Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica
Over the last two decades, spaceborne polarimetric synthetic aperture radar (PolSAR) has been widely used to penetrate sea ice surfaces to achieve fully polarimetric high-resolution imaging at all times of day and in a range of weather conditions. Model-based polarimetric decomposition is a powerful...
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MDPI AG
2023-06-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/15/12/3208 |
| _version_ | 1797592817591123968 |
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| author | Dong Li He Lu Yunhua Zhang |
| author_facet | Dong Li He Lu Yunhua Zhang |
| author_sort | Dong Li |
| collection | DOAJ |
| description | Over the last two decades, spaceborne polarimetric synthetic aperture radar (PolSAR) has been widely used to penetrate sea ice surfaces to achieve fully polarimetric high-resolution imaging at all times of day and in a range of weather conditions. Model-based polarimetric decomposition is a powerful tool used to extract useful physical and geometric information about sea ice from the matrix datasets acquired by PolSAR. The volume scattering of sea ice is usually modeled as the incoherent average of scatterings of a large volume of oriented ellipsoid particles that are uniformly distributed in 3D space. This uniform spatial distribution is often approximated as a uniform orientation distribution (UOD), i.e., the particles are uniformly oriented in all directions. This is achieved in the existing literature by ensuring the canting angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> and tilt angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi></mrow></semantics></math></inline-formula> of particles uniformly distributed in their respective ranges and introducing a factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo></mo><mrow><mi>τ</mi></mrow></mrow></mrow></semantics></math></inline-formula> in the ensemble average. However, we find this implementation of UOD is not always effective, while a real UOD can be realized by distributing the solid angles of particles uniformly in 3D space. By deriving the total solid angle of the canting-tilt cell spanned by particles and combining the differential relationship between solid angle and Euler angles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi></mrow></semantics></math></inline-formula>, a complete expression of the joint probability density function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mfenced separators="|"><mrow><mi>φ</mi><mo>,</mo><mi>τ</mi></mrow></mfenced></mrow></semantics></math></inline-formula> that can always ensure the uniform orientation of particles of sea ice is realized. By ensemble integrating the coherency matrix of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mi>φ</mi><mo>,</mo><mi>τ</mi></mrow></mfenced></mrow></semantics></math></inline-formula>-oriented particle with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mfenced separators="|"><mrow><mi>φ</mi><mo>,</mo><mi>τ</mi></mrow></mfenced></mrow></semantics></math></inline-formula>, a generalized modeling of the volume coherency matrix of 3D uniformly oriented spheroid particles is obtained, which covers factors such as radar observation geometry, particle shape, canting geometry, tilt geometry and transmission effect in a multiplicative way. The existing volume scattering models of sea ice constitute special cases. The performance of the model in the characterization of the volume behaviors was investigated via simulations on a volume of oblate and prolate particles with the differential reflectivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula>, polarimetric entropy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi></mrow></semantics></math></inline-formula> and scattering α angle as descriptors. Based on the model, several interesting orientation geometries were also studied, including the aligned orientation, complement tilt geometry and reflection symmetry, among which the complement tilt geometry is specifically highlighted. It involves three volume models that correspond to the horizontal tilt, vertical tilt and random tilt of particles within sea ice, respectively. To match the models to PolSAR data for adaptive decomposition, two selection strategies are provided. One is based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula>, and the other is based on the maximum power fitting. The scattering power that reduces the rank of coherency matrix by exactly one without violating the physical realizability condition is obtained to make full use of the polarimetric scattering information. Both the models and decomposition were finally validated on the Gaofen-3 PolSAR data of a young ice area in Prydz Bay, Antarctica. The adaptive decomposition result demonstrates not only the dominant vertical tilt preference of brine inclusions within sea ice, but also the subordinate random tilt preference and non-negligible horizontal tilt preference, which are consistent with the geometric selection mechanism that the c-axes of polycrystallines within sea ice would gradually align with depth. The experiment also indicates that, compared to the strategy based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula>, the maximum power fitting is preferable because it is entirely driven by the model and data and is independent of any empirical thresholds. Such soft thresholding enables this strategy to adaptively estimate the negative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula> offset introduced by the transmission effect, which provides a novel inversion of the refractive index of sea ice based on polarimetric model-based decomposition. |
| first_indexed | 2024-03-11T01:58:30Z |
| format | Article |
