QAA Inversion Method for Water Body's inherent Optical Properties Based on Gaussian Process Regression

Abstract

The present invention belongs to the field of water body remote sensing technology, and particularly relates to a method for retrieving the inherent optical properties of water bodies based on Gaussian process regression. In the process of retrieving the inherent optical properties of water bodies using the QAA algorithm, the absorption coefficient a(λ0) of the reference band λ0 and the spectral slope Y of the particulate backscattering coefficient no longer use empirical models, but instead, the first inversion model GPR-a and the second inversion model GPR-Y are constructed using Gaussian process regression, and these two models are used to calculate the absorption coefficient a(λ0) of the reference band λ0 and the spectral slope Y of the particulate backscattering coefficient. Compared with the traditional QAA algorithm, the inversion accuracy of the method of the present invention has been significantly improved, and the water body adaptability has been enhanced. At the same time, due to the introduction of Gaussian process regression, it is possible to evaluate the uncertainty of the inversion results.

Description

Technical Field

[0001] The present invention belongs to the technical field of water body remote sensing, and particularly relates to a method for retrieving the inherent optical properties of water bodies based on Gaussian process regression for the Quasi-Analytical Algorithm (QAA). Background Technique

[0002] The inherent optical properties of water bodies can be used to derive many water body parameters, including the diffuse attenuation coefficient, water transparency, primary productivity, and chlorophyll and suspended sediment concentrations. The inversion accuracy of these derived quantities will directly depend on the accuracy of the inherent optical properties.

[0003] As an algorithm with the best comprehensive performance, the Multi-Band Quasi-Analytical Algorithm (QAA) is superior to other types of algorithms in both inversion accuracy and computational efficiency, and does not involve prior assumptions about water body components, making it particularly suitable for the inversion of large-scale remote sensing images.

[0004] When using the QAA algorithm to retrieve the inherent optical properties of water bodies, empirical models are used for the inversion of the reference band absorption coefficient a(λ 0 ), and the spectral slope Y of the particulate backscattering coefficient, which to a certain extent limits the further improvement of its inversion accuracy and water body adaptability. Summary of the Invention

[0005] The present invention provides a method for retrieving the inherent optical properties of water bodies based on Gaussian process regression for the QAA, aiming to solve the problem of low inversion accuracy caused by the use of an empirical model for the band absorption coefficient a(λ 0 ) in the QAA algorithm.

[0006] To solve the above technical problems, the technical solutions included in the present invention and the corresponding beneficial effects of the technical solutions are as follows:

[0007] The present invention provides a method for retrieving the inherent optical properties of water bodies based on Gaussian process regression for the QAA, including the following steps:

[0008] 1) Obtain the remote sensing reflectance R of the calculation band λ rs ;

[0009] 2) Determine the remote sensing reflectance r just below the water surface of the calculation band λ according to the remote sensing reflectance R of the calculation band λ rs ; rs ;

[0010] 3) Determine the Gordon parameter u(λ) of the calculation band λ according to the remote sensing reflectance r just below the water surface of the calculation band λ rs ;

[0011] 4) Select the reference band λ 0, obtain the input features related to the first inversion model GPR-a, and substitute them into the first inversion model GPR-a to obtain the reference band λ 0 of the absorption coefficient a(λ 0 ); wherein, the first inversion model GPR-a is constructed based on the Gaussian process regression model, and the input of the first inversion model GPR-a is the input features. The input features of the first inversion model GPR-a include the remote sensing reflectance of the selected band and the band ratio combination. The band ratio is the ratio of the remote sensing reflectances of two selected bands. The output of the first inversion model GPR-a is the absorption coefficient a(λ 0 of the reference band λ 0 );

[0012] 5) Determine the particulate backscattering coefficient b 0 (λ 0 ) of the reference band λ 0 according to the absorption coefficient a(λ 0 ) of the reference band λ 0 , the Gordon parameter of the reference band λ bp and the pure water backscattering coefficient of the reference band λ 0 ;

[0013] 6) Determine the spectral slope Y of the particulate backscattering coefficient;

[0014] 7) Determine the backscattering coefficient b 0 (λ bp ) of the calculation band λ according to the spectral slope Y of the particulate backscattering coefficient, the particulate backscattering coefficient b 0 (λ 0 ) of the reference band λ bw and the pure water backscattering coefficient b 0 (λ b ) of the reference band λ

[0015] 8) Determine the absorption coefficient a(λ) of the calculation band λ according to the backscattering coefficient b b (λ) of the calculation band λ and the Gordon parameter u(λ) of the calculation band λ.

[0016] The beneficial effects of the above technical solution are as follows: The present invention uses the QAA algorithm to invert the inherent optical properties of water bodies. During the use of the QAA, the absorption coefficient a(λ 0 ) of the reference band λ 0 no longer uses an empirical model, but uses the Gaussian process regression to construct the first inversion model GPR-a. The first inversion model GPR-a is used to calculate the absorption coefficient a(λ 0 ) of the reference band λ 0)Perform prediction. In terms of the inversion of the inherent optical properties of water bodies, compared with the QAA algorithm in the prior art, the inversion accuracy of the method of the present invention has been significantly improved, and the water body adaptability has been enhanced.

[0017] Further, the means for determining the spectral slope Y of the particulate backscattering coefficient in step 6) is:

[0018] Obtain the input features related to the second inversion model GPR-Y, and substitute them into the second inversion model GPR-Y to obtain the spectral slope Y of the particulate backscattering coefficient; wherein, the second inversion model GPR-Y is constructed based on the Gaussian process regression model, the input of the second inversion model GPR-Y is the input features, the input features of the second inversion model GPR-Y include the remote sensing reflectance of the selected bands, and the output of the second inversion model GPR-Y is the spectral slope Y of the particulate backscattering coefficient.

