Layered water body radiation transfer modeling method based on two-flow approximation

Abstract

The invention relates to a two-flow approximation-based layered water body radiation transmission modeling method, which comprises the following steps of: by analyzing the vertical layering characteristic of water body component concentration, setting a basic assumption condition to realize two-flow approximation-based water body light field radiation quantity modeling, and solving a scene containing a direct component through an iteration method; coupling a sea surface incident irradiance model, comprehensively considering the influence of wind on water surface reflection and transmission, and further optimizing to obtain a coefficient of a two-flow model; and finally, in combination with boundary conditions including initial illumination, water body attribute parameters and the wave water surface under the influence of the wind speed, calculating the downflow irradiance and the direct irradiance of the water surface, and substituting the downflow irradiance and the direct irradiance into a two-flow formula to obtain the remote sensing reflectivity of the water body. According to the analysis method, the layering effect of the water body is considered, the accuracy and reliability of real scene water body radiation transmission modeling are effectively improved, and the analysis method has wide application prospects in the fields of water environment remote sensing monitoring, underwater target detection and recognition, ocean engineering and the like.

Description

Technical Field

[0001] The present invention relates to a layered water body radiation transmission modeling method based on two-stream approximation, which belongs to the field of water body optics and has important significance in the detection and identification of underwater targets and water quality monitoring applications. Background Art

[0002] Water body radiation transfer theory is used to quantitatively study the radiation transfer problem in water bodies. It is the core theoretical problem of water body optics and water color remote sensing, ocean and lake ecological dynamics, etc. In the past studies of ocean optics and ocean color remote sensing, most of them were carried out by assuming that the inherent optical properties and optical components of seawater are uniformly distributed vertically. However, this assumption is not suitable for all water bodies. Some ocean observations show that vertical inhomogeneity will appear significantly in the upper part of the water body. Strictly speaking, vertically non-uniform water bodies are very common. In marine biological studies, it was found that the chlorophyll concentration in the water body has non-uniform characteristics on the vertical scale, especially before the red tide erupts in the ocean surface, the red tide algae will first grow in the sub-surface of the water body. Similarly, marine sedimentology studies have shown that the inflow of fresh water from the estuary will cause the resuspension of sediment, resulting in the vertical non-uniformity of suspended sediment concentration. At the same time, solar radiation transmission occupies a primary position in the atmospheric and ocean circulation process. Therefore, an assessment of the physical process of radiation transmission is crucial to understanding the phenomena produced during the transmission process.

[0003] The present invention establishes a model that can describe the radiation transmission process of solar electromagnetic energy. By using the solution of the two-stream model, the light field distribution in any stratified medium is quickly and accurately evaluated, while retaining the most important physical essence of the radiation transmission model. The model is obtained by solving the improved two-stream formula by an iterative method, and the solution of the stratified two-stream radiation transmission formula is converged by an iterative method. The model established by this method includes the scattering 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, thereby improving the efficiency of remote sensing inversion and providing important theoretical and practical references for the study of stratified water characteristics. Summary of the invention

[0004] The present invention relates to a radiation transmission modeling method for stratified water bodies based on two-stream approximation, and the steps are as follows: by analyzing the characteristics of stratified water bodies, setting basic assumptions to complete the derivation of two-stream formulas, solving the two-stream formulas for whether they contain direct components through an iterative method, and analyzing important characteristics such as absorptivity, scattering rate and attenuation rate in the formulas; based on the sea surface incident irradiance model, comprehensively considering the sea surface reflectivity and transmittance under the influence of wind speed, further optimizing the coefficients of the two-stream model; finally, combining the atmospheric radiation transmission model, calculating the downwelling irradiance and direct irradiance of the water surface, and bringing them into the two-stream model to obtain the remote sensing reflectance of the water body, and the specific steps are as follows: 1 A radiation transmission modeling method for stratified water bodies based on two-stream approximation, characterized in that it comprises the following steps:

[0005] (1) Theoretically analyze the two-flow formula for layered media and whether it contains direct components, derive mathematical expressions, and analyze important characteristics such as absorptivity, scattering rate, attenuation rate, and conversion rate in the formula to find out the method to determine their values ​​and the influencing factors, and finally find the most original input parameters of the model;

[0006] (2) Solve the derived two-stream formula by iterative method. Since Lambertian reflectance cannot fully represent the characteristics of ocean water, the effects of chlorophyll, suspended matter, dissolved organic matter and wind-driven capillary waves on the coefficients in the two-stream formula are considered in the air-sea radiation transmission model. The bidirectional reflection coefficient of the sea surface is calculated, and the spectral variation of the sea surface reflection is also considered.

