A method for inverting water body attenuation coefficient based on two-stream model

Abstract

The present invention relates to a water body diffuse attenuation coefficient inversion method based on a two-stream method model. The inversion method includes obtaining the absorption coefficient, backscattering coefficient and solar zenith angle of the water body; inputting the obtained absorption coefficient, backscattering coefficient and solar zenith angle into the inversion model to obtain the water body diffuse attenuation coefficient, wherein the inversion model is obtained based on the two-stream method model; the obtaining method includes using the two-stream method model to obtain the expression of the diffuse attenuation coefficient and the irradiance reflectivity just below the water surface to obtain the initial expression of the water body diffuse attenuation coefficient inversion model; pre-processing the initial expression to obtain multiple parameters to be determined; using a preset simulation data set to parameterize each of the parameters to be determined to obtain the final expression of each parameter to be determined, and obtaining the final expression of the water body diffuse attenuation coefficient inversion model based on the final expression of each parameter to be determined, thereby obtaining the inversion model. According to the present invention, the problem that the accuracy of the inversion model of the prior art needs to be improved can be solved.

Description

Technical Field

[0001] The invention belongs to the technical field of water environment remote sensing monitoring, and in particular relates to a water body diffuse attenuation coefficient inversion method based on a two-stream method model. Background Art

[0002] As a basic parameter to characterize the underwater light field, the diffuse attenuation coefficient plays a vital role in studying water turbidity, sediment transport and resuspension, heat transfer in the upper water layer, phytoplankton photosynthesis, and primary productivity of natural water bodies. Compared with traditional in situ measurements, satellite-based water color remote sensing is a more effective and faster way to obtain a large range of diffuse attenuation coefficients. In order to obtain the diffuse attenuation coefficient from images, researchers have conducted extensive research and established a large number of inversion models, which can generally be divided into three categories: (1) The optical properties of water bodies are mainly affected by phytoplankton, and a relationship model between the diffuse attenuation coefficient and chlorophyll concentration is established; (2) The relationship model between the diffuse attenuation coefficient and remote sensing reflectance is directly constructed based on the statistical relationship between the two; (3) A semi-analytical algorithm based on radiation transfer theory is used to establish a relationship model between the diffuse attenuation coefficient and the intrinsic optical properties of water and boundary conditions (such as the solar zenith angle).

[0003] The first two categories are both empirical algorithms, which are the most widely studied and used algorithms at present, and are also the operational inversion algorithms for most satellite standard water color products. However, due to the unclear mechanism, these algorithms have great limitations in use and cannot be applied to a large range of highly variable water bodies. Moreover, the existing inversion models are all established for the diffuse attenuation coefficient of the 490nm band. If you want to obtain the diffuse attenuation coefficient of other bands, you need to build a new empirical inversion model or re-parameterize it, which greatly limits its scope of application. The semi-analytical algorithm uses the radiation transfer equation to describe the relationship between the diffuse attenuation coefficient and the inherent optical properties and boundary conditions. The results are universal and will not change with the changes in water body properties and bands. Therefore, it has stronger interpretability and a wider range of applications. At present, there are few diffuse attenuation coefficient inversion models based on semi-analytical algorithms. Some of the existing diffuse attenuation coefficient inversion models based on semi-analytical algorithms use forward scattering probability and scattering coefficient that cannot be accurately inverted from remote sensing images. Some inversion models only rely on water absorption coefficient and backscattering coefficient so that they can be directly used on remote sensing images, but there are usually large deviations when they are applied to turbid water bodies.

[0004] Therefore, the accuracy of the existing inversion models needs to be improved. Summary of the invention

[0005] The present invention provides a water body diffuse attenuation coefficient inversion method based on a two-stream method model, which is used to solve the problem that the accuracy of the inversion model in the prior art needs to be improved.

[0006] In order to solve the above technical problems, the present invention provides a water body diffuse attenuation coefficient inversion method based on a two-stream method model, comprising:

[0007] Obtain the absorption coefficient, backscattering coefficient and solar zenith angle of water bodies;

[0008] The obtained absorption coefficient, backscattering coefficient and solar zenith angle are input into the inversion model to obtain the water body diffuse attenuation coefficient, wherein the inversion model is obtained based on the two-stream method model;

[0009] The methods of obtaining include:

[0010] 1) Using the two-stream method model, the expression of the diffuse attenuation coefficient and the expression of the irradiance reflectivity just below the water surface are obtained;

[0011] 2) Substitute the obtained expression of irradiance reflectance just below the water surface into the expression of diffuse attenuation coefficient to obtain the initial expression of the inversion model of water diffuse attenuation coefficient;

[0012] 3) Preprocessing the initial expression of the water body diffuse attenuation coefficient inversion model to obtain a plurality of undetermined parameters, wherein the plurality of undetermined parameters include two categories, and using the undetermined parameters to update the initial expression of the water body diffuse attenuation coefficient inversion model to obtain an updated expression of the water body diffuse attenuation coefficient inversion model;

[0013] 4) Parameterizing each undetermined parameter using a preset simulation data set to obtain a final expression of each undetermined parameter, wherein the first type of undetermined parameter is related to the solar zenith angle, and the second type of undetermined parameter is related to the absorption coefficient and the backscattering coefficient;

[0014] 5) Based on the final expressions of the unknown parameters and the updated expression of the water body diffuse attenuation coefficient inversion model, the final expression of the water body diffuse attenuation coefficient inversion model is obtained, thereby obtaining the inversion model.

[0015] The beneficial effects of the above technical solution are: the absorption coefficient, backscattering coefficient and solar zenith angle of the water body are input into the inversion model to obtain the diffuse attenuation coefficient of the water body, wherein the inversion model is obtained based on the two-stream method model, wherein the expression of the diffuse attenuation coefficient and the expression of the irradiance reflectivity just below the water surface are obtained by using the two-stream method model, in which case, the rationality and water body adaptability of the inversion model are improved by using the irradiance reflectivity just below the water surface; the expression of the irradiance reflectivity just below the water surface is substituted into the expression of the diffuse attenuation coefficient to obtain the initial expression of the inversion model of the diffuse attenuation coefficient of the water body; the initial expression is preprocessed to obtain multiple pending parameters, and the multiple pending parameters include two categories, and the initial expression is updated using the pending parameters to obtain Updated expression of the water body diffuse attenuation coefficient inversion model; in this case, the degree of freedom of the introduced unknown parameters is lower than the degree of freedom of the actual unknown parameters in the initial expression of the water body diffuse attenuation coefficient inversion model, which enhances the stability of the parameterization result, and because the degree of freedom of the unknown parameters is reduced, the simplicity of the parameterization process is improved; each unknown parameter is parameterized using a preset simulation data set to obtain the final expression of each unknown parameter, the first type of unknown parameter is related to the solar zenith angle, and the second type of unknown parameter is related to the absorption coefficient and the backscattering coefficient; based on the final expression of each unknown parameter and the updated expression of the water body diffuse attenuation coefficient inversion model, the final expression of the water body diffuse attenuation coefficient inversion model is obtained to obtain the final inversion model. Therefore, parameterizing the unknown parameters improves the accuracy of the inversion model.

