A method for mapping sea surface temperature from single point to region under incomplete information

Abstract

A kind of information under the condition of incomplete sea surface temperature single-point to regional mapping method, the optimal window width in asymmetric ellipse information diffusion function is calculated by particle swarm algorithm, and the single-point to regional mapping interpolation of sparse sample is carried out by asymmetric ellipse information diffusion, the extremely sparse sea surface temperature small sample expansion function under the condition of incomplete information is realized;The data set formed by known sparse sample;By non-normal information diffusion function, the known sparse sample point information is diffused into monitoring point space Ω, and the diffusion gain q of all information in each monitoring point in U×V×W is obtained;The gain of all sample points in monitoring point space is summed to obtain information matrix Q jkl The fuzzy relation matrix R is calculated;For any given longitude and latitude coordinate input (x, y), the fuzzy set μ B Is de-fuzzified to obtain the sea surface temperature interpolation result under the coordinate.

Description

Technical Field

[0001] This invention relates to a method for mapping sea surface temperature from a single point to a region under conditions of incomplete information, and is particularly suitable for a high-precision data mapping method for asymmetric, extremely sparse, small samples in the ocean. Background Technology

[0002] Sea surface temperature is a crucial component of the global climate system. Monitoring and analyzing changes in sea surface temperature can provide a better understanding of climate change trends and patterns, thereby enabling predictions of future climate change. However, the limited distribution of observation stations leads to a lack of sufficient data in some regions. In such situations, interpolation techniques become a key means of obtaining comprehensive and accurate sea surface temperature distribution data.

[0003] CN202310173686.3 discloses a spatiotemporal intelligent prediction method for sea surface temperature based on improved variational mode decomposition. This method predicts future changes in sea surface temperature based on historical sea surface temperatures. The method includes: acquiring historical sea surface temperature data; processing the data using an improved denoising module based on historical sea surface temperature changes and dividing it into training and testing sets; extracting spatiotemporal features from the training set using deep learning methods to fully capture the spatial dependence of sea surface temperature; and using the feature data from the training set as input model parameters to obtain corresponding test results. This effectively improves denoising performance while also enhancing prediction accuracy and efficiency.

[0004] CN202110562552.1 discloses a method, apparatus, electronic device, and storage medium for sea surface temperature inversion, including: acquiring Himawari-8 satellite data and measured sea surface temperature data; preprocessing the Himawari-8 satellite data and measured sea surface temperature data to obtain target satellite data and target measured data; performing spatiotemporal matching on the target satellite data and target measured data to generate matched data pairs; simulating sea surface temperature on the matched data pairs based on the least squares method to obtain sea surface temperature inversion coefficients; and inverting sea surface temperature from a Himawari-8 satellite image based on the sea surface temperature inversion coefficients to obtain a sea surface temperature map. This improves the accuracy of temperature inversion results and enables high-precision sea surface temperature maps to be obtained from Himawari-8 satellite images.

[0005] CN202010461315.1 proposes a deep learning method for sea surface temperature prediction based on spatiotemporal multidimensional influence. 1. Quantifying Spatial Influence: The spatial influence on a target observation point is quantified using sea surface temperature data from its neighboring observation points, and a multidimensional spatiotemporal sea surface temperature dataset is constructed over the target sea area. 2. Data Completion Processing: The dataset is completed using the neighbor data mean method. 3. Establishing a Prediction Model: A deep learning prediction model for sea surface temperature based on spatiotemporal multidimensional influence is established by combining deep learning techniques such as GRU, CNN, and MLP, namely a Convolutional GRU with Multilayer Perceptron (CGMP). This method integrates spatiotemporal multidimensional influence and deep learning techniques to establish a high-accuracy sea surface temperature prediction model.

[0006] The goal of interpolation methods is to predict values ​​at unknown locations based on existing data points using appropriate mathematical models or algorithms. Common interpolation methods include Kriging interpolation, inverse distance weighted interpolation, spline interpolation, and Lagrange interpolation. These methods can generally meet most application needs, but their accuracy drops significantly when the sample size is extremely sparse. Even with currently popular neural network methods for prediction interpolation, the model's performance and generalization ability can only be improved with larger datasets; in small sample situations, the performance of neural networks is difficult to fully realize.