[0019] The beneficial effects of the above technical solutions are: during the use of QAA, the spectral slope Y of the particulate backscattering coefficient no longer uses an empirical model, but uses the Gaussian process regression to construct the second inversion model GPR-Y, and uses the second inversion model GPR-Y to predict the spectral slope Y of the particulate backscattering coefficient. In terms of the inversion of the inherent optical properties of water bodies, compared with the QAA algorithm in the prior art, the inversion accuracy of the method of the present invention has been significantly improved, and the water body adaptability has been enhanced.

[0020] Further, in step 4), the selected bands include the 412 nm band, 443 nm band, 490 nm band, 510 nm band, 560 nm band, 620 nm band, and 665 nm band.

[0021] Further, the band ratio combination is a combination of the ratios of the remote sensing reflectance of the long band to the short band; the band ratio combination includes the ratios of the 620 nm band and 665 nm band to the remote sensing reflectance of the 412 nm band, 443 nm band, 490 nm band, 510 nm band, and 560 nm band respectively.

[0022] Further, the kernel functions of the first inversion model GPR-a and the second inversion model GPR-Y both select the Matérn kernel function.

[0023] Further, in step 4), the first inversion model GPR-a is trained and tested using the self-built in-situ measurement dataset SeaBASS2020.

[0024] The beneficial effects of the above technical solution are as follows: The in-situ measurement dataset SeaBASS2020 contains certain measurement errors and the influence of the external environment. Therefore, the inversion model established based on it can fully consider the uncertainties caused by water bodies, the atmosphere, instruments, etc., making it more suitable for water bodies outside the dataset and applicable to remote sensing images.

[0025] Further, in step 6), the second inversion model GPR-Y is obtained by training and testing using the simulation dataset IOCCG2006.

[0026] The beneficial effects of the above technical solution are as follows: The simulation dataset IOCCG 2006 has less uncertainty, a more reasonable Y value range, and is more conducive to the training of the second inversion model GPR-Y. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flowchart of the QAA water inherent optical property inversion method based on Gaussian process regression of the present invention;

[0028] Figure 2-1 is an effect diagram of the a(560) inversion model constructed with the input feature In_Rrs of the present invention;

[0029] Figure 2-2 is an effect diagram of the a(560) inversion model constructed with the input feature In_Ratio of the present invention;

[0030] Figure 2-3 is an effect diagram of the a(560) inversion model constructed with the input feature In_Rrs+Ratio of the present invention;

[0031] Figure 3-1 is an effect diagram of the Y inversion constructed with the input feature In_Rrs of the present invention;

[0032] Figure 3-2 is an effect diagram of the Y inversion constructed with the input feature In_Ratio of the present invention;

[0033] Figure 3-3 is an effect diagram of the Y inversion constructed with the input feature In_Rrs+Ratio of the present invention;

[0034] Figure 4-1 is a relative relationship diagram of the simulation errors generated by the simulation noise GN of the present invention among different bands;

[0035] Figure 4-2 is a relative relationship diagram of the simulation errors generated by the simulation noise GNwK of the present invention among different bands;

[0036] Figure 5-1It is the comparison chart of the a(560) inversion performance between GPR-QAA and QAA_v6 of the present invention;

[0037] Figure 5-2 It is the comparison chart of the a(510) inversion performance between GPR-QAA and QAA_v6 of the present invention;

[0038] Figure 5-3 It is the comparison chart of the a(490) inversion performance between GPR-QAA and QAA_v6 of the present invention;

[0039] Figure 5-4 It is the comparison chart of the a(443) inversion performance between GPR-QAA and QAA_v6 of the present invention;

[0040] Figure 5-5 It is the comparison chart of the a(412) inversion performance between GPR-QAA and QAA_v6 of the present invention. Detailed implementation mode

[0041] The basic concept of the present invention is as follows: when using the QAA algorithm in the present invention, the absorption coefficient a(λ 0 ) and the spectral slope Y of the particulate backscattering coefficient of the reference band no longer use the empirical model, and the Gaussian Process Regression (GPR) is used to replace the empirical model, so as to realize the improvement of QAA, and the improved algorithm is called the GPR-QAA inversion algorithm. The improvement of the GPR-QAA inversion algorithm compared with the QAA algorithm includes two aspects: one is to establish an inversion substitution model of the absorption coefficient a(λ 0 ) of the reference band based on GPR, where the reference band λ 0 is selected as 560nm, and the other part is to establish an inversion substitution model of the spectral slope Y of the particulate backscattering coefficient based on GPR. These two inversion models are respectively called GPR-a and GPR-Y, so as to further improve the inversion accuracy and water body adaptability of QAA.

[0042] The Gaussian regression process will be introduced first below.

[0043] The Gaussian regression process is a type of machine learning regression algorithm. Compared with empirical mode algorithms, the advantage of machine learning regression algorithms is that they do not require assuming an explicit functional relationship between feature quantities and quantities of interest. Instead, they autonomously learn the functional form from the data and have good flexibility in the selection of feature quantities, being able to make full use of spectral information and mine the high-dimensional features existing therein. As a kernel-based machine learning regression algorithm, Gaussian process regression has shown better performance than other machine learning regression algorithms in some studies. And because its calculation is based on the Bayesian framework, it has the ability of posterior evaluation and can obtain the uncertainty of the inversion value, which is of great significance for analyzing the error and rationality of the inversion value.

