Sea ice complex dielectric constant modeling and scattering characteristic analysis method based on very high frequency band

Abstract

The invention belongs to the technical field of sea ice parameter detection, and particularly relates to a sea ice complex dielectric constant modeling and scattering characteristic analysis method based on a very high frequency band, and the method comprises the specific steps: collecting basic physical parameters of various types of sea ice, including sea ice salt content, sea ice temperature and surface roughness parameters; a physical parameter database is constructed according to sea ice type classification; fitting saline water cell volume ratios according to temperature intervals to obtain saline water cell volume ratio data of different sea ice types; a single-component Cole-Cole model is adopted to calculate the complex dielectric constants of the pure ice and the saline water cells respectively, and the sea ice overall complex dielectric constant is calculated on the basis of the dielectric constants of the pure ice and the saline water cells through a Maxwell-Gardt mixed formula; constructing a volume scattering coefficient model based on a Rayleigh scattering theory and calculating a volume scattering coefficient; and constructing a surface scattering coefficient model and calculating a surface scattering coefficient based on a small disturbance model and an initialized polarization mode.

Description

Technical Field

[0001] This invention belongs to the field of sea ice parameter detection technology, and in particular relates to a method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the very high frequency band. Background Technology

[0002] Sea ice, a key component of the Earth's climate system, plays an indispensable role in global energy balance and material cycling. By regulating heat exchange between the atmosphere and ocean, it directly affects global thermal balance and marine ecological stability, and even has a profound impact on global climate patterns. Sea ice of different thicknesses and types produces unique scattering signals under the influence of electromagnetic waves. Accurately obtaining sea ice thickness information is a crucial prerequisite for understanding sea ice change mechanisms and predicting climate change. By analyzing these signal differences, precise inversion of sea ice thickness can be achieved, thereby improving inversion accuracy.

[0003] Currently, sea ice research is mostly concentrated in the microwave frequency band (such as Ku and C bands), where a relatively mature theoretical and applied system has been formed. There is also some exploration of the very low frequency band, but research in the very high frequency band is still relatively scarce. Research in this frequency band is of particular significance: on the one hand, its electromagnetic waves can penetrate sea ice to a greater depth, reaching thick sea ice (thickness ≥ 2m) to probe its internal structure, providing the possibility of revealing the relationship between sea ice physical properties and thickness; on the other hand, the mechanism of electromagnetic scattering of sea ice in this frequency band and its quantitative relationship with sea ice parameters have not yet formed a systematic understanding, and there is an urgent need to supplement relevant research through theoretical modeling and experimental verification in order to fully realize the potential of this frequency band in sea ice thickness inversion. Summary of the Invention

[0004] In view of this, in order to solve the problems of insufficient penetration of microwave frequency band into thick sea ice and lack of modeling of dielectric and scattering of sea ice in VHF band in existing sea ice detection, this invention provides a method for modeling the complex dielectric constant of sea ice and analyzing its scattering characteristics based on VHF band. It does not rely on traditional microwave frequency band models and can accurately characterize the electromagnetic properties of sea ice in this frequency band, laying the foundation for sea ice parameter inversion.

[0005] The technical solution for implementing the present invention is as follows: A method for modeling the complex permittivity and analyzing the scattering characteristics of sea ice based on the VHF band, the specific process of which is as follows: Database construction: Collect basic physical parameters of various types of sea ice, including sea ice salinity. Sea ice temperature The surface roughness parameters were collected, and a physical parameter database was constructed according to sea ice type; the proportion of brine cell volume was fitted for different temperature ranges. Data on the percentage of saline cell volume for different sea ice types were obtained. Complex permittivity calculation: The complex permittivity of pure ice and brine cells was calculated separately using the single-component Cole-Cole model. The overall complex permittivity of sea ice was calculated based on the permittivity of pure ice and brine cells using the Maxwell-Garnett mixing formula. Sea ice scattering coefficient calculation: A volume scattering coefficient model is constructed based on Rayleigh scattering theory and the volume scattering coefficient is calculated; a surface scattering coefficient model is constructed based on a small perturbation model and the polarization mode is initialized and the surface scattering coefficient is calculated.

