Method for estimating lake ice thickness based on four-layer medium reflectivity model

Abstract

The invention discloses a method for estimating the thickness of lake ice based on a four-layer medium reflectivity model. The method comprises the following steps: acquiring FY-3 satellite data, ground actual measurement data and ERA5 reanalysis data; preprocessing the data, including atmospheric correction, geographical registration, resampling and space-time matching among the data; performing accumulated snow parameter inversion to output accumulated snow depth ds, density rho s, dielectric constant epsilons and roughness; a four-layer medium reflectivity model is deduced by combining a Fresnel reflection coefficient and a Snell law and considering the reflectivity of an incident angle, a polarization effect, roughness and loss; inverting the lake ice thickness di based on a four-layer model by adopting a mode of fixing accumulated snow parameters; and performing precision evaluation verification and sensitivity analysis on the result to further optimize the performance of the model. According to the technical scheme, robust estimation of the lake ice thickness can be achieved through the mode that multi-source data is cooperatively combined with the four-layer model and staged inversion, which is another breakthrough of the satellite-borne GNSS-R technology in the lake research field, and an operable technical scheme is provided for lake monitoring.

Description

Technical Field

[0001] The present invention belongs to the cross - research field of GNSS reflection measurement and cryosphere science, and particularly relates to a method for estimating lake ice thickness based on a four - layer medium reflectivity model. Background Technique

[0002] Monitoring the thickness of lake ice is an important task in the research of the cryosphere environment. As a key element of the cold - region ecosystem and hydrological cycle, the change in the thickness of lake ice directly affects regional climate feedback, water body thermodynamic processes, and human activities (such as ice - based transportation and fishing). Existing relevant research shows that the presence or absence of ice cover in a lake plays a key role in the impact on air temperature and even affects the precipitation in the surrounding environment. Moreover, the World Meteorological Organization regards lake ice and lake ice thickness as two indispensable climate variables. Regarding the monitoring of lake ice, traditional measurement methods such as drilling and radar have disadvantages such as small spatial coverage, short time span, and difficult operation. Under the background of global climate change, there is an urgent need for efficient and high - precision remote sensing technology for dynamic monitoring of lake ice.

[0003] Space - borne GNSS - R technology is being widely used in the research of the cryosphere field, especially in calculating sea ice reflectivity using multi - layer models or applying multi - layer models to fields such as soil freeze - thaw. Correspondingly, space - borne GNSS - R technology can also indirectly estimate the thickness of lake ice by using the reflection of signals between surfaces, and can dynamically monitor the changes in lake ice in a large - scale area without contacting the ice surface, with advantages such as non - contact, high efficiency, and high spatial resolution. Therefore, the present invention has derived a four - layer medium reflectivity model that can be used to estimate the thickness of lake ice. Combining with space - borne GNSS - R technology, it can realize the study of the changes in lake ice and its impact on climate in a low - cost monitoring method. The proposal of this idea has promoted the development of using space - borne GNSS - R technology to estimate lake parameters.

[0004] Considering that lake ice exists in the state of air - snow - lake ice - lake water under specific circumstances, there are multiple reflection surfaces and complex parameters in this state, and the physical properties of each layer will also affect the reflection signal. Therefore, it is necessary to analyze and estimate the lake ice thickness by combining the electromagnetic wave propagation characteristics of these layers. Traditional lake ice inversion models mostly assume that the ice layer is bare (i.e., a three - layer structure of air - lake ice - lake water), ignoring the influence of snow cover, resulting in an overestimation of ice thickness (especially in winter snow - covered areas). The innovation of the air - snow - lake ice - lake water four - layer model lies in: First, the medium stratification is refined, and the parameters of the snow layer (dielectric constant, thickness) and the lake ice layer (dielectric constant, thickness) are independently characterized, explicitly analyzing the snow attenuation and interface reflection effects. Second, multi - physical coupling modeling is carried out, introducing a roughness correction factor to quantify the influence of surface scattering, and constructing a recursive reflectivity equation by combining the Fresnel reflection coefficient and the attenuation term. Third, the phase and amplitude are jointly utilized to enhance the sensitivity of thin ice thickness through the interference phase, making up for the deficiencies of the traditional amplitude inversion method.