[0016] Furthermore, in order to improve the simplicity of the subsequent parameterization process, the present invention provides a water body diffuse attenuation coefficient inversion method based on the two-stream method model, and also includes an updated expression of the water body diffuse attenuation coefficient:

[0017]

[0018] Among them, K d is the water body diffuse attenuation coefficient, p 0 and p 3 is the first type of undetermined parameter, p 1 and p 2 is the second type of unknown parameter, a is the absorption coefficient, b b It refers to the backscattering coefficient of radiation caused by water scattering, which is opposite to the direction of radiation transmission.

[0019] Furthermore, in order to better enhance the stability of the inversion model, the present invention provides a water body diffuse attenuation coefficient inversion method based on the two-stream method model, which also includes a first type of undetermined parameters including two undetermined parameters, namely a first undetermined parameter and a fourth undetermined parameter, and the final expressions of the first undetermined parameter and the fourth undetermined parameter are:

[0020]

[0021] Among them, p 0 is the first undetermined parameter, p 3 is the fourth unknown parameter, θ s is the solar zenith angle.

[0022] Furthermore, in order to better enhance the stability of the inversion model, the present invention provides a water body diffuse attenuation coefficient inversion method based on the two-stream method model, and further includes a second type of undetermined parameters including two undetermined parameters, namely, a second undetermined parameter and a third undetermined parameter, and the final expressions of the second undetermined parameter and the third undetermined parameter are:

[0023]

[0024] Among them, p 1 is the second undetermined parameter, p 2 It is the third undetermined parameter.

[0025] Furthermore, in order to better parameterize the to-be-determined parameters, the present invention provides a method for inverting the water body diffuse attenuation coefficient based on the two-stream method model, which also includes step 4), using the following method to obtain the final expression of the first type of to-be-determined parameters: using the solar zenith angle in a preset simulation data set and the corresponding actual value of the to-be-determined parameter to perform quadratic function fitting on the relationship between the two, and fitting to obtain the final expression of the first to-be-determined parameter in the first type of to-be-determined parameters; and then obtaining the final expression of the fourth to-be-determined parameter.

[0026] Furthermore, in order to better parameterize the parameters to be determined, the present invention provides a method for inverting the water body diffuse attenuation coefficient based on the two-stream method model, which also includes step 4), using the following method to obtain the final expression of the second type of parameters to be determined: first obtain the final expression of the first type of parameters to be determined, and substitute it into the updated expression of the water body diffuse attenuation coefficient inversion model to obtain the intermediate expression of the water body diffuse attenuation coefficient inversion model; determine the parameterized variables of the second type of parameters to be determined, and then use the preset simulation data set to obtain the final expression of the second type of parameters to be determined by grouping parameterization. The grouping parameterization method includes: selecting multiple adjacent bands in the same group of simulation data in the preset simulation data set as a group of data, using the actual value of the second type of parameters to be determined in the group of data, and using the median of the parameterized variables of multiple bands as the input for establishing the expression of the second type of parameters to be determined, and then using the iterative parameterization method to obtain the final expression of the second type of parameters to be determined.

[0027] Furthermore, in order to better parameterize the to-be-determined parameters, the present invention provides a method for inverting the water body diffuse attenuation coefficient based on a two-stream method model, and also includes the iterative parameterization method comprising: ① determining a benchmark expression of the second to-be-determined parameter, substituting the benchmark expression into the intermediate expression of the water body diffuse attenuation coefficient inversion model to obtain a current expression of the third to-be-determined parameter; ② substituting the current expression of the third to-be-determined parameter into the intermediate expression of the water body diffuse attenuation coefficient inversion model to obtain the current expression of the second to-be-determined parameter, and judging whether the second to-be-determined parameter and the third to-be-determined parameter meet the requirements. If not, substituting the current expression of the second to-be-determined parameter into the intermediate expression of the water body diffuse attenuation coefficient to obtain the current expression of the third to-be-determined parameter again, and repeating step ② to obtain the final expression of the second type of the to-be-determined parameter.

[0028] Furthermore, in order to better parameterize the parameters to be determined, the present invention provides a water body diffuse attenuation coefficient inversion method based on the two-stream method model, which also includes obtaining a benchmark expression by using the following method: using the actual value of the second parameter to be determined in the preset simulation data set and the corresponding parameterized variable to perform logarithmic function fitting on the relationship between the two, and fitting to obtain a benchmark expression of the second parameter to be determined, and the parameterized variable is the ratio of the backscattering coefficient to the absorption coefficient in the preset simulation data set ω b .

[0029] Furthermore, in order to improve the inversion efficiency, the present invention provides a method for inverting the diffuse attenuation coefficient of a water body based on a two-stream method model, which also includes step 2), wherein the irradiance reflectivity just below the water surface is the irradiance reflectivity just below the water surface after series expansion, and the number of terms in the series expansion is retained to the quadratic term.

[0030] Furthermore, in order to better parameterize the parameters to be determined, the present invention provides a method for inverting the water body diffuse attenuation coefficient based on a two-stream method model, and also includes a preset simulation data set which is a self-built Sim-Kd simulation data set. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1(a) is a scatter plot of different scattering phase functions at a fixed solar zenith angle;

[0032] Figure 1(b) is a scatter plot of different solar zenith angles under a fixed scattering phase function;

[0033] Figure 2 is a scatter plot of the first undetermined parameter and the solar zenith angle;

[0034] Figure 3 It is a flowchart of the iterative steps of the second undetermined parameter and the third undetermined parameter of the present invention;

[0035] Figure 4is a scatter plot of the ratio of the backscattering coefficient to the absorption coefficient in low-scattering water and the second unknown parameter;

[0036] FIG5( a ) is a scatter plot of the final second unknown parameter and the ratio of the backscattering coefficient to the absorption coefficient;

[0037] FIG5( b ) is a scatter plot of the final third undetermined parameter and the ratio of the backscattering coefficient to the absorption coefficient;

