CN114239416B - QAA water body inherent optical characteristic inversion method based on Gaussian process regression - Google Patents
QAA water body inherent optical characteristic inversion method based on Gaussian process regression Download PDFInfo
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Abstract
The invention belongs to the technical field of water remote sensing, and particularly relates to a QAA water inherent optical characteristic inversion method based on Gaussian process regression. In the method, in the process of inversion of inherent optical characteristics of a water body by using a QAA algorithm, an absorption coefficient a (lambda 0) of a reference wave band lambda 0 and a particulate matter backscattering coefficient spectrum slope Y are not used any more, a first inversion model GPR-a and a second inversion model GPR-Y are constructed by using Gaussian process regression, and the absorption coefficient a (lambda 0) of the reference wave band lambda 0 and the particulate matter backscattering coefficient spectrum slope Y are calculated by using the two models. Compared with the traditional QAA algorithm, the inversion accuracy of the method is remarkably improved, the water adaptability is improved, and meanwhile, the uncertainty of an inversion result can be evaluated due to the fact that Gaussian process regression is introduced.
Description
Technical Field
The invention belongs to the technical field of water remote sensing, and particularly relates to a QAA water inherent optical characteristic inversion method based on Gaussian process regression.
Background
The inherent optical characteristics of the water body can be used for deriving numerous water body parameters including diffuse attenuation coefficient, water body transparency, primary productivity, chlorophyll, suspended sediment concentration and the like, and the inversion accuracy of the derived quantities directly depends on the accuracy of the inherent optical characteristics.
The multiband quasi-analysis algorithm (QAA) is used as an algorithm with optimal comprehensive performance, has better inversion precision and calculation efficiency than other types of algorithms, does not involve prior assumption of water components, and is particularly suitable for inversion of a large-range remote sensing image.
When the QAA algorithm is used for inversion of the inherent optical characteristics of the water body, an empirical model is used for inversion of the absorption coefficient a (lambda 0) of the reference wave band and the spectrum slope Y of the particulate matter backscattering coefficient, so that further improvement of inversion accuracy and water body adaptability is limited to a certain extent.
Disclosure of Invention
The invention provides a Gaussian process regression-based inversion method for the inherent optical characteristics of a QAA water body, which is used for solving the problem of low inversion precision caused by the fact that an empirical model is used for a wave band absorption coefficient a (lambda 0) in a QAA algorithm.
In order to solve the technical problems, the technical scheme and the corresponding beneficial effects of the technical scheme are as follows:
the invention provides a Gaussian process regression-based QAA water body inherent optical characteristic inversion method, which comprises the following steps:
1) Acquiring remote sensing reflectivity R rs of a calculated wave band lambda;
2) Determining the remote sensing reflectivity R rs of the calculated wave band lambda just under the water surface according to the remote sensing reflectivity R rs of the calculated wave band lambda;
3) Determining Gordon parameters u (lambda) of the calculated wave band lambda according to the remote sensing reflectivity r rs of the calculated wave band lambda just under the water surface;
4) Selecting a reference wave band lambda 0, acquiring input features related to a first inversion model GPR-a, substituting the input features into the first inversion model GPR-a to obtain an absorption coefficient a (lambda 0) of a reference wave band lambda 0, wherein the first inversion model GPR-a is constructed based on a Gaussian process regression model, the input of the first inversion model GPR-a is the input features, the input features of the first inversion model GPR-a comprise a combination of remote sensing reflectivity of a selected wave band and a wave band ratio, the wave band ratio is the ratio of the remote sensing reflectivities of two screening wave bands, and the output of the first inversion model GPR-a is the absorption coefficient a (lambda 0) of a reference wave band lambda 0;
5) Determining a particulate matter backscattering coefficient b bp(λ0 of the reference band lambda 0 according to an absorption coefficient a (lambda 0) of the reference band lambda 0, a Gordon parameter of the reference band lambda 0 and a pure water backscattering coefficient of the reference band lambda 0;
6) Determining a spectrum slope Y of a backward scattering coefficient of the particulate matter;
7) Determining a backscattering coefficient b b (lambda) of the calculated band lambda according to the spectrum slope Y of the backscattering coefficient of the particulate matter, the backscattering coefficient b bp(λ0 of the particulate matter of the reference band lambda 0 and the pure water backscattering coefficient b bw(λ0 of the reference band lambda 0;
8) The absorption coefficient a (lambda) of the calculated band lambda is determined from the backscattering coefficient b b (lambda) of the calculated band lambda and the Gordon parameter u (lambda) of the calculated band lambda.
The method has the beneficial effects that the QAA algorithm is utilized to invert the inherent optical characteristics of the water body, in the process of using the QAA, the absorption coefficient a (lambda 0) of the reference wave band lambda 0 is not used any more, the Gaussian process regression construction is utilized to obtain the first inversion model GPR-a, and the absorption coefficient a (lambda 0) of the reference wave band lambda 0 is predicted by utilizing the first inversion model GPR-a. In the aspect of inversion of inherent optical characteristics of water, compared with the QAA algorithm in the prior art, the inversion accuracy of the method is remarkably improved, and the water adaptability is improved.
