Application of an improved DINEOF method in inversion of ocean primary productivity

Abstract

The present invention designs an application method of an improved DINEOF method in the inversion of marine primary productivity, which relates to the field of marine productivity inversion; a variety of satellite remote sensing data, such as SST, Chl_a, PAR, Kd(490), need to be used in the process of inverting OPP; however, due to the influence of weather, sensors, etc., satellite remote sensing ocean products generally have data missing phenomena, which leads to the one-sidedness of the OPP inversion results; in order to accurately and comprehensively analyze the distribution characteristics of primary productivity in the Bohai Sea, the remote sensing missing data required in the OPP inversion process are reconstructed; and the abnormal phenomenon of reconstruction values ​​of adjacent time data in the reconstruction process of the traditional DINEOF method is overcome; based on the spatiotemporal characteristics of the ocean, this paper proposes the MS-DINEOF method, and uses the MS-DINEOF method and the DINEOF method to reconstruct the remote sensing data of SST, Chl_a, PAR, Kd(490) of MODIS L3 level respectively; by comparing the reconstruction results of the two, it is concluded that the reconstruction accuracy of the method and the changes in the spatiotemporal characteristics of the original data are superior to the existing DINEOF method.

Description

Technical Field

[0001] The present invention relates to the field of ocean productivity inversion, and in particular to an application method of an improved DINEOF method in ocean primary productivity inversion. Background Art

[0002] With the increasing prominence of resource and environmental issues in my country, research on ocean primary productivity (OPP) has received increasing attention. Analyzing the distribution characteristics of OPP is of great significance to the development and management of my country's marine resources. Missing data are common in satellite remote sensing ocean products due to factors such as weather and sensor errors. Currently, methods used to reconstruct missing data include optimal interpolation, intrinsic mode decomposition, kriging interpolation, variational data assimilation, and empirical orthogonal function interpolation. Among these methods, the Data Interpolation Empirical Orthogonal Function (DINEOF) method reconstructs observations in missing regions by constructing an empirical interpolation model based on a long-term observational dataset. Because the DINEOF method requires no prior information during the reconstruction process, it reduces the workload required for data reconstruction and has been widely used to reconstruct missing data from ocean remote sensing. Zhang Zhiheng et al., Beckers and Rixen, Song Wanjiao et al., and Ma Aohui et al. have applied the DINEOF algorithm to reconstruct missing ocean remote sensing data, such as sea surface temperature (SST) and chlorophyll a (Chl-a) concentration. Traditional DINEOF methods place the data to be reconstructed within the same spatiotemporal field, which can easily lead to anomalies in the reconstructed values ​​of adjacent time points within the spatiotemporal field and fail to accurately reflect the diverse spatiotemporal variations of the data. Summary of the Invention

[0003] Aiming at the shortcomings of the existing DINEOF reconstruction method, the present invention proposes an improved DINEOF method for applying it in the inversion of marine primary productivity. The DINEOF is Multiple Spatiotemporal DINEOF (MS-DINEOF).

[0004] An improved DINEOF method is used to invert ocean primary productivity, which specifically includes the following steps:

[0005] Step 1: Collect D remote sensing data sets at different times and divide the data sets to be reconstructed into different feature subsets X according to their features. (g) ;

[0006] Given D remote sensing datasets collected at D different times, each dataset has m data points, which are defined as a matrix X with m rows and D columns; according to the spatiotemporal characteristics of the dataset, X is decomposed into G sub-matrices, represented as X = {X (g) ,g=1,…,G}, where g is the index of the decomposition submatrix, is a system with m rows and n g g sub-matrices of columns, n g is the number of data sets contained in the submatrix g, satisfying X (g) Missing data values ​​are set to NaN;

[0007] Step 2: Calculate X (g) The average value vector M in the time dimension (g) ; for X (g) After the deviation calculation, the initial matrix Y is obtained (g) ; Select Y (g) A certain proportion of valid data is used as a cross-validation set and is designated as NaN, Y (g) The points assigned to NaN in are replaced by zero and are represented as Y (g)(L)(0) ;

[0008] Specifically: Calculate X (g) The average value vector in the time dimension is the average value of the i-th pixel in the time dimension;

[0009]

[0010] X (g) After the deviation calculation, the initial matrix Y is obtained (g) :

[0011] Y (g) =X (g) -A m×1 ×M (g) (2)

[0012] Among them, A m×1 is a column vector of all 1s; randomly select Y (g) A certain proportion of valid data is used as the cross-validation set Y C , and assign it to NaN; Y (g) The points assigned to NaN in are replaced by zero and are represented as Y (g)(L)(0) ; Through Y (g)(L) Perform multiple singular value decompositions to achieve X (g) Reconstruction of missing data;