[0007] (3) During the entire radiation transmission 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 of the water body. Based on this principle, the irradiance of each layer is calculated through an iterative method for the entire radiation process until the successive values ​​of the upwelling at the sea level converge.

[0008] 2. A stratified water body radiation transmission modeling method based on two-stream approximation according to claim 1, characterized in that: the step (1) of "theoretically analyzing the two-stream formula for stratified media and whether it contains direct components, deriving mathematical expressions, and analyzing important characteristics such as absorptivity, scattering rate, attenuation rate, and conversion rate in the formula, finding methods for determining their values ​​and influencing factors, and finally finding the most original input parameters of the model"; the specific method is as follows:

[0009] Step 1: Setting of basic assumptions:

[0010] Some basic assumptions are made before modeling: it is assumed that the distribution of light is independent of time, so the spectral characteristics are not allowed to change with time; it is assumed that in an ideal layered medium, the spectral characteristics of each layer are uniform; it is assumed that the geometric form of the boundary of this radiation transmission medium can be roughly estimated as a parallel plane plate defined as infinite space between two horizontal parallel planes, which are of finite thickness and uniform horizontally, but not necessarily uniform in the vertical direction, so that the medium of radiation transmission is a stable 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, scatterings and parallel photon flows of the downflow are Lambertian bodies, so the photon flows of the upflow can be completely scattered;

[0011] Step 2: Use the mean cosine to derive the second-rate formula:

[0012] The mean cosine is an apparent optical property that is related to the sea surface conditions, the incident light on the sea surface, and a series of intrinsic optical properties, including absorptivity a, scattering rate b, beam attenuation rate c, and scattering phase function. At the same time, the mean cosine can relate the complete absorptivity of a small volume of water to the scattering attenuation rate of the upwelling and downwelling of a large volume of water and the reflected irradiance. According to the parallel plane assumption, the original transmission equation is as follows:

[0013]

[0014] Integrating this formula in the lower hemisphere gives the downwelling scattered irradiance:

[0015]

[0016] Among them, the shape 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, part of the scattering in the downward direction is determined by the backscattered photons. Further simplification can be obtained:

[0017]

[0018] Similarly, integrating the original transmission equation in the upper hemisphere can obtain the upwelling scattered irradiance:

[0019]

[0020] For the special case of only direct components, the original transmission equation is changed to:

[0021]

[0022] Since the direct irradiance is only attenuated and transmitted in the downwelling direction, the formula is integrated in the lower hemisphere and simplified to obtain the first-order differential formula of the direct downwelling irradiance:

[0023]

[0024] Step 3: Equivalent substitution:

[0025] The above three equations form a two-stream model of irradiance including parallel or direct components, including the mean cosine of upwelling and downwelling, shape factor and backscattering rate, and represent a complex differential system with a greater number of unknown quantities than the number of equations. Transformation is required to remove the unknown quantities, i.e., r d (z),r u (z), b btc (z),b' btc (z), assuming that a(z), b(z), c(z) are the same for upwelling and downwelling irradiances, i.e., r d (z) = r u (z) = 1; Assuming that a(z), b(z), c(z) are intrinsic optical properties, not apparent optical properties, then the scattering absorption rate is: a d (z) = a u (z) = a(z), backscattering rate: B du (z) = B ud (z) = b(z), conversion rate: c f (z) = c b (z) = c(z), beam attenuation rate: c tc (z)secθ=α(z), substituting the above equivalent substitution formula into the two-stream model formula, we can get:

[0026]

[0027] 3. The method for modeling radiation transmission of layered water bodies based on two-stream approximation according to claim 1, characterized in that: in step (2), the derived two-stream formula is solved by an iterative method. Since the Lambert reflection cannot fully represent the characteristics of the ocean water body, the effects of chlorophyll, suspended matter, dissolved organic matter and wind-driven sea surface capillary waves in the ocean water on the coefficients in the two-stream formula are considered in the air-sea radiation transmission model, thereby calculating the sea surface bidirectional reflection coefficient.