Further, the means for determining the spectrum slope Y of the backscattering coefficient of the particulate matter in step 6) is as follows:
And obtaining input features related to the second inversion model GPR-Y, substituting the input features into the second inversion model GPR-Y to obtain the particulate matter backscattering coefficient spectrum slope Y, wherein the second inversion model GPR-Y is constructed based on a Gaussian process regression model, the input features of the second inversion model GPR-Y are input features, the input features of the second inversion model GPR-Y comprise remote sensing reflectivity of a selected wave band, and the output of the second inversion model GPR-Y is the particulate matter backscattering coefficient spectrum slope Y.
The technical scheme has the beneficial effects that in the process of using QAA, an empirical model is not used any more for the spectrum slope Y of the backward scattering coefficient of the particulate matter, a second inversion model GPR-Y is obtained by means of Gaussian process regression construction, and the spectrum slope Y of the backward scattering coefficient of the particulate matter is predicted by means of the second inversion model GPR-Y. In the aspect of inversion of inherent optical characteristics of water, compared with the QAA algorithm in the prior art, the inversion accuracy of the method is remarkably improved, and the water adaptability is improved.
Further, in step 4), the selected wavelength bands include 412nm, 443nm, 490nm, 510nm, 560nm, 620nm and 665 nm.
Further, the combination of the wave band ratio is a combination of the ratio of the remote sensing reflectances of the long wave band and the short wave band, and the combination of the wave band ratio comprises the ratio of the remote sensing reflectances of the 620nm wave band and the 665nm wave band to the 412nm wave band, the 443nm wave band, the 490nm wave band, the 510nm wave band and the 560nm wave band respectively.
Further, the kernel functions of the first inversion model GPR-a and the second inversion model GPR-Y are both selected from Materrn kernel functions.
Further, in step 4), the first inversion model GPR-a is trained and tested using a self-built in situ measurement dataset SeaBASS.
The technical scheme has the beneficial effects that the in-situ measurement dataset SeaBASS contains a certain measurement error and the influence of external environment, so that the uncertainty caused by water, atmosphere, instruments and the like can be fully considered by the inversion model established based on the in-situ measurement dataset SeaBASS, and the inversion model is more suitable for water outside the dataset and applied to remote sensing images.
Further, in step 6), the second inversion model GPR-Y is trained and tested using the simulation dataset IOCCG 2006.
The technical scheme has the beneficial effects that the uncertainty of the simulation dataset IOCCG 2006 is smaller, the more reasonable Y value range is provided, and the training of the second inversion model GPR-Y is facilitated.
Drawings
FIG. 1 is a flow chart of the method of inversion of QAA water body intrinsic optical properties based on Gaussian process regression of the present invention;
FIG. 2-1 is a graph of the effect of the a (560) inversion model of the invention with the input features in_Rrs constructed;
FIG. 2-2 is a graph of the effect of the a (560) inversion model of the invention with the input features In_Ratio build;
FIGS. 2-3 are effect graphs of an a (560) inversion model constructed with the input features In_Rrs+ratio of the present invention;
FIG. 3-1 is a graph of the effect of the Y inversion of the invention with the input features in_Rrs construction;
FIG. 3-2 is a graph of the effect of the Y inversion of the invention with the input features in_Ratio construction;
FIGS. 3-3 are effect graphs of the Y inversion of the invention constructed with the input features In_Rrs+ratio;
FIG. 4-1 is a graph of the relative relationship of the analog error generated for GN by the analog noise of the present invention between different bands;
FIG. 4-2 is a graph of the relative relationship of the analog error generated for GNwK of the present invention between different bands;
FIG. 5-1 is a graph comparing the a (560) inversion performance of GPR-QAA and QAA_v6 of the present invention;
FIG. 5-2 is a graph comparing the a (510) inversion performance of GPR-QAA and QAA_v6 of the present invention;
FIGS. 5-3 are graphs comparing the a (490) inversion performance of GPR-QAA and QAA_v6 of the present invention;
FIGS. 5-4 are graphs comparing the a (443) inversion performance of the GPR-QAA and QAA_v6 of the present invention;
FIGS. 5-5 are graphs comparing the a (412) inversion performance of GPR-QAA and QAA_v6 of the present invention.
Detailed Description
The basic idea of the invention is that when the QAA algorithm is used, an empirical model is not used any more for the absorption coefficient a (lambda 0) of the reference wave band and the spectrum slope Y of the particulate matter backscattering coefficient, and the empirical model is replaced by Gaussian process regression (Gaussian Process Regression, GPR), so that the QAA is improved, and the improved algorithm is called GPR-QAA inversion algorithm. The improvement of the GPR-QAA inversion algorithm compared with the QAA algorithm comprises the following two aspects of firstly establishing an inversion substitution model of a reference wave band absorption coefficient a (lambda 0) based on GPR, wherein the reference wave band lambda 0 is 560nm, and the other part of establishing an inversion substitution model of a particulate matter backward scattering coefficient spectrum slope Y based on GPR, wherein the two inversion models are respectively named as GPR-a and GPR-Y, so that the inversion precision and the water body adaptability of the QAA are further improved.
