A radiative transfer modeling method for stratified water bodies based on the two-stream approximation

Abstract

The present invention relates to a method for modeling the radiative transfer of stratified water bodies based on the two-stream approximation. The steps are as follows: By analyzing the vertical stratification characteristics of the water body component concentration, set basic assumptions to achieve the modeling of the radiative quantity of the water body light field based on the two-stream approximation, and solve the scenario including the direct component through the iterative method; Couple the sea surface incident irradiance model, comprehensively consider the influence of wind on the reflection and transmission of the water surface, and further optimize the coefficients of the two-stream model; Finally, combined with boundary conditions, including the initial light, water body attribute parameters, and the wave water surface under the influence of wind speed, calculate the downwelling irradiance and direct irradiance of the water surface, and substitute them into the two-stream formula to obtain the remote sensing reflectance of the water body. This analytical method takes into account the stratification effect of the water body, effectively improves the accuracy and reliability of the radiative transfer modeling of the water body in the real scene, and has broad application prospects in the fields of water environment remote sensing monitoring, underwater target detection and recognition, and ocean engineering.

Description

Technical Field

[0001] The present invention relates to a method for modeling the radiative transfer of stratified water bodies based on two-stream approximation, belonging to the field of water optics, and is also of great significance in the detection and identification of underwater targets and the application of water quality monitoring. Background Art

[0002] The theory of radiative transfer in water bodies is used to quantitatively study the problem of radiative transfer in water bodies, and is the core theoretical problem in the research of water optics, water color remote sensing, marine and lake ecological dynamics, etc. In the past research on marine optics and ocean color remote sensing, most of them were carried out by assuming that the inherent optical properties and the vertical distribution of optical components of seawater are uniform. However, this assumption does not apply to all water body situations. Some ocean observation results show that vertical inhomogeneity will appear significantly in the upper part of the water body. Strictly speaking, vertically inhomogeneous water bodies are very common. In marine biological research, it is found that the chlorophyll concentration in water bodies has non-uniform characteristics on the vertical scale. Especially before the outbreak of red tides on the ocean surface, red tide algae will first grow in the subsurface layer of the water body. Similarly, marine sedimentology research shows that the inflow of fresh water in estuaries will cause the resuspension of sediment, resulting in non-uniform vertical suspended sediment concentration. At the same time, solar radiative transfer plays a primary role in the atmospheric and oceanic circulation processes. Therefore, an assessment of the physical process of radiative transfer is crucial for understanding the phenomena generated during the transfer process.

[0003] The present invention establishes a model that can describe the radiative transfer process of solar electromagnetic energy, uses the solution of the two-stream model to quickly and accurately evaluate the light field distribution in any stratified medium, and at the same time retains the most important physical essence in the radiative transfer model. The model is obtained by solving the improved two-stream formula through an iterative method, and the iterative method is used to converge the solution of the stratified two-stream radiative transfer formula. The model established by this method includes the scattered and direct irradiance under the water surface, and uses boundary conditions to allow the absorption rate, backscattering rate, beam attenuation rate, and conversion rate to vary with depth, improving the efficiency of remote sensing inversion and providing important theoretical and practical references for the study of stratified water body characteristics. Summary of the Invention

[0004] The present invention relates to a method for modeling the radiative transfer of stratified water bodies based on the two-stream approximation. The steps are as follows: By analyzing the characteristics of stratified water bodies, basic assumptions are set to complete the derivation of the two-stream formula. The two-stream formula with or without the direct component is solved by the iterative method, and at the same time, important characteristics such as the absorption rate, scattering rate, and attenuation rate in the formula are analyzed; Based on the sea surface incident irradiance model, considering the sea surface reflectivity and transmittance under the influence of wind speed, the coefficients of the two-stream model are further optimized; Finally, combined with the atmospheric radiative transfer model, the downward irradiance and direct irradiance of the water surface are calculated and substituted into the two-stream model to obtain the remote sensing reflectivity of the water body. The specific steps are as follows: 1 A method for modeling the radiative transfer of stratified water bodies based on the two-stream approximation, characterized by including the following steps:

[0005] (1) Conduct a theoretical analysis of the two-stream formula for stratified media with or without the direct component, derive a mathematical expression, and at the same time, analyze important characteristics such as the absorption rate, scattering rate, attenuation rate, and conversion rate in the formula, find methods for determining their values and influencing factors, and finally find the most primitive input parameters of the model;

[0006] (2) Solve the derived two-stream formula by the iterative method. Since Lambertian reflection cannot fully represent the characteristics of ocean water bodies, in the air-sea radiative transfer model, consider the effects of chlorophyll, suspended matter, dissolved organic matter, and wind-generated capillary waves on the coefficients in the two-stream formula in ocean water bodies, thereby calculating the sea surface bidirectional reflectance coefficient and considering the spectral variation of sea surface reflection;

[0007] (3) During the entire radiative transfer process, the downward irradiance is attenuated by the two processes of scattering and absorption in the water layer. At the same time, the upward irradiance becomes an increment of the downward irradiance due to the backscattering effect of the water body. Based on this principle, calculate the irradiance of each layer through the iterative method for the entire radiative process until the successive values of the upward irradiance at the sea surface converge.