[0028] And consider the spectral changes of sea surface reflection"; the specific method is as follows:

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

[0030] For a two-stream radiation transfer model in a homogeneous water medium that does not contain direct light components, that is, the absorption rate and backscattering rate do not change with water depth, the boundary condition is used: the surface downwelling irradiance E d (0), z = 0; surface downwelling slope Bottom upwelling irradiance E u (h) = R b E d (h), z = h; bottom upwelling slope Calculate its upwelling and downwelling scattered vector irradiance:

[0031]

[0032] In order to simplify, a variable is defined

[0033] For stratified water bodies that do not contain direct light components, the water body may not be uniform, but the chemical and optical properties are uniform within the same layer, and it is assumed that the downwelling light is completely scattered as soon as it enters the water body. Therefore, the above formula β can be d (0) rewritten as β d (0,i), where i is the i-th layer of the water body, the downflow two-flow formula in this case is:

[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 upwelling vector irradiance at layer i and depth 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 radiation transfer model containing direct light components in a uniform water medium, the solutions of the two-stream formula are divided into general solutions and special solutions. First, integrate and then take the logarithm to obtain the solutions of the two-stream formula for the direct part of the beam and the non-homogeneous differential equations of the downflow and upflow:

[0041] E s (z) = E s (0)e -αz

[0042]

[0043] The particular solution of the downwelling part is a function of the diffuse 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 for the upwelling part is a function of the diffuse attenuation rate α of the direct irradiance and is defined as: E u (z) = ne -αz , and we get:

[0044] Five boundary conditions are further used: surface downwelling irradiance E d (0), z = 0; surface downwelling slope Bottom upwelling irradiance E u (h) = R b (E d (h)+E s (h)), z = h; bottom upwelling slope Surface direct irradiance E s (0), z = 0, and the upwelling and downwelling scattered vector irradiances are obtained:

[0045]

[0046] For stratified water bodies that do not contain direct light components, the above formula β can be d (0) rewritten as β d (0,i), and m is rewritten as m(i), where i is the i-th layer of the water body, and the general solution of the downwelling vector irradiance in the i-th layer and the depth 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 in the i-th layer and the 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 bidirectional reflection coefficient of the sea surface:

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

[0054]

[0055] in, w s is the wind speed, θ n is the surface inclination angle, as As the slope increases, θ n = 0 when P(θ n ,w s ) is the largest, P(θ n ,w s ) decreases as the slope increases;

[0056] At the same time, it is stipulated that the foam reflectivity is isotropic at 55%. In the solar spectrum band, it increases with the increase of the amount of white foam. It is a function of sea surface roughness, wind speed and wind pressure. For the seawater surface reflectivity, each reflectivity can be divided into two parts, mirror reflectivity and 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 reflectance, R dis the external scattering reflectivity, ρ ssp is the direct reflectivity, ρ dsp The specular reflectivity is set to 0.057, ρ f is the foam reflectivity. When the upwelling irradiance reaches the water surface, part of it is reflected back into the water column, and only part of it is projected through the sea surface into the air. The internal reflectivity 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:

[0060]

[0061] The internal reflectivity of the sea surface decreases with increasing wind speed. When the angle of incidence is greater than the semi-conical angle, the upwelling irradiance is completely reflected, which is specified as 0.485 here;

[0062] Step 4: Calculation of the coefficients of the second-rate model:

[0063] A water body mainly contains water molecules, phytoplankton, yellow matter and suspended sediments, all of which can cause the absorption and scattering of direct and indirect irradiance of the downwelling flow, which can be measured by water-leaving radiation or remote sensing radiation. The specific calculation method is as follows:

[0064] Absorption is a function of 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] Among them, 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 solids, c chl is the chlorophyll a concentration, c doc is the dissolved organic carbon concentration, c ss is the concentration of suspended solids;

[0067] Likewise, the backscatter rate and 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] It is assumed that the conversion rates of upwelling and downwelling are the same. At the same time, the two-stream 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 absorptivity, and the attenuation caused by scattering is obtained from the backscattering rate:

[0071] α(λ)=a(λ)+53×b(λ)