The Gaussian regression process is described first.
The gaussian regression process is one of the machine learning regression algorithms. Compared with an empirical mode algorithm, the machine learning regression algorithm has the advantages that the function form is autonomously learned from data without assuming an explicit function relation between the feature quantity and the interest quantity, the machine learning regression algorithm has good flexibility in feature quantity selection, and spectrum information can be fully utilized and high-dimensional features existing in the spectrum information can be mined. Gaussian process regression is used as a kernel-based machine learning regression algorithm, shows better performance than other machine learning regression algorithms in some researches, has the capability of posterior evaluation because the calculation is based on a Bayesian framework, can obtain uncertainty of an inversion value, and has important significance for analyzing errors and rationality of the inversion value.
The gaussian regression process is a predictive implementation of the gaussian process in continuous space, while the basic gaussian process acts as a non-parametric model, describing the relationship between input and output variables without strict modeling, and this capability makes it well suited for the problem of non-linearities of multiple variables.
The gaussian process describes existing data without specifying an explicit class of fitting functions, which is defined as a set of random variables, any number of which in the set obey a joint gaussian distribution. Thus, from a functional point of view, a gaussian process can be completely determined by the expectation function m (x) and the covariance function k (x, x'), where the expectation function and the covariance function are defined as:
m(x)=E[f(x)] (1)
k(x,x′)=E[(f(x)-m(x))(f(x′)-m(x′))] (2)
where E is the desired operator, f is the unknown function to be fitted for the inputs and outputs, x is the input matrix in the training set, and x' is the input matrix in the test set.
The gaussian process can be uniquely determined by the following formulas (1), (2):
f(x)~GP(m(x),k(x,x′)) (3)
For simplicity of representation and computation, the desired function is typically zero, which has no effect on the distribution description of the variables. It can be found that the gaussian process after such operation is completely determined by the covariance function, so that the suitability of the covariance function selection directly affects the how good the gaussian process is for variable distribution description, i.e. how good the covariance function is for unknown function representation. When the regression model is built by using the Gaussian process, certain noise is usually considered in the data in reality, so that a noise item is added to the covariance function in the modeling process of the Gaussian process, and the Gaussian process can be more in line with the real distribution of the variables. The added noise term is represented as an ideal gaussian random distribution with zero mean and fixed covariance, and is independent and co-distributed and additive for the noise terms of the different components in the input vector. At this time, given a known data set with a certain error, a multi-element joint gaussian distribution containing a priori knowledge, that is, the expression of an unknown function, can be learned based on the gaussian process:
Wherein N is Gaussian distribution, x and y are input data and output data respectively, K is covariance matrix function, footmarks are representative test data, no footmarks are representative training data, and sigma n 2 I is Gaussian random noise matrix.
Based on the above, the invention relates to a QAA water body inherent optical characteristic inversion method based on Gaussian process regression, which is described in detail below with reference to the accompanying drawings and examples.
Method embodiment:
The calculation flow of the method for realizing the QAA water body inherent optical characteristic inversion based on Gaussian process regression by using the GPR-QAA algorithm is shown in a figure 1, and the specific process is as follows:
step one, obtaining remote sensing reflectivity R rs of a calculated wave band lambda.
Step two, according to the remote sensing reflectivity R rs of the calculated wave band lambda, the remote sensing reflectivity R rs of the calculated wave band lambda just under the water surface is calculated:
where, t=0.52, γq=1.7.
Thirdly, calculating Gordon parameter u (lambda) of the calculated wave band lambda by utilizing remote sensing reflectivity r rs of the calculated wave band lambda just under the water surface:
Where g 0 and g 1 are both constants, in general, the values of g 0 and g 1 may be g 0＝0.089,g1 = 0.1245.