[0038] FIG6( a ) is an inversion diagram of the water body diffuse attenuation coefficient at different solar zenith angles under the fixed scattering phase function of the present invention;

[0039] Figure 6(b) is the inversion diagram of the water diffuse attenuation coefficient at different solar zenith angles under the fixed scattering phase function of the existing inversion model;

[0040] FIG6( c ) is an inversion diagram of the water body diffuse attenuation coefficient of different scattering phase functions under a fixed solar zenith angle of the present invention;

[0041] Figure 6(d) is the inversion diagram of the water diffuse attenuation coefficient of different scattering phase functions under a fixed solar zenith angle of the existing inversion model;

[0042] FIG. 7( a ) is an inversion diagram of the water body diffuse attenuation coefficient of the present invention under different scattering phase functions in an absorbing water body;

[0043] Fig. 7(b) is the inversion diagram of the water diffuse attenuation coefficient of the existing inversion model under different scattering phase functions in absorbing water;

[0044] FIG. 7( c ) is an inversion diagram of the water body diffuse attenuation coefficient of the present invention under different scattering phase functions in scattering water;

[0045] Fig. 7(d) is the inversion diagram of the water diffuse attenuation coefficient of the existing inversion model under different scattering phase functions in scattering water;

[0046] Figure 8 It is an overall flow chart of the water body diffuse attenuation coefficient inversion method based on the two-stream method model of the present invention. DETAILED DESCRIPTION

[0047] The basic concept of the present invention is: based on the two-stream method model, the downward irradiance, the irradiance reflectivity just below the water surface and the introduced unknown parameters are obtained to obtain the initial inversion model of the water body diffuse attenuation coefficient, and the final inversion model is obtained after parameterizing the unknown parameters in the initial inversion model, thereby obtaining the final water body diffuse attenuation coefficient. In the parameterization process, each unknown parameter is gradually parameterized and iteratively parameterized using a preset simulation data set to obtain the final expression of each unknown parameter, and the final water body diffuse attenuation coefficient is obtained based on the final expression of each unknown parameter.

[0048] In order to make the purpose, technical scheme and technical effect of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] Example of water body diffuse attenuation coefficient inversion method based on two-stream method model:

[0050] An embodiment of a water body diffuse attenuation coefficient inversion method based on a two-stream method model of the present invention has the following overall process: Figure 8 shown.

[0051] The second-stream model is introduced below.

[0052] The two-stream model is a variant of the radiation transfer equation, which is a model that calculates upward and downward radiation separately. The simplified radiation transfer equation is often used in ocean radiation research:

[0053]

[0054] Wherein, z represents the depth, L(θ,φ,z,λ) represents the radiance in the direction of (θ,φ), θ represents the angle between the radiation and the horizontal plane, φ represents the azimuth of the radiation, λ represents the wavelength of the radiation, c(z,λ) represents the attenuation coefficient, c(z,λ) is the sum of the absorption coefficient and the backscattering coefficient, β(θ,θ′,φ,φ′,z,λ) represents the scattering function of the radiation in the direction of (θ',φ') scattered to the direction of (θ,φ), θ′ represents the angle between the scattered radiation and the horizontal plane, φ′ represents the azimuth of the scattered radiation, L(θ′,φ′,z,λ) represents the radiance in the direction of (θ',φ'), and Ω′ represents the solid angle of the scattered radiation.

[0055] Assuming that the inherent optical properties of the same water body are stable within a certain depth, the water body can be regarded as a homogeneous medium. When the external lighting conditions and environment change, the distribution and change patterns of the upward and downward irradiance in the homogeneous medium are synchronized, so one of the directions can be analyzed separately.

[0056] Since the diffuse attenuation coefficient is an apparent optical property used to describe the degree of downward irradiance attenuation, the downward radiation part can be analyzed. In order to extract the downward radiation part, the left equation of equation (1) is integrated over the solid angle of the lower hemisphere to obtain:

[0057]

[0058] Among them, π d represents the lower hemisphere solid angle, E d represents the downward irradiance, Ω represents the solid angle of radiation, and the other symbols are consistent with formula (1).

[0059] By integrating the right side of equation (1) over the solid angle of the lower hemisphere, we can obtain:

[0060]

[0061] Among them, E od represents the downward scalar irradiance, π u represents the upper hemisphere solid angle, and the other symbols are consistent with those in equations (1) and (2). In particular, c has the same meaning as c(z, λ) in equation (1).

[0062] Based on the physical meaning of the integral formula, two new parameters are introduced. The two new parameters satisfy equations (4) and (5) respectively:

[0063]

[0064]

[0065] Among them, r d represents the average upward scattering coefficient caused by the downward radiation part of the radiation, r u Represents the average downward scattering coefficient caused by the upward radiation part of the radiation. b It refers to the backscattering coefficient of radiation caused by water scattering in the opposite direction of radiation transmission, E od represents the downward scalar irradiance, β(θ,φ,θ′,φ′,λ) represents the scattering function of the radiation in the direction of (θ',φ') being scattered to the direction of (θ,φ), and for simplicity, the depth z in the symbol is omitted, E ou Represents the upward scalar irradiance.

[0066] Substituting equations (4) and (5) into equations (2) and (3), we can obtain the expression of the downward radiation part:

[0067]

[0068] Among them, E d represents downward irradiance, z represents depth, c represents attenuation coefficient, b represents scattering coefficient, E ou Represents the upward scalar irradiance.

[0069] Based on the definition of scalar irradiance, equation (6) can be transformed into equation (7):

[0070]

[0071] Where a represents the absorption coefficient, μ d represents the downward mean cosine, μ u represents the upward mean cosine, E u Indicates upward irradiance.

[0072] Referring to the method of obtaining the downward radiation part, the expression of the upward radiation part can be obtained:

[0073]

[0074] Formula (7) and formula (8) constitute the two-stream method model.

[0075] An initial inversion model is constructed based on the above-mentioned two-stream method model, and the initial inversion model is introduced below.

[0076] Specifically, based on the definition of diffuse attenuation coefficient, the left side of equation (7) is similar to the definition of diffuse attenuation coefficient, and the difference between the two is a proportionality factor of -1 / E d , divide both sides of equation (7) by -E d You can get:

[0077]

[0078] Among them, K d represents the diffuse attenuation coefficient of the water body, and R represents the irradiance reflectance just below the water surface. In this case, the definition of the diffuse attenuation coefficient is transformed into a relationship including the absorption coefficient and the backscattering coefficient using equation (9).