[0006] Optionally, this invention selects thin annual ice (TFYI), annual ice (FYI), and multi-year ice (MYI) from the World Meteorological Organization's sea ice classification as research objects.

[0007] Optionally, this invention uses the Frankenstein and Garner empirical formula to calculate the volume fraction of saline cells. for: .

[0008] Optionally, the complex permittivity of the pure ice and saline cells described in this invention is:

[0009] in, It is the high-frequency limiting dielectric constant. It is the low-frequency limiting dielectric constant. It is the angular frequency of the electromagnetic wave; For relaxation time, The vacuum permittivity, DC resistivity; The relaxation index, It represents the imaginary unit.

[0010] Optionally, the relaxation index of the present invention can be 0 < <1.

[0011] Optionally, in calculating the overall complex permittivity of sea ice, the present invention treats the tiny brine cells and bubbles within the sea ice as ideal spherical particles, and only considers the contribution of the brine cells to the complex permittivity of sea ice in the calculation. for:

[0012] Among them, the matrix dielectric constant Take the dielectric constant of pure ice; the dielectric constant of particles Determine the dielectric constant of the saline cell.

[0013] Optionally, the volume scattering coefficient of the medium in this invention... for:

[0014]

[0015] in, It is the thickness of the medium; It is the angle of refraction in the medium; It is the extinction coefficient of the medium; It is the unidirectional loss factor of the medium. It is the volume scattering coefficient that ignores multiple reflections between particles in the mixed medium.

[0016] Optionally, the volume scattering coefficient of the present invention for:

[0017] in, It is the number of scattering particles per unit volume; It is the volume fraction of the scattered particles; The scattering cross section of a single scattering particle. To initialize the radius of the scattering particles.

[0018] Optionally, the surface scattering coefficient of the present invention for:

[0019] in, It is a polarization mode, including HH polarization and VV polarization, Indicates the polarization term; It is the angle of incidence; The wave number of electromagnetic waves in a vacuum; For the relevant length; This is the root mean square height.

[0020] Optionally, the present invention Under-polarization term The expression is:

[0021] Under-polarization term The expression is:

[0022] in, The complex permittivity is given by the sea ice background.

[0023] Beneficial effects: This invention provides a method for modeling the complex permittivity and analyzing the scattering characteristics of sea ice based on the VHF band. It is the first method to construct a research system for the electromagnetic properties of sea ice adapted to the VHF band, overcoming the technical limitations of traditional microwave bands in penetrating thick sea ice and filling the gap in dielectric modeling and scattering analysis of sea ice in this band. This method abandons the Matzler empirical formula, which is only effective in the microwave band, and uses a single-component Cole-Cole model to accurately describe the dielectric relaxation characteristics of pure ice and brine cells. It combines the Maxwell-Garnett mixture formula to quantify the influence of the brine cell volume ratio. Simultaneously, it models the microstructure differences of thin one-year ice (TFYI), one-year ice (FYI), and multi-year ice (MYI), without relying on a fixed and uniform simplified model, and can dynamically model dielectric properties according to sea ice type. Furthermore, this method constructs volume scattering and surface scattering coefficient calculation models through Rayleigh scattering theory and small perturbation models, respectively. In the VHF band, the small perturbation model has a better fit between wavelength and scale of sea ice surface roughness than the Kirchhoff model. Attached Figure Description

[0024] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A schematic diagram of the layered structure of sea ice; Figure 2 The graph shows the variation of penetration depth of different sea ice and saline cells with incident wave frequency. The black dashed line represents saline, the blue solid line represents TFYI, the red solid line represents FYI, and the green area represents the range of penetration depth variation of MYI. Figure 3 for VV A comparison of surface scattering coefficients of sea ice under polarization, where the green line represents the surface scattering coefficient of MYI, the red line represents the surface scattering coefficient of FYI, and the blue line represents the surface scattering coefficient of TFYI. Figure 4 for HH A comparison of surface scattering coefficients of sea ice under polarization, where the green line represents the surface scattering coefficient of MYI, the red line represents the surface scattering coefficient of FYI, and the blue line represents the surface scattering coefficient of TFYI. Detailed Implementation