[0005] In summary, the method for estimating lake ice thickness based on the four - layer medium reflectivity model breaks through the bottleneck of traditional remote sensing means in the monitoring of snow - covered lake ice through multi - physical mechanism modeling and multi - source data collaboration, providing a new reference scheme for high - precision and all - weather dynamic monitoring of lakes in alpine regions. Combining the global observation ability of the Fengyun - 3 (FY - 3) satellite, this technology is expected to become an important tool in the field of cryosphere remote sensing, contributing to climate change research and the realization of sustainable development goals. Summary of the Invention

[0006] In order to break through the barriers in the monitoring of snow - covered lake ice by traditional inversion models, deeply explore the influence of adding snow factors on estimating lake ice thickness, and more accurately estimate lake ice thickness, the present invention provides a method for estimating lake ice thickness based on the four - layer medium reflectivity model. This method adopts a phased inversion approach. First, the snow parameters are inverted, and then the four - layer medium reflectivity model is simplified by fixing the snow parameters. Then, the lake ice thickness is preliminarily estimated based on the four - layer medium reflectivity model. Finally, the influence of snow parameter errors on lake ice thickness is quantified and output in the form of a confidence interval.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for estimating lake ice thickness based on the four - layer medium reflectivity model, comprising the following steps:

[0009] Step S1, obtaining Fengyun - 3 (FY - 3) satellite data, ground measured data, and ERA5 re - analysis data;

[0010] Step S2, pre - processing the data, including atmospheric correction, georegistration and resampling, and spatio - temporal matching between various data.

[0011] Step S3, performing snow parameter inversion to output snow depth, density, dielectric constant and roughness;

[0012] Step S4, combining the Fresnel reflection coefficient and Snell's law, taking into account the incident angle, polarization effect, roughness and loss reflectivity to derive a four-layer medium reflectivity model;

[0013] Step S5, fixing the snow cover parameters and inverting the lake ice thickness based on the four-layer model;

[0014] Step S6: perform accuracy evaluation and sensitivity analysis on the results to further optimize the performance of the model;

[0015] Preferably, the Fengyun-3 (FY-3) satellite data in step S1 is specifically the MWRI L1 data of FY-3D, the MERSI L1 (resolution 250M) data of FY-3E, and the GNSS-R data of FY-3E. The ground measured data specifically includes lake ice parameters, snow cover parameters, and roughness. The ERA5 reanalysis data includes surface temperature, air temperature, humidity, and wind speed data.

[0016] Preferably, the data is pre-processed in step S2, including firstly performing atmospheric correction on the MWRI L1 microwave brightness temperature data of FY-3D using the atmospheric radiation transfer model (RTTOV) to remove atmospheric effects. Then, georeferencing is performed to unify the coordinates to the WGS84 coordinate system to match the research scope. The spatial resolution of the data of different frequencies is unified to 250km using bilinear interpolation, and finally outliers are removed. Then, snow cover is extracted from the MERSI L1 (resolution of 250M) data of FY-3E, specifically by calculating the normalized snow cover index (NDSI).

[0017]

[0018] Using the threshold method, NDSI>0.4 is judged as snow-covered area, and NDSI≤0.4 is judged as non-snow-covered area. Here, the typical threshold judgment is used, and special scenes such as wet snow and cloud cover are not considered. In formula (1), Band 0.65μm Indicates the reflectivity value of the MERSI sensor in the visible light band (0.65μm, red light band). Snow has high reflectivity in the visible light band. 1.6μm This represents the reflectance value of the MERSI sensor in the shortwave infrared band (1.6μm). Since snow crystals absorb shortwave infrared radiation, the reflectance decreases at this time. Finally, all data are aligned with the FY-3 data in time and space to ensure data consistency.

[0019] Preferably, step S3 performs snow parameter inversion to output snow depth, density, dielectric constant, and roughness as an auxiliary method for lake ice thickness inversion. The purpose is to fix the snow layer parameters and simplify the four-layer medium reflectivity model. Specifically, it includes the following sub-steps:

[0020] Step S3.1: Use the random forest (RF) model to input multi-band brightness temperature and auxiliary data to retrieve snow depth;

[0021] Step S3.2: Use the polarization difference index (PDI) of the FY-3D MWRI combined with an empirical formula to invert the snow density, and then calculate the dielectric constant based on the empirical formula of snow density and dielectric constant;

[0022] In step S3.3, the roughness is inverted based on the AIEM model using the GNSS-R data of FY-3E.