[0007] To overcome the difficulty of scarce sample information, Huang Chongfu proposed a small-sample data information diffusion method and algorithm model based on the information matrix and information diffusion concept in his paper "Information Diffusion Principle and Computational Thinking and Its Application in Earthquake Engineering," and applied it to the estimation of epicentral intensity. Currently, information diffusion is mostly used for small-sample risk assessment problems. For example, Yang Nannan et al. assessed the potential ecological risk of heavy metals in the soil of Fengdong New City based on the information diffusion model, and Li Xia et al. assessed the lightning disaster risk in Jiangsu Province based on the information diffusion theory. Given the excellent performance of the information diffusion concept in small-sample risk assessment, Liu Wei et al. proposed a sparse sample interpolation method based on information diffusion theory in their paper "Sparse Data Interpolation Algorithm Based on Information Diffusion," verifying the feasibility of information diffusion for sea surface temperature interpolation. Huang Chongfu et al., taking the flood disaster in Sichuan Province as an example, applied information diffusion to geographic interpolation in their paper "Empirical Research on Geospatial Information Diffusion Technology—Taking the Flood Disaster in Santai County, Sichuan Province as an Example" to fill data gaps in geographic units. Zhang Ren et al., addressing the limitations of normal information diffusion for non-uniformly distributed samples, proposed an elliptical information diffusion function in their paper "Liu Wei, Zhang Ren, Xu Zhisheng, et al. Interpolation Algorithm for Sparse Marine Observation Data Based on Information Diffusion—Elliptical Model," but the window width was not improved. Summary of the Invention

[0008] To address the aforementioned technical problems, the purpose of this invention is to provide a high-precision data mapping method suitable for asymmetric, extremely sparse, small samples in the ocean.

[0009] The present invention solves the above-mentioned technical problems by adopting the following technical solution: a method for mapping sea surface temperature from a single point to a region under conditions of incomplete information, which uses the particle swarm optimization algorithm (PSO) to optimize the optimal window width theory and uses an elliptical information diffusion function to realize the mapping of a small sample of extremely sparse sea surface temperature under conditions of incomplete information from a single point to a region.

[0010] The optimal window width in the asymmetric elliptical information diffusion function is calculated by particle swarm optimization. The asymmetric elliptical information diffusion is then used to perform single-point to region mapping interpolation on sparse samples, thereby enabling the expansion of extremely sparse sea surface temperature small samples under incomplete information conditions.

[0011] The specific steps are as follows:

[0012] Step 001. Let S = {(x1,y1,z1),…,(x n ,y n ,z n Let x be a dataset consisting of known sparse samples, where x i For longitude, y i For latitude, z iGiven the monthly average sea surface temperature at that latitude and longitude; determine the fundamental universe of discourse U = {u1, ..., u2} corresponding to latitude and longitude x, y and sea surface temperature z from the known sparse dataset based on the step size. J},V={v1,…,v K}, W={w1,…,w L In this context, each element in the universe of discourse represents a monitoring point for its corresponding component. The three universes of discourse, U, V, and W, correspond to the longitude, latitude, and sea surface temperature in the known sample, respectively. The number of monitoring points in each universe of discourse does not need to be the same for different components. The step size for U and V is 1, and the step size for W is 0.5. Let the three-dimensional Cartesian coordinate system be Ω = U × V × W, then Ω... J×K×L Representative (x) i ,y i ,z i The possible values, i.e., the monitoring point space.

[0013] Step 002. Using a non-normal information diffusion function, the known sparse sample point information is diffused into the monitoring point space Ω to obtain the diffusion gain q of all information at each monitoring point in U×V×W.

[0014] The non-normal elliptic information diffusion function is as follows:

[0015]

[0016] In the formula, h is the diffusion coefficient, i.e., the window width. λ i k is the scaling factor. i is the slope of the major axis of the ellipse.

[0017] Where the slope of the major axis of the ellipse is k i Calculated using the following formula: In the formula, Scaling coefficient λ i It is obtained by calculating the ratio of the average distance of all sample points from the line containing the minor axis to the average distance of all sample points from the line containing the major axis.