[0026] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0027] It should be noted that, unless otherwise specified, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0028] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0029] This embodiment presents a method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the very high frequency band (VHF). The VHF band is specifically 30~300MHz. This band was chosen because its electromagnetic waves have deep penetration into thick sea ice (thickness ≥2m) and are different from the microwave bands that are the focus of existing research. This embodiment selects Thin One-Year Ice (TFYI), One-Year Ice (FYI), and Multi-Year Ice (MYI) from the World Meteorological Organization (WMO) sea ice classification as the core research objects. By collecting physical parameters of the three types of sea ice, calculating the saline cell volume ratio, and constructing models of complex permittivity and scattering coefficients, it achieves accurate characterization of the electromagnetic properties of sea ice in this frequency band, providing technical support for the inversion of sea ice thickness and type. The sea ice model adopts a three-layer medium structure of air-sea ice-seawater. Figure 1 This is a schematic diagram of the layered structure of sea ice. The specific process is as follows: S1: The acquisition of sea ice physical parameters needs to match the electromagnetic characteristic calculation requirements of the VHF band. The parameter values ​​refer to the typical ranges known in the field of sea ice remote sensing: sea ice salinity. Regarding sea ice temperature, TFYI is 10-15‰ (short formation time, insufficient desalination), FYI is 5‰ (moderate desalination), and MYI is 1‰ (deep desalination after multiple thawing cycles); TFYI is -10 to -2℃, FYI is -13℃, and MYI is -20 to -15℃, which matches the actual temperature distribution of various types of sea ice in polar environments; regarding surface roughness parameters, the root mean square height of the air-sea ice interface is... TFYI is 0.23cm, FYI is 0.05-0.4cm, and MYI is 0.15-0.8cm, for the relevant lengths The TFYI values ​​are 0.19–1.36 cm, FYI values ​​are 0.82–2.51 cm, and MYI values ​​are 0.31–2.92 cm. For a Gaussian distribution, the root mean square height is... Relevant length With root mean square slope The conversion relationship between them is: These parameters provide input data for subsequent model building.

[0030] S2: Based on the collected sea ice physical parameters, the volume ratio of brine cells in sea ice is calculated using the Frankenstein and Garner empirical formula. This formula is based on the influence of sea ice salinity and temperature on the survival capacity of brine cells and is fitted across different temperature ranges. The specific formula is as follows: (1) in, These values ​​represent the salinity of sea ice; when calculating the saline cell volume fraction of typical sea ice types, these typical values ​​provide key input parameters for the complex permittivity model.

[0031] S3: Construction and calculation of complex dielectric constant model of sea ice: divided into calculation of dielectric constant of pure ice and saline cells, and calculation of overall dielectric constant of sea ice.

[0032] Because the Matzler empirical formula commonly used in the microwave band cannot accurately characterize the dielectric properties of pure ice in the VHF band, the relative complex permittivity of pure ice and salt water cells is calculated using the single-component Cole-Cole model, with the following formula: (2) in, The dielectric constant is the high-frequency limiting dielectric constant. Based on the polarization response characteristics of pure ice in this frequency band, the value is 3.17 to 3.19 for pure ice and 4.3 to 4.8 for saline cells. The low-frequency limiting dielectric constant is defined with reference to the low-frequency dielectric properties of ice-like media. For pure ice, the value is 90–100, and for saline cells, the value is 80–90. It is the angular frequency of the electromagnetic wave; The relaxation time reflects the speed of dipole polarization response in sea ice; It is the vacuum permittivity; DC resistivity; The relaxation index (0 < <1), which quantifies the width of the relaxation time distribution. Pure ice is dominated by orientation polarization relaxation, with a narrow relaxation time distribution close to Debye relaxation, with values ​​ranging from 0.7 to 0.9. Salt cells are dominated by interfacial polarization relaxation originating from ion conduction, with a very wide distribution, with values ​​ranging from 0.1 to 0.3.