[0023] Preferably, the reflectivity model of the four-layer medium derived in step S4 by combining the Fresnel reflection coefficient and Snell's law, taking into account the incident angle, polarization effect, roughness and loss, comprises the following main formulas:

[0024] Considering four media layers of air, snow, lake ice, and lake water, a reflectivity calculation model including incident angle, polarization effect, roughness, and loss is derived:

[0025] First, the Fresnel reflection coefficient is used for polarization separation. For oblique incidence from the jth layer to the j+1th layer, the incident angle θ j The transfer changes in the four-layer model can be expressed as:

[0026]

[0027] Where s represents the snow layer, i represents the lake ice layer, and w represents the lake water layer. To facilitate the subsequent derivation of formulas, when j and j+1 appear at the same time, j=0, 1, 2, and j+1 represents s, i, and w. The Fresnel reflection coefficient is expressed as follows:

[0028] Vertical polarization (TE wave):

[0029]

[0030] Horizontal polarization (TM wave):

[0031]

[0032] Here, the incident angles of each layer are constrained by Snell's law:

[0033]

[0034] Next, the interface root mean square height is introduced, and the roughness of each interface is corrected by combining the incident angle and the wave number. The correction formula is as follows:

[0035]

[0036] Among them, σ j represents the interface root mean square height, represents the real part of the wave number (related to the phase). The dielectric constant ε of each layer after loss j is a complex number. The complex wave number can be decomposed into a phase constant β j and an attenuation constant α j , as shown in formulas (7) and (8):

[0037] ε j = ε j + iε j (j = s, i, w) (7)

[0038]

[0039] Finally, the equivalent reflection coefficient is calculated recursively. For the lake ice - lake water interface, the reflection coefficient after roughness correction is After multiple reflections and losses, the total reflection contribution of the lake ice layer is:

[0040]

[0041] For the snow - lake ice interface, the reflection coefficient after roughness correction is The total reflection contribution of the snow layer is:

[0042]

[0043] For the air - snow interface, after roughness correction is The total reflection coefficient is:

[0044]

[0045] It should be noted that considering the polarization characteristics of the receiver antenna, the reflectivity R needs to be projected onto the receiving polarization basis:

[0046]

[0047] Among them, and are the total reflection coefficients for vertical and horizontal polarization respectively.

[0048] Preferably, step S5 adopts the method of fixing the snow parameters to invert the lake ice thickness based on the four - layer model. The specific implementation process is as follows: input the incident angle, dielectric constant (it should be specified here that the snow dielectric constant is fixed according to step 3), and roughness → use the formula described in step S4 to calculate and R→invert the lake ice thickness d according to formula (13) i , the lake ice thickness d i can be extracted through the periodic change of R, and the formula can be expressed as:

[0049]

[0050] where f is the frequency, and the phase change rate has a linear relationship with the ice thickness.

[0051] Preferably, in step S6, accuracy evaluation verification and sensitivity analysis are performed on the results to further optimize the performance of the model, including calculating the mean absolute error (MAE), root mean square error (RMSE), quantifying the snow cover parameter error, i.e., the snow cover density ρ s ±10% impact on the lake ice thickness, and finally generate a lake ice thickness distribution map. The relevant calculation formulas are as follows:

[0052]

[0053] where n is the number of samples, and y i is the true lake ice thickness value of the i-th sample, is the predicted lake ice thickness value of the i-th sample by the lake ice model, and the smaller the MAE value, the better the model prediction effect.

[0054]

[0055] where m is the number of samples, y i,M is the estimated lake ice thickness value by the model, and y i,T is the lake ice thickness value from the reference data set. Description of the Drawings

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below.

[0057] Attached Figure 1 is the basic flowchart of a method for estimating lake ice thickness based on a four-layer medium reflectivity model in an embodiment of the present invention;

[0058] Attached Figure 2 is the schematic diagram of the most core four-layer medium reflectivity model in an embodiment of the present invention;

[0059] Attached Figure 3 is the specific experimental detail diagram for estimating lake ice thickness based on a four-layer medium reflectivity model in an embodiment of the present invention. Detailed Description of the Invention

[0060] The present invention will be specifically described below in conjunction with specific embodiments and examples, and the advantages and various effects of the present invention will be presented more clearly therefrom. Those skilled in the art should understand that these specific embodiments and examples are used to illustrate the present invention, rather than to limit the present invention.

[0061] Throughout the specification, unless otherwise specifically stated, the terms used herein should be understood as having the meanings commonly used in the art. Therefore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as the general understanding of those skilled in the art to which the present invention pertains. In case of contradiction, this specification shall prevail.

[0062] Unless otherwise specifically stated, various raw materials, reagents, instruments, and equipment used in the present invention can be obtained through market purchases or can be prepared by existing methods.

