Spatial refined interpolation method for sea ice concentration based on cokriging

Abstract

The application discloses a spatial fine interpolation method for sea ice density based on a collaborative Kriging method, and comprises the following steps: S1, dividing an interpolation area and obtaining sea ice density observation values and climate parameter observation values at observation points; S2, taking the sea ice density of the observation points as a main variable and taking the climate parameter with the highest correlation with the sea ice density as a covariant; S3, calculating the distance between all the observation points, the main variable variation function value and the covariant variation function value; calculating the covariant variation function value between the observation points; S4, obtaining the autocorrelation distance of the covariant variation function value based on a fitting curve; S5, calculating the distance between the observation points and the interpolation point within the autocorrelation distance range of each interpolation point and obtaining the covariant variation function value between the observation points and the interpolation point; S6, constructing a Lagrange equation and solving the Lagrange equation to obtain a weight coefficient; and S7, constructing a quality control equation of the collaborative Kriging method and calculating a sea ice density prediction value of the interpolation point.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of polar ship safety navigation information technology, in particular to a sea ice density spatial refinement interpolation method based on a collaborative Kriging method. BACKGROUND

[0002] In recent decades, with the gradual increase in temperature, the sea ice has accelerated melting, and the Arctic sea ice coverage area has been decreasing. Changes in sea ice coverage affect the global transportation industry. For example, as the sea ice coverage decreases, the possibility of merchant ships crossing the Arctic passage gradually increases, especially the navigation window period of the Northeast Passage gradually extends, and the navigation capacity significantly improves. However, due to the rapid climate change in polar waters, it often leads to the phenomenon of "ice block" of ships. From the perspective of navigation in the Arctic region, sea ice density has a greater impact on safe navigation in the polar region.

[0003] Currently, the sea ice density data obtained by ships before polar navigation is mostly 0.25°x0.25° latitude and longitude grid data, which cannot meet the needs of polar navigation and path planning. For this reason, many scholars have studied the prediction of sea ice density from the perspective of time series, which can be mainly divided into two categories based on numerical mode prediction and statistical prediction. Numerical mode is based on the known physical law, and realizes the simulation and prediction of the above sea ice change process based on the law of sea ice dynamics, thermodynamics and thickness distribution; however, due to the uncertainty of the physical model caused by the lack of clear physical law of sea ice dynamics and deformation. Statistical prediction is data-driven, which starts from the data itself, and uses statistical methods to mine and fit the change law of sea ice; among them, deep learning is the most widely used, but deep learning model has time dependence, when the time series input is too long, it will forget the historical information, and the gradient will disappear or explode, which will lead to the model unable to converge. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the present application provides a sea ice density spatial refinement interpolation method based on a collaborative Kriging method, which is used to solve at least one of the above technical problems.

[0005] The present application is realized by the following technical solutions:

[0006] The sea ice density spatial refinement interpolation method based on the collaborative Kriging method comprises the following steps:

[0007] S1: dividing the interpolation area according to the latitude and longitude grid, setting the grid points of the latitude and longitude grid as observation points, setting the middle points of the four sides of the latitude and longitude grid and the center points of the grid as interpolation points, and obtaining the sea ice density observation value and climate parameter observation value at the observation points;

[0008] S2: taking the sea ice concentration of the observation point as a principal variable, performing correlation analysis on the sea ice concentration observation value and the climate parameter observation value of the observation point, and taking the climate parameter with the highest correlation with the sea ice concentration as a covariate;

[0009] S3: calculating the distance between all observation points, the principal variable variogram value and the covariate variogram value; and constructing a covariogram equation between the observation points based on the principal variable variogram value and the covariate variogram value, and calculating the covariogram value between the observation points;

[0010] S4: finding a fitting curve between the distance and the covariogram value between all observation points, and obtaining the autocorrelation distance of the covariogram value based on the fitting curve;

