Rice canopy optics and microwave integrated radiation modeling method

Abstract

The invention relates to a rice canopy optical and microwave integrated radiation modeling method, which comprises the following steps of: acquiring and uniformly processing rice canopy and environmental parameters, and constructing a same physical parameter system shared by optical and microwave models; the optical part is used for calculating bidirectional reflection factors and optical reflectivity of the rice canopy under different observation conditions based on an aquatic vegetation radiation transmission model; the microwave part is based on a vector radiation transfer equation, adopts a matrix multiplication method to calculate canopy multiple scattering, and simulates underlying surface scattering in combination with an improved integral equation model to obtain a multi-polarization backscattering coefficient; the optical reflectivity and the microwave backscattering coefficient are output under a unified parameter system, and optical and microwave collaborative forward modeling is achieved. According to the invention, a rice canopy optical and microwave integrated collaborative simulation framework is established based on a radiation transfer principle, a physical consistent basis is provided for crop parameter inversion, multi-source remote sensing data application and farmland environment monitoring, and the application prospect is wide.

Description

(I) Technical Field

[0001] This invention relates to an integrated optical and microwave radiation modeling method for rice canopy, belonging to the field of agricultural remote sensing and crop monitoring technology. It is particularly suitable for the joint modeling and simulation of rice canopy optical reflectivity and microwave backscattering, and has important significance in crop trait inversion, yield estimation and collaborative application of multi-source remote sensing data. (II) Background Technology

[0002] Rice is an important food crop, and its growth status and yield have a significant impact on food security. Utilizing remote sensing technology to acquire optical and microwave information of the rice canopy is a crucial method for monitoring crop growth, estimating biomass, and retrieving farmland environmental parameters. Traditional optical remote sensing, by measuring the bidirectional reflectance factor (BRF) of the rice canopy, can reflect information such as leaf area index (LAI), chlorophyll content, and canopy structure; while microwave remote sensing, through the backscattering coefficient (σ... 0 ) Obtain parameters such as rice plant water content, geometric structure, and soil moisture.

[0003] However, most current optical and microwave forward modeling models are built and run independently, lacking a unified input parameter system, which leads to inconsistencies in multi-source remote sensing collaborative studies. For example, optical models can usually complete simulations based on macroscopic canopy parameters, while microwave models require explicit geometric parameterization. Furthermore, the two types of models differ in dielectric constants, structural parameters, and underlying surface treatment. This separate modeling approach limits the collaborative use of optical and microwave data and hinders the comprehensive inversion of crop physiological parameters within a physically consistent framework.

[0004] Therefore, there is an urgent need for a collaborative forward modeling method that can simultaneously output the optical reflectivity and microwave backscattering coefficient of rice canopy based on a unified physical parameter system. This method can not only improve the consistency between optical and microwave models, but also provide a solid physical foundation for cross-validation of multi-source satellite observation data and agricultural monitoring. (III) Summary of the Invention

[0005] 1. A method for integrated optical and microwave radiation modeling of rice canopy, characterized by comprising the following steps:

[0006] (1) Based on the obtained rice canopy and environmental parameters, and after unifying them, the optical and microwave models share the same physical parameter system. At the same time, a formula relationship is established between the optical bidirectional reflectance factor and the microwave backscattering coefficient to achieve synergy between input and output. The specific method is as follows:

[0007] The input parameters required for the model are obtained through field measurements or statistical analysis, including leaf area index, leaf tilt angle distribution, leaf water content, dry matter content, plant height, soil moisture, canopy density, component geometry, and sensor characteristic parameters. Some input variables are shown in Table 1. Some variables cannot be used simultaneously in different models and need to be standardized using formulas.

[0008] Unifying leaf weight water content with leaf transmittance and reflectance: The optical model references the PROSPECT leaf radiative transfer model for the leaf portion, and can be adjusted based on water content C. w and dry matter content C m Calculate the reflectance and transmittance spectra of vegetation leaves. The input parameter for the microwave model is the weight water content (Gmc). leaf Water content refers to the percentage of water weight in an object relative to its total weight. By using specific leaf weight (SLW), i.e., the weight of a leaf per unit leaf area, we can unify the optical and microwave models regarding leaf water content, thereby establishing the relationship between leaf weight water content and leaf transmittance and reflectance.