[0013] Step 3: For Y obtained in step 2 (g)(L)(t)Perform SVD calculation, where L = 1,…,n g ,t=0, is the maximum number of iterations;

[0014] Y (g)(L)(t) =U (g)(L)(t) S (g)(L)(t) (V (g)(L)(t) ) T (3)

[0015] in, and Y (g)(L)(t) The spatial eigenmode matrix, singular value matrix and time eigenmode matrix of ;

[0016] Step 4: Reconstruct the matrix Y (g)(L)(t) The missing data in the reconstruction matrix Y is obtained (g)(L)(t+1) ;

[0017] Reconstruct the matrix Y according to Equation 4 (g)(L)(t) The missing data in the reconstruction matrix is ​​obtained

[0018]

[0019] Where, l = 1, ..., L; It's U (g)(L)(t) The i-th data in the l-th column of It is V (g)(L)(t) Transpose the jth data in the lth row of the matrix, It's S (g)(L)(t) The singular value of the lth column of (g)(L)(t+1) Zhong and Y C ={Y C d ,d=1,...,N}, the data points at the same position of the data in are recorded as (Y (g)(L)(t+1) ) C ={(Y (g)(L)(t+1) ) C d ,d=1,...,N}, N is Y C The number of data points in ; then, calculate (Y (g)(L)(t+1) ) C and Y C The root mean square error is denoted as R (g)(L)(t+1) ;

[0020]

[0021] Step 5: Reconstruct the matrix Y again according to step 3 (g)(L)(t+1) Perform SVD until its And record the RMSE value each time; take R (g)(L) =[R (g)(L)(1) ,…,R (g)(L)(t+1) ] and record it as R (g)(L) ;

[0022] Step 6: Let L = 1,…,n g ; Repeat steps 2 to 4 and record the corresponding R (g)(L) ;choose The minimum value of The optimal mode number k is The corresponding L value;

[0023] Step 7: Take the optimal modal number k and reconstruct Y according to steps 3 and 4 (g) The missing data in the matrix is ​​still represented as Y (g) ; for Y (g) Each column of is added with the average value of its corresponding time dimension to obtain the final reconstruction matrix X re(g) ;

[0024] X re(g) =Y (g) +A×M (g) (6)

[0025] Beneficial technical effects of the present invention:

[0026] This paper proposes an improved DINEOF method for applying it in the inversion of marine primary productivity. The data to be reconstructed are divided into different subsets according to their different spatiotemporal characteristics, and the different subsets are reconstructed. Compared with the existing DINEOF reconstruction method, the error between the reconstruction result and the true value of the MS-DINEOF method is much smaller than that of the DINEOF method, and the reconstruction result of the MS-DINEOF method is more specific in depicting the spatiotemporal changes of the original data. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flow chart of an application method of an improved DINEOF method in the inversion of ocean primary productivity according to an embodiment of the present invention;

[0028] Figure 2 The DINEOF and MS-DINEOF reconstruction results and their original data of Chl_a, SST, Kd(490) and PAR in the embodiments of the present invention;

[0029] Figure 3 Time series of original data, reconstruction results of the DINEOF method, and reconstruction results of the MS-DINEOF method in an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The specific embodiments of the present invention are described in further detail below with reference to the accompanying drawings and examples;

[0031] The present invention proposes an improved DINEOF method for the inversion of marine primary productivity. By utilizing the different characteristics of the ocean in different time and space, the reconstruction data set is divided into different feature subsets, and a dedicated space-time field is established for each feature subset to reconstruct the missing data.

[0032] An improved DINEOF method is used to invert ocean primary productivity. Figure 1 As shown, the following steps are included:

[0033] Step 1: Collect D remote sensing data sets at different times and divide the data sets to be reconstructed into different feature subsets X according to their features. (g) ;

[0034] Given D remote sensing datasets collected at D different times, the remote sensing datasets are MODIS data collected by satellites, where each dataset has m data points and is defined as a matrix X with m rows and D columns; according to the spatiotemporal characteristics of the dataset, X is decomposed into G sub-matrices, expressed as X = {X (g) ,g=1,…,G}, where g is the index of the decomposition submatrix, is a system with m rows and n g g sub-matrices of columns, n g is the number of data sets contained in the submatrix g, satisfying X (g) Missing data values ​​are set to NaN;

[0035] Step 2: Calculate X (g) The average value vector M in the time dimension (g) ; for X (g) After the deviation calculation, the initial matrix Y is obtained (g) ; Select Y (g) A certain proportion of valid data is used as a cross-validation set and is designated as NaN, Y (g) The points assigned to NaN in are replaced by zero and are represented as Y (g)(L)(0) ;