[0063] Example 1

[0064] To verify the feasibility of the method proposed by the present invention, FY-3 data, ECMWF ERA5 reanalysis data, and ground measured data covering the entire two months from January to February 2024 in the Qinghai region were collected for experiments.

[0065] The basic configuration of the experimental platform is shown in Table 1:

[0066] Table 1

[0067]

[0068] A method for estimating lake ice thickness based on a four-layer medium reflectivity model, as shown in the appendix Figure 1 is shown and includes the following steps:

[0069] Step S1, obtaining FY-3 satellite data, ground measured data, and ERA5 reanalysis data;

[0070] Step S2, preprocessing the data, including atmospheric correction, georegistration and resampling, and spatio-temporal matching between the data;

[0071] Step S3, performing snow parameter inversion to output snow depth, density, dielectric constant, and roughness;

[0072] Step S4, combining the Fresnel reflection coefficient and Snell's law, and deriving a four-layer medium reflectivity model considering the incident angle, polarization effect, roughness, and loss reflectivity;

[0073] Step S5, fixing the snow parameters and inversely calculating the lake ice thickness based on the four-layer model;

[0074] Step S6: Conduct accuracy evaluation verification and sensitivity analysis on the results to further optimize the performance of the model;

[0075] As an implementation manner of this embodiment, in step S1, the Fengyun-3 (FY-3) satellite data specifically includes the MWRI L1 data of FY-3D, the MERSI L1 (with a resolution of 250M) data of FY-3E, and the GNSS-R data of FY-3E. The ground measured data specifically includes lake ice parameters, snow cover parameters, and roughness. The ERA5 reanalysis data includes surface temperature, air temperature, humidity, and wind speed data.

[0076] As an implementation manner of this embodiment, step S2 includes the following steps:

[0077] Preprocessing the data includes first performing atmospheric correction on the MWRI L1 data of FY-3D using the atmospheric radiative transfer model (RTTOV) to remove the atmospheric influence. Conducting georegistration to unify it into the WGS84 coordinate system and then matching the research scope. Using the bilinear interpolation method to unify the spatial resolution of different frequency data to 250KM, and finally removing outliers; then extracting the snow cover from the MERSI L1 (with a resolution of 250 m ) data of FY-3E, which is specifically manifested as: calculating the normalized difference snow index (NDSI)

[0078]

[0079] Using the threshold method, NDSI > 0.4 is determined as the snow-covered area, and NDSI ≤ 0.4 is determined as the non-snow-covered area. Here, typical thresholds are used for judgment, and special scenarios such as wet snow and cloud cover are not considered yet. In formula (1), Band 0.65μm represents the reflectance value of the MERSI sensor in the visible light band (0.65μm, red light band). Snow has a high reflectance in the visible light band. Band 1.6μm represents the reflectance value of the MERSI sensor in the shortwave infrared band (1.6μm). Since snow crystals absorb shortwave infrared radiation, the reflectance will decrease at this time; finally, align all the data in time and space with the FY-3 data to ensure data consistency;

[0080] As an implementation manner of this embodiment, step S3 is an auxiliary work for constructing a four-layer medium reflectivity model. First, a random forest (RF) model is used, and multi-band brightness temperature and auxiliary data are input to invert the snow depth; then, the polarization difference index (PDI) of MWRI of FY-3D is combined with an empirical formula to invert the snow density, and then the dielectric constant is deduced according to the empirical formula of snow density and dielectric constant; finally, the roughness is inverted based on the AIEM model using the GNSS-R data of FY-3E. After obtaining all snow parameters, these physical characteristic parameters of the snow layer are set as known constants instead of inversion variables. This operation aims to reduce the model complexity and the inversion uncertainty caused by multi-parameter coupling.

[0081] As an implementation manner of this embodiment, for the principle of deriving the four-layer medium reflectivity model by combining the Fresnel reflection coefficient and Snell's law and considering the incident angle, polarization effect, roughness, and loss in step S4, see Appendix Figure 2 , which includes the following main formulas:

[0082] Considering four layers of media: air, snow, lake ice, and lake water, a reflectivity calculation model including the incident angle, polarization effect, roughness, and loss is derived:

[0083] First, the Fresnel reflection coefficient is used for polarization separation. For the oblique incidence from the j-th layer to the (j + 1)-th layer, the incident angle θ j The transfer change in the four-layer model can be expressed as:

[0084]