[0011] S5: calculating the distance between the observation points within the autocorrelation distance range of each interpolation point and the interpolation point, and obtaining the covariogram value between the observation points and the interpolation point from the fitting curve based on the distance;

[0012] S6: constructing a Lagrange equation based on the covariogram value between the observation points and the interpolation point obtained in step S5, and solving the Lagrange equation to obtain a set of weight coefficients assigned to each covariate and a set of weight coefficients assigned to each principal variable;

[0013] S7: constructing a quality control equation of the collaborative Kriging method, and calculating the sea ice concentration prediction value of the interpolation point based on the set of weight coefficients assigned to each covariate and the set of weight coefficients assigned to each principal variable.

[0014] In the above technical solution, based on the sea ice concentration observation data of the observation points in the interpolation region and the observation data of the climate parameters with the highest correlation with the sea ice concentration observation value, the collaborative Kriging interpolation method is used to realize the prediction of the sea ice concentration at the interpolation point on the basis of considering spatial heterogeneity and dependence, to improve the grid precision in the interpolation region by one time, and to obtain sea ice concentration data with higher spatial precision, thereby providing a ship with a sea ice concentration data set with higher spatial resolution on the sailing route or in the region.

[0015] Further, the climate parameters include sea surface pressure, sea surface temperature and average sea level pressure.

[0016] Among the numerous climate parameters, the climate parameters that have a greater impact on the sea ice concentration mainly include sea surface pressure, sea surface temperature and average sea level pressure, and the above three parameters are selected as potential covariates, thereby improving the accuracy of the sea ice concentration prediction at the interpolation point.

[0017] Further, the interpolation method further comprises:

[0018] S8: comparing the sea ice concentration prediction value of the interpolation point in S7 with the sea ice concentration prediction value of the interpolation point, and evaluating the model by mean absolute error MAE, root mean square error RMSE and mean square error MSE.

[0019] By comparing the sea ice concentration prediction value at the interpolation point with the sea ice concentration prediction value at the interpolation point, the model is evaluated by mean absolute error MAE, root mean square error RMSE and mean square error MSE, so as to ensure that the model has high accuracy.

[0020] The calculation formulas of MAE, MSE and RMSE are as follows:

[0021]

[0022]

[0023]

[0024] In the formula, Y(x j ) and Y*(x j ) are the observed value and the prediction value at x j , respectively; and n is the number of interpolation point samples.

[0025] Further, the calculation methods of the principal variable variation function value and the covariant variation function value in the step S3 are as follows:

[0026]

[0027] In the formula, γ1(h) is the covariant variation function value, γ2(h) is the principal variable variation function value, h is the separation distance, n is the number of covariant point pairs with a separation distance of h, m is the number of principal variable point pairs with a separation distance of h, Y(x i ) and Y(x i +h) are the observed values of the covariant at positions x i and x i +h, respectively, Y(x j ) and Y(x j +h) are the observed values of the principal variable at positions x j and x j +h, respectively; and i and j are both observation point serial numbers.

[0028] The covariant variation function equation in the step S3 is as follows:

[0029]

[0030] In the formula, γ 12 (h) is the covariant variation function value.

[0031] Further, the Lagrange equation in step S6 is:

[0032]

[0033] wherein ψ1 and ψ2 are two Lagrange coefficients; γ 11 and γ 22 are the covariant variogram model and the principal variogram model respectively; γ 12 and γ 21 are the variogram models of the two variables and γ 12 (h) = γ 21 (h); ω 1i is a set of weight coefficients given to each covariant, ω 2j is a set of weight coefficients given to each principal variable; a is the number of covariants, b is the number of principal variables; x0 is the interpolation point; x1 is the covariant, and x2 is the principal variable.

[0034] The unbiased estimation condition of the collaborative Kriging method is that the sum of the principal variable weight coefficients is 1 and the sum of the covariant weight coefficients is 0, and by using the Lagrange multiplier method, the Lagrange coefficients (ψ1 and ψ2) are introduced, that is, the Lagrange function equation set can be constructed.