[0036] Specifically: Calculate X (g) The average value vector in the time dimension is the average value of the i-th pixel in the time dimension;

[0037]

[0038] X (g)After the deviation calculation, the initial matrix Y is obtained (g) :

[0039] Y (g) =X (g) -A m×1 ×M (g) (2)

[0040] Among them, A m×1 is a column vector of all 1s; randomly select Y (g) 3% of the valid data is used as the cross-validation set Y C , and assign it to NaN; Y (g) The points assigned to NaN in are replaced by zero and are represented as Y (g)(L)(0) ; Through Y (g)(L) Perform multiple singular value decompositions (SVD) to achieve X (g) Reconstruction of missing data;

[0041] Step 3: For Y obtained in step 2 (g)(L)(t) Perform SVD calculation, where L = 1,…,n g ,t=0, is the maximum number of iterations; in this paper

[0042] Y (g)(L)(t) =U (g)(L)(t) S (g)(L)(t) (V (g)(L)(t) ) T (3)

[0043] in, and Y (g)(L)(t) The spatial eigenmode matrix, singular value matrix and time eigenmode matrix of ;

[0044] Step 4: Reconstruct the matrix Y (g)(L)(t) The missing data in the reconstruction matrix Y is obtained (g)(L)(t+1) ;

[0045] Reconstruct the matrix Y according to Equation 4 (g)(L)(t) The missing data in the reconstruction matrix is ​​obtained

[0046]

[0047] Where, l = 1, ..., L; It's U (g)(L)(t) The ith data in the lth column of (g)(L)(t) ) Tj,l It is V (g )(L)(t) Transpose the jth data in the lth row of the matrix, It's S (g)(L)(t) The singular value of the lth column of (g)(L)(t+1) Zhong and Y C ={Y C d ,d=1,...,N}, the data points at the same position of the data in are recorded as (Y (g)(L)(t+1) ) C ={(Y (g )(L)(t+1) ) C d ,d=1,...,N}, N is Y C The number of data points in ; then, calculate (Y (g)(L)(t+1) ) C and Y C The root mean square error (RMSE) is denoted as R (g)(L)(t+1) ;

[0048]

[0049] Step 5: Reconstruct the matrix Y again according to step 3 (g)(L)(t+1) Perform SVD until its And record the RMSE value each time; take R (g)(L) =[R (g)(L)(1) ,…,R (g)(L)(t+1) ] and record it as R (g)(L) ;

[0050] Step 6: Let L = 1,…,n g ; Repeat steps 2 to 4 and record the corresponding R (g)(L) ;choose The minimum value of The optimal modal number k is The corresponding L value;

[0051] Step 7: Take the optimal modal number k and reconstruct Y according to steps 3 and 4 (g) The missing data in the matrix is ​​still represented as Y (g) ; for Y (g) Each column of is added with the average value of its corresponding time dimension to obtain the final reconstruction matrix X re(g) ;

[0052] X re(g) =Y (g) +A×M (g) (6)

[0053] To verify the authenticity of the present invention, under the same experimental conditions, the DINEOF algorithm and the MS-DINEOF algorithm were used to analyze the SST, Chl_a concentration, photosynthetically active radiation data (PAR) and the diffuse attenuation coefficient data of water at 490nm (K) from April to October 2021. d (490)) (all from MODIS L3 products) were reconstructed, and the reconstruction results are shown in Table 1;

[0054] Table 1 Monthly average values ​​of Chl_a, SST, Kd(490) and par from DINEOF method, MS-DINEOF method and original data respectively;

[0055]

[0056] The absolute errors of the DINEOF and MS-DINEOF reconstruction values ​​of each parameter and the original data were calculated, and the calculation results are shown in Table 2.

[0057] Table 2 Monthly mean values ​​of Chl_a, SST, Kd(490) and PAR from the AE of the DINEOF method and the absolute errors of the MS-DINEOF method, respectively;

[0058]

[0059]

[0060] Combining Table 1 and Table 2, the reconstruction accuracy of the MS-DINEOF method is much higher than that of the DINEOF method. Take the daily data of Chl_a, SST and KD490 on June 30, 2021 and PAR on June 4, 2021 as examples. The reconstruction results are as follows Figure 2 As shown in Figure 2, both the DINEOF and MS-DINEOF methods can completely reconstruct the missing data. Furthermore, the MS-DINEOF reconstruction is more detailed than the DINEOF reconstruction in depicting the temporal and spatial variations of the original data.