[0079] Based on the above two-stream model, the relationship between the irradiance reflectance R just below the water surface and the inherent optical properties in equation (9) is obtained. The relationship between the irradiance reflectance R just below the water surface is:

[0080]

[0081] Among them, b in the formula u , b d 、c u and c d are the scattering coefficient and attenuation coefficient with directional information, which are defined as:

[0082]

[0083] Among them, a in the formula u / d Indicates the upward absorption coefficient a u Or downward absorption coefficient a d , b u / d represents the upward scattering coefficient b u Or the downward scattering coefficient b d , c u / d represents the downward attenuation coefficient c u Or upward attenuation coefficient c d , μ u / d represents the upward mean cosine μ u or downward mean cosine μ d , ru / d The definition of is the same as that of formula (3) and formula (4).

[0084] Since 4b in formula (10) d b u / (c d +c u ) 2 is less than 1, so the bracket terms in formula (10) are expanded in series to obtain:

[0085]

[0086] Formula (10) is retained to obtain the retained formula (10). During the retention process, the error and computational complexity after the retention process are comprehensively compared to determine the number of terms to be retained. Specifically, compared with formula (12), the error of formula (12) when retained to the quadratic term is smaller, and the computational complexity of formula (12) when retained to the quadratic term is significantly less than the computational complexity of formula (12) when retained to the cubic term, so formula (12) is retained to the quadratic term. Since formula (12) is the content in the curly bracket term in formula (10), when formula (10) is retained, the curly bracket term in formula (10) is also retained to the quadratic term, and then formula (11) is substituted into the retained formula (10) to obtain:

[0087]

[0088] Substituting formula (13) into formula (9) yields:

[0089]

[0090] Formula (14) is the initial expression of the water body diffuse attenuation coefficient inversion model of the initial inversion model of this embodiment. The initial expression of the water body diffuse attenuation coefficient inversion model is the diffuse attenuation coefficient expression determined by the absorption coefficient, the backscattering coefficient and a number of coefficients to be optimized. Among them, formula (14) includes the absorption coefficient a and the backscattering coefficient b b The two variables and the actual undetermined parameter are the downward mean cosine μ u , upward mean cosine μ d , the average downward scattering coefficient r caused by the upward radiation part u and the average upward scattering coefficient r caused by the downward radiation part d .

[0091] Based on the above initial inversion model, the initial inversion model is parameterized to obtain the final inversion model.

[0092] The process of parameterization is as follows:

[0093] Step 1: Preprocess the initial expression of the water body diffuse attenuation coefficient inversion model in the initial inversion model to obtain the unknown parameters.

[0094] In step 1, the preprocessing is deformation simplification. Since a and b are involved in formula (14) b Two variables, and the number of parameters to be parameterized exceeds the actual number of parameters to be determined μ u , μ d 、r u and r d Therefore, new unknown parameters are introduced to simplify equation (14) to reduce the degree of freedom of unknown parameters and enhance the stability of parameterization results. The conditions that need to be met when selecting new unknown parameters are: the form of the new unknown parameters themselves should be as simple as possible to ensure high stability and simplicity when parameterizing them later; when substituting the new unknown parameters into equation (14), multiple parameter combinations should be avoided as much as possible; at the same time, the parameters used in the new unknown parameters should be relevant and consistent to ensure that they have certain physical meanings. The new unknown parameters selected based on the above conditions meet the following conditions:

[0095]

[0096] Among them, p 0 、p 1 、p 2 and p 3 are the four unknown parameters introduced, p 0 represents the first undetermined parameter, p 1 represents the second undetermined parameter, p 2 represents the third undetermined parameter, p 3 In order to ensure the simplicity of the subsequent parameterization process, the backscattering coefficient b is introduced. b The ratio of the absorption coefficient a to ω b Simplify equation (14). Substituting equation (15) into equation (14) can obtain the updated expression of the water body diffuse attenuation coefficient inversion model:

[0097]

[0098] Among them, K d represents the water body diffuse attenuation coefficient, a represents the absorption coefficient. Compared with formula (14), the form of formula (16) is simpler, and the correlation degree of the undetermined parameters is lower and the degree of freedom is also lower. Therefore, parameterizing formula (16) can enhance the stability of the parameterization results.

[0099] Step 2: Classify the pending parameters and determine the parameterization order of each category.

[0100] In step 2, since there are p in formula (16) 0 -p 3 Four undetermined parameters, the four undetermined parameters are distributed in the numerator and denominator of the function, and except for the first undetermined parameter p 0 The other three parameters appear in multiple positions and the existence of product between the parameters makes it difficult to directly obtain stable parameterization results of the four. Therefore, the parameters are evaluated and ranked by analyzing their importance, stability and the degree of influence of additional factors.

[0101] For the four unknown parameters p 0 -p 3 After analysis, the four unknown parameters p 0 -p 3 Divided into two categories, the first undetermined parameter p 0 and the fourth undetermined parameter p 3 It is classified into the first category because the values ​​of both depend only on the upward mean cosine μ u and the downward mean cosine μ d Therefore, both are little affected by the inherent optical properties and are mainly affected by the solar zenith angle, that is, the first type of undetermined parameters are related to the solar zenith angle; the second undetermined parameter p 1 and the third undetermined parameter p 2 It is classified into the second category because both of them are not only related to the upward mean cosine μ u and the downward mean cosine μ d It is also related to the forward scattering coefficient r which contains information about the scattering phase function. u and the backscatter coefficient r d Therefore, the values ​​of both will be affected by both the inherent optical properties and the solar zenith angle, that is, the second type of undetermined parameters are related to the absorption coefficient and the backscattering coefficient. 1 and the third undetermined parameter p 2 The parameterization difficulty is relatively large. Therefore, the first parameter to be determined is p 0 and the fourth undetermined parameter p 3 The parameterization of has higher priority.

[0102] Step 3: Based on the parameterization order of each category, the parameterization order of the undetermined parameters in each category is obtained, and parameterization is performed step by step.

[0103] In step 3, during the step-by-step parameterization process, after a pending parameter is parameterized, it is regarded as a known quantity and substituted back into the original parameterized expression, and then the remaining pending parameters are evaluated and solved. The parameterization process of this embodiment selects the simulated annealing algorithm for the pending parameter p 0 -p 3Optimization is performed. This can avoid falling into the local optimum during the parameterization process. In addition, the Sim-Kd simulation data set generated by the commercial software HydroLight 6.0 is also needed during the optimization.