[0033] The overall complex dielectric constant of sea ice was calculated using the Maxwell-Garnett hybrid formula, which is applicable to the dielectric calculation of composite materials in which spherical particles are dispersed in a continuous matrix. The formula is as follows: (3) Among them, the matrix dielectric constant Take the dielectric constant of pure ice; the dielectric constant of particles The dielectric constant of the brine cell is taken. Since the difference in dielectric constant between bubbles and sea ice is much smaller than that of the brine cell in the VHF band, only the contribution of the brine cell is considered in the calculation. Under typical conditions, TFYI... It is 8.529 + 0.265 FYI ranges from 3.387 to 5.121, plus 0.024 to 0.150. MYI is 3.202~3.229 +0.013~0.080 ， The imaginary unit is defined as follows: .

[0034] S4: Construction and calculation of sea ice scattering coefficient model: including volume scattering coefficient model and surface scattering coefficient model; The volume scattering coefficient model is based on Rayleigh scattering theory and is applicable when the radius of the scattering particle is less than 1 / 10 of the wavelength of the incident electromagnetic wave. This condition is met by saltwater cells with radii of 3–5 mm and bubbles with radii of 2–4 mm in sea ice. The scattering cross-section of a single scattering particle... The formula is: (4) in, For dielectric contrast factor, The dielectric constant of the scattering particle is taken as FYI and TFYI, which are taken as the dielectric constant of the salt water cell, and MYI is taken as the dielectric constant of the bubble. The dielectric constant is the background dielectric constant of sea ice. The wavelength of electromagnetic waves in the very high frequency band. To initialize the radius of the scattering particles (salt cells and bubbles).

[0035] Ignoring multiple reflections between particles in the mixed medium, the volume scattering coefficient Represented as: (5) The volume scattering coefficient of the medium The expression is: (6) (7) in, It is the number of scattering particles per unit volume; It is the volume fraction of the scattered particles; It is the thickness of the medium; It is the angle of refraction in the medium; It is the extinction coefficient of the medium; It is the unidirectional loss factor of the medium.

[0036] Electromagnetic waves attenuate due to dielectric loss when propagating in sea ice. Penetration depth Defined as the field strength decaying to the surface value The propagation distance, extinction coefficient With penetration depth They are reciprocals of each other. , characterizes the attenuation rate of electromagnetic waves in a medium: (8) in, and These are the real and imaginary parts of the relative permittivity of the dielectric, respectively. Figure 2 The penetration depth of different sea ice and saline cells varies with incident wave frequency. As the incident wave frequency increases, the penetration depth of sea ice... The penetration depth of the signal gradually decreases, and the penetration depth of the signal through MYI is greater than that through FYI and TFYI in all frequency bands. Calculations show that at an incident radio frequency of 200MHz, the penetration depth of the signal through FYI is 15.6998m; the penetration depth through TFYI is 2.2872m; the penetration depth through permafrost varies from 18.5935m to 20.3421m; and the penetration depth through pure brine is 0.0065m.

[0037] The surface scattering coefficient model is based on the small perturbation model (SPM) and is applicable when the root-mean-square height of the sea ice surface is much smaller than the VHF band wavelength. The calculation formula is: (9) in, It is a polarization mode, including polarization and polarization; It is the angle of incidence; The wave number of an electromagnetic wave in a vacuum can be obtained from... calculate; For the relevant length; This is the root mean square height.

[0038] Under-polarization term The expression is: (10) Under-polarization term The expression is: (11) in, The complex permittivity is given by the sea ice background. Based on model calculations, it can be known that... Under polarization, the surface scattering coefficient of various types of sea ice decreases slightly with increasing incident angle. Under polarization, the surface scattering coefficient increases slightly with the increase of the incident angle, and because MYI has a higher surface roughness, its surface scattering coefficient is greater than that of FYI and TFYI under both polarization modes. Figure 3 , Figure 4 They are respectively and Comparison of scattering coefficients of sea ice surface under polarization.