[0072] 4. The method for modeling radiation transfer of stratified water bodies based on two-stream approximation according to claim 1, characterized in that: the step (3) states that "in the entire radiation 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 of the water body. According to this principle, the irradiance of each layer is calculated by an iterative method for the entire radiation process until the successive values ​​of the upwelling at the sea level converge." The specific method is as follows:

[0073] 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 Lambertian reflection of the bottom of the sea. When the upwelling irradiance is at the bottom of the water body, it 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 Lambertian reflection. The upwelling irradiance is transmitted to the surface at the bottom and becomes the upwelling radiation energy. Therefore, the upwelling irradiance is related to the bottom type and the composition of the water body. The upwelling irradiance is affected by the bottom reflectivity. Strong backscattering can be caused by bottom particles and sediments. It is assumed that the bottom of the water body is assumed to be a Lambertian surface, that is, the incident light is isotropic when scattered and converted. 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 optical shallow water bodies, the bottom type has a great influence on the bottom reflectivity. Therefore, for the convenience of analysis, the bottom type is defined as the seaweed type. The specific situation can be measured by a spectroradiometer or a fiber optic probe to 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 on the sea surface are:

[0076]

[0077] Remote sensing reflectivity:

[0078]

[0079] Among them, the water-leaving radiation L w With E u and L u The Q factor is used to convert the upwelling irradiance into upwelling radiation:

[0080]

[0081] Remote sensing algorithms operate on upwelling irradiance, avoiding solar glare. That is, the sensor measures the portion of irradiance that leaves the water. Upwelling irradiance must be converted to upwelling radiation by the Q factor. If the bottom of the water body is a Lambertian surface, then Q = π, which is a function of wavelength, solar apex angle, solar azimuth angle, and lighting conditions.

[0082] For a stratified water medium, the two-flow 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. In order 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 and added to the downwell irradiance converted from the parallel irradiance. The upwelling irradiance is also obtained in this way. During the first iteration, the upwelling backscattering irradiance entering each layer is initialized to 0. The entire iterative process is to repeatedly use the current backscattering irradiance and the converted irradiance for calculation until the successive values ​​of the upwelling at sea level converge.

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

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

[0085] (2) When dealing with layer changes in water bodies, the background noise and measurement saturation effects affect the measurement of water body characteristic parameters, resulting in inaccurate measurement. The two-stream approximation method for simulating layered 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 water bodies and significantly enhancing the performance of the model in complex water environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 The technical process of the present invention; Figure 2 Comparison of the results of the MC-two-stream model, where (a) is the simulation result of the two-stream approximate model, and (b) is the simulation result of the Monte Carlo model (MC); Figure 3 This is the accuracy verification of the MC-two-stream model, (a) is pure water body, and (b) is turbid water body. DETAILED DESCRIPTION

[0087] In order to better illustrate the stratified water body radiation transfer modeling method based on two-stream approximation involved in the present invention, the model of the present invention and the Monte Carlo model were used to test and analyze, and good results were achieved. The specific implementation method is as follows:

[0088] (1) Theoretically analyze the two-flow formula for layered media and whether it contains direct components, derive mathematical expressions, and analyze important characteristics such as absorptivity, scattering rate, attenuation rate, and conversion rate in the formula to find out the method to determine their values ​​and the influencing factors, and finally find the most original input parameters of the model;

[0089] (2) Solve the derived two-stream formula by iterative method. Since Lambertian reflectance cannot fully represent the characteristics of ocean water, the effects of chlorophyll, suspended matter, dissolved organic matter and wind-driven capillary waves on the coefficients in the two-stream formula are considered in the air-sea radiation transmission model. The bidirectional reflection coefficient of the sea surface is calculated, and the spectral variation of the sea surface reflection is also considered.

[0090] (3) During the entire radiation transmission 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 of the water body. Based on this principle, the irradiance of each layer is calculated through an iterative method for the entire radiation process until the successive values ​​of the upwelling at the sea level converge.