[0104] In step 3, when parameterizing the first type of undetermined parameters with high priority, first determine the first undetermined parameter p 0 and the fourth undetermined parameter p 3 The parameterization priority of 0 It is an undetermined parameter independent of other parameters, so the first undetermined parameter p 0 Compared to the fourth undetermined parameter p 3 It has higher parameterization stability and priority.

[0105] In the first category, we first determine the first parameter p 0 Specifically, the form of equation (16) is adjusted and both sides are divided by a to obtain:

[0106]

[0107] Among them, if ω b Considered as an independent variable, K d / a is regarded as the dependent variable, then the first undetermined parameter p 0 This is the ordinate value of the intersection of equation (17) and the y-axis.

[0108] Based on formula (15), we can know that the first undetermined parameter p 0 Depends on the downward mean cosine μ d , so it is little affected by the inherent optical characteristics and is mainly affected by the solar zenith angle, among which the influence of the inherent optical characteristics can be ignored. Therefore, only the solar zenith angle is used to establish the first unknown parameter p 0 The final expression of . For this embodiment, the data forming the scatter plot comes from the Sim-Kd simulation data set. Figure 1(a) is a scatter plot of different scattering phase functions under a fixed solar zenith angle (30°); Figure 1(b) is a scatter plot of different solar zenith angles under a fixed scattering phase function (Fournier-Forand scattering phase function when the backscattering ratio B is 0.018, denoted as FF018). The horizontal axis of Figures 1(a) and 1(b) is the ratio of the backscattering coefficient to the absorption coefficient ω b , the ordinate is the ratio of the diffuse attenuation coefficient to the absorption coefficient K d / a, it can be found from Figure 1(a) that when the solar zenith angle is fixed at 30°, for different scattering phase functions (for example, the backscattering ratio B is 0.012, 0.024, and 0.060), the three function scatter curves are close to ω b= 0, which almost completely coincides with each other, indicating that the first unknown parameter p under different scattering phase functions 0 The difference is very small. It can be found from Figure 1(b) that when the scattering phase function is FF018, for different solar zenith angles (such as solar zenith angles 0°, 30° and 60°), the first undetermined parameter p 0 In close to ω b = 0, and shows a trend of increasing with the increase of the solar zenith angle. Therefore, based on Figure 1(a) and Figure 1(b), it can be seen that the first undetermined parameter p 0 The value of is greatly affected by the solar zenith angle and is almost unaffected by the inherent optical properties of water.

[0109] The first undetermined parameter p is obtained by using multiple different solar zenith angles in the Sim-Kd simulation data set and multiple solar zenith angles and parameterization corresponding to each solar zenith angle. 0 (i.e., the actual value of the undetermined parameter) is plotted, and a quadratic function is fitted based on the scatter plot to obtain the first undetermined parameter p 0 The relationship between the solar zenith angle and the

[0110] p 0 =4.12e -5 θ s 2 +2.13e -3 θ s +1.01 (18)

[0111] Among them, θ s is the solar zenith angle. Formula (18) is the first unknown parameter p 0 The final expression of .

[0112] For this embodiment, Figure 2 is a scatter plot of the first undetermined parameter and the solar zenith angle. For example, the first undetermined parameter p obtained by parameterizing 6 different solar zenith angles in the Sim-Kd simulation data set is 0 and the solar zenith angle θ to obtain Figure 2 The scatter plot shown in Figure 1 and the formula (18) are used to obtain Figure 2 Waveform A and waveform B in the figure are curves obtained using the existing formula. Figure 2 It can be seen that the fitting accuracy of this embodiment is higher than that of the existing formula.

[0113] In the first category, the fourth undetermined parameter p 3 Specifically, based on formula (15), the fourth undetermined parameter p 3 With the first undetermined parameter p 0 The power is consistent (that is, the numerator is one order higher than the denominator), and the fourth unknown parameter p3 After deformation, we get:

[0114]

[0115] Based on formula (19), we can know that the fourth undetermined parameter p 3 and the first undetermined parameter p 0 The difference between d and the upward mean cosine μ u The fourth parameter p is determined by the ratio of 3 Greater than the first undetermined parameter p 0 Since the downward mean cosine μ d and the upward mean cosine μ u The relationship between them is relatively stable, and usually tends to decrease with the increase of water depth, and the ratio μ between them is u / μ d is approximately equal to 0.5. Substituting this ratio into equation (19) we can get the fourth unknown parameter p 3 The final expression of is:

[0116] p 3 =3p 0 (20)

[0117] In step 3, the first undetermined parameter p of the first category is completed 0 and the fourth undetermined parameter p 3 After parameterization, we continue to analyze the second unknown parameter p of the second type. 1 and the third undetermined parameter p 2 Parameterization is performed. At this time, the first undetermined parameter p can be 0 and the fourth undetermined parameter p 3 The final expressions of the first type of unknown parameters, equations (18) and (20), are substituted into the updated expressions of the water body diffuse attenuation coefficient inversion model to obtain the intermediate expressions of the water body diffuse attenuation coefficient inversion model.

[0118] In step 3, when parameterizing the second type of undetermined parameters with low priority, first determine the second undetermined parameter p 1 and the third undetermined parameter p 2 Specifically, Equation (18) and Equation (20) are substituted into Equation (17) to simplify the elimination term and obtain the intermediate expression of the water body diffuse attenuation coefficient inversion model. The intermediate expression of the water body diffuse attenuation coefficient inversion model is related to the second unknown parameter p 1 and the third undetermined parameter p 2 The functional form mainly includes 1 / p 1 and p 1 and p 2 The second undetermined parameter p1 There are independent terms in the formula, and the third unknown parameter p 2 There are no independent terms and the function terms involved are in the form of ratios or products. Therefore, in the process of optimization, it is considered that the second unknown parameter p 1 The parameterization priority is higher than the third undetermined parameter p 2 higher.

[0119] In step 3, after determining the second undetermined parameter p 1 and the third undetermined parameter p 2 After the priority, the second parameter p is determined. 1 and the third undetermined parameter p 2 The parameterized variables need to be able to describe the relationship between the backscatter ratio and the backscatter degree of the water body, and also need to be accurately obtained from remote sensing images.