[0018] The steps for calculating the optimal window width h are as follows:

[0019] Step 0021. Set the objective function for solving the optimal window width h, i.e., the fitness function in the particle swarm optimization algorithm. in Population probability density estimation n is the number of known sample points, q(x) is the diffusion function, h is the diffusion window width, and l i For the observed values ​​of the variable.

[0020] Step 0021. Calculate the range of values ​​for the window width h. Among them, htrad This represents the calculated value from the traditional window width calculation formula. In the formula, a and b are the minimum and maximum values ​​of the components corresponding to the known samples, respectively.

[0021] Step 0023. Generate an initial population of 50 particles within the range of the window width h in step 0022, that is, randomly initialize the velocity V and position X of each particle in the feasible solution space and velocity space;

[0022] Step 0024. Input the window-width particles into the fitness function, and iteratively update the velocity and position of each particle based on the current fitness value and the historical best fitness value.

[0023]

[0024] In the above formula, c1 = c2 = 2; r1 and r2 are random numbers in the range [0,1]; T max =300, which is the maximum number of iterations; t is the current number of iterations; w max =0.9, which is the maximum inertia weight; w min =0.4, which is the minimum inertia weight.

[0025] Step 0025. When the maximum number of iterations is reached, end the iteration calculation and output the historical best position of the entire population, which is the current observation value l. i The corresponding optimal window width value d i .

[0026] Step 0026. Calculate h for each observation. i The average value is used as the final window width. n is the number of samples.

[0027] Step 003. After the sample point information is diffused to the monitoring points, the gain of all sample points in the monitoring point space is summed to obtain the information matrix.

[0028] Step 004. Based on the information matrix Q jkl The fuzzy relation matrix R is calculated.

[0029]

[0030] Step 005. Perform fuzzification processing on any given latitude and longitude coordinate input (x, y) through information allocation.

[0031] in,

[0032] Δx=u j+1 -u j Δy=v j+1-v j .

[0033] Step 006. Normalize the input fuzzy set obtained in step 005. This yields the final input fuzzy set A;

[0034] Step 007. Perform max-min fuzzy rule synthesis on the input fuzzy set A and the fuzzy relation matrix R to obtain the output fuzzy set. For fuzzy set μ B Deblurring is performed to obtain the sea surface temperature interpolation result at this coordinate.

[0035] The beneficial effects of this invention are as follows: This invention proposes a single-point to regional mapping method for sea surface temperature under incomplete information conditions. This method is particularly effective for high-precision mapping and interpolation of sea surface temperature under asymmetric and extremely sparse information conditions in nature. Based on this invention's single-point to regional mapping method for sea surface temperature under incomplete information conditions, it can fully mine information from a small amount of data, achieving effective interpolation of asymmetric sea surface temperature samples in small sample situations. It solves the problem of inaccurate interpolation of non-normal data by information diffusion interpolation methods, and has advantages such as high accuracy and ease of implementation. It is especially suitable for mapping and interpolation of asymmetric, extremely sparse, and small samples in nature, providing important information for marine science, marine surveys, and other fields. A prediction model is established based on the analysis of the method of optimizing the penalty factor C, insensitive loss parameter e, and kernel function parameter y of the Support Vector Regression Machine (SVR) using the Particle Swarm Optimization (PSO) algorithm, followed by a neural network method using chaotic phase space reconstruction. Using the Particle Swarm Optimization (PSO) algorithm, based on a dataset composed of sparse samples, the optimal window width *h* is determined by solving the constraint objective function, i.e., the fitness function in the PSO algorithm. Choosing appropriate window width and diffusion function is crucial to interpolation accuracy. Compared with the above-mentioned technique and existing Kriging interpolation methods, the root mean square error (RMSE) and mean absolute error (MAE) of the interpolation results are reduced by approximately 20% when the known sample sizes are 30 and 100. Therefore, the algorithm mentioned in this technique is practically effective, with advantages such as high accuracy and ease of implementation. Compared with Kriging interpolation, the method of this invention reduces the RMS and MAE by approximately 19.5% when the known sample sizes are 30 and 100. The effect is particularly good when the sample size is extremely sparse, providing a practical and effective technical basis for mapping and expanding sea surface temperature and other similar sparse samples. Attached Figure Description