[0061] Figure 3The figure shows the time series of the reconstruction results and the original valid data. The reconstruction results of the DINEOF method and the MS-DINEOF method have the same time variation trend as the original data. Among them, the reconstructed values ​​of Chl_a, SST, and Kd(490) based on the DINEOF method are mostly much larger or much smaller than the true values, and the reconstructed values ​​of PAR based on the DINEOF method are much smaller than the true values. The reconstructed values ​​of Chl_a, SST, Kd(490), and PAR based on the MS-DINEOF method almost coincide with the true values. In summary, the MS-DINEOF method is superior to the DINEOF method in all aspects.

Claims

1. An improved DINEOF method for applying inversion of ocean primary productivity, characterized in that: The specific steps include: Step 1: Collect D remote sensing data sets at different times and divide the data sets to be reconstructed into different feature subsets X according to their features. (g) ; Given D remote sensing datasets collected at D different times, each dataset has m data points, which are defined as a matrix X with m rows and D columns; according to the spatiotemporal characteristics of the dataset, X is decomposed into G sub-matrices, represented as X = {X (g) ,g=1,…,G}, where g is the index of the decomposition submatrix, is a system with m rows and n g g sub-matrices of columns, n g is the number of data sets contained in the submatrix g, satisfying X (g) Missing data values ​​are set to NaN; Step 2: Calculate X (g) The average value vector M in the time dimension (g) ; for X (g) After the deviation calculation, the initial matrix Y is obtained (g) ; Select Y (g) A certain proportion of valid data is used as a cross-validation set and is designated as NaN, Y (g) The points assigned to NaN in are replaced by zero and are represented as Y (g)(L)(0) ; Step 3: For Y obtained in step 2 (g)(L)(t) Perform SVD calculation, where L = 1,…,n g , is the maximum number of iterations; Step 4: Reconstruct the matrix Y (g)(L)(t) The missing data in the reconstruction matrix Y is obtained (g)(L)(t+1) ; Step 5: Reconstruct the matrix Y again according to step 3 (g)(L)(t+1) Perform SVD until its And record the RMSE value each time; take R (g)(L) =[R (g)(L)(1) ,…,R (g)(L)(t+1) ] and record it as R (g)(L) ; Step 6: Let L = 1,…,n g ; Repeat steps 2 to 4 and record the corresponding R (g)(L) ;choose The minimum value of The optimal mode number k is The corresponding L value; Step 7: Take the optimal modal number k and reconstruct Y according to steps 3 and 4 (g) The missing data in the matrix is ​​still represented as Y (g) ; for Y (g) Each column of is added with the average value of its corresponding time dimension to obtain the final reconstruction matrix X re(g) .

2. The method for applying the improved DINEOF method in inversion of marine primary productivity according to claim 1, characterized in that: Step 2 is as follows: Calculate X (g) The average value vector in the time dimension is the average value of the i-th pixel in the time dimension; X (g) After the deviation calculation, the initial matrix Y is obtained (g) : Y ( g ) =X ( g ) -A m×1 ×M ( g ) (2) Among them, A m×1 is a column vector of all 1s; randomly select Y (g) A certain proportion of valid data is used as the cross-validation set Y C , and assign it to NaN; Y (g) The points assigned to NaN in are replaced by zero and are represented as Y (g)(L)(0) ; Through Y (g)(L) Perform multiple singular value decompositions to achieve X (g) Reconstruction of missing data.

3. The method for applying the improved DINEOF method in inversion of marine primary productivity according to claim 1, characterized in that: Step 3 is as follows: Y (g)(L)(t) =U (g)(L)(t) S (g)(L)(t) (V (g)(L)(t) ) T (3) in, and Y (g )(L)(t) The spatial eigenmode matrix, singular value matrix and time eigenmode matrix of .

4. The method for applying the improved DINEOF method in inversion of marine primary productivity according to claim 1, characterized in that: Step 4 is as follows: Reconstruct the matrix Y according to Equation 4 (g)(L)(t) The missing data in the reconstruction matrix is ​​obtained Where, l = 1, ..., L; It's U (g)(L)(t) The i-th data in the l-th column of It is V (g)(L)(t) Transpose the jth data in the lth row of the matrix, It's S (g)(L)(t) The singular value of the lth column of (g)(L)(t+1) Zhongyu The data points at the same position as the data in are recorded as N is Y C The number of data points in ; then, calculate (Y (g)(L)(t+1) ) C and Y C The root mean square error is denoted as R (g)(L)(t+1) ; 5. The method for applying the improved DINEOF method in inversion of marine primary productivity according to claim 2, characterized in that: Step 7 Final reconstruction matrix X re(g) for: X re(g) =And (g) +A×M (g) (6)。

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