[0120] The parameterized variables are determined according to the influence of the solar zenith angle and the scattering phase function on the solar zenith angle and the scattering phase function. Specifically, for the second undetermined parameter p 1 and the third undetermined parameter p 2 Based on the simplified formula (17) and combined with the distribution and variation structure of the actual underwater light field, it can be seen that the two unknown parameters are not independent of each other. The second unknown parameter p 1 and the third undetermined parameter p 2 is a description of the distribution of downward and upward scattered radiation in the underwater light field. The two unknown parameters affect each other, and based on formula (15), the second unknown parameter p 1 and the third undetermined parameter p 2 It is affected by the inherent optical properties and the solar zenith angle. In general, the downward mean cosine μ d and the upward mean cosine μ u The value variation of is smaller than that of the intrinsic optical properties, so the second unknown parameter p 1 and the third undetermined parameter p 2 The degree of influence of the inherent optical properties of water is greater than that of the solar zenith angle.

[0121] In order to better confirm the influence of the inherent optical properties of water and the solar zenith angle, the data in the Sim-Kd simulation data set were used to calculate the second unknown parameter p 1 and the third undetermined parameter p 2 Group parameterization is performed to observe the degree to which the two undetermined parameters are affected by the solar zenith angle and the scattering phase function. For this embodiment, for example, 30 sets of data formed by combining 6 sets of solar zenith angles and 5 sets of scattering phase functions in the Sim-Kd simulation data set are used to analyze the second undetermined parameter p 1 and the third undetermined parameter p2 After parameterization, it is found that the second undetermined parameter p 1 and the third undetermined parameter p 2 The parameterization result is not like the first undetermined parameter p 0 It also shows a single change law that is obviously affected by only one factor, but the second unknown parameter p 1 The parameterization results show that the backscattering ratio of the scattering phase function increases. The third unknown parameter p 2 The trend of is opposite, and both are less affected by the solar zenith angle than the scattering phase function. Therefore, based on the group parameterization, the backscattering ratio is initially selected as the second unknown parameter p 1 and the third undetermined parameter p 2 The parameterized variables, and in order to minimize the influence of the solar zenith angle on the final expressions of the two parameters to be determined, the solar zenith angle is 30°. However, since the backscattering ratio of the initially selected scattering phase function cannot be accurately obtained from remote sensing images, the ω that can be accurately obtained from remote sensing images and can express the relationship between the backscattering ratio and the backscattering degree of the water body is used. b As the second undetermined parameter p 1 and the third undetermined parameter p 2 parameterized variables.

[0122] In step 3, after determining the parameterized variables, the second undetermined parameter p is parameterized using the Sim-Kd simulation data set in a grouped manner. 1 and the third undetermined parameter p 2 Parameterization is performed to obtain the final expression of the second type of undetermined parameters. Specifically, five adjacent bands in the same group of simulation data in the Sim-Kd simulation data set are selected as a group of data, which is used to obtain the parameterized second undetermined parameter p 1 and the third undetermined parameter p 2 (i.e. the actual value of the second type of undetermined parameter), and the ω of the five bands b The median value of is used as the input to establish the expression of the second type of undetermined parameter, and then the iterative parameterization method is used to obtain the final expression. In this case, since the intrinsic optical properties and diffuse attenuation coefficients between adjacent bands vary little for the same set of simulation data, the relationship is relatively stable. 1 and the third undetermined parameter p 2 is relatively fixed, so it can ensure that the second undetermined parameter p 1 and the third undetermined parameter p 2 The stability of the parameterization results is to avoid the first unknown parameter p 0 and the fourth undetermined parameter p 3After substituting into equation (17), the parameterization result becomes unstable due to the presence of two undetermined parameters.

[0123] Figure 3 FIG. 1 is a flowchart of the iterative steps of the second and third parameters to be determined of the present invention. Figure 3 As shown, the iteration steps include: first based on the low scattering water body (such as ω b <0.1) Using simulated annealing algorithm to obtain the initial second unknown parameter p 1 Parameterize the result to determine the second parameter p 1 The benchmark expression is then regarded as a known intermediate expression for the water body diffuse attenuation coefficient inversion model; the third unknown parameter p 2 Parameterize and establish the third undetermined parameter p 2 The current expression is then repeated for the second undetermined parameter p 1 The parameterization process obtains the second undetermined parameter p 1 The current expression; until the second undetermined parameter p 1 and the third undetermined parameter p 2 The expression of b , which can remain relatively stable (i.e., meet the requirements) in the range of 1 and the third undetermined parameter p 2 The parameter variation of the expression is less than 5%, and the second undetermined parameter p is output. 1 and the third undetermined parameter p 2 The final expression of .

[0124] For this embodiment, Figure 4 It is a scatter plot of the relationship between low-scattering water and the second unknown parameter. Figure 4 The low scattering water in ω b Scattering water with a value less than 0.1. Figure 4 It can be seen that the second undetermined parameter p 1 With ω b The relationship between is similar to the form of logarithmic function. The second parameter p in the first iteration is 1 Parameterized expressions (i.e., base expressions) can be obtained from Figure 4 get:

[0125] p 1 =0.041ln(ω b )+0.348 (21)

[0126] After the iteration steps, the second unknown parameter p is obtained. 1 and the third undetermined parameter p 2 The final expression of .

[0127] For this embodiment, FIG5(a) is a scatter plot of the final second parameter to be determined and the low-scattering water body; FIG5(b) is a scatter plot of the final third parameter to be determined and the low-scattering water body. FIG5(a) and FIG5(b) are based on Figure 4 The second unknown parameter p in Figure 5(a) is 1 The final expression satisfies:

[0128] p 1 =0.036ln(ω b )+0.301 (22)

[0129] The third undetermined parameter p in Figure 5(b) 2 The final expression satisfies:

[0130] p 2 =0.848ω b -0.959 +2.79 (23)

[0131] In step 3, based on the first undetermined parameter p 0 , the second undetermined parameter p 1 、The third undetermined parameter p 2 and the fourth undetermined parameter p 3 The final expression of and the updated expression of the water body diffuse attenuation coefficient inversion model are used to obtain the final expression of the water body diffuse attenuation coefficient inversion model to obtain the final inversion model. The final inversion model is:

[0132]

[0133] Based on the expression of the above final inversion model, the final water body diffuse attenuation coefficient is obtained.

[0134] Next, the first undetermined parameter p of this embodiment is simulated using the Sim-Kd data set. 0 , the second undetermined parameter p 1 、The third undetermined parameter p 2 and the fourth undetermined parameter p 3 The stability and correctness of the final expression and the inversion performance of the final inversion model are verified. The specific process is as follows:

[0135] The existing inversion model used for comparison during verification is the Kd_Lee model. The evaluation index for verification is R 2 , RMSE and MRE.