[0036] Figure 1 This is a functional module diagram of the sea surface temperature single-point to regional mapping method under incomplete information conditions of the present invention;

[0037] Figure 2This is a schematic diagram of fuzzy two-dimensional approximate reasoning under the condition of incomplete information in this invention. Detailed Implementation

[0038] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0039] The optimal window width in the asymmetric elliptical information diffusion function is calculated by particle swarm optimization. The asymmetric elliptical information diffusion is then used to perform single-point to region mapping interpolation on sparse samples, thereby enabling the expansion of extremely sparse sea surface temperature small samples under incomplete information conditions.

[0040] Step 001. As Figure 1 As shown, let S = {(x1,y1,z1),…,(x...} n ,y n ,z n Let x be a dataset consisting of known sparse samples, where x i For longitude, y i For latitude, z i This represents the monthly average sea surface temperature at that latitude and longitude. From the known sparse dataset, determine the fundamental universe of discourse U = {u1, ..., u2} corresponding to latitude and longitude x, y, and sea surface temperature z, based on the step size. J},V={v1,…,v K}, W={w1,…,w L In this context, each element in the universe of discourse represents a monitoring point for its corresponding component. The three universes U, V, and W correspond to longitude, latitude, and sea surface temperature, respectively. The number of monitoring points in each universe of discourse may differ for different components. The step size for U and V is 1, and the step size for W is 0.5. Let the three-dimensional Cartesian coordinate system be Ω = U × V × W, then Ω... J×K×L Representative (x) i ,y i ,z i The possible values, i.e., the monitoring point space.

[0041] Step 002. Using a non-normal information diffusion function, the known sparse sample point information is diffused into the monitoring point space Ω to obtain the diffusion gain q of all information at each monitoring point in U×V×W.

[0042] The information diffusion function for the nonnormal elliptic is:

[0043]

[0044] In the formula, h is the diffusion coefficient, i.e., the window width. λ i k is the scaling factor. i is the slope of the major axis of the ellipse.

[0045] Where the slope of the major axis of the ellipse is k i Calculated using the following formula: In the formula, Scaling coefficient λ i It is obtained by calculating the ratio of the average distance of all sample points from the line containing the minor axis to the average distance of all sample points from the line containing the major axis.

[0046] The steps for calculating the optimal window width h are as follows:

[0047] Step 0021. Set the objective function for solving the optimal window width h, i.e., the fitness function in the particle swarm optimization algorithm. in Population probability density estimation n is the number of known sample points, q(x) is the diffusion function, h is the diffusion window width, and l i For the observed values ​​of the variable.

[0048] Step 0021. Calculate the range of values ​​for the window width h. Among them, h trad This represents the calculated value from the traditional window width calculation formula. In the formula, a and b are the minimum and maximum values ​​of the components corresponding to the known samples, respectively. The values ​​of a and b are calculated based on the known samples. For example, (x, y, z) represents a known point, where x, y, and z correspond to (longitude, latitude, and sea surface temperature), respectively. There are a total of 20 similar known sample points. h needs to be calculated based on the latitude, specifically h0. x ,h y ,h z In this context, a and b, which are needed to obtain hx, refer to the maximum and minimum longitude values ​​among the known sample points. hy and hz are the maximum and minimum values ​​of the corresponding latitude and temperature, respectively, and are not fixed values.

[0049] Step 0023. Generate an initial population of 50 particles within the range of the window width h in step 0022, that is, randomly initialize the velocity V and position X of each particle in the feasible solution space and velocity space;

[0050] Step 0024. Input the window-width particles into the fitness function, and iteratively update the velocity and position of each particle based on the current fitness value and the historical best fitness value.

[0051]

[0052] In the above formula, c1 = c2 = 2; r1 and r2 are random numbers in the range [0,1]; T max =300, which is the maximum number of iterations; t is the current number of iterations; w max =0.9, which is the maximum inertia weight; w min=0.4, which is the minimum inertia weight.