[0009] C w =SLW×Gmc leaf

[0010] Unified blade tilt angle distribution: In the microwave model, the blade is geometrically equivalent to a slender and thin elliptical disk, uniformly distributed in the vertical direction, and its blade tilt angle distribution is determined according to the following empirical function:

[0011]

[0012] Where β is the leaf tilt angle, this function describes the proportion of leaves with different tilt angles in the entire vegetation canopy. To achieve uniformity, the optical model also follows this leaf tilt angle distribution pattern.

[0013] Unifying Leaf Area Index (LAI) and Leaf Volume Density: In the optical model, the LAI continues the definition from the SAIL model, referring to the sum of the single-sided areas of leaves within a unit of ground surface vegetation canopy cover. In the microwave model, parameters related to leaves within the canopy include the equivalent diameter of the leaves, canopy height, and the number of leaves per unit volume of the canopy. The LAI can be given by the following formula:

[0014]

[0015] Where, N leaf H is the leaf volume density, D is the canopy height, and H is the leaf volume density. leaf This is the equivalent diameter of the blade. This formula unifies the LAI with the canopy parameters.

[0016] Unifying the Two-Way Reflection Distribution Function (BRF) and Backscattering Coefficient: In the scenario of planar targets, there is a clear mathematical relationship between the two-way reflection distribution function (BRDF) and the radar cross section (RCS). The BRDF describes the reflection characteristics of the ground surface from a certain incident direction to the scattering direction, while the RCS is an indicator in a radar system that measures the target's ability to intercept and reflect radar signals. The two can be converted using the following formula:

[0017] RCS(θ i ,φ i ;θ s ,φ s )=BRDF(θ i ,φ i ;θ s ,φ s )×(4πA0 cosθ i cosθ s )

[0018] Where A0 is the irradiation area, that is, the effective area of ​​the surface irradiated by the incident electromagnetic wave; and It is the azimuth angle between the incident wave and the scattered wave, θ i and θ s That is, the zenith angle between the incident and scattered waves. Since BRF is π times BRDF, the above equation can be written as:

[0019] RCS(θ i ,φ i ;θ s ,φ s ) = BRF(θ i ,φ i ;θ s ,φ s )×(4A0cosθ i cosθ s )

[0020] The unification of BRF and backscattering coefficients has been achieved.

[0021] Table 1. Some input parameters of the collaborative model

[0022]

[0023] (2) Simplified geometric modeling of rice leaves, stems, and panicles is performed, and scattering characteristics and dielectric constants are calculated. Optical simulation is directly based on macroscopic canopy parameters, without the need for geometric modeling. The simplification process is as follows:

[0024] Step 1: Geometric simplification and calculation of scattering characteristics. The interaction between microwave band and vegetation depends more on the geometry and size of vegetation elements. This invention employs certain geometric simplifications to retain key features while reducing computational load, enabling the calculation of single scatterer characteristics. The rice canopy considers leaves, stems, and panicles that appear after heading. Geometrically, leaves are equivalent to slender, thin elliptical disks, uniformly distributed vertically, with leaf tilt angles distributed according to an empirical function:

[0025]

[0026] According to the Rayleigh-Gans approximation, the formula for calculating the scattering amplitude of an elliptical blade is as follows:

[0027]

[0028] Among them, f vv f represents the amplitude of vv polarization scattering. hv f represents the amplitude of hv polarization scattering. vh f represents the amplitude of vh polarization scattering. hh The amplitude of the hh-polarized scattering is represented; k is the wavenumber of the background medium—air, ∈ r v0 is the complex permittivity of the blade, and v0 is the volume of the blade. Let θ represent the unit vectors of the scattering and incident directions, respectively. i ,φ i θ represents the zenith angle and azimuth angle of the incident wave direction. s ,φ s ) represents the zenith angle and azimuth angle of the scattered wave direction, a tt It is a term related to the polarizability of the blade, which depends on the blade's shape and dielectric constant, while μ is a factor describing the blade shape and scattering phase.