[0044] The Gaussian regression process is the prediction implementation of the Gaussian process in the continuous space. And the basic Gaussian process, as a non-parametric model, can describe the relationship between input variables and output variables without a strict model form. This ability enables it to be well applicable to multi-variable non-linear problems.

[0045] When the Gaussian process describes the existing data, it does not need to specify the explicit category of the fitting function. It is defined as a set of a series of random variables, and any number of random variables in this set follow a joint Gaussian distribution. Therefore, from a functional perspective, a Gaussian process can be completely determined by the mean function m(x) and the covariance function k(x, x′), where the mean function and the covariance function are defined as:

[0046] m(x) = E[f(x)] (1)

[0047] k(x, x′) = E[(f(x) - m(x))(f(x′) - m(x′))] (2)

[0048] In the formula, E is the expectation operator; f is the unknown function about input and output to be fitted; x is the input matrix in the training set; x′ is the input matrix in the test set.

[0049] The Gaussian process can be uniquely determined by the following formulas (1) and (2):

[0050] f(x) ∼ GP(m(x), k(x, x′)) (3)

[0051] For the sake of simplicity in representation and calculation, generally, the expectation function is usually taken as zero, which will not affect the description of the distribution of variables. It can be found that the Gaussian process after such an operation is completely determined by the covariance function. Therefore, whether the covariance function is appropriately selected will directly affect the quality of the Gaussian process in describing the variable distribution, that is, the quality of representing the unknown function. When using the Gaussian process to establish a regression model, considering that the data in reality usually has a certain amount of noise, a noise term is added to the covariance function during the modeling of the Gaussian process so that it can better conform to the true distribution of the variables. The added noise term is represented as an ideal Gaussian random distribution with zero mean and fixed covariance, and for the noise terms of different components in the input vector, they are independently and identically distributed and additive. At this time, given a known data set with a certain error, a multivariate joint Gaussian distribution containing prior knowledge can be learned based on the Gaussian process, that is, the expression of the unknown function:

[0052]

[0053] where N is the Gaussian distribution; x and y are the input and output data respectively; K is the covariance matrix function; the subscript with * represents the test data, and the one without subscript represents the training data; σ n 2 I is the Gaussian random noise matrix.

[0054] On this basis, the following combines the drawings and embodiments to elaborate in detail on a QAA water inherent optical property inversion method based on Gaussian process regression of the present invention.

[0055] Method embodiment:

[0056] The calculation process of using the GPR-QAA algorithm to implement a QAA water inherent optical property inversion method based on Gaussian process regression of the present invention is as Figure 1 shown, and the specific process is as follows:

[0057] Step 1, obtain the remote sensing reflectance R of the calculation band λ rs .

[0058] Step 2, according to the remote sensing reflectance R of the calculation band λ rs , calculate the remote sensing reflectance r just under the water surface of the calculation band λ rs :

[0059]

[0060] where T = 0.52 and γQ = 1.7.

[0061] Step 3, use the remote sensing reflectance r just under the water surface of the calculation band λ rs, the Gordon parameter u(λ) of the calculation band λ is calculated:

[0062]

[0063] where g 0 and g 1 are both constants. Generally, the values of g 0 and g 1 can be g 0 = 0.089 and g 1 = 0.1245.

[0064] Step 4, select the reference band λ 0 = 560 nm, and obtain 17 input features related to the first inversion model GPR-a, including In_Rrs and In_Ratio. In_Rrs includes R rs (412), R rs (443), R rs (490), R rs (510), R rs (560), R rs (620) and R rs (665). In_Ratio includes the ratios of R rs (620) and R rs (665) to R rs (412) - R rs (560). Substitute these 17 input features into the first inversion model GPR-a to obtain the absorption coefficient a(λ 0 ) of the reference band λ 0 . Among them, the construction and training process of the first inversion model GPR-a is as follows:

[0065] The first inversion model GPR-a is constructed based on Gaussian process regression. The input of the model is the input feature, and the output of the model is the absorption coefficient a(λ 0 ) of the reference band λ 0 . Considering the OLCI band settings, the bands covered by SeaBASS2020 and IOCCG2006, the remote sensing reflectances of the 412, 443, 490, 510, 560, 620, and 665 nm bands are selected as alternative input features, and are respectively denoted as R rs (412), R rs (443), R rs (490), R rs (510), R rs (560), R rs (620) and R rs(665), and these 7 features are denoted as In_Rrs. At the same time, considering that the empirical inversion model of the water body absorption coefficient is often constructed using band ratios, so R is added. rs (620) and R rs (665) and R rs (412) - R rs (560) ratios are used as alternative input features, denoted as Ratio1 - Ratio10 respectively, and these 10 features are denoted as In_Ratio. In this embodiment, the input features of the first inversion model GPR - a are selected as In_Rrs and In_Ratio, that is, a(λ 0 ) = a(560) = GPR(In_Rrs, In_Ratio).