[0136] The final inversion model of this embodiment and the existing inversion model are grouped and plotted using the Sim-Kd simulation data set to obtain inversion maps showing the inversion results of the water body diffuse attenuation coefficient, and the R values ​​of the two models are obtained by grouping. 2, RMSE and MRE evaluation indicators. Figure 6 (a) is an inversion diagram of the water body diffuse attenuation coefficient at different solar zenith angles under the fixed scattering phase function of the present invention;

[0137] Figure 6(b) is an inversion diagram of the water body diffuse attenuation coefficient at different solar zenith angles under a fixed scattering phase function of the existing inversion model; Figure 6(c) is an inversion diagram of the water body diffuse attenuation coefficient at different scattering phase functions at a fixed solar zenith angle of the present invention; Figure 6(d) is an inversion diagram of the water body diffuse attenuation coefficient at different scattering phase functions at a fixed solar zenith angle of the existing inversion model; The grouping performance index statistics of Two-Flow-Kd (the present invention) and Kd_Lee on the Sim-Kd simulation data set are shown in Table 1. Figure 6(a) to Figure 6(d) The horizontal axis is the diffuse attenuation coefficient of the simulated data, and the vertical axis is the diffuse attenuation coefficient calculated based on the inversion model. Figure 6(a) to Figure 6(d) It can be seen that the inversion performance of Two-Flow-Kd is very good in the whole range, and the inversion values ​​are evenly distributed near the 1:1 line. -1 The performance of Kd_Lee is significantly worse than that of Two-Flow-Kd, and the inversion values ​​are generally too large. Figure 6(a) to Figure 6(b) It can be seen that the influence of different solar zenith angles (i.e. solar altitude angles) on the inversion accuracy of the two models is relatively small, and only causes small changes, which is consistent with the trend of the statistical indicators in Table 1. Figure 6(c) to Figure 6(d) It can be seen that different scattering phase functions have little effect on the final inversion model of the present invention, but have a great impact on Kd_Lee. Among them, Figure 6 (d) shows that the inversion accuracy of Kd_Lee in water bodies with high backscattering ratios is very poor, and the scattering phase function corresponding to the most obvious overestimation happens to be the one with the largest backscattering ratio, indicating that Kd_Lee has poor inversion performance in water bodies with high backscattering ratios. The two models in Table 1 are statistically different in terms of the indicators of the scattering phase function grouping. Figure 6(c) to Figure 6(d) The results show the same trend, and when the backscattering ratio of the scattering phase function is 0.012, the accuracy of Kd_Lee is comparable to that of Two-Flow-Kd, but as the backscattering ratio gradually increases, the inversion accuracy of Kd_Lee decreases rapidly. This proves that the final inversion model of this embodiment has higher inversion performance than the existing inversion model.

[0138] Table 1 Grouping performance index statistics of Two-Flow-Kd and Kd_Lee on Sim-Kd simulation data set

[0139]

[0140] In addition, water bodies with high backscatter ratios are usually turbid water bodies. In turbid water bodies, in addition to scattering water bodies with high backscatter ratios, there are also absorbing water bodies dominated by colored dissolved organic matter. For absorbing and scattering water bodies, ω b To distinguish, ω b The simulated value less than 0.1 can be regarded as absorbing water. b The simulation value greater than 0.5 is regarded as a scattering water body, and the water body diffuse attenuation coefficient inversion diagram of different scattering phase functions under absorbing water body and scattering water body is drawn for Two-Flow-Kd and Kd_Lee. Figure 7(a) is the inversion diagram of the water body diffuse attenuation coefficient of different scattering phase functions under absorbing water body of the present invention; Figure 7(b) is the inversion diagram of the water body diffuse attenuation coefficient of different scattering phase functions under absorbing water body of the existing inversion model; Figure 7(c) is the inversion diagram of the water body diffuse attenuation coefficient of different scattering phase functions under scattering water body of the present invention; Figure 7(d) is the inversion diagram of the water body diffuse attenuation coefficient of different scattering phase functions under scattering water body of the existing inversion model. Figure 7(a) to Figure 7(d) The horizontal axis is the diffuse attenuation coefficient of the simulated data, and the vertical axis is the diffuse attenuation coefficient calculated based on the inversion model. Figure 7(a) to Figure 7(b) It can be seen that Two-Flow-Kd and Kd_Lee can achieve high inversion accuracy in absorbing water bodies. Figure 7(c) to Figure 7(d) It can be seen that the inversion accuracy of Two-Flow-Kd is still very high, while Kd_Lee shows obvious overestimation in the entire domain, which further proves that the final inversion model of this embodiment has higher inversion performance than the existing inversion model.

[0141] Based on the inversion results of Two-Flow-Kd and Kd_Lee on the Sim-Kd simulation data set, it can be seen that for clean and absorbing water bodies, both can achieve good inversion accuracy, but Two-Flow-Kd has better performance in scattering water bodies. Therefore, the comprehensive inversion performance of Two-Flow-Kd is better than that of Kd_Lee, and reliable inversion results can be obtained.

[0142] The water body diffuse attenuation coefficient inversion method based on the two-stream method model involved in this embodiment includes: obtaining the absorption coefficient, backscattering coefficient and solar zenith angle of the water body; inputting the obtained absorption coefficient, backscattering coefficient and solar zenith angle into the inversion model to obtain the water body diffuse attenuation coefficient. Among them, the absorption coefficient, backscattering coefficient and solar zenith angle of the water body can be obtained from the water body remote sensing image or the water body. After receiving the absorption coefficient, backscattering coefficient and solar zenith angle, the inversion model performs inversion processing to obtain the required water body diffuse attenuation coefficient.