[0035] Further, the quality control equation of the collaborative Kriging method is:

[0036]

[0037] wherein Y* CoK (x0) is the sea ice density prediction value at the interpolation point x0, Y CoK (x i ) and Y CoK (x j ) are the covariant observation value and the principal variable observation value of the observation point within the autocorrelation range of the interpolation point x0 respectively.

[0038] In order to obtain the most accurate result, the difference between the estimated value and the true value at the interpolation point x0 should be minimized (unbiased estimation); the variance of the difference between the estimated value and the true value should be as small as possible; the space is stationary, and the value at any point in the space is composed of the regional average value μ and the random deviation R, wherein the variances of the deviations are all constants.

[0039] Further, the Pearson correlation analysis method is used to analyze the correlation between the sea ice density observation value and the climate parameter observation value of the observation point in step S2.

[0040] Further, the distance is the Euclidean distance of two points in the latitude and longitude coordinate system.

[0041] Compared with the prior art, the beneficial effects of the present application are:

[0042] This invention provides a spatially refined interpolation method for sea ice concentration based on co-kriging. Using sea ice concentration observation data from observation points within the interpolation region and the climate parameter observations most correlated with the sea ice concentration observations, the co-kriging interpolation method, considering spatial heterogeneity and dependence, enables sea ice concentration prediction at the interpolation points. This doubles the grid accuracy within the interpolation region, obtaining higher-resolution sea ice concentration grid data. This provides more refined sea ice concentration data at the ship's deck for polar vessels, ensuring their safe navigation in polar regions. Attached Figure Description

[0043] Figure 1 This is a flowchart of a method for spatial fine interpolation of sea ice concentration according to an embodiment of the present invention;

[0044] Figure 2 Satellite imagery of sea ice concentration distribution in the research area according to an embodiment of the present invention;

[0045] Figure 3 This is a distribution map of observation points within the research sea area according to an embodiment of the present invention;

[0046] Figure 4 This is a map showing the sea ice concentration distribution in the region of 20°E-180°E and 65°N-90°N according to an embodiment of the present invention.

[0047] Figure 5 This is a distribution map of sea ice concentration data at 0.25°×0.25° latitude and longitude grid observation points according to an embodiment of the present invention;

[0048] Figure 6 This is a distribution map of sea ice concentration data in a 0.125°×0.125° latitude and longitude grid after interpolation according to an embodiment of the present invention;

[0049] Figure 7 This is a schematic diagram of the interpolation region division method according to an embodiment of the present invention. Detailed Implementation

[0050] The technical solutions of various embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment provides a spatially refined interpolation method for sea ice concentration based on co-kriging, including the following steps:

[0053] S1: divide the interpolation area according to the latitude and longitude grid, set the grid points of the latitude and longitude grid as observation points, set the midpoints of the four edges of the latitude and longitude grid and the center point of the grid as interpolation points (as shown in Figure 7 ), and obtain the sea ice concentration observation value and the climate parameter observation value at the observation points;

[0054] In this embodiment, the sea area of the part of the Laptev Sea and the East Siberian Sea of the Northeast Passage in the Arctic (geographical position between 113°E-170°E, 70°N-75°N, as shown in Figure 2 ), is taken as the sea ice concentration interpolation area, the interpolation area is divided according to the latitude and longitude grid of 0.5°x0.5°, and the observation points and interpolation points are determined according to the above. After interpolation, the sea ice concentration data of 0.25°x0.25° latitude and longitude grid can be obtained. The spatial distribution map of the observation point data of the study area in this embodiment is shown in Figure 3 .