[0066] At the same time, it can be known from the principle of Gaussian process regression that the key to determining the performance of the Gaussian process regression model lies in whether the covariance function can accurately describe the distribution of variables. Therefore, the selection of the covariance function will have a direct impact on the inversion performance of the GPR - QAA algorithm. The covariance function is usually called the kernel function in engineering applications. The kernel function is a function that describes the variable distribution and measures the distance between variables, and its role is usually described as mapping the non - linear relationship that is not easy to describe in the low - dimensional space into a simple and easy - to - describe linear relationship in the high - dimensional space. According to the kernel function theorem, as long as the kernel matrix corresponding to a symmetric function is positive semi - definite, then it can be used as a kernel function. Therefore, the types of kernel functions are very diverse. The commonly used kernel functions in Gaussian process regression mainly include the radial basis kernel function, the exponential kernel function, the rational polynomial kernel function, and the Matérn kernel function. At present, there is no kernel function that can be applied to all problems. Therefore, in order to enable Gaussian process regression to better solve problems, the selection of the kernel function often needs to be determined according to the problems to be solved and the data characteristics used. By analyzing the input features of GPR - a, the remote sensing reflectance and band ratios, it is found that the optical characteristics distribution of clean water bodies is continuous and the difference between remote sensing reflectances is small, while the optical characteristics distribution of turbid water bodies is discrete and the shape of remote sensing reflectances is variable. Considering the above characteristics, in this embodiment, the Matérn function is selected as the kernel function of the first inversion model GPR - a because it can well adapt to smooth and non - smooth data, and its definition is:

[0067]

[0068] In the formula, x and x' are the input vectors for training and testing respectively; Γ and K v are the gamma function and the modified Bessel function respectively; l is the scale parameter that can be automatically learned through maximum likelihood; v is the weight parameter used to adjust the smoothness of the Matérn kernel; and both l and v are positive parameters.

[0069] The first inversion model GPR-a is trained and tested using the in-situ measurement dataset SeaBASS2020. This is because for the absorption coefficient, the in-situ measurement dataset contains certain measurement errors and the influence of the external environment. Therefore, the inversion model established based on it can fully consider the uncertainties caused by water bodies, the atmosphere, and instruments, making it more suitable for generalization to water bodies outside the dataset and application in remote sensing images. After training and testing the constructed first inversion model GPR-a using the in-situ measurement dataset SeaBASS2020, the absorption coefficient a(λ 0 ) of the reference band λ 0 can be calculated using the first inversion model GPR-a.

[0070] Step five, calculate the particulate backscattering coefficient b 0 of the reference band λ bp (λ 0 ):

[0071]

[0072] In the formula, u(λ 0 ) represents the Gordon parameter of the reference band λ 0 ; b bw (λ 0 ) represents the backscattering coefficient of pure water of the reference band λ 0 .

[0073] Step six, obtain 7 input features related to the second inversion model GPR-Y, including In_Rrs, and In_Rrs includes R rs (412), R rs (443), R rs (490), R rs (510), R rs (560), R rs (620), and R rs (665). Substitute these 7 input features into the second inversion model GPR-Y to obtain the spectral slope Y of the particulate backscattering coefficient. Among them, the construction and training process of the second inversion model GPR-Y are as follows:

[0074] The second inversion model GPR-Y is constructed based on Gaussian process regression. The input of the model is the input feature, and the output of the model is the spectral slope Y of the particulate backscattering coefficient. In this embodiment, the input feature of the second inversion model GPR-Y is selected as In_Rrs. That is, Y = GPR(In_Rrs).

[0075] Moreover, the kernel function of the second inversion model GPR-Y also selects the Matérn kernel function.

[0076] The training and testing of the second inversion model GPR-Y uses the simulated data set IOCCG2006. In this embodiment, the training and testing of the second inversion model GPR-Y does not select the in-situ measurement data set SeaBASS2020. This is because the amount of backscatter coefficient data in the SeaBASS2020 data set is small and most of it is located in clean water bodies, and the distribution is very unbalanced and lacks representativeness, which is not conducive to the training of the model. Moreover, compared with the absorption coefficient, the measurement of the backscatter coefficient is more complicated and has greater uncertainty, because it is not directly measured but obtained by measuring the scattering phase function at a certain angle and multiplying it by a certain constant conversion coefficient. Since the scattering phase function is not easy to measure and the value of the constant coefficient is not fixed, a large uncertainty is introduced, which will cause Y as a derivative of the backscatter coefficient to have a greater uncertainty, so SeaBASS2020 is not suitable for constructing the inversion formula of Y. Therefore, IOCCG 2006, which is more representative and has less uncertainty, is selected. At the same time, considering that the negative value in the value range of Y is not conducive to the comparison of evaluation indicators, it is normalized to ensure that its value range falls within a range greater than zero.

[0077] Step 7: Based on the particle backscattering coefficient spectral slope Y and reference band λ 0 The particle backscatter coefficient b bp (λ 0 ), reference band λ 0 The backscattering coefficient of pure water is b bw (λ 0 ), calculate the backscattering coefficient b of the calculation band λ b (λ):

[0078]

[0079] Where b bw (λ) represents the pure water backscattering coefficient in the calculated band λ.

[0080] Step 8: Calculate the backscatter coefficient b of band λ b (λ) and the Gordon parameter u(λ) of the calculation band λ, the absorption coefficient a(λ) of the calculation band λ is calculated:

[0081]

[0082] At this point, the backscattering coefficient b of the calculation band λ can be calculated bp (λ) and absorption coefficient a(λ). Following the same processing method as steps 1 to 8, the backscattering coefficients and absorption coefficients of all other bands can be calculated to complete the inversion of the inherent optical properties of the water body.

