Z, Wang Z, Zhang Q, et al.Drifting ionospheric scintillation simulation for L-band geosynchronous SAR.IEEE J Sel Top Appl Earth Obs Remote Sens 2023; 17:842-854.

[27]	Carrano CS, Groves KM, Caton RG.Simulating the impacts of ionospheric scintillation on L band SAR image formation.Radio Sci 2012; 47(4):1-14.

[28]	Belcher DP, Cannon PS.Amplitude scintillation effects on SAR.IET Radar Sonar Navig 2014; 8(6):658-666.

[29]	Mohanty S, Singh G.Improved POLSAR model-based decomposition interpretation under scintillation conditions.IEEE Trans Geosci Remote Sens 2019; 57(10):7567-7578.

[30]	Gomba G, de F Zan.Bayesian data combination for the estimation of ionospheric effects in SAR interferograms.IEEE Trans Geosci Remote Sens 2017; 55(11):6582-6593.

[31]	Roth AP, Huxtable BD, Chotoo K, Chotoo SD, Caton RG.Detection and mitigation of ionospheric stripes in PALSAR data.In: Proceedings of the 2012 IEEE International Geoscience and Remote Sensing Symposium; 2012 Jul 22–27; Munich, Germany. Piscataway: IEE E; 2012. p. 1621–4.

[32]	Gama FF, Wiederkehr NC, Bispo PC.Removal of ionospheric effects from Sigma naught images of the ALOS/PALSAR-2 satellite.Remote Sens 2022; 14(4):962.

[33]	Mohanty S, Khati U, Singh G, Chandrasekharb E.Correction of amplitude scintillation effect in fully polarimetric SAR coherency matrix data.ISPRS J Photogramm Remote Sens 2020; 164:184-199.

[34]	Gan N, Ji Y, Tang F, Zhang Y, Dong Z.Correcting and measuring ionospheric scintillation amplitude stripes in L-band SAR images.IEEE Geosci Remote Sens Lett 2022; 19:4515505.

[35]	Monhanty S, Singh G, Carrano CS, Sripathi S.Ionospheric scintillation observation using space-borne synthetic aperture radar data.Radio Sci 2018; 53(10):1187-1202.

[36]	Monhanty S, Carrano CS, Singh G.Effect of anisotropy on ionospheric scintillations observed by SAR.IEEE Trans Geosci Remote Sens 2019; 57(9):6888-6899.

[37]	Kim JS, Papathanassiou K.SAR observation of ionosphere using range/azimuth sub-bands.In: Proceedings of the 10th European Conference on Synthetic Aperture Radar; 2014 Jun 3–5; Berlin, Germany. Frankfurt: VD E; 2014.

[38]	Kim JS, Sato H, Papathanassiou K.Estimation of drift of equatorial ionosphere of post sunset-sector by means of low frequency space-borne SAR.In: Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium; 2016 Jul 10–15; Beijing, China. Piscataway: IEE E; 2016. p. 6946–9.

[39]	Rino CL.A power law phase screen model for ionospheric scintillation: 1. Weak scatter.Radio Sci 1979; 14(6):1135-1145.

[40]	Rino CL.A power law phase screen model for ionospheric scintillation: 2. Strong scatter.Radio Sci 1979; 14(6):1147-1155.

[41]	Rino CL.The theory of scintillation with applications in remote sensing.Wiley & Sons, Inc., Hoboken (2011)

[42]	Yeh KC, Liu CH.Radio wave scintillations in the ionosphere.Proc IEEE 1982; 70(4):324-360.

[43]	Rino CL.Double-passage radar cross section enhancements.Radio Sci 1994; 29(2):495-501.

[44]	Rino C, Yokoyama T, Carrano C.Dynamic spectral characteristics of high-resolution simulated equatorial plasma bubbles.Prog Earth Planet Sci 2018; 5(83):1-13.

[45]	Rino C, Yokoyama T, Carrano C.A three-dimensional stochastic structure model derived from high-resolution isolated equatorial plasma bubble simulations.Earth Planets Space 2023; 75(1):64.

[46]	Rino C, Carrano C.On the characterization of intermediate-scale ionospheric structure.Radio Sci 2018; 53(11):1316-1327.

RIGHTS & PERMISSIONS

THE AUTHOR

PDF (5177KB)

2646

Accesses

Citation

Detail

Sections

Recommended

Browse

Authors & reviewers

About the journal

Abstract

Graphical abstract

Keywords

Cite this article

1. Introduction

2. Theoretical background

2.1. PS theory

2.2. Spectrum mechanism

2.3. Amplitude stripes in SAR images

3. Methodology

3.1. Extraction of the amplitude stripe pattern

3.2. Estimation and fitting of the amplitude SDF

4. Experimental results and validation

4.1. Extraction and correction of amplitude stripes

4.2. Estimation of the PS height

4.3. Ionospheric scintillation measurement in the along-track direction

4.4. Comparison of ionospheric scintillation measurement without sublook processing

4.5. Refined 2D measurement with higher resolution

4.6. Self-validation using measurements of azimuth lines

4.7. Cross-validation using GPS measurement

5. Discussion

5.1. Overview of the experimental procedure and results

5.2. Highlight of the proposed methodology

6. Conclusion and prospect

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgments

References

RIGHTS & PERMISSIONS