[0055] The grid data from the fifth generation ECMWF reanalysis in the Copernicus Climate Service Center is obtained, so as to obtain the monthly average data of the sea ice concentration SIC and the climate parameters (in this embodiment, the climate parameters include sea surface pressure SP, sea surface temperature SST and mean sea level pressure MSLP) of the observation points in the study area. As shown in Figure 4 , it is the sea ice concentration distribution map of the common navigation area (20°E-180°E, 65°N-90°N) of the Northeast Passage in the Arctic in a year. From the figure, it can be seen that the sea ice concentration shows great difference in different months, so the monthly average data is taken as the observation value when interpolating the sea ice concentration, and the study area is interpolated according to the month.

[0056] S2: take the sea ice concentration of the observation point as the main variable, use the Pearson correlation analysis method to analyze the correlation between the sea ice concentration observation value and the climate parameter observation value of the observation point, and take the climate parameter with the highest correlation with the sea ice concentration as the covariate;

[0057] As shown in Table 1, the correlation analysis results of SIC with SP, SST and MSLP in the embodiment are shown, from Table 1, among January, May, June, August, October and November, the Pearson coefficient of SST and SIC is the highest, and the absolute value of the Pearson coefficient is greater than 0.5 except January, thus in the example, SST is used as the covariant in these months; in February, April, July and December, the correlation (the absolute value is greater than 0.3) of SP and SIC is greater than the correlation of MSLP and SIC, and SP is used as the covariant in these three months; in March and September, the absolute value of the Pearson coefficient of the three correlation auxiliary variables and SIC is less than 0.3, and it can be considered that there is no correlation between them, thus the CoKriging interpolation in March and September is cancelled.

[0058] Table 1 Pearson correlation distribution of sea ice density and climate parameters

[0059]

[0060] e: indicates that the variable has only one constant.

[0061] **: indicates that the correlation is significant at the 0.01 level (two-tailed).

[0062] S3: calculating the distance between all observation points, the main variable variogram value and the covariant variogram value, and constructing the covariant variogram equation between the observation points based on the main variable variogram value and the covariant variogram value, and calculating the covariant variogram value between the observation points;

[0063] The distance is the Euclidean distance of two points in the longitude and latitude coordinate system, after the interpolation region is divided and the observation points and the interpolation points are determined, the longitude and latitude coordinates of each interpolation point and observation point are obtained, and the Euclidean distance between two points can be calculated based on the longitude and latitude coordinates.

[0064] Specifically, the calculation methods of the main variable variogram value and the covariant variogram value are as follows:

[0065]

[0066] In the formula, γ1(h) is the covariant variogram value, γ2(h) is the main variable variogram value, h is the separation distance, n is the number of covariant point pairs with the separation distance h, m is the number of main variable point pairs with the separation distance h, Y(x i ) and Y(x i +h) are the observation values of the covariant at positions x i and x i +h respectively, Y(x j ) and Y(x j +h) are the observation values of the main variable at positions xj and x j observed value at point h; i and j are both observation point serial numbers;

[0067] The covariogram equation in step S3 is:

[0068]

[0069] In the formula, γ 12 (h) is the covariogram value.

[0070] S4: Find the fitting curve between the distance between all observation points and the covariogram value, and obtain the autocorrelation distance of the covariogram value based on the fitting curve;

[0071] S5: Calculate the distance between the observation points within the autocorrelation distance range of each interpolation point and the interpolation point, and obtain the covariogram value between the observation points and the interpolation point from the fitting curve based on the distance;

[0072] S6: Construct the Lagrange equation based on the covariogram value between the observation points and the interpolation point obtained in step S5, and solve the Lagrange equation to obtain a set of weight coefficients assigned to each covariant and a set of weight coefficients assigned to each principal variable;

[0073] Specifically, the Lagrange equation is:

[0074]

[0075] In the formula, ψ1 and ψ2 are two Lagrange coefficients; γ 11 and γ 22 are the covariant variogram model and the principal variable variogram model, respectively; γ 12 and γ 21 are the variogram models of the two variables, and γ 12 (h) = γ 21 (h); ω 2i is a set of weight coefficients assigned to each covariant, ω 1j is a set of weight coefficients assigned to each principal variable; a is the number of covariants, b is the number of principal variables; x0 is the interpolation point; x1 is the covariant, and x2 is the principal variable.