[0083] To further analyze the inversion performance of the GPR-a and GPR-Y models, three other machine regression algorithms were also selected for comparison, namely Elastic Net Regression (ENR), Support Vector Regression (SVR), and Random Forest Regression (RFR). All three are widely used in various regression inversion problems and can achieve good results, which can help better analyze the advantages of the model of the present invention. To ensure that the models obtained by training the machine learning regression algorithms have sufficient reliability and robustness, in this embodiment, the train_test_split function of sklearn was used to randomly split SeaBASS2020 and IOCCG2006, where the training set accounted for 70% and the test set accounted for 30%, and the random_state was set to 42. Considering that several hyperparameters are included in all models and they have a direct impact on the model performance, improper values may cause underfitting or overfitting. Therefore, 10-fold cross-validation was used on the training set to determine the optimal hyperparameters of the model. The model performance evaluation metrics used were R 2 , RMSE, MRE, Slope, and Intercept.

[0084] 1. Performance evaluation of the GPR-a inversion model.

[0085] Figures 2-1 to 2-3 , and Table 1 statistically compared the performance of the GPR models constructed based on different input features and the other three types of machine regression models. The results showed that the GPR-a model constructed using In_Rrs+Ratio as the input feature had the best inversion performance among all models.

[0086] As Figures 2-1 to 2-3 shown, GPR achieved good inversion accuracy when using three input features. The R of the three inversion models 2All exceeded 0.9, indicating that GPR has excellent potential in retrieving the water absorption coefficient. It can be seen from the figure that the inversion values of the three models are concentrated near the 1:1 line, which means that GPR can fully extract information related to a(560) from the input features, enabling the inversion model to take into account both low and high values. However, there are still certain differences among the three groups of inversion models. The inversion performance of the model constructed using In_Rrs as the input is the worst, with some inversion values significantly deviating from the 1:1 line in both high and low value regions. When using In_Ratio as the input, the performance of the inversion model is significantly improved compared to the former, indicating that for the inversion of a(560), the band ratio is a better feature than remote sensing reflectance. The model with the best inversion performance is GPR-a established using In_Rrs+Ratio, indicating that using only the band ratio will lose some information beneficial to the inversion of a(560). Therefore, better accuracy is achieved when both are used as inputs, which also shows that even features with a very low correlation with the inversion quantity may still contain information beneficial to explaining the inversion quantity.

[0087] As shown in Table 1, GPR achieved the best inversion performance on all three groups of inputs, and its performance was far superior to that of the other models. Among the four machine regression algorithms, the inversion accuracy of ENR was the lowest because it belongs to regularized multiple linear regression and is not applicable to non-linear data, while the relationships between both remote sensing reflectance and band ratio and a(560) are highly non-linear. Both SVR and RFR have strong non-linear fitting capabilities, so the inversion models they constructed also performed excellently, but generally SVR was slightly better than RFR. In terms of the comparison of input features, all algorithms performed the worst on In_Rrs, but GPR still achieved higher accuracy than the other three machine regression algorithms, indicating that GPR has stronger information mining capabilities. The inversion performance of all algorithms was almost better when using In_Rrs+Ratio as the input than when using In_Ratio, further indicating that the remote sensing reflectance contains a(560) inversion information that cannot be covered by the band ratio. Therefore, it should be retained as a feature input.

[0088] Table 1 Comparison of the results of GPR and the other three machine regression models

[0089]

[0090] 2. Performance evaluation of the GPR-Y inversion model.

[0091] Figures 3-1 to 3-3、The inversion results of the 4 algorithms in Table 2 on three groups of inputs and the conclusions of the absorption coefficient are similar. The inversion model established with In_Rrs+Ratio as the input has the highest accuracy. The errors on In_Rrs and In_Ratio are slightly larger, and there is almost no difference between the other algorithms except ENR. From the indicators, it can be seen that the inversion accuracy of the model established with In_Rrs+Ratio as the feature input is the best, but the difference between it and the other two models is very small. Through the comparison between algorithms, it is found that the algorithm with the best inversion accuracy is still GPR, and all evaluation indicators on the three inputs are at the forefront, fully demonstrating the excellent performance of GPR in mining data features and establishing inversion models. Among the other 4 algorithms, the inversion accuracy of ENR is the worst, only slightly better than RFR on In_Ratio; the accuracy of SVR, which belongs to the kernel method, is also very good, especially the error on In_Rrs+Ratio is comparable to that of GPR and significantly smaller than the other algorithms; although RFR performs poorly on In_Rrs and In_Ratio, its inversion accuracy on In_Rrs+Ratio is second only to GPR and SVR, indicating that its performance is greatly affected by the input features. It can be seen that when constructing the Y inversion formula, in terms of the usage priority of the feature input amount, In_Rrs+Ratio>In_Rrs≈In_Ratio, and in terms of the algorithm inversion accuracy, GPR>SVR≈RFR>ENR.

[0092] Table 2 Comparison of the accuracy of the Y inversion model based on IOCCG 2006

[0093]

[0094] 3. Comparison of model robustness.

[0095] From the analysis of the inversion accuracy of each model in the above two parts, it is found that when using In_Rrs+Ratio as the input feature, the a(560) and Y inversion models constructed based on GPR both show the best inversion accuracy. However, if it is required to still have a relatively high accuracy when applying it to new data, it is necessary for it to have sufficient robustness to resist data with different error levels, especially when it needs to be applied to remote sensing images. More than 90% of the radiation value of water bodies on the image is caused by atmospheric scattering. To obtain the remote sensing reflectance that only contains water body information, atmospheric correction is required, which results in the data input to the model containing atmospheric correction errors, and its error is often larger than that of in-situ measurement. Therefore, higher requirements are imposed on the robustness of the model. For this reason, in this embodiment, the method of adding simulated errors to the remote sensing reflectance in the SeaBASS2020 and IOCCG2006 test sets is used to test the model robustness.