Step four, selecting a reference wave band lambda 0 =560 nm, acquiring 17 input features related to a first inversion model GPR-a, wherein the 17 input features comprise In_Rs and In_Ratio, the In_Rs comprises R rs(412)、Rrs(443)、Rrs(490)、Rrs(510)、Rrs(560)、Rrs (620) and R rs (665), the In_Ratio comprises the Ratio of R rs (620) and R rs (665) to R rs(412)-Rrs (560), and substituting the 17 input features into the first inversion model GPR-a to obtain an absorption coefficient a (lambda 0) of the reference wave band lambda 0. The construction and training process of the first inversion model GPR-a is as follows:
The first inversion model GPR-a is constructed based on Gaussian process regression, the input of the model is an input characteristic, and the output of the model is the absorption coefficient a (lambda 0) of a reference wave band lambda 0. The remote sensing reflectivities of the 412, 443, 490, 510, 560, 620, and 665nm bands are selected as alternative input features, denoted R rs(412)、Rrs(443)、Rrs(490)、Rrs(510)、Rrs(560)、Rrs (620) and R rs (665), respectively, and these 7 features are denoted in_rrs, combining the bands covered by OLCI band settings SeaBASS2020 and IOCCG 2006. Meanwhile, an empirical inversion model considering the absorption coefficient of the water body is often constructed by using the wave band Ratio, so that the Ratio of R rs (620) and R rs (665) to R rs(412)-Rrs (560) is increased to serve as an alternative input characteristic, which is respectively denoted as Ratio1-Ratio10, and the 10 characteristics are denoted as in_ratio. In this embodiment, the input features of the first inversion model GPR-a select in_rrs and in_ratio, i.e., a (λ 0) =a (560) =gpr (in_rrs, in_ratio).
Meanwhile, as can be known from the principle of Gaussian process regression, the key for determining the performance of the Gaussian process regression model is whether the covariance function can accurately describe the distribution of variables, so that the selection of the covariance function directly affects the inversion performance of the GPR-QAA algorithm, and the covariance function is generally called a kernel function in engineering application. A kernel function is a function that describes the distribution of variables and is used to measure the distance between variables, whose function is typically described as mapping a non-linear relationship that is not easily described in a low-dimensional space to a linear relationship that is simply easily described in a high-dimensional space. According to the theorem of the kernel function, the kernel matrix corresponding to one symmetric function can be used as the kernel function, so that the kernel function has various kinds, and the kernel functions commonly used in the Gaussian process regression mainly comprise radial basis kernel functions, exponential kernel functions, rational polynomial kernel functions and Materrn kernel functions. At present, there is no kernel function applicable to the problem, so in order to enable the gaussian process to return to solve the problem better, the kernel function needs to be selected according to the solved problem and the used data characteristics. Analysis of the input characteristic remote sensing reflectivity and the band ratio of the GPR-a shows that the optical characteristic distribution of the clean water body is continuous, the difference between the remote sensing reflectances is small, the optical characteristic distribution of the turbid water body is discrete, and the shape of the remote sensing reflectivity is changeable. In view of the above features, the present embodiment selects the Materrn function as the kernel function of the first inversion model GPR-a, since it is well adapted to smooth and non-smooth data, defined as:
Wherein x and x' are respectively input vectors for training and testing, Γ and K v are respectively a gamma function and an optimized Bessel function, l is a scale parameter which can be obtained through maximum likelihood automatic learning, v is a weight parameter for adjusting the smoothness of a Matlern kernel, and l and v are both positive parameters.
Training and testing of the first inversion model GPR-a uses the in situ measurement dataset SeaBASS2020. The method is characterized in that for the absorption coefficient, the in-situ measurement data set contains a certain measurement error and the influence of external environment, so that the uncertainty caused by water, atmosphere, instruments and the like can be fully considered by the inversion model established based on the in-situ measurement data set, and the inversion model is more suitable for being popularized to water outside the data set and applied to remote sensing images. After the first inversion model GPR-a constructed using the in situ measurement dataset SeaBASS2020 is trained and tested, the absorption coefficient a (λ 0) of the reference band λ 0 can be calculated for the first inversion model GPR-a.
Step five, calculating a particulate matter backscattering coefficient b bp(λ0 of the reference wave band lambda 0):
Where u (lambda 0) denotes the Gordon parameter of the reference band lambda 0 and b bw(λ0 denotes the pure water backscattering coefficient of the reference band lambda 0.
Step six, 7 input features related to the second inversion model GPR-Y are obtained, wherein the input features comprise In_Rrs, the In_Rrs comprises R rs(412)、Rrs(443)、Rrs(490)、Rrs(510)、Rrs(560)、Rrs (620) and R rs (665), and the 7 input features are substituted into the second inversion model GPR-Y to obtain the particulate matter backscattering coefficient spectrum slope Y. The construction and training process of the second inversion model GPR-Y is as follows:
The second inversion model GPR-Y is constructed based on Gaussian process regression, the input of the model is an input characteristic, and the output of the model is the spectrum slope Y of the particulate matter backscattering coefficient. In this embodiment, the input features of the second inversion model GPR-Y are selected from In_Rrs. That is, y=gpr (in_rrs).
Furthermore, the kernel function of the second inversion model GPR-Y is likewise selected from the Matrn kernel functions.