[0085] where s represents the snow layer, i represents the lake ice layer, w represents the lake water layer. For the convenience of subsequent formula derivation, when j and j + 1 appear simultaneously, j = 0, 1, 2, and j + 1 represents s, i, and w. The Fresnel reflection coefficient is expressed in polarization as:

[0086] Vertical polarization (TE wave):

[0087]

[0088] Horizontal polarization (TM wave):

[0089]

[0090] Here, the incident angles of each layer are constrained by Snell's law:

[0091]

[0092] Then, the root mean square height of the interface is introduced to correct the roughness of each interface in combination with the incident angle and wave number. The correction formula is:

[0093]

[0094] Among them, σ j represents the root mean square height of the interface, represents the real part of the wave number (related to the phase), and the dielectric constant ε of each layer after loss j is a complex number, and the complex wave number can be decomposed into a phase constant β j and an attenuation constant α j , as shown by formulas (7) and (8):

[0095] ε j = ε j + iε j (j = s, i, w) (7)

[0096]

[0097] Finally, the equivalent reflection coefficient is calculated recursively. For the lake ice - lake water interface, the reflection coefficient after roughness correction is After multiple reflections and losses, the total reflection contribution of the lake ice layer is:

[0098]

[0099] For the snow - lake ice interface, the reflection coefficient after roughness correction is The total reflection contribution of the snow layer is:

[0100]

[0101] For the air - snow interface, after roughness correction is The total reflection coefficient is:

[0102]

[0103] It should be noted that considering the polarization characteristics of the receiver antenna, the reflectivity R needs to be projected onto the receiving polarization basis:

[0104]

[0105] Among them, and are the total reflection coefficients for vertical and horizontal polarization, respectively.

[0106] As an implementation manner of this embodiment, the specific implementation process of step S5 for inversely calculating the lake ice thickness based on the four - layer model by fixing the snow parameters is as follows: input the incident angle, dielectric constant (it should be specified here that the snow dielectric constant is fixed according to step 3), and roughness → use the formula described in step S4 to calculate and R → inversely calculate the lake ice thickness d according to formula (13) i The lake ice thickness d iIt can be extracted through the periodic change of R, and the formula can be expressed as:

[0107]

[0108] where f is the frequency and the phase change rate has a linear relationship with the ice thickness.

[0109] As an implementation manner of this embodiment, step S6 performs accuracy evaluation verification and sensitivity analysis on the results, and further optimizes the performance of the model, including calculating the mean absolute error (MAE) and the root mean square error (RMSE), and quantifying the snow cover parameter error, that is, the snow cover density ρ s ±10%'s influence on the lake ice thickness, and finally generates a lake ice thickness distribution map. The relevant calculation formulas are as follows:

[0110]

[0111] where n is the number of samples, and y i is the true lake ice thickness value of the i-th sample, is the predicted lake ice thickness value of the i-th sample by the lake ice model. The smaller the MAE value, the better the model prediction effect.

[0112]

[0113] where m is the number of samples, y i,M is the estimated lake ice thickness value of the model, and y i,T is the lake ice thickness value from the reference data set.

[0114] Appendix Figure 3 Details show the specific experimental details of using the four-layer medium reflectivity model to estimate the lake ice thickness, including some specific methods used for data preprocessing. This model provides a theoretical framework for the spaceborne GNSS-R lake ice thickness inversion, but in the future, it is still necessary to optimize the parameters and solve the phase ambiguity problem in combination with the measured data.

[0115] The above-described embodiments only describe the method of the present invention and do not impose any formal limitations on the present invention. Any person skilled in the art of this patent, without departing from the design spirit of the present invention, can make various changes and improvements using the technical content prompted above. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution of the present invention still fall within the scope of the present invention's solution.

Claims

1. A method for estimating lake ice thickness based on a four-layer medium reflectivity model, characterized in that The following steps are involved: S1. Acquire Fengyun-3 satellite data, ground-based data, and ERA5 reanalysis data; S2. Preprocess the data, including atmospheric correction, georeferencing, and time-space matching; S3. Invert snow parameters and output snow depth d s , density ρ s , dielectric constant ε s and roughness; S4. Combining the Fresnel reflection coefficient and Snell's law, the reflectivity model of the four-layer medium is derived by considering the incident angle, polarization effect, roughness and loss; S5. Fixed snow cover parameters and inverted lake ice thickness based on the four-layer model; S6. Conduct accuracy assessment and sensitivity analysis to optimize model performance.