[0053] Step 0025. When the maximum number of iterations is reached, end the iteration calculation and output the historical best position of the entire population, which is the current observation value l. i The corresponding optimal window width value d i .

[0054] Step 0026. Calculate h for each observation. i The average value is used as the final window width. n is the number of samples.

[0055] Step 003. After the sample point information is diffused to the monitoring points, the gain of all sample points in the monitoring point space is summed to obtain the information matrix.

[0056] Step 004. Based on the information matrix Q jkl The fuzzy relation matrix R is calculated.

[0057]

[0058] Q jkl It is a three-dimensional matrix whose element size is related to the known samples, the range of the universe of discourse, and the step size, and has no fixed value.

[0059] Step 005. Figure 2 As shown, any given latitude and longitude coordinate input (x, y) is fuzzified through information allocation. Where, Δx=u j+1 -u j Δy=v j+1 -v j .

[0060] Step 006. Normalize the input fuzzy set obtained in step 005. This yields the final input fuzzy set A;

[0061] Step 007. Perform max-min fuzzy rule synthesis on the input fuzzy set A and the fuzzy relation matrix R to obtain the output fuzzy set. For fuzzy set μ B Deblurring is performed to obtain the sea surface temperature interpolation result at this coordinate. A refers to the input fuzzy set matrix, μ(u i ,v k ) represents the function needed to obtain the input fuzzy matrix A, where u i ,v k The elements represent the preceding domains U and V, while x and y represent the longitude and latitude of the point to be interpolated.

[0062] Current techniques generally assume that when the number of known samples is less than 30, the result of Kriging interpolation will approach a fixed value, regardless of the input latitude and longitude. Therefore, it can be considered that Kriging interpolation performs poorly in this case. Table 1 shows the errors of the two methods under different sparsity levels.

[0063] To verify the superiority of the algorithm in interpolating small sample data, monthly average sea surface temperature data of China's coastal waters in 2019 were used for the experiment. The dataset comes from the reanalysis data of the South China Sea Institute of Oceanology, Chinese Academy of Sciences, a co-construction unit of the Ocean Big Science Research Center of the Chinese Academy of Sciences. The data range is from 0° to 40° north latitude and 100° to 130° east longitude, with a resolution of 0.5° × 0.5°, and a total of 80 (meridian) × 60 (zonal) = 4800 grid points. After removing land, there are 2647 grid points.

[0064] In the monthly average sea surface temperature data of 2019, the distribution range of sea surface temperature in January and December was relatively dispersed, while the distribution range was more concentrated in August and September. Therefore, this paper selects data from these four representative months for interpolation experiments, and the interpolation results are shown below:

[0065] Table 1. Interpolation results of monthly average sea surface temperature error

[0066]

[0067]

[0068] In the table above, OK represents Kriging interpolation, and PSO-AFD represents the interpolation method proposed in this paper. Based on the average error over four months, with a known sample size of 30, the PSO-AFD interpolation algorithm reduces both the root mean square error and mean absolute error by approximately 19.5% compared to Kriging interpolation; with a known sample size of 100, the PSO-AFD interpolation algorithm reduces the root mean square error by approximately 14% and the mean absolute error by approximately 24% compared to Kriging interpolation.

[0069] This invention presents a single-point to regional mapping method for sea surface temperature under incomplete information conditions. It is particularly suitable for high-precision mapping and interpolation of sea surface temperature under asymmetric and extremely sparse information conditions in nature. The algorithm is practical and effective, offering advantages such as high accuracy and ease of implementation. Compared with existing Kriging interpolation methods, it performs better, especially under extremely sparse sample conditions. When the known sample size is less than 100, the root mean square error and mean absolute error can be reduced by approximately 20% compared to Kriging interpolation. This difference gradually decreases as the known sample size increases. This algorithm provides a practical and effective technical foundation for mapping and expanding sea surface temperature and other similar sparse samples. It can also be extended to the interpolation and expansion of coefficient samples in other natural fields, such as remote areas like the polar regions and the Qinghai-Tibet Plateau where observational data for temperature and air pressure are scarce. This provides crucial basic data for economic industries related to meteorological and oceanographic elements, possessing broad market application prospects and economic value.