[0029] The morphology of rice stalks is simplified as a cylindrical medium with a certain length and radius. In terms of orientation, rice stalks are typically considered approximately vertical, and their tilt distribution is described by a narrow probability density function centered on the vertical direction to simulate natural micro-swaying. Their azimuth angle is usually assumed to be uniformly distributed within the range of 0° to 360°. Scattering amplitude is calculated based on the calculation principle of an infinitely long cylinder, and length corrections are applied to obtain the characteristics of a single scatterer.

[0030]

[0031] Where h is half the length of the cylinder, ∈ r It is the complex permittivity of the stem, (θ) i ,φ i θ represents the zenith angle and azimuth angle of the incident wave direction. s ,φ s) represents the zenith angle and azimuth angle of the scattered wave direction, μ is the length correction factor, and A n and B n It is the nth-order scattering coefficient used to assist in the solution, e nq and h nq These are the nth-order expansion coefficients used to describe the electromagnetic field inside a cylinder. The subscript q indicates the polarization mode v or h, and z n It is the nth order radial integral term, and η is the intrinsic impedance of the background medium;

[0032] The rice spike is also simplified as a short cylinder, and its geometric parameters include length, equivalent radius and number density. The calculation method for scattering amplitude is the same as that for the stalk.

[0033] Step 2: Calculate the complex dielectric constant of each leaf, stem, and panicle component of the canopy. The real part of the dielectric constant is related to the propagation speed and energy storage of electromagnetic waves in the medium, while the imaginary part characterizes the medium's ability to absorb electromagnetic energy. This invention uses the vegetation dielectric constant model proposed by Ulaby to describe the dielectric properties of each component of rice. This model treats the plant as a mixture of water, dry matter, and air, and separately handles the contributions of free water and bound water due to the significant differences in their dielectric responses in the microwave band. Its expression is:

[0034] ε veg =A+B·ε fw +C·ε bw

[0035] Where, ε veg It is the complex permittivity of vegetation, where A represents the basis term contributed by vegetation dry matter and some tightly bound water, B and C are empirical parameters, and ε fw The free water contribution term describes the Debye-type dispersion characteristics of free water in the high-frequency range and takes into account the losses caused by ionic conductivity; ε bw The contribution of the first type of bound water, which is more closely integrated with the vegetation structure, is usually expressed as another dispersion spectrum at a lower characteristic frequency. The complex permittivity of rice leaves, stems and panicles is calculated based on their respective physiological characteristics (mainly weight water content and dry matter density, combined with the current vegetation temperature and the observed microwave frequency).

[0036] (3) Based on radiative transfer theory, input unified parameters into the optical-microwave cooperative model, and run the model to calculate the optical reflectivity and microwave backscattering coefficient of the rice canopy under different observation conditions. The specific steps are as follows:

[0037] The first step involves standardizing the input rice biophysical parameters to meet the requirements of both the optical radiative transfer model and the microwave radiative transfer model. This process is implemented at the code level; after determining the input parameters, the Python program reads all parameters and passes them to the co-model to begin calculations.

[0038] Step 2: The optical part, based on the existing aquatic vegetation radiative transfer model AVRT, uses the four-flow approximation method to handle diffuse radiation within the medium. The radiative transfer equation can be expressed as:

[0039]

[0040] The four radiative flows are the direct solar irradiance Es, the downward and upward diffuse irradiance Es, and the upward diffuse irradiance Es. – and E + Flux equivalent radiance E in the observation direction o =πL o Where Lo is the radiance in the observation direction. Coefficients k and K are the extinction coefficients of direct radiation in the solar and observation directions, respectively, α is the attenuation coefficient of diffuse radiation, and the others are various scattering coefficients. Based on the optical properties and boundary conditions of the dielectric layer, the radiative transfer equations are solved to obtain the matrix representation of the relationship between incident and emitted radiation from the dielectric layer:

[0041]

[0042] It can be abbreviated as E out =ZE in E in and E out These are the incident and emitted radiation matrices, respectively. The coefficient matrix Z is called the "layer scattering matrix." In the radiation notation, 0 represents the top of the layer, and -1 represents the bottom of the layer. The coefficients in the layer scattering matrix are divided into reflection factor ρ and transmission factor τ, with double subscripts indicating the type of incident and emitted radiation: s represents direct solar radiation E. s d represents diffuse radiation E – or E + o represents the radiation E in the direction of observation. o The AVRT model calculates the bidirectional reflectance factor (BRF) of the canopy in the visible to near-infrared bands and outputs the optical reflectance results under different solar zenith angles, azimuth angles, and sensor observation angles.

[0043] Step 3: Design a new microwave model suitable for rice. This model is based on the vector radiative transfer equation and uses the matrix multiplication method. First, the canopy is divided into multiple uniform thin layers, and the radiation characteristics of each thin layer are calculated. Then, the matrix multiplication formula is used to obtain the scattering and transmission characteristics of the entire canopy.

[0044]

[0045] Where S is the scattering matrix of the sublayer and T is the transmission matrix. Simultaneously, the scattering contribution of the rough surface beneath the paddy field water surface is calculated using the integral equation model AIEM. Then, the total radiation characteristics are calculated using the matrix multiplication formula for the radiation characteristics of the canopy and the underlying surface, and simulation results for different polarization channels (VV, HH, HV, HH) are output.

[0046] Ultimately, within a unified simulation framework, the optical reflectivity and microwave backscattering coefficient of the rice canopy under different observation geometries and electromagnetic bands can be obtained simultaneously.

[0047] 2. Compared with the prior art, the advantages of the present invention are:

[0048] (1) The integrated simulation of optical reflectivity and microwave backscattering coefficient of rice canopy has been realized, avoiding the problem of independent optical model and microwave model and inconsistent input and output in traditional research. It has greatly improved the physical consistency and reliability of simulation results, and can output optical reflectivity and multi-polarization backscattering coefficient at the same time, which is convenient for joint verification and application with multi-source remote sensing observation data. It has good versatility and scalability.

[0049] (2) Through the parameter unification method, key parameters such as leaf area index, leaf water content and leaf tilt angle distribution can be shared and transformed within a framework, which effectively reduces the uncertainty caused by repeated modeling and parameter mismatch.

[0050] The innovation of this invention is mainly reflected in:

[0051] (1) A rice optical-microwave collaborative modeling method with a unified physical parameter system as the core was proposed. The optical reflectivity and microwave backscattering coefficient were established in terms of formulas at the input parameter and output index levels, realizing an integrated framework for cross-band and multi-source modeling.

[0052] (2) In the microwave section, a geometric simplification and dielectric constant calculation method was designed for the characteristics of rice plants. Combined with the matrix multiplication method and AIEM model, a comprehensive modeling method was formed that considers multiple scattering of the canopy and can accurately describe the rough scattering of the underlying surface. (iv) Description of the attached drawings

[0053] Figure 1 This is the technical process of the present invention.

[0054] Figure 2 The BRF variation with zenith angle is simulated for the present invention.

[0055] Figure 3The variation of the VV polarization backscattering coefficient with incident angle is simulated by the model of this invention. (V) Detailed Implementation

[0056] To better illustrate the rice canopy optical and microwave integrated radiation modeling method involved in this invention, tests and simulations were conducted on typical rice-growing areas using this invention, achieving good results. The specific implementation method is as follows:

[0057] (1) The rice canopy and environmental parameters of the study area were obtained through satellite data and field measurements, including leaf area index, leaf water content, dry matter content, plant height, leaf tilt angle distribution, soil moisture, canopy density, etc. The parameters were then standardized using code so that the optical and microwave models could share the same physical parameters. At the same time, a formula relationship was established between the optical bidirectional reflectance factor and the microwave backscattering coefficient to achieve the coordination between input parameters and output results.