[0008] 2 A method for modeling the radiative transfer of stratified water bodies based on the two-stream approximation, characterized in that: the "conduct a theoretical analysis of the two-stream formula for stratified media with or without the direct component, derive a mathematical expression, and at the same time, analyze important characteristics such as the absorption rate, scattering rate, attenuation rate, and conversion rate in the formula, find methods for determining their values and influencing factors, and finally find the most primitive input parameters of the model" described in step (1); The specific method is as follows:

[0009] The first step: Setting of basic assumptions:

[0010] Some basic assumptions are specified before modeling: It is assumed that the light distribution is independent of time, so the spectral characteristics are not allowed to change with time; It is assumed that in an ideal stratified medium, the spectral characteristics of each layer are uniform; It is assumed that the geometric form of the boundary of this radiative transfer medium can be roughly estimated as a parallel plane slab with infinite space defined between two horizontally parallel planes, and these slabs are of finite thickness and horizontally uniform, but not necessarily uniform in the vertical direction, such that the radiative transfer medium is in a steady state, the refractive index is a constant and there are no other light sources; It is assumed that there is no internal scattered irradiance, but this model can include parallel light sources, and direct sunlight can be converted into scattered light emitted by elastic scattering; It is assumed that at the bottom of the medium, all reflections, scattering, and parallel photon fluxes of the downwelling flux are Lambertian bodies, so that the photon flux of the upwelling flux can be fully scattered;

[0011] Step 2: Derive the two-stream formula using the average cosine:

[0012] The average cosine is an apparent optical property related to the sea surface condition, the incident light on the sea surface, and a series of inherent optical properties, including: absorption coefficient a, scattering coefficient b, beam attenuation coefficient c, and scattering phase function. At the same time, the average cosine can relate the total absorption coefficient of a small-volume water body to the scattering attenuation coefficients of the upwelling and downwelling fluxes and the reflected irradiance of a large-volume water body. According to the parallel plane assumption, the original transfer equation is as follows:

[0013]

[0014] Integrating this equation over the lower hemisphere gives the downwelling scattered irradiance:

[0015]

[0016] where the form factor r d (z) represents the main upward scattering rate of photons moving in the downward direction, and r u (z) represents the main downward scattering rate of photons moving in the upward direction. Therefore, a part of the downward scattering is determined by the backscattered photons, and further simplification gives:

[0017]

[0018] Similarly, integrating the original transfer equation over the upper hemisphere gives the upwelling scattered irradiance:

[0019]

[0020] For the special case that only contains the direct component, the original transfer equation is changed to:

[0021]

[0022] Since the direct irradiance only attenuates and propagates in the downward flow direction, integrating the equation over the lower hemisphere and simplifying gives the first-order differential equation of the direct downward flow irradiance:

[0023]

[0024] Step 3: Equivalent substitution:

[0025] The above three equations form a two-stream model equation for irradiance containing parallel or direct components, including the average cosine of the upward and downward flows, the shape factor, and the backscattering rate. At the same time, it represents a complex differential system with the number of unknowns greater than the number of equations, and transformation is needed to remove the unknowns, that is, r d (z), r u (z), b btc (z), b' btc (z), assuming that a(z), b(z), c(z) are the same for the upward and downward flow irradiances, that is, r d (z) = r u (z) = 1; assuming that a(z), b(z), c(z) are inherent optical properties, not apparent optical properties, then the scattering absorption coefficient: a d (z) = a u (z) = a(z), the backscattering rate: B du (z) = B ud (z) = b(z), the conversion rate: c f (z) = c b (z) = c(z), the beam attenuation rate: c tc (z)secθ = α(z). Substituting the above equivalent substitution equations into the two-stream model equation gives:

[0026]

[0027] 3. A method for modeling the radiative transfer of stratified water bodies based on the two-stream approximation, characterized in that: in step (2), "solving the derived two-stream formula by the iterative method. Since the Lambert reflection cannot fully represent the characteristics of ocean water bodies, in the air-sea radiative transfer model, the effects of chlorophyll, suspended matter, dissolved organic matter, and wind-generated capillary waves on the coefficients in the two-stream formula in ocean water bodies are considered, and thus the sea surface bidirectional reflection coefficient is calculated,

[0028] and the spectral variation of the sea surface reflection is considered"; the specific method is as follows:

[0029] Step 1: Solving the two-stream formula without the direct component:

[0030] For the two-stream radiative transfer model without the direct light component in a homogeneous water medium, that is, the absorption rate and the backscattering rate do not change with the water depth, using the boundary conditions: the downward irradiance of the surface E d (0), z = 0; the slope of the downward flow at the surface The upward irradiance of the bottom E u (h) = R b E d (h), z = h; the slope of the upward flow at the bottom Calculate the upward and downward scattered vector irradiances:

[0031]

[0032] Among them, for simplification, a variable is defined

[0033] For a stratified water body without the direct light component, the water body may not be homogeneous, but the chemical properties and optical properties are homogeneous within the same layer, and it is assumed that the downward light is completely scattered as soon as it enters the water body. Therefore, the above formula β d (0) can be rewritten as β d (0, i), where i is the i-th layer of the water body, and the two-stream formula for the downward flow in this case is obtained:

[0034]

[0035] Among them, due to the energy transfer principle, E d (z, i) = E d (0, i + 1);

[0036] Similarly, the general solution of the upward flow vector irradiance at the i-th layer and a depth of 0 can be obtained:

[0037]

[0038] Among them, due to the energy transfer principle, E u (0, i) = E u (z, i - 1);

[0039] Step 2: Solve the two-stream formula including the direct component:

[0040] For the two-stream radiative transfer model with the direct light component in a homogeneous water medium, the solution of the two-stream formula is divided into the general solution and the particular solution. First, perform integration and then take the logarithm to obtain the solution of the two-stream formula for the direct part of the light beam and the non-homogeneous differential equations for the downward and upward flows:

[0041] E s (z) = E s (0)e -αz

[0042]

[0043] The particular solution of the downwelling part is a function of the scattering attenuation rate α of the direct irradiance and is defined as: E d (z) = me -αz , where the constant m can be obtained by taking its second derivative: Similarly, the particular solution of the upwelling part is a function of the scattering attenuation rate α of the direct irradiance and is defined as: E u (z) = ne -αz , and the solution is:

[0044] Further, using five boundary conditions: the downwelling irradiance E d (0), z = 0; the slope of the downwelling at the surface the upwelling irradiance E u (h) = R b (E d (h) + E s (h)), z = h; the slope of the upwelling at the bottom the direct irradiance E s (0), z = 0, the upwelling and downwelling scattering vector irradiances are obtained:

[0045]

[0046] For a stratified water body without a direct light component, similar to the first step, the above β d (0) can be rewritten as β d (0, i), and m can be rewritten as m(i), where i is the i-th layer of the water body, and the general solution of the downwelling vector irradiance at the i-th layer with a depth of h is obtained:

[0047]

[0048] Among them, due to the energy transfer principle, E d (z, i) = E d (0, i + 1);

[0049] Similarly, n is rewritten as n(i), where i is the i-th layer of the water body, and finally the general solution of the upwelling vector irradiance at the i-th layer with a depth of 0 is obtained:

[0050]

[0051] Among them, due to the energy transfer principle, E u (0, i) = E u (z, i - 1);

[0052] Step 3: Calculation of the sea surface bidirectional reflectance coefficient:

[0053] The irradiance of the seawater surface downwelling current is affected by the reflection and refraction at the air-sea interface. A rough sea surface is conducive to more light entering the water body. The seawater surface slope and the surface foam coverage rate are functions of the wind speed, the observation angle, and the zenith angle. The sea surface reflectivity can be obtained through the seawater surface slope and the sea surface foam coverage rate. At the same time, the internal scattering surface reflectivity of the upwelling current irradiance can also be obtained. The data shows that when the wind speed is less than or equal to 10 m / s, the irradiance of the seawater surface downwelling current increases with the increase of the wind speed. Subsequently, when the wind speed is greater than 10 m / s, it basically remains unchanged. The wind-blown surface is a function of the surface slope and the wind speed. The seawater surface is divided into many small planes with random slopes, and a probability distribution function P(θ n ,w s ) can be obtained, which can be used to predict the probability of observing sunlight incident from the direction of (θ0, φ0) in the direction of (θ, φ), and is defined as follows:

[0054]

[0055] Among them, w s is the wind speed, θ n is the surface inclination angle. As increases, the slope rises. When θ n = 0, P(θ n ,w s ) is the largest, and P(θ n ,w s ) decreases with the increase of the slope;

[0056] At the same time, it is stipulated that the foam reflectivity is isotropic at 55%. In the solar spectral band, it increases with the increase of the white foam quantity and is a function of the sea surface roughness, the wind speed, and the wind pressure. For the seawater surface reflectivity, each reflectivity can be divided into two parts: the specular reflectivity and the foam reflectivity:

[0057] R s (ω,w s ) = ρ ssp (ω,w s ) + ρ f (w s )

[0058] R d (w s ) = ρ dsp (w s ) + ρ f (w s )

[0059] Among them, R s is the external specular reflectivity, R dis the external scattering reflectance, ρ ssp is the direct direct reflectance, ρ dsp is the specular scattering reflectance specified as 0.057, ρ f is the foam reflectance. When the upwelling irradiance reaches below the water surface, a part of the irradiance is reflected back into the water body, and only a part passes through the sea surface and projects into the air. The internal reflectance of the sea surface is set independent of the wavelength and the incident angle of the upwelling irradiance is a function of the wind speed:

[0060]

[0061] The internal reflectance of the sea surface decreases with the increase of the wind speed. When the incident angle is greater than the half-cone angle, the upwelling irradiance is completely reflected, which is specified as 0.485 here;

[0062] Step 4: Calculation of the two-stream model coefficients:

[0063] A water body mainly contains water molecules, phytoplankton, yellow substances, and suspended sediments, etc. These can all cause the absorption and scattering processes of the downwelling direct and diffuse irradiance, which can be measured by the radiance leaving the water or remote sensing radiance. The specific calculation method is as follows:

[0064] The absorption rate is a function of the wavelength and is related to chlorophyll a, dissolved organic carbon, and inorganic suspended matter:

[0065] a(λ) = a water (λ) + a chl (λ)c chl + a doc (λ)c doc + a ss (λ)c ss

[0066] where, a chl is the chlorophyll a absorption rate, a doc is the dissolved organic carbon absorption rate, a ss is the absorption rate of suspended matter, c chl is the chlorophyll a concentration, c doc is the dissolved organic carbon concentration, c ss is the suspended matter concentration;

[0067] Similarly, the backscattering rate and the conversion rate:

[0068] b(λ) = b water (λ) + b chl (λ)c chl + b ss (λ)c ss

[0069] c(λ) = 2.85 × b(λ)

[0070] Assume that the upwelling and downwelling conversion rates are the same. Meanwhile, the two-stream model requires the beam attenuation rate, which is defined as the combination of attenuation caused by absorption and scattering. The attenuation caused by absorption is obtained from the absorption rate, and the attenuation caused by scattering is obtained from the backscattering rate:

[0071] α(λ) = a(λ) + 53 × b(λ)

[0072] 4 A method for modeling the radiative transfer of stratified water bodies based on the two-stream approximation, characterized in that: in step (3), "during the entire radiative transfer process, the downwelling irradiance is attenuated by the two processes of scattering and absorption when passing through the water layer. At the same time, due to the backscattering effect of the water body, the upwelling irradiance becomes an increment of the downwelling irradiance. Based on this principle, the irradiance of each layer is calculated by the iterative method for the entire radiative process until the successive values of the upwelling current at the sea surface converge"; the specific method is as follows:

[0073] When the downwelling irradiance passes through the water body, a part of it is absorbed, a part is backscattered into the upwelling irradiance, and the last part reaches the bottom of the water body. The upwelling irradiance under the sea surface comes from the backscattering of the downwelling irradiance and the Lambert reflection at the bottom of the sea. The upwelling irradiance at the bottom of the water body is a function of the downwelling irradiance and the bottom reflectivity. In shallow water bodies, the upwelling irradiance under the water surface is composed of the backscattering of the downwelling irradiance and the bottom Lambert reflection. The upwelling irradiance is transmitted from the bottom to the surface and becomes the upwelling radiant energy. Therefore, the upwelling irradiance is related to the bottom type and the water body composition. The upwelling irradiance is affected by the bottom reflectivity. Strong backscattering can be caused by bottom particles and sediments. Assume that the bottom of the water body is a Lambert surface, that is, the incident light is isotropic during scattering and conversion. When the direct irradiance reaches the bottom, it is completely reflected into the upwelling irradiance. The bottom reflectivity is defined as the ratio of the upwelling irradiance to the sum of the downwelling irradiance and the direct irradiance:

[0074]

[0075] In optically shallow water bodies, the bottom type has a great influence on the bottom reflectivity. Therefore, for the convenience of analysis, it is stipulated that the bottom type is the seagrass type, and the specific situation can be measured by a spectroradiometer or an optical fiber probe, which can avoid the shadow problem. The surface reflectivity is defined as the ratio of the upwelling irradiance to the sum of the downwelling irradiance and the direct irradiance. The reflectivity under the sea surface and the reflectivity above the sea surface:

[0076]

[0077] Remote sensing reflectivity:

[0078]

[0079] Among them, the radiance leaving the water L w and E u and L u are related. The upwelling irradiance is converted into upwelling radiance through the Q factor:

[0080]

[0081] The remote sensing algorithm operates on the upwelling irradiance, avoiding the situation of solar glint. That is to say, for the part where the sensor measures the radiance leaving the water, the upwelling irradiance must be converted into upwelling radiance through the Q factor. If the bottom of the water body is a Lambertian surface, then Q = π, which is a function of wavelength, solar zenith angle, solar azimuth angle, and illumination conditions;

[0082] For a stratified water body medium, the two - stream formula cannot be easily obtained because the upwelling irradiance at the bottom is unknown until the downwelling scattering and direct irradiance reach the bottom. However, this limitation can be solved by an iterative method. To calculate the downwelling irradiance at the next interface, the downwelling irradiance at the top of this layer can be added to the irradiance of the upwelling irradiance backscattered into this layer plus the downwelling irradiance converted from the parallel irradiance. The upwelling irradiance is obtained in the same way. During the first iteration, the upwelling backscattered radiance entering each layer is initialized to 0. The entire iterative process is to repeatedly calculate using the current backscattered irradiance and the converted irradiance until the successive values of the upwelling at the sea surface converge.