Training and testing of the second inversion model GPR-Y uses a simulation dataset IOCCG2006. In this embodiment, the training and testing of the second inverse model GPR-Y does not select the in situ measurement dataset SeaBASS, 2020 because the amount of data for the backscatter coefficients in the SeaBASS2020 dataset is small and mostly in the clean water, the distribution is very unbalanced and lacks representativeness, which is detrimental to the training of the model. Moreover, the measurement of the backscattering coefficient is more complex than the absorption coefficient, with greater uncertainty, since it is not obtained by direct measurement but by measuring the scattering phase function at an angle and multiplying it by a certain conversion coefficient. Since the scattering phase function is not easy to measure and the value of the constant coefficient is not fixed, larger uncertainty is introduced, and larger uncertainty exists in the derivative of Y as the backscattering coefficient, seaBASS2020 is not suitable for constructing an inversion formula of Y, and therefore IOCCG2006 with more representativeness and smaller uncertainty is selected. Meanwhile, considering that the negative value contained in the value range of Y is unfavorable for the comparison of the evaluation index, normalization processing is carried out on the value range of Y so as to ensure that the value range of Y falls in a range larger than zero.
Step seven, according to the spectrum slope Y of the particulate matter backscattering coefficient, the particulate matter backscattering coefficient b bp(λ0 of the reference wave band lambda 0 and the pure water backscattering coefficient b bw(λ0 of the reference wave band lambda 0, the backscattering coefficient b b (lambda) of the calculated wave band lambda is calculated:
where b bw (λ) represents the pure water backscattering coefficient of the calculated band λ.
Step eight, according to the backscattering coefficient b b (lambda) of the calculated wave band lambda and the Gordon parameter u (lambda) of the calculated wave band lambda, calculating to obtain the absorption coefficient a (lambda) of the calculated wave band lambda:
Thus, the backscattering coefficient b bp (λ) and the absorption coefficient a (λ) of the calculated band λ can be calculated. And according to the same processing mode from the first step to the eighth step, the backscattering coefficient and the absorption coefficient of other all wave bands can be calculated, and the inversion of the inherent optical characteristics of the water body is completed.
To further analyze the inversion performance of the GPR-a and GPR-Y models, three additional machine Regression algorithms were also selected for comparison, namely, elastic network Regression (ELASTIC NET Regression, ENR), support vector Regression (Support Vector Regression, SVR), and random forest Regression (Random Forest Regression, RFR). All three are widely used for various regression inversion problems, can obtain good effects, and can be helpful for better analyzing the advantages of the model. In order to ensure that a model obtained by training a machine learning regression algorithm has sufficient reliability and robustness, the embodiment adopts sklearn train_test_split functions to randomly divide SeaBASS, 2020 and IOCCG2006, wherein a training set accounts for 70%, a testing set accounts for 30%, and a random_state is set to be 42. Considering that all models contain a plurality of super-parameters which directly affect the performance of the models, if the values are incorrect, the under-fitting or the over-fitting can be caused, and therefore, 10-fold cross-validation is adopted on a training set to determine the optimal super-parameters of the models. The model performance evaluation index used was R 2, RMSE, MRE, slope, intersept.
1. Performance evaluation of GPR-a inversion model.
Fig. 2-1 to 2-3, and table 1 statistically compare the performance of the GPR model constructed based on different input features and the other three types of machine regression models, showing that the GPR-a model constructed using in_rrs+ratio as the input feature has the best inversion performance among all models.
2-1-2-3, GPR achieves good inversion accuracy when three input features are used, R 2 of three inversion models exceeds 0.9, and GPR has excellent potential in inverting the water absorption coefficient. From the figure, it can be found that the inversion values of the three models are distributed intensively around the 1:1 line, which means that the GPR can fully extract the information related to a (560) from the input features, so that the inversion model can simultaneously give a low value and a high value. However, there is a certain difference among the three sets of inversion models, the inversion performance of the model constructed by using In_Rrs as input is worst, inversion values which are partially and obviously deviated from 1:1 lines appear In the high-value and low-value areas, and the performance of the inversion model is obviously improved compared with the former by using In_ratio as input, which shows that the band Ratio is a better characteristic than the remote sensing reflectivity for inversion of a (560). The best inversion performance model is GPR-a established when In_Rrs+ratio is used, which shows that only using the band Ratio can lose part of the information beneficial to a (560) inversion, so that better accuracy is obtained when the two are used as input, and the model also shows that even the characteristics with low correlation with inversion quantity can still contain information beneficial to the interpretation of the inversion quantity.
As shown in table 1, GPR achieved optimal inversion performance over all three inputs, and performance far superior to the rest of the model. The inversion accuracy at ENR is the lowest among the four machine regression algorithms because it belongs to regularized multiple linear regression and cannot be applied to nonlinear data, whether the relationship between the remote sensing reflectivity or the band ratio and a (560) is highly nonlinear. And SVR and RFR have strong nonlinear fitting capability, so that the constructed inversion model is excellent, but the SVR is slightly better than the RFR as a whole. In comparison of input feature usage, all algorithms are worst In In_Rrs, but the GPR still obtains precision superior to other three machine regression algorithms, and the GPR has stronger information mining capability. The inversion performance of all algorithms when using in_rrs+ratio as input is almost superior to in_ratio, further illustrating that the remote sensing reflectivity contains a (560) inversion information that cannot be contained In the band Ratio, so it should be kept as a feature input.