[0039] The rationality of this method is verified by theoretical calculations. Based on the above model, in the VHF band, both the real and imaginary parts of the complex permittivity of sea ice decrease with increasing incident wave frequency, which is consistent with the basic physical law of dielectric relaxation. For every 10% increase in the volume ratio of brine cells, the real part of the complex permittivity of TFYI increases by an average of 1.2–1.5, and the imaginary part increases by an average of 0.03–0.05, consistent with the influence of the high dielectric properties of brine cells. The volume scattering coefficient increases significantly with the increase of the radius of the scattering particles. When the radius of the brine cell in FYI increases from 3 mm to 5 mm, the volume scattering coefficient increases by 6–8 dB, which is consistent with the theoretical expectation of Rayleigh scattering that "the scattering cross-section is proportional to the sixth power of the radius". The surface scattering coefficient increases with the increase of the root mean square height of the surface. The surface scattering coefficient of MYI is 5–7 dB higher than that of FYI, which is consistent with the enhancing effect of surface roughness on scattering. The consistency between the above theoretical calculation results and the basic laws of electromagnetism verifies the rationality of this method in characterizing the electromagnetic properties of sea ice in this frequency band.

[0040] Contents not described in detail herein are existing technologies known to those skilled in the art. The foregoing description illustrates and describes several preferred embodiments of the invention; however, as mentioned above, it should be understood that the invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various combinations, modifications, and environments related to sea ice remote sensing, and can be modified within the scope of the inventive concept described herein through the foregoing teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the invention should be within the protection scope of the appended claims.

[0041] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band, characterized in that, The specific process is as follows: Database construction: Collect basic physical parameters of various types of sea ice, including sea ice salinity. Sea ice temperature The surface roughness parameters were collected, and a physical parameter database was constructed according to sea ice type; the proportion of brine cell volume was fitted for different temperature ranges. Data on the percentage of saline cell volume for different sea ice types were obtained. Complex permittivity calculation: The complex permittivity of pure ice and brine cells was calculated separately using the single-component Cole-Cole model. The overall complex permittivity of sea ice was calculated based on the permittivity of pure ice and brine cells using the Maxwell-Garnett mixing formula. Sea ice scattering coefficient calculation: A volume scattering coefficient model is constructed based on Rayleigh scattering theory and the volume scattering coefficient is calculated; a surface scattering coefficient model is constructed based on a small perturbation model and the polarization mode is initialized and the surface scattering coefficient is calculated.

2. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, The study focused on thin annual ice (TFYI), annual ice (FYI), and multi-year ice (MYI) as defined by the World Meteorological Organization's sea ice classification system.

3. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, The volume fraction of saline cells was calculated using the Frankenstein and Garner empirical formula. for: 。 4. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, The complex permittivity of the pure ice and salt water cells is: in, It is the high-frequency limiting dielectric constant. It is the low-frequency limiting dielectric constant. It is the angular frequency of the electromagnetic wave; For relaxation time, The vacuum permittivity, DC resistivity; The relaxation index, It represents the imaginary unit.

5. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 4, characterized in that, The relaxation index takes the value of: 0 < <1.

6. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, When calculating the overall complex permittivity of sea ice, the tiny brine cells and bubbles within the sea ice are considered as ideal spherical particles. The calculation only considers the contribution of the brine cells to the overall complex permittivity of the sea ice. for: Among them, the matrix dielectric constant Take the dielectric constant of pure ice; the dielectric constant of particles Determine the dielectric constant of the saline cell.

7. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, The volume scattering coefficient of the medium for: in, It is the thickness of the medium; It is the angle of refraction in the medium; It is the extinction coefficient of the medium; It is the unidirectional loss factor of the medium. It is the volume scattering coefficient that ignores multiple reflections between particles in the mixed medium.

8. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, The volume scattering coefficient for: in, It is the number of scattering particles per unit volume; It is the volume fraction of the scattered particles; The scattering cross section of a single scattering particle. To initialize the radius of the scattering particles.

9. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, The surface scattering coefficient for: in, It is a polarization mode, including HH polarization and VV polarization, Indicates the polarization term; It is the angle of incidence; The wave number of electromagnetic waves in a vacuum; For the relevant length; This is the root mean square height.

10. The method for modeling the complex permittivity of sea ice and analyzing its scattering characteristics based on the VHF band according to claim 1, characterized in that, Under-polarization term The expression is: Under-polarization term The expression is: in, The complex permittivity is given by the sea ice background.

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