[0083] The advantages of the present invention compared with the prior art are as follows:

[0084] (1) The existing technologies usually assume a single water body layer, ignoring the multi - layer structure existing in the water body, such as the optical property differences between the surface layer and the bottom layer. This simplified assumption may be applicable in a homogeneous water body environment, but in a complex stratified water body environment, the propagation and reflection of light are more complexly affected. The two - stream approximation method for simulating stratified water bodies can more accurately simulate the optical behavior of the water body by considering different layers of the water body and their optical properties, thereby improving the simulation accuracy of the reflectance of various components (such as plankton, sediment, etc.) in the water body;

[0085] (2) When dealing with the layer changes in the water body, it is affected by background noise and measurement saturation effects, resulting in inaccurate measurement of the water body characteristic parameters. The two - stream approximation method for simulating stratified water bodies effectively reduces the interference of background noise and saturation effects on the simulation results by introducing a hierarchical optical model, thereby improving the sensitivity to the optical properties of the water body and significantly enhancing the performance of the model in a complex water body environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is the technical process of the present invention; Figure 2 is the comparison of the MC-two-stream model results, where (a) is the simulation result of the two-stream approximation model, and (b) is the simulation result of the Monte Carlo model (MC); Figure 3 is the accuracy verification of the MC-two-stream model, (a) is pure water body, and (b) is turbid water body. Specific embodiments

[0087] To better illustrate a method for modeling the radiative transfer of stratified water bodies based on two-stream approximation involved in the present invention, the model of the present invention and the Monte Carlo model were tested and analyzed, and good results were obtained. The specific implementation methods are as follows:

[0088] (1) Conduct a theoretical analysis of the two-stream formula for stratified media and the case of whether it includes a direct component, and derive a mathematical expression. At the same time, analyze important characteristics such as the absorption rate, scattering rate, attenuation rate, and conversion rate in the formula, find methods to determine their values and influencing factors, and finally find the most original input parameters of the model;

[0089] (2) Solve the derived two-stream formula by the iterative method. Since Lambert reflection cannot fully represent the characteristics of ocean water bodies, in the air-sea radiative transfer model, consider the effects of chlorophyll, suspended matter, dissolved organic matter, and wind-generated capillary waves on the sea surface in the two-stream formula, thereby calculating the sea surface bidirectional reflectance coefficient, and consider the spectral variation of sea surface reflection;

[0090] (3) During the entire radiative transfer process, the downwelling irradiance is attenuated by the two processes of scattering and absorption through the water layer. At the same time, the upwelling irradiance becomes an increment of the downwelling irradiance due to the backscattering effect of the water body. Based on this principle, calculate the irradiance of each layer through the iterative method for the entire radiative process until the successive values of the upwelling irradiance at the sea surface converge.

[0091] Compare the results of the two-stream model calculated by stratified iteration of the water body with the results simulated by the MC model. Apply and verify the two-stream model of water body stratification by calculating the surface reflectance and the irradiance distribution in natural water bodies at different wavelengths. And the absorption rate and scattering rate that change due to the change of biochemical factors in the water body will change the irradiance distribution of the surface light field. Figure 2It shows the variation curve of surface irradiance reflectance with wavelength when two kinds of seawater optically active substances are quantified and another optically active substance changes. The hierarchical thickness of the two-stream model uses optical thickness. When the chlorophyll a concentration is less than or equal to 1 μg / L, in the wavelength range from 400 nm to 685 nm, the performance of the two-stream model is better than that of the MC model, but in the wavelength range greater than 685 nm, the performance of the two-stream model is inferior to that of the MC model. When the chlorophyll a concentration is 5 μg / L, the two-stream model performs better than the MC model in the wavelength range from 475 nm to 600 nm, but performs worse than the MC model in the wavelength ranges from 400 nm to 475 nm and from 600 nm to 700 nm. When the chlorophyll a concentration is greater than or equal to 10 μg / L, the performance of the two-stream model is inferior to that of the MC model in the wavelength range from 400 nm to 700 nm.