Table 1 GPR compares the results of the other three machine regression models
2. Performance evaluation of GPR-Y inversion model.
The inversion results of the 4 algorithms In fig. 3-1 to 3 and table 2 on the three sets of inputs are similar to the conclusion of the absorption coefficients, again with the highest accuracy of the inversion model established with inrrs+ratio as input, with slightly larger errors on inrrs and inratio, and with little difference between the two algorithms other than ENR. From the index, the model inversion established when in_rrs+ratio is taken as the characteristic input has the best accuracy, but the other two models have little difference. The algorithm with the optimal inversion precision is found to be GPR through comparison among algorithms, all evaluation indexes on three inputs are in the front, and the excellent performance of GPR in the aspects of mining data characteristics and establishing an inversion model is fully represented. The inversion accuracy of ENR is the worst In the other 4 algorithms, and is only slightly better than that of RFR In In_Ratio, the SVR accuracy of the homonuclear method is the same good, especially the error In In_Rs+Ratio is equivalent to that of GPR and is obviously smaller than that of the other algorithms, and the inversion accuracy of RFR In In_Rs and In_Ratio is inferior to that of GPR and SVR although the performance of RFR In In_Rs and In_Ratio is poor, so that the performance of the inversion accuracy of ENR is greatly influenced by input characteristics. It can be seen that when constructing the Y inversion formula, in_Rrs+ratio > In_Rrs≡In_ratio on the use priority of the feature input quantity, and GPR > SVR house-RFR > ENR on the algorithm inversion accuracy.
TABLE 2 IOCCG 2006 based Y-inversion model accuracy contrast
3. Model robustness contrast.
From the inversion accuracy analysis of the individual models In section 2 above, it was found that when in_rrs+ratio was used as an input feature, both the a (560) and Y inversion models constructed based on GPR exhibited the best inversion accuracy, but were required to be robust enough to resist data of different error levels, especially when applied to remote sensing images, if it was to be ensured that they still had relatively high accuracy when applied to new data. The radiation value of the water body on the image exceeds 90% due to atmospheric scattering, and atmospheric correction is needed to obtain the remote sensing reflectivity only containing the water body information, so that the data input into the model contains atmospheric correction errors, and the errors are larger than the errors of in-situ measurement, so that the robustness of the model is required. To this end, the present embodiment employs a method of adding simulation errors to the remote sensing reflectances in SeaBASS2020 and IOCCG2006 test sets to verify model robustness.
Two methods are used to generate the analog noise, one is Gaussian Noise (GN) which does not consider the relative relationship of errors between bands, and a noise level of 10% is chosen to represent the low error condition in the in-situ measurement. The other is Gaussian noise with a reference kernel (Gaussian noise WITH REFERENCE KERNEL, GNwK), which can take into account the relative relationship of the errors between the bands, i.e. when the value of a certain band is larger (smaller) than the value of the value, the remaining bands are also larger (smaller) with a high probability. GNwK comprises two steps, namely firstly randomly generating a group of reference kernels according to the relative amplitude of errors between wave bands, and then adding 10% Gaussian random noise on the reference kernels to improve the reality of the simulation noise, wherein GNwK is used for representing the high error condition of atmospheric correction errors on remote sensing images. Referring to current studies on OLCI atmospheric correction accuracy in the determination of simulated noise levels, the noise levels of 412nm, 443nm, 490nm, 510nm, 620nm, and 665nm were set to 50%, 20%, 40%, and 40% [90-92], respectively. To demonstrate the rationality of GNwK, fig. 4-1 through 4-2 depict the relative relationships between the analog errors generated by GN and GNwK at the noise level corrected by the atmosphere, and it can be found that there is no correlation between the relative errors of the respective bands in GN, only a difference in the amplitude range, and the analog error generated by GNwK has a clear relative relationship between the bands, but the relationship is not strict but includes a certain randomness, which is more in line with the actual atmospheric correction error than GN. In addition, to avoid the specificity of Gaussian random noise, 50 times of noise simulation are performed on each group of models, the mean value of MRE and RMSE is selected to evaluate the robustness of the models, and SVR with performance inferior to GPR is selected for comparison.
As shown In table 3, for a (560), GPR shows good robustness, either with 10% low error GN or with atmospheric corrected high error GNwK, and GPR-a model built with in_rrs+ratio as input is the most robust, while SVR is significantly weaker than GPR. GPR-a constructed with In_Rrs+ratio as input on the low error set achieves the best performance on both MRE and RMSE, while SVR models with In_ratio have the lowest MRE and RMSE. In the MRE increment, the increment of two groups of inversion models including in_ratio and in_Rrs+ratio of the band Ratio is less than half of the noise level, and the increment of 8.01% of the other group of input models is used, which shows that the band Ratio has important influence on the inversion robustness of the low value a (560), the MRE increment of the three groups of models does not exceed the noise level of 10%, which indicates that the three groups of models have stronger robustness, and the MRE increment of SVR is higher than the corresponding GPR inversion model. For RMSE delta, the model of GPR when using in_rrs as input has minimum delta, in_rrs+ratio times, with maximum in_ratio increase, indicating that the telemetry reflectivity has a more important impact on the robustness of the inversion model In the high-value part.