[0058] (2) Simplified geometric modeling was performed on rice leaves, stems, and panicles, and their scattering characteristics and dielectric constants were calculated. Leaves were simplified to elliptical thin plates, stems to finite-length cylinders, and panicles to short cylinders. The complex dielectric constants were calculated using the vegetation dielectric constant model proposed by Ulaby based on the physiological characteristics of the vegetation. The optical part was calculated directly based on the unified macroscopic canopy parameters, without the need for geometric modeling.

[0059] (3) The optical-microwave co-model receiving parameters were calculated. The optical part adopted the aquatic vegetation radiative transfer model AVRT and the canopy bidirectional reflectance factor BRF under different observation conditions was calculated by the four-flow approximation method. The microwave part adopted the vector radiative transfer equation and combined the matrix multiplication method to calculate the canopy scattering and transmission characteristics. At the same time, the AIEM model was used to calculate the scattering contribution of the rough surface of the paddy field. Finally, the microwave backscattering coefficients of different polarization channels were obtained, and the simulation results of the study area under multispectral and microwave conditions were generated.

[0060] This invention establishes a collaborative simulation method for optical and microwave data by unifying rice canopy parameters. It can simultaneously output optical reflectivity and microwave backscattering coefficient, which not only truly reflects the optical characteristics of the rice canopy but also accurately describes its microwave scattering characteristics. This provides a scientific tool for crop parameter inversion, satellite remote sensing product verification, and multi-source data collaborative application, and has strong reliability and application value.