[0092] When the suspended sediment concentration is from 0 to 1 mg / L, the water layer thickness is 1 m. When the suspended sediment concentration is 5 mg / L, the water layer thickness is 0.5 m; when the suspended sediment concentration is from 10 to 20 mg / L, the water layer thickness is 0.1 m. When the suspended sediment concentration is from 0 to 1 mg / L, the performance of the two-stream model is better than that of the MC model in the wavelength range from 400 nm to 700 nm; when the concentration is 5 mg / L, the two-stream model performs worse than the MC model in the wavelength range from 400 nm to 510 nm, but performs better than the MC model in the wavelength range from 510 nm to 700 nm; when the suspended sediment concentration is from 10 to 20 mg / L, the performance of the two-stream model is better than that of the MC model in the wavelength range from 400 nm to 700 nm. For all ranges of dissolved organic carbon concentration, the performance of the two-stream model is inferior to that of the MC model in the wavelength range from 400 nm to 500 nm, but is better than that of the MC model in the wavelength range from 500 nm to 700 nm.

[0093] Figure 3 It shows the comparative scatter plots of the MC model and the two-stream model in the cases of pure water body and relatively turbid water body. The R values of the two cases are 0.9579 and 0.9806 respectively. In the case of pure water, when all variables, the concentrations of chlorophyll a, dissolved organic carbon and suspended sediment are 0, only the pure water absorption rate and the pure water backscattering rate affect the total reflectance. Regardless of water depth and bottom type, the error in pure water is higher than that in turbid water. At the same time, the errors of the two hierarchical two-stream models and the MC model are related to the choice of hierarchical thickness. Smaller hierarchies can better approximate the reflectance values. However, because all variables in the previous hierarchy are used to calculate the input values of the next hierarchy, a larger number of hierarchies will affect the error distribution of the entire water body. These errors will be particularly prominent in clear water in the blue light band (400 nm to 480 nm) because the backscattering and absorption rates are high. 2

[0094] ​The two-stream approximation simulation method for stratified water bodies established by the present invention helps to explore the relationship between the water body stratification structure and optical properties more deeply and scientifically, and at the same time significantly improves the spatio-temporal continuous simulation ability of water body optical properties. This method can accurately simulate the optical behaviors of different layers in the water body, and significantly improves the simulation accuracy of the water body reflectivity. By effectively reducing the interference of background noise and measurement saturation effects, the sensitivity to water body optical properties and stratification changes is enhanced, ensuring the generality and reliability of the model in complex water body environments.

Claims

1. A method for modeling the radiative transfer in stratified water bodies based on the two-stream approximation, characterized in that The steps include the following: (1) Conduct theoretical deduction on the radiation transfer equation for the vertically stratified water medium and in the case of including the direct component, and derive the mathematical expression of the radiation quantity of the light field in the water body with vertical concentration stratification, that is, the two-stream approximation model. The specific implementation method is as follows: According to the parallel plane assumption, integrating the radiation transfer equation in the lower hemisphere can obtain the downward diffuse irradiance: where E represents irradiance, z represents the vertical position coordinate, a represents the absorption coefficient, B represents the conversion coefficient caused by the scattering process, c represents the total attenuation coefficient, the subscripts d and u respectively represent the downward and upward directions, the subscript s represents the solar incident direction, and the subscript f represents forward scattering; similarly, integrating the radiation transfer equation in the upper hemisphere can obtain the upward diffuse irradiance: where the subscript b represents backscattering; for the special case of only including the direct component, integrating the original transfer equation in the lower hemisphere to obtain the first-order differential form of the direct downward irradiance: Among them, c tc represents the attenuation coefficient of downward radiation; θ represents the observed zenith angle; At the same time, analyze the important optical properties in the model: absorption rate, scattering rate, attenuation rate, and conversion rate, find the methods to determine their values and influencing factors, and finally find the most original input parameters of the model; (2) Numerically solve the derived two-stream approximation model by the iterative method. Since Lambert reflection cannot fully represent the characteristics of ocean water, in the radiation transfer model of the atmosphere-ocean coupled system, consider the effects of chlorophyll, suspended matter, dissolved organic matter, and wind-generated capillary waves on the sea surface in the two-stream approximation model, thereby calculating the bidirectional reflectance of the sea surface and considering the spectral variation of the sea surface reflection; (3) In the radiation transfer process of the entire water medium layer, consider the conversion mechanism of the backward scattering in the scattering process of the downward and upward irradiances, and calculate the downward irradiance and upward irradiance of each layer by the iterative method until the successive values of the upward irradiance at the sea surface converge.