2. The method according to claim 1, wherein The Fengyun-3 data includes (FY-3) satellite data, specifically GNSS-R data in the MWRI L1 data of FY-3D, the MERSI L1 data of FY-3E, and the GNSS-R data in the GNOS LI data of FY-3E; the ground measured data specifically includes lake ice parameters, snow cover parameters, and roughness; and the ERA5 reanalysis data includes surface temperature, air temperature, humidity, and wind speed data.

3. The method according to claim 1, wherein The preprocessing of step S2 includes: S2.1: Perform atmospheric correction on the FY-3D MWRIL1 data using the Radiative Transfer of Air (RTTOV) model to remove atmospheric effects. Georeference the data to the WGS84 coordinate system to match the study area. Use bilinear interpolation to unify the spatial resolution of the data at different frequencies to 250 km, and finally remove outliers. S2.2 Calculate the Normalized Difference Snow Cover Index (NDSI) for the FY-3E MERSI L1 data: The threshold method (NDSI>0.4) was used to extract snow areas; Step 2.3 aligns all data with the FY-3 data in time and space to ensure data consistency.

4. The method according to claim 1, wherein The snow parameter inversion in step S3 includes: S3.1 uses the random forest (RF) model to input multi-band brightness temperature and auxiliary data to retrieve snow depth; S3.2 Use the MWRI polarization difference index (PDI) of FY-3D and the empirical formula to invert the snow density and dielectric constant. S3.3 Use the GNSS-R data of FY-3D and the AIEM model to invert the roughness.

5. The method according to claim 1, wherein In step S4, the reflectivity model of the four-layer medium is derived by combining the Fresnel reflection coefficient and Snell's law, taking into account the incident angle, polarization effect, roughness and loss, and includes the following main formulas: First, the Fresnel reflection coefficient is used for polarization separation. For the oblique incidence from the j-th layer to the (j + 1)-th layer, the incident angle θ j The transfer change in the four-layer model can be expressed as: Where s represents the snow layer, i represents the lake ice layer, and w represents the lake water layer. To facilitate the subsequent derivation of formulas, when j and j+1 appear at the same time, j=0, 1, 2, and j+1 represents s, i, and w. The Fresnel reflection coefficient is expressed as follows: Vertical polarization (TE wave): Horizontal polarization (TM wave): Here, the incident angles of each layer are constrained by Snell's law: Then, the interface root mean square height is introduced to correct the roughness of each interface in combination with the incident angle and wave number. The correction formula is: Among them, σ j represents the root mean square height of the interface, represents the real part of the wave number (related to the phase), and the dielectric constants ε of the layers with losses j are complex numbers. The complex wave number can be decomposed into a phase constant β j and an attenuation constant α j , as shown by formulas (7) and (8): ε j = ε j + iε j (j = s, i, w) (7) Finally, the equivalent reflection coefficient is calculated recursively. For the lake ice-lake water interface, the reflection coefficient after roughness correction is After multiple reflections and losses, the total reflection contribution of the lake ice layer is: The snow-ice interface, the reflectivity after roughness correction is The total reflection contribution of the snow layer is: Air-snow interface, after roughness correction is The total reflectance coefficient is: It is worth noting that, considering the polarization characteristics of the receiver antenna, the reflectivity R needs to be projected onto the receiving polarization basis: wherein, and are the total reflection coefficients of vertical and horizontal polarizations, respectively.

6. The method according to claim 1, characterized in that, The specific implementation process of the step S5 for inversely calculating the lake ice thickness based on the four-layer model by adopting the method of fixing the snow parameters is as follows: input the incident angle, the dielectric constant (it should be specified here that the snow dielectric constant is fixed according to step 3), and the roughness → calculate and R → inversely calculate the lake ice thickness d according to formula (13) i , the lake ice thickness d i can be extracted through the periodic change of R, and the formula can be expressed as: where f is the frequency and the phase change rate has a linear relationship with the ice thickness.

7. The method according to claim 1, wherein In step S6, the mean absolute error (MAE) and root mean square error (RMAE) are used to evaluate the accuracy, and the impact of snow parameter errors on the inversion results is quantified through sensitivity analysis: where n is the number of samples, and y i is the true lake ice thickness value of the i-th sample, is the predicted lake ice thickness value of the i-th sample. The smaller the MAE value, the better the model prediction effect. where m is the number of samples, and y i,M is the lake ice thickness value estimated by the model, and y i,T is the lake ice thickness value from the reference dataset.

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