Claims

1. A method for integrated optical and microwave radiation modeling of rice canopy, characterized in that... Includes the following steps: (1) Obtain typical rice canopy and environmental parameters and standardize them so that the optical and microwave radiative transfer models share the same physical parameter system. At the same time, establish the formula relationship between the optical bidirectional reflectance factor and the microwave backscattering coefficient to achieve synergy between input and output. The specific method is as follows: The input parameters required for the model are obtained through actual measurement or statistics, including plant height, leaf area index, leaf tilt angle distribution, leaf water content, dry matter content, soil moisture content, canopy density, solar azimuth and observation geometry, and sensor characteristic parameters. Since some variables cannot be used simultaneously in different models, they are uniformly processed as follows: 1) Unification of leaf weight water content and leaf transmittance and reflectance: The rice canopy optical radiative transfer model references the PROSPECT model for the leaf portion, based on the water content C w and dry matter content C m The reflectance and transmittance spectra of vegetation leaves are calculated; the input parameter for the microwave model is the weight water content (Gmc). leaf By using specific leaf weight (SLW), i.e., leaf weight per unit leaf area, the rice canopy optical radiation model and microwave radiation model were unified regarding leaf water content, thereby establishing the relationship between leaf weight water content and leaf transmittance and reflectance: C w =SLW×Gmc leaf 2) Unified leaf tilt angle distribution: In the microwave model, the leaf is geometrically equivalent to a slender and thin elliptical disk, uniformly distributed in the vertical direction. Its leaf tilt angle distribution (pdf) leaf Based on the empirical function, it can be described as follows: Where β represents the leaf tilt angle, this function describes the proportion of leaves with different tilt angles in the entire vegetation canopy. To achieve uniformity, the optical model also follows this leaf tilt angle distribution pattern. 3) Unification of Leaf Area Index and Leaf Volume Density: In the optical model, the leaf area index follows the definition in the SAIL model, referring to the sum of the single-sided areas of leaves within a unit of ground surface vegetation canopy cover; in the microwave model, parameters related to leaves within the canopy include the equivalent diameter of the leaves, canopy height, and the number of leaves per unit volume of the canopy. The leaf area index (LAI) is given by the following formula: Where, N leaf H is the leaf volume density, D is the canopy height, and H is the leaf volume density. leaf It is the equivalent diameter of the blade; this formula unifies the LAI with the canopy parameters. 4) Unification of two-way reflection factor (BRF) and backscattering coefficient: In the scenario of planar targets, there is a clear mathematical relationship between the two-way reflection distribution function (BRDF) and the radar cross section (RCS). BRDF describes the reflection characteristics of the ground surface from a certain incident direction to the scattering direction, while RCS is an indicator in the radar system that measures the target's ability to intercept and reflect radar signals. The two can be converted using the following methods: RCS(θ i ,f i ;θ s ,f s )=BRDF(θ i ,f i ;θ s ,f s )×(4πA0cosθ i cosθ s ) Where A0 is the irradiation area, that is, the effective area of ​​the surface irradiated by the incident electromagnetic wave; and It is the azimuth angle between the incident wave and the scattered wave, θ i and θ s This is the zenith angle between the incident wave and the scattered wave; according to the quantitative relationship between BRF and BRDF, the above formula can be expressed as: RCS(θ i ,f i ;θ s ,f s )=BRF(θ i ,f i ;θ s ,f s )×(4A0cosθ i cosθ s ) It achieves the unification of BRF and backscattering coefficient; (2) Simplified geometric modeling of rice leaves, stems, and panicles is performed, and scattering characteristics and dielectric constants are calculated. Optical simulation is directly based on macroscopic canopy parameters, without the need for geometric modeling. The simplification process is as follows: Step 1: Geometric simplification and calculation of scattering characteristics; the interaction between microwave bands and vegetation depends more on the geometry and size of vegetation elements. This invention employs certain geometric simplifications, retaining key features while reducing computational load, to achieve the calculation of single scatterer characteristics; the rice canopy considers leaves, stems, and panicles appearing after heading; the leaves are geometrically equivalent to slender, thin elliptical disks, uniformly distributed vertically, with their leaf tilt angle distribution following an empirical function: The scattering amplitude of an elliptical blade can be calculated using the Rayleigh-Gans approximation as follows: Among them, f vv f represents the amplitude of vv polarization scattering. hv f represents the amplitude of hv polarization scattering. vh f represents the amplitude of vh polarization scattering. hh The amplitude of the hh-polarized scattering is represented; k is the wavenumber of the background medium—air, ∈ r v0 is the complex permittivity of the blade, and v0 is the volume of the blade. Let θ represent the unit vectors of the scattering and incident directions, respectively. i ,φ i θ represents the zenith angle and azimuth angle of the incident wave direction. s ,φ s ) represents the zenith angle and azimuth angle of the scattered wave direction, a 11 ,a 22 and a 33 These are the polarizability-related terms of the blade, which depend on the blade's shape and dielectric constant, while μ is a factor describing the blade shape and scattering phase. The morphology of rice stalks is simplified as a cylindrical medium with a certain length and radius. In terms of orientation, rice stalks are typically considered approximately vertical, and their tilt distribution is described by a narrow probability density function centered on the vertical direction to simulate natural micro-swaying. Their azimuth angle is usually assumed to be uniformly distributed within the range of 0° to 360°. Scattering amplitude is calculated based on the