2. The method for modeling radiation transfer of layered water bodies based on two-stream approximation according to claim 1 is characterized by: The specific method of step (1) is as follows: The first step: Setting of basic assumption conditions: The following assumptions are made in the modeling: Assume that the distribution of light is independent of time, that is, the spectral characteristics do not change with time; Assume that in an ideal stratified medium, the spectral characteristics of each layer are uniform; Assume that the geometric form of the boundary of this radiation transfer medium can be roughly estimated as a parallel plate with infinite space defined between two parallel planes. These plates are of finite thickness and horizontally uniform, but not necessarily uniform in the vertical direction, so that the radiation transfer medium is in a stable state, the refractive index is a constant and there are no other light sources; Assume that there is no internal diffuse irradiance, but this model can include parallel light sources, and the direct sunlight can be converted into scattered light emitted by elastic scattering; Assume that at the bottom of the medium, all reflections, scatterings, and parallel photon fluxes of the downward currents are Lambertian, so that all the photon fluxes of the upward current can be scattered; The second step: Derive the two-stream approximation model expression using the mean cosine; Step 3: Equivalent substitution: The above three equations form a two-stream approximate model expression for irradiance containing parallel or direct components, including the mean cosine of upwelling and downwelling, the shape factor, and the backscattering rate. At the same time, it represents a complex differential system with the number of unknowns greater than the number of equations. It is necessary to perform a transformation to remove the unknowns. Assume that a(z), b(z), and c(z) are the same for upwelling and downwelling; that is, a d (z) = a u (z) = a(z), B du (z) = B ud (z) = b(z), c f (z) = c b (z) = c(z), c tc (z)secθ = α(z). Substituting the above equivalent substitution equations into the two-stream approximate model expression, we get:

3. A method for modeling the radiative transfer of stratified water bodies based on the second-order approximation according to claim 1, characterized in that: The specific method of step (2) is as follows: The first step: Solving the two-stream approximation model without the direct component: For the two - stream approximate radiative transfer model without direct light component in a homogeneous water medium, that is, the absorption rate and the backscattering rate do not change with the water depth, using the boundary conditions: the downward irradiance of the surface E d (0), z = 0; the slope of the downward flow at the surface the upward irradiance of the bottom E u (h)=R b E d (h), z = h; the slope of the upward flow at the bottom Calculate its upward and downward scattered irradiances: Wherein, for simplicity, a variable is defined For a stratified water body that does not contain a direct light component, the water body may not be homogeneous, but the chemical and optical properties are homogeneous within the same layer. And it is assumed that the downwelling light is completely scattered once it enters the water body. Therefore, the above formula β d (0) can be rewritten as β d (0, i), where i is the i-th layer of the water body, and the expression of the downwelling two-stream approximation model in this case is obtained: where, due to the energy transfer principle, E d (z, i) = E d (0, i + 1); Similarly, the general solution of the upward irradiance at the i-th layer with a depth of 0 can be obtained: Among them, due to the energy transfer principle, E u (0, i) = E u (z, i - 1); Step 2: Solving the two-stream approximation formula containing the direct component: For the two-stream approximation radiative transfer model containing the direct light component in a homogeneous water medium, the solution of the two-stream approximation formula is divided into the general solution and the particular solution. First, perform integration to obtain the solution of the two-stream approximation formula for the direct part of the light beam and the inhomogeneous differential equations of the downwelling and upwelling fluxes: E s (z) = E s (0)e -αz The particular solution of the downwelling part is a function of the scattering attenuation rate α of the direct irradiance and is defined as: E d (z) = me -αz , where the constant m can be obtained by taking its second derivative: Similarly, the particular solution of the upwelling part is a function of the scattering attenuation rate α of the direct irradiance and is defined as: E u (z) = ne -αz , and the solution is: Further utilize five boundary conditions: the irradiance E of the surface downwelling current d (0), z = 0; the slope of the surface downwelling current the irradiance E of the bottom upwelling current u (h) = R b (E d (h) + E s (h)), z = h; the slope of the bottom upwelling current the direct irradiance E of the surface s (0), z = 0, and obtain the irradiance of the scattering vectors of the upwelling and downwelling currents: For a stratified water body that does not contain a direct light component, similar to the first step, the above β d (0) can be rewritten as β d (0, i), and m can be rewritten as m(i), where i is the i-th layer of the water body, to obtain the general solution of the downward flow vector irradiance at the i-th layer with a depth of h: Among them, due to the energy transfer principle, E d (z, i) = E d (0, i + 1); Similarly, rewrite n as n(i), where i is the i-th layer of the water body. Finally, obtain the general solution of the upwelling vector irradiance at the i-th layer with a depth of 0: Among them, due to the energy transfer principle, E u (0, i) = E u (z, i - 1); Step 3: Calculation of the sea surface bidirectional reflectance coefficient: The irradiance of the downward current on the sea surface is affected by the reflection and refraction at the air-sea interface. The wind-blown surface is a function of the surface slope and wind speed, dividing the sea surface into many small planes with random slopes, resulting in a probability distribution function P(θ n ,w s ), which can be used to predict the probability of observing sunlight incident from the direction of (θ0, φ0) in the direction of (θ, φ), defined as follows: Among them, w s is the wind speed, and θ n is the surface tilt angle; At the same time, assume that the sea surface foam reflectance is isotropic and is 55%. In the solar spectral band, it increases with the increase in the foam amount and is a function of the sea surface roughness, wind speed, and wind pressure. For the seawater surface reflectance, each reflectance can be divided into two parts: the specular reflectance and the foam reflectance: R s (ω, w s ) = ρ ssp (ω, w s ) + ρ f (w s ) R d (w s ) = ρ dsp (w s ) + ρ f (w s ) Among them, R s is the specular reflectance, R d is the external scattering reflectance, ρ ssp is the direct direct reflectance, ρ dsp is the specular scattering reflectance, given as 0.057, ρ f is the foam reflectance. When the upwelling irradiance reaches below the water surface, a part of the irradiance is reflected back into the water body, and only a part passes through the sea surface and projects into the air. The internal reflectance of the sea surface is set to be independent of the wavelength, and the incident angle of the upwelling irradiance is a function of the wind speed: The internal reflectance of the sea surface decreases with the increase in wind speed. When the incident angle is greater than the half-cone angle, the upwelling irradiance is completely reflected, which is given as 0.485 here; Step 4: Calculation of the two-stream approximation model coefficients: The optically active substances in the water body include water molecules, phytoplankton, yellow substances, and suspended matter, all of which can cause the absorption and scattering processes of the downwelling direct and diffuse irradiances and can be measured by the water-leaving radiance or remote sensing radiance. The specific calculation methods are as follows: The absorption rate is a function of wavelength and is related to chlorophyll a, dissolved organic carbon, and inorganic suspended matter: a(λ) = a water (λ) + a chl (λ)c chl + a doc (λ)c doc + a ss (λ)c ss where a chl is the chlorophyll a absorption coefficient, a doc is the dissolved organic carbon absorption coefficient, a ss is the phytoplankton absorption coefficient, c chl is the chlorophyll a concentration, c doc is the dissolved organic carbon concentration, c ss is the phytoplankton concentration; Similarly, the backscattering coefficient and the conversion coefficient: b(λ) = b water (λ) + b chl (λ)c chl + b ss (λ)c ss c(λ) = 2.85 × b(λ) And assume that the upwelling and downwelling conversion rates are the same. At the same time, the two-stream approximation model requires the beam attenuation rate, which is defined as the combination of the attenuation caused by absorption and scattering. The attenuation caused by absorption is obtained from the absorption rate, and the attenuation caused by scattering is obtained from the backscattering rate: α(λ) = a(λ) + 53 × b(λ).