The conclusion on the high error group of the atmospheric correction is basically consistent with the low error group, and the GPR-a model constructed by In_Rrs+ratio still shows the strongest robustness, the increment of MRE is still that two groups of models containing the band Ratio are better than the model taking In_Rrs as input, the trend of the increment of RMSE is the same, and the increment of the MRE is better than SVR. However, the model constructed when in_rrs is taken as an input reaches 21.96% on the MRE increment, is the only one that exceeds 20% of the lowest noise level of the atmospheric correction, and further illustrates the importance of the band ratio to the robustness of the model low value inversion. The relative differences between the three models are less obvious than the low error group in RMSE increment, indicating that the remote sensing reflectivity has a positive effect but is limited on improving the inversion robustness of the model in the high value part. The MRE increment of all three inversion models of SVR In a high-error group exceeds the lowest noise level of atmospheric correction, and besides the model using In_Rrs+ratio as input, the MRE increment is higher than that of the GPR inversion models In the same group, which indicates that SVR is more influenced by errors and weaker In robustness than GPR.
However, for Y, the most robust model In table 3 is the GPR-Y model built with in_rrs as input, and is far superior to the inversion model built with the other two input features, and is minimal In both MRE, RMSE, and corresponding increments. While the inversion model constructed using In_Rrs+ratio is slightly better In accuracy than the GPR-Y model, but has poor robustness, the MRE increment reaches up to 68.53% surprisingly, approximately 7 times the noise level In the face of 10% noise level GN, and even more up to approximately 100% on atmospheric corrected simulation error GNwK, the MRE increment reaches up to 20% even when the noise level of GN is reduced to 5%, indicating that the model is not suitable for remote sensing images with large errors.
Another set of inversion models constructed using in_ratio as input had inversion accuracy similar to GPR-Y, but showed significantly less robustness than GPR-Y In table 3, and MRE delta over 10% GN also exceeded noise level. The robustness trend shown by the inversion model constructed by SVR based on three groups of inputs is consistent with that of GPR, the model constructed by strong to weak In_Rrs-In_Ratio-In_Rrs+Ratio is larger than the inversion model constructed by GPR of the same group In terms of four indexes of MRE, RMSE and corresponding increment, and the model constructed by using In_Rrs+Ratio as the input has extremely poor robustness. Analysis may be caused by the fact that In the existing research, the backward coefficient of the particulate matter has strong correlation with the magnitude of the remote sensing reflectivity, especially In a long wave band, but the wave band Ratio in_ratio used In the embodiment is exactly the Ratio of two long wave bands to a short wave band, so that the correlation between the backward scattering coefficient of the particulate matter and the remote sensing reflectivity is destroyed, and the derivative of Y as the backward scattering coefficient is influenced more, so that the model constructed by using the wave band Ratio has weak stability and is easy to be influenced by errors.
After the performance of the integrated inversion accuracy and model robustness, the GPR-a model constructed using In_Rrs+ratio as an input feature and the GPR-Y model constructed using In_Rrs as an input feature are the models with the best integrated performance of inversion a (560) and Y, respectively.
TABLE 3 robustness contrast of GPR and SVR inversion models
4. In contrast to the inversion performance of QAA.
To verify the performance of the improved algorithm GPR-QAA, the GPR-QAA was compared to the latest version of QAA, QAA_v6, using SeaBASS2020 test set, with the results shown in FIGS. 5-1 to 5-4, and Table 4. From the above analysis, it is clear that the inversion accuracy of the backscattering coefficient and the inversion accuracy of the absorption coefficient are highly correlated and the accuracy of both are consistent for the QAA algorithm with strict optical closure, and GPR-QAA is also strictly optical closure like QAA, thus also possessing this property. And the inversion performance of the GPR-QAA is evaluated in this section using the inversion accuracy of the absorption coefficient, considering that the SeaBASS2020 test set contains few groups of backscatter coefficients and none are representative of being located in a clean body of water. Because the span of the absorption coefficient exceeds more than three orders of magnitude and there is a more concentrated distribution in the low value region, logarithmic plot is employed for display effect.