| id | doaj.art-f441ea4912d649e08d5a7481816fa81b |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-11T01:58:30Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-f441ea4912d649e08d5a7481816fa81b2023-11-18T12:27:59ZengMDPI AGRemote Sensing2072-42922023-06-011512320810.3390/rs15123208Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in AntarcticaDong Li0He Lu1Yunhua Zhang2CAS Key Laboratory of Microwave Remote Sensing, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, ChinaCAS Key Laboratory of Microwave Remote Sensing, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, ChinaCAS Key Laboratory of Microwave Remote Sensing, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, ChinaOver the last two decades, spaceborne polarimetric synthetic aperture radar (PolSAR) has been widely used to penetrate sea ice surfaces to achieve fully polarimetric high-resolution imaging at all times of day and in a range of weather conditions. Model-based polarimetric decomposition is a powerful tool used to extract useful physical and geometric information about sea ice from the matrix datasets acquired by PolSAR. The volume scattering of sea ice is usually modeled as the incoherent average of scatterings of a large volume of oriented ellipsoid particles that are uniformly distributed in 3D space. This uniform spatial distribution is often approximated as a uniform orientation distribution (UOD), i.e., the particles are uniformly oriented in all directions. This is achieved in the existing literature by ensuring the canting angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> and tilt angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi></mrow></semantics></math></inline-formula> of particles uniformly distributed in their respective ranges and introducing a factor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo></mo><mrow><mi>τ</mi></mrow></mrow></mrow></semantics></math></inline-formula> in the ensemble average. However, we find this implementation of UOD is not always effective, while a real UOD can be realized by distributing the solid angles of particles uniformly in 3D space. By deriving the total solid angle of the canting-tilt cell spanned by particles and combining the differential relationship between solid angle and Euler angles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi></mrow></semantics></math></inline-formula>, a complete expression of the joint probability density function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mfenced separators="|"><mrow><mi>φ</mi><mo>,</mo><mi>τ</mi></mrow></mfenced></mrow></semantics></math></inline-formula> that can always ensure the uniform orientation of particles of sea ice is realized. By ensemble integrating the coherency matrix of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mi>φ</mi><mo>,</mo><mi>τ</mi></mrow></mfenced></mrow></semantics></math></inline-formula>-oriented particle with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mfenced separators="|"><mrow><mi>φ</mi><mo>,</mo><mi>τ</mi></mrow></mfenced></mrow></semantics></math></inline-formula>, a generalized modeling of the volume coherency matrix of 3D uniformly oriented spheroid particles is obtained, which covers factors such as radar observation geometry, particle shape, canting geometry, tilt geometry and transmission effect in a multiplicative way. The existing volume scattering models of sea ice constitute special cases. The performance of the model in the characterization of the volume behaviors was investigated via simulations on a volume of oblate and prolate particles with the differential reflectivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula>, polarimetric entropy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi></mrow></semantics></math></inline-formula> and scattering α angle as descriptors. Based on the model, several interesting orientation geometries were also studied, including the aligned orientation, complement tilt geometry and reflection symmetry, among which the complement tilt geometry is specifically highlighted. It involves three volume models that correspond to the horizontal tilt, vertical tilt and random tilt of particles within sea ice, respectively. To match the models to PolSAR data for adaptive decomposition, two selection strategies are provided. One is based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula>, and the other is based on the maximum power fitting. The scattering power that reduces the rank of coherency matrix by exactly one without violating the physical realizability condition is obtained to make full use of the polarimetric scattering information. Both the models and decomposition were finally validated on the Gaofen-3 PolSAR data of a young ice area in Prydz Bay, Antarctica. The adaptive decomposition result demonstrates not only the dominant vertical tilt preference of brine inclusions within sea ice, but also the subordinate random tilt preference and non-negligible horizontal tilt preference, which are consistent with the geometric selection mechanism that the c-axes of polycrystallines within sea ice would gradually align with depth. The experiment also indicates that, compared to the strategy based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula>, the maximum power fitting is preferable because it is entirely driven by the model and data and is independent of any empirical thresholds. Such soft thresholding enables this strategy to adaptively estimate the negative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>D</mi><mi>R</mi></mrow></msub></mrow></semantics></math></inline-formula> offset introduced by the transmission effect, which provides a novel inversion of the refractive index of sea ice based on polarimetric model-based decomposition.https://www.mdpi.com/2072-4292/15/12/3208polarimetric decompositionradar polarimetrysynthetic aperture radarsea icevolume scattering model |
| spellingShingle | Dong Li He Lu Yunhua Zhang Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica Remote Sensing polarimetric decomposition radar polarimetry synthetic aperture radar sea ice volume scattering model |
| title | Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica |
| title_full | Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica |
| title_fullStr | Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica |
| title_full_unstemmed | Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica |
| title_short | Solid Angle Geometry-Based Modeling of Volume Scattering with Application in the Adaptive Decomposition of GF-3 Data of Sea Ice in Antarctica |
| title_sort | solid angle geometry based modeling of volume scattering with application in the adaptive decomposition of gf 3 data of sea ice in antarctica |
| topic | polarimetric decomposition radar polarimetry synthetic aperture radar sea ice volume scattering model |
| url | https://www.mdpi.com/2072-4292/15/12/3208 |
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