4. A method for modeling the radiative transfer in stratified water bodies based on the two-stream approximation according to claim 1, characterized in that: The specific method of step (3) is as follows: When the downwelling irradiance passes through the water body, part of it is absorbed, part of it is backscattered into the upwelling irradiance, and the last part reaches the bottom of the water body. The upwelling irradiance under the sea surface comes from the backscattering of the downwelling irradiance and the Lambert reflection at the bottom of the sea. The upwelling irradiance at the bottom of the water body is a function of the downwelling irradiance and the bottom reflectance. In the shallow water body, the upwelling irradiance under the water surface is composed of the backscattering of the downwelling irradiance and the bottom Lambert reflection. The upwelling irradiance is transmitted from the bottom to the surface and becomes the upwelling radiation energy. Therefore, the upwelling irradiance is related to the bottom type and the water body composition. The upwelling irradiance is affected by the bottom reflectance. Strong backscattering can be caused by bottom particles and sediments. Assume that the bottom of the water body is a Lambert surface, that is, the incident light is isotropic during scattering and conversion. When the direct irradiance reaches the bottom, it is completely reflected into the upwelling irradiance. The bottom reflectance is defined as the ratio of the upwelling irradiance to the sum of the downwelling irradiance and the direct irradiance: The surface reflectance is defined as the ratio of the upwelling irradiance to the sum of the downwelling irradiance and the direct irradiance, and the reflectance R w below the sea surface and the reflectance R a above the sea surface are expressed as: Remote sensing reflectance: where the upwelling radiation L w is related to E u and L u where the subscript a represents air, the subscript w represents water body, 0 represents the position just at the water surface, and the upwelling irradiance is converted into upwelling radiation by the Q factor: Remote sensing algorithms operate on the upwelling irradiance, avoiding the situation of solar glint. That is, the sensor measures the in-water irradiance part. The upwelling irradiance must be converted into upwelling radiance through the Q factor. Q is a function of wavelength, solar zenith angle, solar azimuth angle, and illumination conditions. If the bottom is a Lambertian surface, then Q = π. For a stratified water medium, the two-stream approximation model cannot be easily solved because the upwelling irradiance at the bottom is unknown until the downwelling scattered and direct irradiance reach the bottom. However, this limitation can be solved by an iterative method. To calculate the downwelling irradiance at the next interface, the downwelling irradiance at the top of this layer is added to the upwelling irradiance scattered back into this layer, plus the downwelling irradiance converted from the parallel irradiance; the upwelling irradiance is obtained in the same way. During the first iteration, the upwelling backscattered radiance entering each layer is initialized to 0. The entire iterative process is to repeatedly calculate using the current backscattered irradiance and the converted irradiance until the successive values of the upwelling irradiance at the sea surface converge.

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