[0096] Two methods are used to generate simulated noise. One is Gaussian noise (GN) that does not consider the relative relationship of inter-band errors. A noise level of 10% is selected to represent the low-error situation in in-situ measurements. The other is Gaussian noise with reference kernel (GNwK), which can consider the relative relationship of inter-band errors, that is, when a certain band is larger (smaller) than the true value, the other bands are also likely to be larger (smaller). The generation of GNwK includes two steps. First, a group of reference kernels are randomly generated according to the relative amplitude of inter-band errors, and then 10% Gaussian random noise is added to this reference kernel to improve the authenticity of the simulated noise. GNwK is used to represent the high-error situation of atmospheric correction errors on remote sensing images. In determining the simulated noise level, referring to the current research on the atmospheric correction accuracy of OLCI, the noise levels of 412nm, 443nm, 490nm, 510nm, 620nm, and 665nm are set to 50%, 50%, 20%, 20%, 20%, 40%, and 40% respectively. [90-92] . To demonstrate the rationality of GNwK, Figures 4-1 to 4-2 Figure 1 plots the relative relationship of simulated errors generated by GN and GNwK at different bands with the atmospheric correction as the noise level. It can be found that there is no correlation between the relative errors of each band in GN, and there are only differences in the amplitude range. However, the simulated errors generated by GNwK have an obvious relative relationship between bands, but this relationship is not strict and contains a certain degree of randomness, which is more in line with the actual atmospheric correction errors compared to GN. In addition, to avoid the specificity of Gaussian random noise, 50 noise simulations are performed for each group of models. The mean values of MRE and RMSE are selected to evaluate the robustness of the models, and SVR, whose performance is second only to GPR, is selected for comparison.

[0097] As shown in Table 3, for a(560), whether it is the low-error GN of 10% or the high-error GNwK of atmospheric correction, GPR shows good robustness, and the GPR-a model constructed with In_Rrs+Ratio as the input has the strongest robustness. The robustness of SVR is significantly weaker than that of GPR. When using In_Rrs+Ratio as the input in the low-error group, the GPR-a constructed has the best performance in both MRE and RMSE. The SVR has the lowest MRE and RMSE in the model established using In_Ratio. In terms of the MRE increment, the increments of the two inversion models of In_Ratio and In_Rrs+Ratio containing band ratios are less than half of the noise level, while the model with the other group of inputs has an increment of 8.01%, indicating that the band ratio has an important impact on the inversion robustness of low-value a(560). And the MRE increments of the three groups of models do not exceed the 10% noise level, indicating that all three have strong robustness, while the MRE increment of SVR is higher than that of the corresponding GPR inversion model. For the RMSE increment, the model of GPR using In_Rrs as the input has the smallest increment, followed by In_Rrs+Ratio, and the increment of In_Ratio is the largest, indicating that the remote sensing reflectance has a relatively important impact on the robustness of the inversion model in the high-value part.

[0098] The conclusions obtained in the high-error group of atmospheric correction are basically the same as those in the low-error group. Still, the GPR-a model constructed with In_Rrs+Ratio shows the strongest robustness. The increment of MRE is still better for the two groups of models containing band ratios than the model using In_Rrs as the input. The trend of the RMSE increment is the same, and both are better than SVR. However, the model constructed with In_Rrs as the input reaches 21.96% in terms of the MRE increment, which is the only model that exceeds 20% of the lowest noise level of atmospheric correction, further illustrating the importance of the band ratio for the low-value inversion robustness of the model. In terms of the RMSE increment, the relative gap between the three groups of models is not as obvious as that in the low-error group, indicating that the remote sensing reflectance has a positive but limited impact on improving the inversion robustness of the model in the high-value part. The MRE increments of all three inversion models of SVR in the high-error group exceed the lowest noise level of atmospheric correction, and except for the model using In_Rrs+Ratio as the input, its MRE increment is higher than that of the GPR inversion model in the same group, indicating that SVR is more affected by errors and its robustness is weaker than that of GPR.

[0099] However, for Y, the GPR-Y model established with In_Rrs as the input has the strongest robustness in Table 3, far superior to the inversion models established with the other two input features, and has the smallest values in terms of MRE, RMSE, and the corresponding increments. Although the inversion model constructed with In_Rrs+Ratio is slightly more accurate than the GPR-Y model, its robustness is very poor. When facing GN with a 10% noise level, the MRE increment reaches an astonishing 68.53%, nearly 7 times the noise level. Moreover, the MRE increment on the simulated error GNwK of atmospheric correction reaches nearly 100%. Even when the noise level of GN is reduced to 5%, the MRE increment still reaches 20%, indicating that this model is not suitable for remote sensing images with large errors.

[0100] Another group of inversion models constructed with In_Ratio as the input have an inversion accuracy similar to that of GPR-Y, but the robustness shown in Table 3 is significantly weaker than that of GPR-Y, and the MRE increment on 10% GN also exceeds the noise level. The robustness trends of the inversion models constructed by SVR based on the three groups of inputs are the same as those of GPR, from strong to weak are the models constructed by In_Rrs—In_Ratio—In_Rrs+Ratio. The four indicators of MRE, RMSE, and the corresponding increments are all greater than those of the inversion models constructed by GPR in the same group, and the model constructed with In_Rrs+Ratio as the input also shows extremely poor robustness. The reason for this situation may be that in existing studies, it is found that there is a strong correlation between the particulate backscattering coefficient and the magnitude of remote sensing reflectance, especially in the long wavelength band. The band ratio In_Ratio used in this embodiment is exactly the ratio of two long wavelength bands to a short wavelength band, thus destroying the correlation between the particulate backscattering coefficient and the remote sensing reflectance. As a derivative of the backscattering coefficient, Y is more affected by it. Therefore, the model constructed with the band ratio has poor stability and is easily affected by errors.