[0143] In the water body diffuse attenuation coefficient inversion method based on the two-stream method model of the present embodiment, the acquired absorption coefficient, backscattering coefficient and solar zenith angle of the water body are input into the inversion model to obtain the water body diffuse attenuation coefficient, wherein the inversion model is obtained based on the two-stream method model, wherein the expression of the diffuse attenuation coefficient and the expression of the irradiance reflectivity just below the water surface are obtained by using the two-stream method model. In this case, the rationality and water body adaptability of the inversion model can be improved by using the irradiance reflectivity just below the water surface; the expression of the irradiance reflectivity just below the water surface is substituted into the expression of the diffuse attenuation coefficient to obtain the initial expression of the water body diffuse attenuation coefficient inversion model; the initial expression of the water body diffuse attenuation coefficient inversion model is preprocessed to obtain multiple pending parameters, and the multiple pending parameters include two categories, and the pending parameters are used to update the initial expression of the water body diffuse attenuation coefficient inversion model. The initial expression is used to obtain the updated expression of the water body diffuse attenuation coefficient inversion model; in this case, the correlation between the introduced unknown parameters is lower than the correlation between the actual unknown parameters in the initial expression of the water body diffuse attenuation coefficient inversion model, which enhances the stability of the parameterization result, and because the degree of freedom of the unknown parameters is reduced, the simplicity of the parameterization process is improved; the priority of each unknown parameter is determined, and each unknown parameter is parameterized according to the priority using the preset simulation data set to obtain the final expression of each unknown parameter. The first type of unknown parameter is related to the solar zenith angle, and the second type of unknown parameter is related to the absorption coefficient and the backscattering coefficient; based on the final expression of each unknown parameter and the updated expression of the water body diffuse attenuation coefficient inversion model, the final expression of the water body diffuse attenuation coefficient inversion model is obtained to obtain the final inversion model. Therefore, parameterizing the unknown parameters improves the accuracy and water body adaptability of the inversion model, for example, it can be applied to various types of clean, absorbing and scattering water bodies. The inversion model obtained by this method can be directly applied to in-situ measurement and remote sensing images.

Claims

1. A water body diffuse attenuation coefficient inversion method based on a two-stream method model, characterized in that: include: Obtain the absorption coefficient, backscattering coefficient and solar zenith angle of water bodies; The obtained absorption coefficient, backscattering coefficient and solar zenith angle are input into the inversion model to obtain the water body diffuse attenuation coefficient, wherein the inversion model is obtained based on the two-stream method model; The methods of obtaining include: 1) Using the two-stream method model, the expression of the diffuse attenuation coefficient and the expression of the irradiance reflectivity just below the water surface are obtained; 2) Substituting the expression of the irradiance reflectivity just below the water surface into the expression of the diffuse attenuation coefficient, the initial expression of the inversion model of the water diffuse attenuation coefficient is obtained; 3) Preprocessing the initial expression of the water body diffuse attenuation coefficient inversion model to obtain a plurality of undetermined parameters, wherein the plurality of undetermined parameters include two categories, and using the undetermined parameters to update the initial expression of the water body diffuse attenuation coefficient inversion model to obtain an updated expression of the water body diffuse attenuation coefficient inversion model; 4) Parameterizing each undetermined parameter using a preset simulation data set to obtain a final expression of each undetermined parameter, wherein the first type of undetermined parameter is related to the solar zenith angle, and the second type of undetermined parameter is related to the absorption coefficient and the backscattering coefficient; 5) Based on the final expressions of the unknown parameters and the updated expression of the water body diffuse attenuation coefficient inversion model, the final expression of the water body diffuse attenuation coefficient inversion model is obtained, thereby obtaining the inversion model.

2. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 1 is characterized in that: The updated expression of the water body diffuse attenuation coefficient inversion model is: Among them, K d is the water body diffuse attenuation coefficient, p0 and p3 are the first type of unknown parameters, p1 and p2 are the second type of unknown parameters, a is the absorption coefficient, b b It refers to the backscattering coefficient of radiation caused by water scattering, which is opposite to the direction of radiation transmission.

3. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 2 is characterized in that: The first type of undetermined parameters includes two undetermined parameters, namely the first undetermined parameter and the fourth undetermined parameter. The final expressions of the first undetermined parameter and the fourth undetermined parameter are: Among them, p0 is the first parameter to be determined, p3 is the fourth parameter to be determined, θ s is the solar zenith angle.

4. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 2 is characterized in that: The second type of undetermined parameters includes two undetermined parameters, namely the second undetermined parameter and the third undetermined parameter. The final expressions of the second undetermined parameter and the third undetermined parameter are: Among them, p1 is the second parameter to be determined, and p2 is the third parameter to be determined.

5. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 3 is characterized in that: In step 4), the final expression of the first type of undetermined parameters is obtained by the following method: The solar zenith angle in the preset simulation data set and the corresponding actual value of the undetermined parameter are used to perform quadratic function fitting on the relationship between the two, and the final expression of the first undetermined parameter in the first category of undetermined parameters is obtained by fitting; and then the final expression of the fourth undetermined parameter is obtained.

6. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 4 is characterized in that: In step 4), the final expression of the second type of undetermined parameters is obtained by the following method: First, the final expression of the first type of undetermined parameters is obtained, and substituted into the updated expression of the water body diffuse attenuation coefficient inversion model to obtain the intermediate expression of the water body diffuse attenuation coefficient inversion model; Determine the parameterized variables of the second type of undetermined parameters, and then use the preset simulation data set to obtain the final expression of the second type of undetermined parameters by adopting a group parameterization method, wherein the group parameterization method includes: Multiple adjacent bands in the same group of simulation data in a preset simulation data set are selected as a group of data, the actual values ​​of the second type of undetermined parameters in the group of data are used, and the median values ​​of the parameterized variables of the multiple bands are used as input for establishing the expression of the second type of undetermined parameters, and then the iterative parameterization method is used to obtain the final expression of the second type of undetermined parameters.

7. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 6 is characterized in that: The iterative parameterization method includes: ① Determine the benchmark expression of the second undetermined parameter, substitute the benchmark expression into the intermediate expression of the water body diffuse attenuation coefficient inversion model to obtain the current expression of the third undetermined parameter; ②Substitute the current expression of the third undetermined parameter into the intermediate expression of the water body diffuse attenuation coefficient inversion model to obtain the current expression of the second undetermined parameter, and judge whether the second undetermined parameter and the third undetermined parameter meet the requirements. If not, substitute the current expression of the second undetermined parameter into the intermediate expression of the water body diffuse attenuation coefficient to obtain the current expression of the third undetermined parameter again, and repeat step ② to obtain the final expression of the second type of undetermined parameters.

8. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 7 is characterized in that: The benchmark expression is obtained as follows: The relationship between the two parameters is fitted by a logarithmic function using the actual value of the second parameter to be determined in the preset simulation data set and the corresponding parameterized variable, and the benchmark expression of the second parameter to be determined is obtained by fitting. The parameterized variable is the ratio of the backscattering coefficient to the absorption coefficient in the preset simulation data set ω b .

9. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 1 is characterized in that: In step 2), the irradiance reflectance just below the water surface is the irradiance reflectance just below the water surface after series expansion, and the number of terms in the series expansion is retained to the quadratic term.

10. The water body diffuse attenuation coefficient inversion method based on the two-stream method model according to claim 1 is characterized in that: The preset simulation data set is the self-built Sim-Kd simulation data set.

Images