calculation principle of an infinitely long cylinder, and length corrections are applied to obtain the characteristics of a single scatterer. Where h is half the length of the cylinder, ∈ r It is the complex permittivity of the stem, (θ) i ,φ i θ represents the zenith angle and azimuth angle of the incident wave direction. s ,φ s ) represents the zenith angle and azimuth angle of the scattered wave direction, μ is the length correction factor, and A n and B n It is the nth-order scattering coefficient used to assist in the solution, e nq and h nq These are the nth-order expansion coefficients used to describe the electromagnetic field inside a cylinder. The subscript q indicates the polarization mode v or h, and z n It is the nth order radial integral term, and η is the intrinsic impedance of the background medium; The rice spike is also simplified as a short cylinder, and its geometric parameters include length, equivalent radius and number density. The calculation method for scattering amplitude is the same as that for the stalk. Step 2: Calculate the complex dielectric constant of each leaf, stem, and panicle component of the canopy. The real part of the dielectric constant is related to the propagation speed and energy storage of electromagnetic waves in the medium, while the imaginary part characterizes the medium's ability to absorb electromagnetic energy. This invention uses the vegetation dielectric constant model proposed by Ulaby to describe the dielectric properties of each component of rice. This model treats the plant as a mixture of water, dry matter, and air, and separately handles the contributions of free water and bound water due to the significant differences in their dielectric responses in the microwave band. Its expression is: e veg =A+B·e fw +C·e bw Where, ε veg It is the complex permittivity of vegetation, where A represents the basis term contributed by vegetation dry matter and some tightly bound water, B and C are empirical parameters, and ε fw The free water contribution term describes the Debye-type dispersion characteristics of free water in the high-frequency range and takes into account the losses caused by ionic conductivity; ε bw The contribution of the first type of bound water, which is more closely integrated with the vegetation structure, is usually expressed as another dispersion spectrum at a lower characteristic frequency. Based on the physiological characteristics of rice leaves, stems and panicles, mainly the weight water content and dry matter density, and combined with the current vegetation temperature and the observed microwave frequency, their complex permittivity was calculated respectively. (3) Based on the radiative transfer theory, input unified parameters into the optical-microwave cooperative model, and run the model to calculate the optical reflectivity and microwave backscattering coefficient of the rice canopy under different observation conditions; the specific steps are as follows: Step 1: The input rice biophysical parameters are standardized to meet the parameter requirements of both the optical radiative transfer model and the microwave radiative transfer model. This process is implemented at the program code level. After the input parameters are determined, the program reads all parameters and passes them to the collaborative model to start the calculation. Step 2: The optical part, based on the existing aquatic vegetation radiative transfer model AVRT, uses the four-flow approximation method to handle diffuse radiation within the medium. The radiative transfer equation can be expressed as: The four radiative flows are the direct solar irradiance Es, the downward and upward diffuse irradiance Es, and the upward diffuse irradiance Es. – and E + Flux equivalent radiance E in the observation direction o =πL o Where Lo is the radiance in the observation direction; coefficients k and K are the extinction coefficients of direct radiation in the sun and in the observation direction, respectively; α is the attenuation coefficient of diffuse radiation; and the others are various scattering coefficients. Based on the optical properties and boundary conditions of the medium layer, the radiative transfer equations are solved to obtain the matrix representation of the relationship between incident and outgoing radiation from the medium layer: It can be abbreviated as E out =ZE in E in and E out These are the incident and emitted radiation matrices, respectively. The coefficient matrix Z is called the "layer scattering matrix." In the radiation notation, 0 represents the top of the layer, and -1 represents the bottom of the layer. The coefficients in the layer scattering matrix are divided into the reflection factor ρ and the transmission factor τ, and the double subscripts indicate the type of incident and emitted radiation, respectively: s represents direct solar radiation E. s d represents diffuse radiation E – or E + o represents the radiation E in the direction of observation. o The AVRT model calculates the bidirectional reflectance factor (BRF) of the canopy in the visible to near-infrared bands and outputs the optical reflectance results under different solar zenith angles, azimuth angles, and sensor observation angles. Step 3: Design a new microwave model suitable for rice. This model is based on the vector radiative transfer equation and uses the matrix multiplication method. First, the canopy is divided into multiple uniform thin layers, and the radiation characteristics of each thin layer are calculated. Then, the matrix multiplication formula is used to obtain the scattering and transmission characteristics of the entire canopy. Where S is the scattering matrix of the sublayer, T is the transmission matrix, 1 and 2 represent different sublayers, and the negative sign indicates upward scattering; at the same time, the scattering contribution of the rough surface of the paddy field underlying surface is calculated by combining the integral equation model AIEM, and then the radiation characteristics of the canopy and underlying surface are calculated by matrix multiplication formula to obtain the total radiation characteristics, and the simulation results of different polarization channels VV, HH, HV, and HH are output; finally, under a unified simulation framework, the optical reflectivity and microwave backscattering coefficient of the rice canopy under different observation geometry and electromagnetic bands can be obtained simultaneously.

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