[0076] S7: Construct the collaborative Kriging method quality control equation, and calculate the interpolation point sea ice density prediction value based on the set of weight coefficients assigned to each covariant and the set of weight coefficients assigned to each principal variable.

[0077] Specifically, the collaborative Kriging method quality control equation is:

[0078]

[0079] In the formula: Y* CoK (x0) is the predicted sea ice concentration at interpolation point x0, Y CoK (x i ) and Y CoK (x j ) are the covariate observations and main variable observations at the observation points within the autocorrelation range of the interpolation point x0, respectively.

[0080] In a preferred embodiment, the interpolation method further includes:

[0081] S8: Compare the sea ice concentration prediction values ​​at the interpolation points in S7 with the sea ice concentration prediction values ​​at the interpolation points, and evaluate the model using the mean absolute error (MAE), root mean square error (RMSE), and mean square error (MSE).

[0082] By comparing and analyzing the predicted sea ice concentration values ​​at the interpolation points, the model is evaluated using mean absolute error (MAE), root mean square error (RMSE), and mean square error (MSE) to ensure that the model has high accuracy.

[0083] The formulas for calculating MAE, MSE, and RMSE are as follows:

[0084]

[0085]

[0086]

[0087] In the formula: Y(x j ) and Y*(x j ) respectively in x j The observed and predicted values ​​are given; n is the number of interpolation points.

[0088] Table 2 shows the comparison between the predicted data obtained by interpolation from the 0.5°×0.5° latitude and longitude grid and the observed 0.25°×0.25° data. As shown in Table 2, February and December have the best interpolation accuracy, with mean absolute errors (MAE) of 0.00222 and 0.00221, respectively; June has the lowest interpolation accuracy, with an MAE of 0.06378. The root mean square error (RMSE) is highest in June, at 0.09513. Furthermore, the analysis comparing the original data reveals that the difference in accuracy is due to the fluctuations in sea ice concentration data across months; the smaller the variance of the source data, the higher the interpolation accuracy, and vice versa.

[0089] Table 2. Interpolation Accuracy Error Analysis Table for 0.25°×0.25°

[0090]

[0091] Example 2

[0092] In this embodiment, the interpolation area is divided according to a 0.25°x0.25° latitude and longitude grid, the data on the 0.25°x0.25° grid points are taken as observation points, the midpoints of the four sides of the 0.25°x0.25° latitude and longitude grid and the center points of the grid are taken as interpolation points, the interpolation points are predicted based on the method in Example 1, and 0.125°x0.125° latitude and longitude grid sea ice density data are obtained. Figure 5 is a data distribution diagram of the 0.25°x0.25° latitude and longitude grid observation points, Figure 6 is a data distribution diagram of the 0.125°x0.125° latitude and longitude grid data obtained after interpolation. Through comparative analysis of the two diagrams, it can be seen that for the 1st month, 2nd month, 4th month and 12th month with small fluctuations in the source data, the collaborative Kriging interpolation method performs excellently; at the same time, for the 5th month, 6th month, 7th month, 8th month and 11th month with obvious data fluctuations and floating up and down of a certain value, the collaborative Kriging interpolation method can also well capture the data fluctuation and perform excellently in data feature extraction. The results show that the use of the collaborative Kriging method can convert low-resolution sea ice data into high-resolution sea ice data to ensure safe navigation of polar ships.

[0093] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present application.