[0091] The results of the two-stream model for water stratification iterative calculation are compared with the results of the MC model simulation. The two-stream model for water stratification is applied and verified by calculating the surface reflectance and irradiance distribution in natural water bodies at different wavelengths. In addition, the changes in the absorptivity and scattering rate due to changes in biochemical factors in the water body will change the irradiance distribution of the surface light field. Figure 2The curves of surface irradiance reflectance changing with wavelength are shown when two optically active substances in seawater are quantitative and the other optically active substance changes. The layer thickness of the two-stream model uses optical thickness. When the chlorophyll a concentration is less than or equal to 1μg / L, the performance of the two-stream model is worse than the MC model in the 400nm to 685nm band, but it is not as good as the MC model in the band greater than 685nm. When the chlorophyll a concentration is 5μg / L, the two-stream model performs better than the MC model in the 475nm to 600nm band, but it is not as good as the MC model in the 400nm to 475nm and 600nm to 700nm bands. When the chlorophyll a concentration is greater than or equal to 10μg / L, the performance of the two-stream model in the 400nm to 700nm band is not as good as the MC model.

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

[0093] Figure 3 The scatter plots of the MC model and the two-stream model in pure water and turbid water are shown. 2 They are 0.9579 and 0.9806 respectively. In the case of pure water, when all variables, chlorophyll a, dissolved organic carbon and suspended solids concentrations are 0, only pure water absorptivity and pure water backscattering rate affect the total reflectivity. Regardless of water depth and bottom type, the error in pure water is higher than that in muddy water. At the same time, the errors of the two stratified two-stream models and the MC model are related to the choice of layer thickness. Smaller layers can better approximate the reflectivity value. However, because all variables in the upper layer are used to calculate the input values ​​of the lower layer, a large number of layers will affect the error distribution of the entire water body. These errors will be particularly prominent in clear water bodies in the blue light band (400nm to 480nm) because of the high backscattering and absorptivity.

[0094] The two-stream approximate simulation method for stratified water bodies established in this invention helps to explore the relationship between the stratified structure of water bodies and optical properties in a more in-depth and scientific manner, and at the same time significantly improves the ability to simulate the time-space continuous optical properties of water bodies. This method can accurately simulate the optical behavior of different layers in water bodies and significantly improve the simulation accuracy of water body reflectivity. By effectively reducing the interference of background noise and measurement saturation effects, the sensitivity to the optical properties and layer changes of water bodies is enhanced, ensuring the versatility and reliability of the model in complex water environments.

Claims

1. A stratified water body radiation transfer modeling method based on two-stream approximation, characterized by The following steps are involved: (1) Theoretically deduce the two-flow formula for vertically stratified water media and whether it contains direct radiation components, and derive the mathematical expression of the light field radiation of vertically stratified water bodies; at the same time, analyze the important optical properties such as absorptivity, scattering rate, attenuation rate, and conversion rate in the formula, find out the method to determine their values ​​and the influencing factors, and finally find the most original input parameters of the model; (2) The derived two-stream model is numerically solved by an iterative method. Since the Lambertian reflectance cannot fully represent the characteristics of the ocean water, the effects of chlorophyll, suspended matter, dissolved organic matter, and wind-driven capillary waves on the coefficients of the two-stream model are considered in the radiation transmission model of the atmosphere-ocean coupling system. The bidirectional reflection coefficient of the sea surface is calculated, and the spectral variation of the sea surface reflection is also considered. (3) In the radiation transmission process of the entire water medium layer, the conversion mechanism of the backscattering of the downwelling and upwelling irradiance in the scattering process is considered, and the downwelling irradiance and upwelling irradiance of each layer are calculated by the iterative method until the successive values ​​of the upwelling at the sea level 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 step (1) "conducts theoretical analysis on the two-flow formula for vertically stratified water medium and whether it contains direct radiation components, derives the mathematical expression of the light field radiation of vertically stratified water, and analyzes important optical properties such as absorptivity, scattering rate, attenuation rate, and conversion rate in the formula, finds out the method for determining their values ​​and the influencing factors, and finally finds the most original input parameters of the model"; the specific method is as follows: Step 1: Setting of basic assumptions: The following assumptions are made in the modeling: the distribution of light is independent of time, that is, the spectral characteristics do not change with time; in an ideal layered medium, the spectral characteristics of each layer are uniform; Assume that the geometry of the boundary of this radiation transmission medium can be roughly estimated as a parallel plate defined as infinite space between two parallel planes, which are of finite thickness and uniform horizontally, but not necessarily uniform vertically, so that the radiation transmission medium is a stable state, the refractive index is a constant and there are no other light sources; Assume that there is no internal scattered irradiance, but the model can include parallel light sources, and 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 flows of the downflow are Lambertian, so the photon flow of the upflow can be completely scattered; Step 2: Use the mean cosine to derive the second-rate formula: According to the parallel plane assumption, integrating the radiation transfer equation in the lower hemisphere can obtain the downwelling scattered irradiance: Among them, 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, subscripts d and u represent the downward and upward directions respectively, subscript s represents the solar incidence direction, and subscript f represents forward scattering; similarly, integrating the radiation transfer equation in the upper hemisphere can obtain the upward scattering irradiance: The subscript b indicates backscattering. For the special case of only direct radiation, the original transmission equation is integrated in the lower hemisphere to obtain the first-order differential of the direct downwelling irradiance: Among them, c tc represents the attenuation coefficient of downlink radiation; θ represents the observation zenith angle; Step 3: Equivalent substitution: The above three equations form a two-stream model of irradiance including parallel or direct components, including the mean cosine of upwelling and downwelling, shape factor and backscattering rate, and represent a complex differential system with a greater number of unknown quantities than the number of equations. Transformations are required to remove the unknown quantities. Assume that a(z), b(z), 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 formula into the two-stream model formula yields:

3. The method for modeling radiation transfer of layered water bodies based on two-stream approximation according to claim 1 is characterized by: Step (2) states that "the derived two-stream model is numerically solved by an iterative method. Since the Lambert reflectance cannot fully represent the characteristics of the ocean water body, the effects of chlorophyll, suspended matter, dissolved organic matter and wind-driven sea surface capillary waves in the ocean water body on the coefficients in the two-stream model are considered in the radiation transmission model of the atmosphere-ocean coupling system, thereby calculating the sea surface bidirectional reflection coefficient and considering the spectral changes of the sea surface reflection". The specific method is as follows: Step 1: Solve the two-stream formula without direct component: For the two-stream radiation transfer model in a uniform water medium that does not contain direct light components, that is, the absorption rate and backscattering rate do not change with water depth, the boundary condition is used: the surface downwelling irradiance E d (0), z = 0; surface downwelling slope Bottom upwelling irradiance E u (h) = R b E d (h), z = h; bottom upwelling slope Calculate the upwelling and downwelling scattered irradiance: For simplicity, a variable is defined. For stratified water bodies that do not contain direct light components, the water body may not be uniform, but the chemical and optical properties are uniform within the same layer, and it is assumed that the downwelling light is completely scattered as soon as it enters the water body. Therefore, the above formula β can be d (0) rewritten as β d (0,i), where i is the i-th layer of the water body, the downflow two-flow formula in this case is: Among them, due to the energy transfer principle, E d (z,i)=E d (0,i+1); Similarly, the general solution of upwelling irradiance at layer i and depth 0 can be obtained: Among them, due to the energy transfer principle, E u (0,i)=E u (z,i-1); Step 2: Solve the two-stream formula including the direct component: For the two-stream radiation transfer model containing direct light components in a uniform water medium, the solutions of the two-stream formula are divided into general solutions and special solutions. First, integration is performed to obtain the solutions of the two-stream formula for the direct part of the light beam and the non-homogeneous differential equations of the downflow and upflow: E s (z)=E s (0)e -αz The particular solution of the downwelling part is a function of the diffuse 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 for the upwelling part is a function of the diffuse attenuation rate α of the direct irradiance and is defined as: E u (z) = ne -αz , and we get: Five boundary conditions are further used: surface downwelling irradiance E d (0), z = 0; surface downwelling slope Bottom upwelling irradiance E u (h) = R b (E d (h)+E s (h)), z = h; bottom upwelling slope Surface direct irradiance E s (0), z = 0, and the scattered vector irradiance of the upwelling and downwelling is obtained: For stratified water bodies that do not contain direct light components, the above formula β can be d (0) rewritten as β d (0,i), and m is rewritten as m(i), where i is the i-th layer of the water body, and the general solution of the downwelling vector irradiance in the i-th layer and the depth h is obtained: Among them, due to the energy transfer principle, E d (z,i)=E d (0,i+1); 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 in the i-th layer and the depth of 0 is obtained: Among them, due to the energy transfer principle, E u (0,i)=E u (z,i-1); Step 3: Calculation of the bidirectional reflection coefficient of the sea surface: The downwelling irradiance on the sea surface is affected by the reflection and refraction of the air-sea interface. The wind-blown surface is a function of the surface slope and wind speed. The sea surface is divided into many small planes with random slopes, and a probability distribution function P(θ n ,w s ), can be used to predict the probability of observing sunlight incident from the direction (θ0, φ0) in the direction (θ, φ), and is defined as follows: in, w s is the wind speed, θ n is the face tilt angle; At the same time, assuming that the sea surface foam reflectivity is isotropic and is 55%, it increases with the amount of white foam in the solar spectrum band and is a function of sea surface roughness, wind speed and wind pressure. For the sea surface reflectivity, each reflectivity can be divided into two parts, mirror reflectivity and foam reflectivity: R s (ω,w s )=ρ ssp (ω,w s )+r f (w s ) R d (w s )=ρ dsp (w s )+r f (w s ) Among them, R s is the specular reflectance, R d is the external scattering reflectivity, ρ ssp is the direct reflectivity, ρ dsp is the specular reflectivity, given as 0.057, ρ f is the foam reflectivity. When the upwelling irradiance reaches the water surface, part of it is reflected back into the water column, and only part of it is projected through the sea surface into the air. The internal reflectivity 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 reflectivity of the sea surface decreases with increasing wind speed, and when the angle of incidence is greater than the semi-conical angle, the upwelling irradiance is completely reflected, which is given as 0.485 here; Step 4: Calculation of the coefficients of the second-rate model: The optically active substances in the water body mainly include water molecules, phytoplankton, yellow substances and suspended matter, all of which can cause the absorption and scattering of the direct and indirect irradiance of the downwelling flow, which can be measured by water-leaving radiation or remote sensing radiation. The specific calculation method is as follows: Absorption 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 Among them, a chl is the chlorophyll a absorption coefficient, a doc is the dissolved organic carbon absorption coefficient, a ss is the floating matter absorption coefficient, c chl is the chlorophyll a concentration, c doc is the dissolved organic carbon concentration, c ss is the concentration of suspended solids; Likewise, the backscatter 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) It is assumed that the conversion rates of upwelling and downwelling are the same. At the same time, the two-stream 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 absorptivity, and the attenuation caused by scattering is obtained from the backscattering rate: α(λ)=a(λ)+53×b(λ) 4. 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 (3) as follows: "In the radiation transmission process of the entire water medium layer, the conversion mechanism of the backscattering of the downwelling and upwelling irradiances in the scattering process is considered, and the downwelling irradiance and upwelling irradiance of each layer are calculated by iteration until the successive values ​​of the upwelling at the sea level converge." 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 Lambertian reflection of the bottom of the sea. When the upwelling irradiance is at the bottom of the water body, it 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 Lambertian reflection. The upwelling irradiance is transmitted to the surface at the bottom and becomes the upwelling radiation energy. Therefore, the upwelling irradiance is related to the bottom type and the composition of the water body. The upwelling irradiance is affected by the bottom reflectivity. Strong backscattering can be caused by bottom particles and sediments. It is assumed that the bottom of the water body is assumed to be a Lambertian surface, that is, the incident light is isotropic when scattered and converted. 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: The surface reflectivity is defined as the ratio of the upwelling irradiance to the sum of the downwelling irradiance and the direct irradiance. w and the reflectivity R on the sea surface a : Remote sensing reflectivity: Among them, the water-leaving radiation L w With E u and L u The upwelling irradiance is converted into upwelling radiation through the Q factor: Remote sensing algorithms operate on upwelling irradiance, avoiding solar glare, i.e. the sensor measures the portion of irradiance that is out of the water. Upwelling irradiance must be converted to upwelling radiation by the Q factor, where Q is a function of wavelength, solar apex angle, solar azimuth angle, and lighting conditions. If the water bottom is a Lambertian surface, then Q = π. For a stratified water medium, the two-flow 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. In order to calculate the downwelling irradiance at the next interface, the downwelling irradiance at the top of this layer is added to the irradiance of the upwelling irradiance backscattered into this layer, and then added to the downwell irradiance converted from the parallel irradiance. The upwelling irradiance is also obtained in this way. During the first iteration, the upwelling backscattering irradiance entering each layer is initialized to 0. The entire iterative process is to repeatedly use the current backscattering irradiance and the converted irradiance for calculation until the successive values ​​of the upwelling at sea level converge.

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