From FIGS. 5-1 to 5-4, it can be seen that the inversion accuracy of GPR-QAA is far better than QAA_v6 in all bands, the difference between the two is smaller in the low value region, namely clean water body, while the inversion accuracy of GPR-QAA is significantly superior in the middle and high value region, namely turbid water body, and the difference between the two in the high value region is visually weakened due to the logarithmic drawing, but the difference between R 2, MRE and RMSE can still obviously reflect the accuracy advantage of GPR-QAA. a (560) is taken as the absorption coefficient of the GPR-QAA reference wave band, and is directly obtained by GPR inversion, with extremely high precision, RMSE and MRE are only 1/3 and 2/3 of QAA_v6, and the inversion value of GPR-QAA can be seen in FIG. 5-1 to be uniformly distributed in the vicinity of the 1:1 line, and no obvious systematic deviation occurs. Whereas qaa_v6 inverted a (560) is more discrete in distribution, especially for turbid water bodies, due to poor performance of the empirical model used in its reference band.
For the water absorption coefficients of the bands except the reference band 560nm, the inversion accuracy is jointly influenced by a (560) and Y, and although a GPR-Y model in the GPR-QAA is established based on a simulation data set, the accuracy of the water absorption coefficients of 412nm to 510nm obtained by inversion can be found to be still higher in accuracy from the figures 5-2 to 5-5, and the accuracy is better than QAA_v6, the RMSE and the MRE are respectively reduced by 24.25% -59.32% and 9.55% -29.40%, so that reasonable Y can be obtained by inversion by using the GPR-Y model. However, there is a clear rule in the change trend of inversion accuracy of the five wave bands, and the inversion accuracy of both qaa_v6 and GPR-QAA decreases with decreasing wavelength, that is, far from the reference wave Duan Yue, the lower the inversion accuracy is, and this is more clear in the high value region. The analysis results in the phenomenon mainly comprise two reasons, namely, the remote sensing reflectivity measurement of the blue-violet light short wave band has larger uncertainty compared with the yellow-green wave band, particularly, the strong absorption effect of high-concentration colored dissolved organic matters is caused for turbid water bodies, radiation is attenuated rapidly in the water bodies, the penetrating capacity of the radiation is limited, the underwater light field change of the surface water bodies is rapid due to the influence of stormy waves, the remote sensing reflectivity measurement is unstable, the relation between the remote sensing reflectivity measurement and the inherent optical characteristics is difficult to accurately describe, and the remote sensing reflectivity is directly used for calculating the absorption coefficient of the non-reference wave bands by GPR-QAA and QAA_v6, so that the uncertainty existing in the measurement can cause the water absorption coefficient obtained by inversion to have large error with the actual environment measured value. The second reason is that because the relationship between the particulate matter backscattering coefficient and the wavelength is not a strict power law function, especially for a water body with a higher phytoplankton content, and the water body absorption coefficients of other wave bands derived from the reference wave band water body absorption coefficient just depend on the assumed relationship, this can also be explained why the inversion accuracy is worse as far from the reference wave Duan Yue, but for most water bodies, the errors introduced thereby are relatively smaller, so that still higher inversion accuracy can be ensured.
In addition, to highlight the performance advantage of GPR-QAA in turbid water bodies, the data in the verification set are divided into clean water bodies and turbid water bodies, and inversion performance indexes of the clean water bodies and the turbid water bodies are respectively counted, and the results are shown in Table 4. It can be seen that both GPR-QAA and QAA_v6 have relatively high inversion accuracy in clean water and are not very different, with the exception of a (412), GPR-QAA being only slightly better than QAA_v6. However, for turbid water bodies, the inversion performance of GPR-QAA is significantly better than QAA_v6, and RMSE and MRE are reduced by 24.72% -59.91% and 18.06% -31.10%, respectively. Thus, taken together, it is clear that GPR-QAA can achieve reliable inversion results for both clean and turbid water.
TABLE 4 comparison of inversion Performance of GPR-QAA and QAA_v6 in clean and turbid Water bodies
In summary, QAA is taken as a semi-analytical inversion algorithm of inherent optical characteristics of water, has good inversion performance and calculation efficiency when facing data with huge water difference and large data volume, but the key steps of the algorithm are that the reference wave band water absorption coefficient a (lambda 0) and the particulate matter backward scattering coefficient spectral slope Y limit the further improvement of water adaptability and inversion precision due to the adoption of an empirical model. To this end, the invention uses Gaussian process regression to improve QAA and proposes a GPR-QAA inversion algorithm, wherein the improvement work mainly comprises two parts, namely (1) taking 412, 443, 490, 510, 560, 620, 665nm remote sensing reflectivity and the ratio of 620 and 665nm remote sensing reflectivity to other 5 wave band remote sensing reflectivity as characteristic inputs, establishing an inversion model GPR-a of an absorption coefficient reference wave band based on an in-situ measurement dataset SeaBASS, and (2) taking 412, 443, 490, 510, 560, 620, 665nm remote sensing reflectivity as characteristic inputs, and establishing an inversion model GPR-Y of Y based on a simulation dataset IOCCG 2006. Experimental results show that compared with the original QAA algorithm, the inversion algorithm provided by the invention has obviously improved precision, and particularly for turbid water bodies, the RMSE and MRE of 412-560nm wave band absorption coefficients are respectively reduced by 24.72% -59.91% and 18.06% -31.10%.
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