[0070] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for mapping sea surface temperature from a single point to a region under conditions of incomplete information, characterized in that, The optimal window width in the asymmetric elliptical information diffusion function is calculated by the particle swarm algorithm. The asymmetric elliptical information diffusion is used to perform single-point to region mapping interpolation on sparse samples, thereby realizing the function of expanding the small sample of extremely sparse sea surface temperature under the condition of incomplete information. The specific steps are as follows: Step 001. Let S = {(x1,y1,z1),…,(x... n ,y n ,z n Let x be a dataset consisting of known sparse samples, where x i For longitude, y i For latitude, z i This represents the average monthly sea surface temperature at that latitude and longitude. Determine the fundamental universe of discourse U = {u1, ..., u2} corresponding to latitude and longitude x, y, and sea surface temperature z from a known sparse dataset based on the step size. J },V={v1,…,v K },W={w1,…,w L In the universe of discourse, each element represents a monitoring point for its corresponding component. The three universes U, V, and W correspond to longitude, latitude, and sea surface temperature, respectively. The number of monitoring points in each universe does not need to be the same for different components. The step size for U and V is 1, and the step size for W is 0.

5. Let the three-dimensional Cartesian coordinate system be Ω = U × V × W, then Ω... J×K×L Representative (x) i ,y i ,z i The possible values, i.e., the monitoring point space; Step 002. Using a non-normal information diffusion function, the known sparse sample point information is diffused into the monitoring point space Ω to obtain the diffusion gain q of all information at each monitoring point in U×V×W; The information diffusion function for the nonnormal elliptic is: In the formula, h is the diffusion coefficient, i.e., the window width. λ i k is the scaling factor. i The slope of the major axis of the ellipse; Where the slope of the major axis of the ellipse is k i Calculated using the following formula: In the formula, Scaling coefficient λ i It is obtained by calculating the ratio of the average distance of all sample points from the line containing the minor axis to the average distance of all sample points from the line containing the major axis; Step 003. After the sample point information is diffused to the monitoring points, the gain of all sample points in the monitoring point space is summed to obtain the information matrix. Step 004. Based on the information matrix Q jkl The fuzzy relation matrix R is calculated. Step 005. Perform fuzzification processing on any given latitude and longitude coordinate input (x, y) through information allocation. Where, Δx=u j+1 -u j Δy=v j+1 -v j ; Step 006. Normalize the input fuzzy set obtained in step 005. This yields the final input fuzzy set A; Step 007. Perform max-min fuzzy rule synthesis on the input fuzzy set A and the fuzzy relation matrix R to obtain the output fuzzy set. For fuzzy set μ B Deblurring is performed to obtain the sea surface temperature interpolation result at this coordinate.

2. The method for mapping sea surface temperature from a single point to a region under conditions of incomplete information as described in claim 1, characterized in that, In step 002, the calculation steps for the optimal window width h are as follows: Step 0021. Set the objective function for solving the optimal window width h, i.e., the fitness function in the particle swarm optimization algorithm. in Population probability density estimation n is the number of known sample points, q(x) is the diffusion function, h is the diffusion window width, and l i For the observed values ​​of the variable; Step 0021. Calculate the range of values ​​for the window width h. Among them, h trad This represents the calculated value from the traditional window width calculation formula. In the formula, a and b are the minimum and maximum values ​​of the components corresponding to the known samples, respectively; Step 0023. Generate an initial population of 50 particles within the range of the window width h in step 0022, that is, randomly initialize the velocity V and position X of each particle in the feasible solution space and velocity space; Step 0024. Input the window-width particles into the fitness function, and iteratively update the velocity and position of each particle based on the current fitness value and the historical best fitness value. In the above formula, c1 = c2 = 2; r1 and r2 are random numbers in the range [0,1]; T max =300, which is the maximum number of iterations; t is the current number of iterations; w max =0.9, which is the maximum inertia weight; w min =0.4, which is the minimum inertia weight; Step 0025. When the maximum number of iterations is reached, end the iteration calculation and output the historical best position of the entire population, which is the current observation value l. i The corresponding optimal window width value d i ; Step 0026. Calculate h for each observation. i The average value is used as the final window width. , where n is the number of samples.

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