[0101] After comprehensively considering the inversion accuracy and model robustness, the GPR-a model constructed with In_Rrs+Ratio as the input feature and the GPR-Y model constructed with In_Rrs as the input feature are the models with the best comprehensive performance for inverting a(560) and Y respectively.

[0102] Table 3 Comparison of the robustness of GPR and SVR inversion models

[0103]

[0104]

[0105] 4. Comparison of the inversion performance with QAA.

[0106] To verify the performance of the improved algorithm GPR-QAA, the GPR-QAA and the latest version of QAA, QAA_v6, were compared using the SeaBASS2020 test set, and the results are as Figures 5-1 to 5-4 shown in Table 4. From the above analysis, it can be seen that for the QAA algorithm with strict optical closure, the inversion accuracy of the backscattering coefficient is highly correlated with the inversion accuracy of the absorption coefficient, and the accuracy performance of both is consistent. Since GPR-QAA is also strictly optically closed like QAA, it also has this property. And considering that there are few groups containing the backscattering coefficient in the SeaBASS2020 test set and they are all in clean water bodies and not representative, the inversion accuracy of the absorption coefficient is used in this section to evaluate the inversion performance of GPR-QAA. Since the span of the absorption coefficient exceeds three orders of magnitude and there is a relatively concentrated distribution in the low-value region, logarithmic plotting is used for display effects.

[0107] From Figures 5-1 to 5-4 it can be found that the inversion accuracy of GPR-QAA in all bands is far better than that of QAA_v6. The difference between the two is small in the low-value region, that is, in clean water bodies, while in the medium-high value region, that is, in turbid water bodies, the inversion accuracy of GPR-QAA is significantly superior. Since logarithmic plotting is used, the difference between the two in the high-value region is visually weakened, but the difference between R 2 , MRE and RMSE can still clearly reflect the accuracy advantage of GPR-QAA. a(560) is used as the absorption coefficient of the reference band of GPR-QAA and is directly inverted by GPR with extremely high accuracy. The RMSE and MRE are only 1 / 3 and 2 / 3 of QAA_v6, respectively, and it can be seen from Figure 5-1 that the inversion values of GPR-QAA are evenly distributed near the 1:1 line without obvious systematic deviation. The a(560) inverted by QAA_v6 is more discretely distributed, especially for turbid water bodies, which is due to the poor performance of the empirical model used in its reference band.

[0108] For the water body absorption coefficient in bands other than the reference band of 560 nm, the inversion accuracy is jointly affected by a(560) and Y. Although the GPR-Y model in GPR-QAA is established based on the simulation dataset, from Figures 5-2 to 5-5It can be found that the accuracy of the water absorption coefficient obtained by inversion in the range of 412 nm to 510 nm still remains at a relatively high level, and all are better than QAA_v6. The RMSE and MRE are reduced by 24.25% - 59.32% and 9.55% - 29.40% respectively, indicating that a reasonable Y can be obtained by inversion using the GPR-Y model. However, there is an obvious pattern in the variation trend of the inversion accuracy for the five bands. The inversion accuracies of QAA_v6 and GPR-QAA both decrease with the decrease of wavelength, that is, the farther away from the reference band, the lower the inversion accuracy, and this is more obvious in the high-value region. There are mainly two reasons for this phenomenon. One is that the measurement of remote sensing reflectance in the short-wave blue and violet bands has greater uncertainty compared to the yellow and green bands. Especially for turbid waters, due to the strong absorption effect of high-concentration chromophoric dissolved organic matter, the radiation attenuates rapidly in the water body, so the penetration ability of the radiation is very limited. And the underwater light field changes rapidly due to the influence of wind and waves on the surface water body, making the measurement of remote sensing reflectance very unstable, and thus it is difficult to accurately describe the relationship between it and the inherent optical properties. Since GPR-QAA and QAA_v6 directly use remote sensing reflectance to calculate the absorption coefficient of non-reference bands, the uncertainty in this measurement will cause a large error between the retrieved water absorption coefficient and the actual environmental measurement value. The second reason is that the relationship between the particulate backscattering coefficient and wavelength is not a strictly power-law function form, especially for waters with a high phytoplankton content. And the derivation of the water absorption coefficient of other bands from the water absorption coefficient of the reference band precisely depends on this assumed relationship. Therefore, this can also explain why the farther away from the reference band, the worse the inversion accuracy. However, for most water bodies, the error introduced thereby is relatively small, so a relatively high inversion accuracy can still be ensured.

[0109] In addition, to highlight the performance advantages of GPR-QAA in turbid waters, the data in the validation set were divided into clean waters and turbid waters, and the inversion performance indicators of the two were respectively counted. The results are shown in Table 4. It can be found that the inversion accuracies of GPR-QAA and QAA_v6 in clean waters are both relatively high and not much different. Except for a(412), GPR-QAA is only slightly better than QAA_v6. But for turbid waters, the inversion performance of GPR-QAA is significantly better than QAA_v6, and the RMSE and MRE are reduced by 24.72% - 59.91% and 18.06% - 31.10% respectively. Therefore, in summary, whether for clean waters or turbid waters, GPR-QAA can obtain reliable inversion results.