Claims

1. A spatial refinement interpolation method for sea ice concentration based on the method of collocated cokriging, characterized in that, The method comprises the following steps: S1: dividing the interpolation area according to a latitude-longitude grid, setting the grid points of the latitude-longitude grid as observation points, setting the midpoints of the four sides of the latitude-longitude grid and the center point of the grid as interpolation points, and obtaining sea ice density observation values and climate parameter observation values at the observation points; S2: taking the sea ice density of the observation points as a main variable, performing correlation analysis on the sea ice density observation values and the climate parameter observation values of the observation points, and taking the climate parameter with the highest correlation with the sea ice density as a covariate; S3: calculating the distances between all observation points, the main variable variogram values, and the covariate variogram values; and constructing a covariogram equation between the observation points based on the main variable variogram values and the covariate variogram values, and calculating the covariogram values between the observation points; S4: finding a fitting curve between the distances and the covariogram values of all observation points, and obtaining the autocorrelation distance of the covariogram values based on the fitting curve; S5: calculating the distances between the observation points within the autocorrelation distance range of each interpolation point and the interpolation point, and obtaining the covariogram values between the observation points and the interpolation point based on the distances; S6: constructing a Lagrange equation based on the covariogram values between the observation points and the interpolation point obtained in step S5, and solving the Lagrange equation to obtain a set of weight coefficients assigned to each covariate and a set of weight coefficients assigned to each main variable; S7: constructing a quality control equation of the collaborative Kriging method, and calculating the sea ice density prediction value of the interpolation point based on the set of weight coefficients assigned to each covariate and the set of weight coefficients assigned to each main variable.

2. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 1, characterized in that, The climate parameters include sea surface pressure, sea surface temperature, and average sea level pressure.

3. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 1, characterized in that, The interpolation method further comprises: S8: comparing the sea ice density prediction value of the interpolation point in S7 with the sea ice density prediction value of the interpolation point, and evaluating the model by mean absolute error (MAE), root mean square error (RMSE), and mean square error (MSE).

4. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 1, characterized in that, In step S3, the calculation methods of the main variable variogram values and the covariate variogram values are as follows: In the formula: γ1(h) is the covariance function value, γ2(h) is the principal variable variance function value, h is the separation distance, n is the number of covariance pairs with a separation distance of h, m is the number of principal variable pairs with a separation distance of h, and Y(x i ) and Y(x i +h) represent the covariates at position x. i and x i The observed value at +h, Y(x) j ) and Y(x j +h) represent the positions of the main variables at x and x respectively. j and x j The observation value at +h; i and j are both observation point numbers; The covariogram equation in step S3 is as follows: where: γ 12 (h) is the covariogram value.

5. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 4, characterized in that, In step S6, the Lagrange equation is as follows: where: ψ1 and ψ2 are two Lagrange coefficients; γ 11 and γ 22 are the covariate variogram model and the principal variogram model, respectively; γ 12 and γ 21 are the variogram models of these two variables and γ 12 (h) = γ 21 (h); ω 1i is a set of weight coefficients assigned to each covariate, ω 2j is a set of weight coefficients assigned to each principal variable; a is the number of covariates and b is the number of principal variables; x0 is the interpolation point; x1 is the covariate and x2 is the principal variable.

6. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 5, characterized in that, The quality control equation of the collaborative Kriging method is as follows: where: Y CoK (x0) is the sea ice concentration forecast value at the interpolation point x0, Y CoK (x0) is the sea ice concentration forecast value at the interpolation point x0, Y i (x0) is the sea ice concentration forecast value at the interpolation point x0, Y CoK (x0) is the sea ice concentration forecast value at the interpolation point x0, Y j (x0) is the sea ice concentration forecast value at the interpolation point x0, Y 7. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 1, characterized in that, In step S2, the Pearson correlation analysis method is used to perform correlation analysis on the sea ice density observation values and the climate parameter observation values of the observation points.

8. The spatial refinement interpolation method of sea ice concentration based on the method of collocated cokriging according to claim 1, characterized in that, The distance is the Euclidean distance of two points in a latitude-longitude coordinate system.

Images