[0110] Table 4 Comparison of the inversion performance of GPR-QAA and QAA_v6 in clean and turbid waters

[0111]

[0112]

[0113] In summary, as a semi - analytical inversion algorithm for the inherent optical properties of water bodies, QAA has good inversion performance and computational efficiency when facing water bodies with huge differences and large amounts of data. However, for the key steps, the absorption coefficient a(λ 0 ) of the reference band in water and the spectral slope Y of the backscattering coefficient of particulate matter are limited in further improving the water body adaptability and inversion accuracy due to the use of empirical models. Therefore, the present invention uses Gaussian process regression to improve QAA and proposes the GPR - QAA inversion algorithm. The improvement work mainly includes two parts: (1) Taking the remote sensing reflectance at 412, 443, 490, 510, 560, 620, 665 nm and the ratios of the remote sensing reflectance at 620 and 665 nm to the remote sensing reflectance of the other 5 bands as feature inputs, an inversion model GPR - a for the absorption coefficient reference band is established based on the in - situ measurement dataset SeaBASS2020; (2) Taking the remote sensing reflectance at 412, 443, 490, 510, 560, 620, 665 nm as feature inputs, an inversion model GPR - Y for Y is established based on the simulation dataset IOCCG2006. The experimental results show that the inversion algorithm proposed by the present invention has been significantly improved in accuracy compared with the original QAA algorithm. Especially for turbid water bodies, the RMSE and MRE of the absorption coefficient in the 412 - 560 nm band are reduced by 24.72% - 59.91% and 18.06% - 31.10% respectively.

Claims

1. A method for retrieving the inherent optical properties of water bodies based on Gaussian process regression, characterized in that, it includes the following steps: 1) Obtain the remote sensing reflectance R of the calculation band λ rs ; 2) Determine the remote sensing reflectance r just below the water surface for the calculation band λ based on the remote sensing reflectance R of the calculation band λ rs ; rs ; 3) Determine the Gordon parameter u(λ) of the calculation band λ according to the remote sensing reflectance r just below the water surface rs , and determine the Gordon parameter u(λ) of the calculation band λ; 4) Select the reference band λ 0 , obtain the input features related to the first inversion model GPR-a, and substitute them into the first inversion model GPR-a to obtain the absorption coefficient a(λ 0 ) of the reference band λ 0 ; wherein, the first inversion model GPR-a is constructed based on the Gaussian process regression model, and the input of the first inversion model GPR-a is the input feature. The input features of the first inversion model GPR-a include the remote sensing reflectance and the band ratio combination of the selected bands. The band ratio is the ratio of the remote sensing reflectances of two selected bands. The output of the first inversion model GPR-a is the absorption coefficient a(λ 0 ) of the reference band λ 0 ; The kernel function of the first inversion model is selected as the Matérn kernel function; 5) According to the absorption coefficient a(λ 0 ) of the reference band λ 0 , the Gordon parameter of the reference band λ 0 , and the backscattering coefficient of pure water of the reference band λ 0 , determine the particulate backscattering coefficient b 0 (λ bp ) of the reference band λ 0 ; 6) Determine the spectral slope Y of the particulate backscattering coefficient; 7) According to the spectral slope Y of the particulate matter backscattering coefficient, the particulate matter backscattering coefficient b 0 at the reference band λ bp (λ 0 ), the backscattering coefficient b 0 of pure water at the reference band λ bw (λ 0 ), determine the backscattering coefficient b b (λ) at the calculation band λ; 8) Determine the absorption coefficient a(λ) of the calculation band λ based on the backscattering coefficient b b (λ) of the calculation band λ and the Gordon parameter u(λ) of the calculation band λ.

2. The method for retrieving the inherent optical properties of water bodies based on Gaussian process regression according to claim 1, characterized in that, the means for determining the spectral slope Y of the particulate backscattering coefficient in step 6) is: Obtain the input features related to the second inversion model GPR-Y and substitute them into the second inversion model GPR-Y to obtain the spectral slope Y of the particulate backscattering coefficient; wherein, the second inversion model GPR-Y is constructed based on the Gaussian process regression model, the input of the second inversion model GPR-Y is the input features, the input features of the second inversion model GPR-Y include the remote sensing reflectance of the selected bands, and the output of the second inversion model GPR-Y is the spectral slope Y of the particulate backscattering coefficient.

3. The method for retrieving the inherent optical properties of water bodies based on Gaussian process regression according to claim 1 or 2, characterized in that, in step 4), the selected bands include the 412 nm band, 443 nm band, 490 nm band, 510 nm band, 560 nm band, 620 nm band and 665 nm band.

4. The method for retrieving the inherent optical properties of water bodies based on Gaussian process regression according to claim 1, characterized in that, the band ratio combination is a combination of the ratios of the remote sensing reflectance of the long band to the short band; the band ratio combination includes the ratios of the 620 nm band and 665 nm band to the remote sensing reflectance of the 412 nm band, 443 nm band, 490 nm band, 510 nm band, 560 nm band respectively.

5. The method for retrieving the inherent optical properties of water bodies based on Gaussian process regression according to claim 2, characterized in that, the kernel function of the second inversion model GPR-Y selects the Matérn kernel function.

6. The method for retrieving the inherent optical properties of water bodies based on Gaussian process regression according to claim 1, characterized in that, in step 4), the first inversion model GPR-a is trained and tested using the self-built in-situ measurement dataset SeaBASS2020.

7. The method for retrieving the inherent optical properties of water bodies based on Gaussian process regression according to claim 2, characterized in that, in step 6), the second inversion model GPR-Y is trained and tested using the simulated dataset IOCCG2006.

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